Airports and ground handling Essay Example | Topics and Well Written Essays - 1500 words - 2

Airports and ground handling - Essay Example te a close collaboration between the top management of air transportation system including airline managers, handling agents, government agencies, as well as specialist agencies and the airport operators. The airport operators vary significantly in relation to the ownership, management structure, funding and degree of autonomy, thus making the manner with which one airport is managed to be significantly different from the other. Nevertheless, each airport operator is faced with challenging tasks of coordinating all services to enable the efficient functionality of the airport system. Each airport operator has a unique responsibility, but all assume the overall responsibility for control and coordination of the operations of the airport. In an attempt to understand the nature of work of the airport operations and the management system of the airports, this paper will analyze some of the future challenges operators are faced with, as well as analyze some of the consequences of these challenges. The paper will also provide an analysis of some of the mitigation measures that can be employed by the airport operators in the event of the potential future challenges. Airport operators are charged with the responsibility of ensuring the safety of passengers and freight through the development of a safe airport environment. However, in some instances, there have been reported incidences when terrorist have managed to evade the security checks and measures in some of the modern and technologically sophisticated airports and managed to spill terror to the airline passengers and crew. An example of the June 8th 2014 terrorist attack on Jinnah international airport, Pakistan, resulting to the death of 36 people is an indication of the sophistication of terrorist attack on airports. Current terrorist attacks on airports are indications that terrorism in the 21st century has revolutionized and points to the development of more sophisticated methods that could be used by

Compare and contrast Essay Example for Free

Compare and contrast Essay Over the last few weeks, I have learned about what makes an essay an essay, after reading the required chapters of â€Å"Essentials of College Writing† (Connell Soles, 2013) the knowledge needed to compare and contrast a narrative and descriptive essay is at my grasp. The essays I have chosen to use as support are â€Å"Homeless† by Anne Quindlen and â€Å"Are the Rich Happy?† by Stephen Leacock. While the differences between these two essays are apparent, the similarities are more recognizable. By using information, I have gained from the class I hope this paper can help you form your own opinion on which essay is superior. There are many different reasons why an author would write a narrative or descriptive essay and for each form, there is a main purpose, though it does not always have to be evident right away. A narrative story is to entertain or engage the reader, maybe for fun or to teach a lesson. In difference to a narrative, which can be truth or fiction, a descriptive is about a true event, person or place. The purpose of a descriptive essay is to create an accurate and vivid â€Å"picture† by using specific details. Details help you focus the reader’s attention on characteristics that make people, places, objects, and events unique and help them â€Å"come alive† for readers, a descriptive essay is about an actual person, place and/or event (Connell Soles, 2013). The author Stephen Leacock started his essay,† Are the Rich Happy?† with, â€Å"Let me admit at the outset that I write this essay without adequate material. I have never known, I have never seen, any rich people. Very often, I have thought I have found them. However, it turned out that it was not so. They were not rich at all. They were quite poor. They were hard up. They were pushed for money. They did not know where to turn for ten thousand dollars.† The essays purpose was not openly stated, I had to finish reading before I understood what point the author was trying to get across. In contrast, Quindlen began her essay â€Å"Homeless† by getting to the point from the very beginning, using words to describe exactly who and what she was writing about in her paper â€Å"Her name was Ann, and we met in the port authority Bus Terminal several Januarys ago. I was doing a story on homeless people. She said I was wasting my time talking to her; she was just passing through, although shed been passing through for more than two weeks. To prove to me that this was true, she rummaged through a tote bag and a manila envelope and finally unfolded a sheet of typing paper and brought out her photographs.† The author of both a narrative and a descriptive essay need to use elements to make sure that they maintain the reader’s attention. Like, the topic they have chosen to write about has to be interesting to others. Just because one person thinks something is interesting does not mean others will feel the same (Connell Soles, 2013). The author of ‘Are the Rich Happy? †˜ Stephen Leacock knew that money will always be an issue among man and no matter how much money one has they will always want more, because there will always be reason to need more and that they will never be happy with what they have. Anne Quindlen also knew that homeless is a major issue in the world and that others would have a related emotion attachment to this. Another element is the use of language that allows the readers’ senses to create the whole picture. A narrative uses words to represent physical objects rather than ideas, qualities, or concepts that help make characters come to life and give those personalities (Connell Soles, 2013). In contrast, a descriptive essay demands emotion and expressive details that are more precise when describing certain aspects such as the characters, the plot and the main idea of why the essay was wrote. As written in â€Å"Are the Rich Happy† By Stephen Leacock, â€Å" I know a man, for example his name is Spugg- whose private bank account was overdrawn last month by twenty thousand dollars. He told me so at dinner at his club, with apologies for feeling out of sorts. He said it was bothering him. He said he thought it rather unfair of his bank to have called this to his attention.†(Para 7) In her essay Homeless, Anna Quindlen wrote, â€Å"Home is where the heart is; there is no place like it. I love my home with ferocity totally out of proportion to it appearance and location† (Para 4). By expressing, her emotions about her home I feel Anna hoped to make the reader reflect on how they feel about there own home. Another example of a strong tone would be, â€Å"People find it curious that  those without homes would rather sleep sitting up on benches or huddled in doorways than go to shelters. Certainly some prefer to do so because they are emotionally ill, because they have been locked up before and they are determined no to be again. Others are afraid of the violence and trouble they may find there. But some seem to want something that is not available in a shelter and they will not compromise, not for cot, or oatmeal, or a shower.’(Quindlen, â€Å"Homeless†, Para 7) So far, we have compared the purpose for each essay, how each essay has an audience that the author must keep in mind and the language used to intrigue the readers. Finally, I want to compare their structures. All essays need organization, writers use a number of different strategies to organize information and, often, the choice of how to organize is based on one own judgment of what would be most effective (Connell Soles, 2013). The structures between the two essays are similar however; each has their own particular form. An author of a narrative essay can use chronological order, events arr anged in a chronological order that are organized by time, and may start with the earliest event and go forward in time to the present or start from the present and go backward in time and spatial order which means organized by direction.(Connell Soles, 2013). A third organizational structure that I have found to be very useful for a narrative is dramatic order The dramatic structure is common in many types of writing and uses these five elements, an opening paragraphs that has an introduction, the introduction should have a strong thesis that helps create questions in the readers mind; it should also captivate their imagination. The rising action should take up the majority of the story and should include interaction, dialogue and detailed descriptions of the characters and the environment. It should also explain the reason for writing the essay; the climax or turning point, which will be the moment the conflict comes into sharp focus and is resolved. The falling action is where the rest of the story falls into place and, the concluding paragraph that will end the essay with answers to the reader’s questions. The essay may conclude with a discussion of why the topic of interest is important (Connell Soles, 2013). As stated in Esse ntials of College writing second edition, a descriptive is very similar to a narrative because it to must have a sound structure, There must be an introduction that â€Å"tells readers what you will tell them†, a body that â€Å"tells them†, and a conclusion thatbbrings closure to your paper (Connell Soles, 2013). For the introduction, the author must accomplish a few goals: capture the readers’ attention by revealing the purpose of the paper, have a strong thesis statement and briefly describe the main points covered in the paper. For the body, which is the heart of your paper, the author must explain, describe, argue, explore, or elaborate on the point or thesis of the paper. The final part of the essay, the conclusion is where the author makes his or her final stand, they state they final opinion on the topic and they end the essay (Connell Soles, 2013, chap. 5). Are narrative and descriptive essay similar? Do they share the same purpose? My answer is yes. The similarities out weigh the differences and with this knowledge I have formed my opinion that neither form of essay is superior, but both equally matched. I believe that both essays inspire the readers’ creativity and help bring forth their own opinions on the topics. I have formed my opinion using the facts described ab ove, such as they both use expressive words to take a hold of their audience, they are wrote to create a clear picture of the characters and the plot, and they both have a similar structure. Based on the information I have gained I can say that the similarities are more recognizable than the differences. References Connell, Christine M Sole, Kathy Essentials of College Writing, 2013 Leacock, S. (1916). Are the rich happy? In R. Nordquist (Ed.), About.com Guide to Grammar Composition. Retrieved from http://grammar.about.com/od/classicessays/a/Are-the-Rich-Happy-by-Stephen-Leacock.htm Quindlen, A. (n.d.). Homeless. Retrieved from http://pers.dadeschools.net/prodev/homelesstext.htm

Gift Giving in the Medical Industry Essay -- Healthcare

In a recent article from St. Paul Pioneer Press (http://www.cbsnews.com/8301-505245_162-57348681/drug-company-money-on-rise-for-2-minn-clinics/), the University of Minnesota and the Mayo Clinic came under public scrutiny after it was revealed that they received $650,000 between them in 2010. Gift giving has always been a touchy subject in the medical industry. Various articles have been written regarding the subject exploring the benefits and its disadvantages. But the tug of war between ethics and the effects of commercialism has yet to be seen in the stand of medical institutions and health care providers. In 2008, Fortune 500 magazine reported the Pharmaceutical Industry as one of the top three most profitable industries in America. This should not come as a surprise since there will always be sickness and disease and as a necessary consequent there will be patients who will need medicine for these illnesses. â€Å"It is a lucrative industry that utilizes different strategies to gain revenue.† said James Rhee, a professor in the Department of Physician Assistants Studies of Eastern Virginia Medical School, when he described the industry in his article in the Internet Journal of Academic Physician Assistants(http://www.ispub.com/journal/the-internet-journal-of-academic-physician-assistants/volume-7-number-1/the-influence-of-the-pharmaceutical-industry-on healthcare-practitioners-prescribing-habits.html). Business is business for these large pharmaceutical industries and they employ marketing techniques that will ensure their profitability. In realizing these gains, Pharmaceutic al companies employ variations on the tried and tested theme of gift giving. GIFT GIVING, IS IT APPROPRIATE? As early as 2003, Arnold Relman a Harvard ... ...dress conflict of interest issues, key people in strategic position like the director of the office of institutional compliance at the University of Minnesota, Lynn Zentner had this to say: â€Å"An unmanaged conflict is a problem,† â€Å"Having a conflict of interest is not.† # # # Works Cited (http://www.cbsnews.com/8301-505245_162-57348681/drug-company-money-on-rise-for-2-minn-clinics/),(http://www.ispub.com/journal/the-internet-journal-of-academic-physician-assistants/volume-7-number-1/the-influence-of-the-pharmaceutical-industry-on healthcare-practitioners-prescribing-habits.html),(http://www.bmj.com/content/326/7400/1189.extract),(http://www.twincities.com/ci_19619583?source=pkg),http://www.msnbc.msn.com/id/45796673/ns/technology_and_science-science/t/drug-company-money-rise-minn-clinics/#.TwFJtDX9Mlc)

Qualitative Anion Tests Essay

Procedure 1. Before beginning, set up a data table similar to the Data Table: Qualitative Anion Tests in the Lab Report Assistant section. 2. Each anion tested will require the use of three separate test tubes. Complete all of the following tests on one solution, record your observations, and then thoroughly clean and dry the test tubes before beginning tests on the next solution. 3. After consecutively testing the identified anions, perform the same tests on the unknown solution to conclusively determine its identity. 4. First test tube: a. Put 8 drops of the anion to be tested in a clean small test tube. b. Add 8 drops of hydrochloric acid to the anion solution. Note the appearance of the solution plus any evolution of gas and odors of gas. 5. Second test tube: a. Put 8 drops of the anion solution in a second test tube. b. Add 3 drops of silver nitrate solution. c. Note the colors of any precipitates formed. d. Write a net ionic equation for any reaction that produces a precipitate. e. Acidify the test tube by adding a few drops of nitric acid. f. Mix well and note if the precipitate dissolves or remains. 6. Third test tube: Per the following, perform the appropriate confirmation test for this anion. NOTE: Where the following instructions call for â€Å"gently warming† a chemical place the test tube containing the chemical into a 50-mL beaker of hot tap water for a few minutes. ââ€"  Bromide (Br-) and Iodide (I-): (First make fresh chlorine water by combining in a graduated cylinder approximately 1ml of bleach, 5ml of tap water, and 6 drops of HCl; stir or shake. Then label an empty pipet and suck up this chlorine solution for use here.)To 10 drops of the test solution add 2 to 3 drops of the organic reagent (hexanes or similar) and several drops of chlorine water. Shake well and allow the lower layer to settle out. Note the color in the organic reagent layer. A brown or gold color indicates bromine and a reddish-violet or pink color indicates iodine. Carbonate(CO32-): Acidify 20 drops of the solution with 2 drops of HCl. Carbonates produce an odorless gas (CO2) which should produce a precipitate when bubbled through a saturated calcium hydroxide solution. For the purpose of this experiment you may distinguish this gas from hydrogen sulfide by its lack of odor (See sulfide test, S2-). ââ€"  Chloride (Cl-): To 6 drops of the test solution add 2 drops of AgN03, silver nitrate solution. A white precipitate that dissolves readily when the solution is made definitely basic with aqueous ammonium indicates the presence of the chloride ion. ââ€"  Phosphate(PO43-): Acidify 10 drops of the test solution with 1 drop of HNO3, nitric acid, and add 7 drops of ammonium molybdate solution (shake it well before using). Wait 30 seconds. The phosphate should produce a yellow precipitate. Gentle warming may be necessary to obtain the precipitate. ââ€"  Sulfate (SO4 2-): To 10 drops of the test solution add 5 drops of the BaCl2, barium chloride solution. A white precipitate that is insoluble in HCl indicates the presence of sulfate. ââ€"  Sulfide (S2-):Acidify 10 drops of the test solution with HCl. The odor of hydrogen sulfide (H2S) should be apparent (it smells like rotten eggs!). Warm the solution moderately and then hold a small piece of moist lead acetate paper at the mouth of the test tube. If the paper turns black (caused by PbS) this indicates the presence of sulfide. Thoroughly clean and dry the test tubes before beginning tests on the next solution. Cleanup: Tightly cap the bottle of silver nitrate solution and put it in the Experiment 11 bag so it will be easy to find when you need it for the next experiment. Flush any other remaining solutions down the drain with lots of water. Properly rinse all equipment used, then dry and store for future use. Data and Observation Data Table: Qualitative Anion Tests Name Test tube 1 w/HCI Test tube 2 w/AgNO3 w/HNO3 Test tube 3 Confirmation Bromide Gas and no smell Precipitate, didn’t dissolve Didn’t dissolve Iodine separated from Bromide Carbonate Gas and no smell Cloudy Precipitate Clear gas present Clear and no smell Chloride Gas and no smell, No precipitate Cloudy precipitate present Didn’t dissolve Dissolve with precipitate present Iodine Gas and no smell Precipitate, didn’t dissolve Didn’t dissolve Iodine separated from Bromide Phosphate Gas and no smell Cloudy and yellow precipitate present Dissolve Yellow with precipitate present Sulfate Gas and no smell Precipitate present Didn’t dissolve White precipitate present Sulfide Gas and clear Precipitate present Didn’t dissolve Had an odor with precipitate present. Turned Black Unknown No change No change White precipitate present Sulfate didn’t dissolve Questions: Group 1: Anions that WILL NOTPRECIPITATE in the presence of silver nitrate. Sulfate Group 2: Anions that WILL PRECIPITATE in the presence of silver nitrate and the resulting precipitates WILL DISSOLVE upon acidification with nitric acid. Carbonate, Phosphate Group 3: Anions that WILL PRECIPITATE in the presence of silver nitrate and the resulting precipitates WILL NOT DISSOLVE upon acidification with nitric acid. Bromide, Chloride, Iodide, Sulfide A. Write a net ionic equation for any reaction that produces a precipitate. Sodium Bromide: Ag+(aq) + Br-(aq) ( AgBr(s) Sodium Carbonate: 2Ag+(aq) + CO32-(aq) ( Ag2CO3(s) Sodium Chloride: Ag+(aq) + Cl-(aq) ( AgCl(s) Sodium Iodide: Ag+(aq) + I-(aq) ( AgI(s) Sodium Phosphate: Ag+(aq) + PO4-(aq) ( Ag3PO4(s) Sodium Sulfide: 2Ag+(aq) & S-2(aq) ( Ag2S(s) B. Identify the anions that produce gas upon addition of HCl. Carbonate, Sulfide C. Identify the anions that do not precipitate with silver nitrate. Sulfate D. Identify the anions that react with silver nitrate to form precipitates that dissolve when acidified with nitric acid. Carbonate, Phosphate E. Identify the anions that react with silver nitrate to form precipitates that do not dissolve when acidified with nitric acid. Bromide, Chloride, Iodide, Sulfide F. What simple test (other than a specific confirmation test) would distinguish between CO3 2-and NO- ? Add Barium Chloride. If there is CO32- a white precipitate of BaCO3 will appear. Conclusions: Through this experiment, I learned how to identify commonly occurring anions. I also learned how to use the characteristics of their reactions with HCl and AgNO3 to identify an unknown solution. Using my observations with the different anion mixtures, I was able to identify the Unknown anion to be Sodium Sulfate. I figured this out because when HCl was added, no gas was formed. This ruled out Sodium Carbonate and Sodium Sulfide. The gas I observed for the Sodium Carbonate & Sulfide was very subtle. Even then I was not 100% sure. This is where I think there could have been room for error because I did not read the results correctly, therefore possibly interfering  with my unknown. However, the unknown did not form a precipitate and there was only one other anion that did this.

Political Disputes In Early Nineteenth Century Essay

The North and South in the nineteenth century were different in lifestyle and morale as well as economy. The north had a booming industrial economy while in the South, cotton was king. Because of this, congress was continuously addressing controversial matters and providing answers that did not satisfy either one side or both. The early 1800s were full of the North and the South making many attempts at reconciliation that just fell short. Among those were the Missouri Compromise of 1820, and the Great Compromise of 1850. Other tempestuous attempts led to the Tariff/Nullification Controversy, anti slavery debates in congress, and the Kansas-Nebraska Act. Whether it was one side or the other, there was always someone to oppose – and in some cases, defy – the laws put in place, which eventually led to the succession of the southern states and the Civil War. The issue of slavery became an even greater concern when the Louisiana Purchase territories were to enter the Union a s states. The question was, would new territories enter the Union as slave or free states? The South wanted a balance of power. They knew that if the North were to have more free states, then slavery in the south could be facing extinction through congress. In an attempt to conciliate with the South, the North agreed upon the Missouri Compromise of 1820. Through this, slavery was banned above the 36 degrees 30 minute line and Missouri entered as a slave state, Maine a free state. For a while, it retained the balance of power. However, tempers in the south rose again later in the 1820s over high tariffs. The tariffs benefitted the north but threatened southern cotton exports. In 1828, the tariff was around 50%. President Jackson modified it to around 33% in 1832 only to have South Carolina nullify it in the state. It raised the question of whether or not the federal government could legally impose protective tariffs and whether it was constitutional for a state to nullify a federal law. â€Å"South Carolina†¦by a course of legislation†¦can defeat the execution of certain laws of the United States†¦.it is utterly impracticable†¦Ã¢â‚¬  [Document A] Henry Clay believed it impractical for South Carolina to oppose the federal law and also believed that South Carolina had no intention of leaving the Union, which depicts just how blind people were to just how great the rift really was. In 1833, the Compromise Tariff was put into place and would reduce rates to 20% by 1842. At this time, most people considered compromise to still be possible. As time goes on, slavery becomes as much of a moral  issue as a political one. The American Anti-Slavery Society believed that the practice of slavery was against God’s teaching and that those who kept slaves were man stealers. [Document B] Slaves should be set free and slaveholders shouldn’t be compensated a dime. â€Å"†¦we concede the Congress†¦has no right to interfere with any of th e slave states†¦But we maintain that Congress has a right†¦to suppress the domestic slave trade†¦Ã¢â‚¬  [Document B] As abolitionists started to make an even greater fuss over slavery, congress was backed into a corner. To release the slaves and prevent slavery in the new territories would incite the wrath of the South, however to allow more slave states to enter the Union would anger the abolitionists. Eventually, the gag rule was put into place. â€Å"All petitions, memorials, [etc.]†¦to the subject of slavery or the abolition of slavery, shall†¦be laid on the table and that no further action whatever shall be had thereon.† [Document C] However, each time a territory wanted to become a state, whether slavery would be permitted or not was a forefront issue – starting with the lands gained from the Mexican War. The Compromise of 1850 was put into place here. California was admitted as a free state and New Mexico and Utah entered under popular sovereignty (the citizens would decide whether they wanted slavery or not.) From this compromise also came a stronger Fugitive Slave L aw (all escaped slaves were to be turned in and returned.) Northerners blatantly ignored this federal law which angered the Southerners, for when they had tried not to comply to a federal law, they had been punished. [Document D] The Southerners felt wronged, and rightly so. Compromise seemed less and less possible. In 1854, there were questions on whether there should be slavery in the Kansas-Nebraska territories, even though it was prohibited by the Missouri Compromise. The South was unhappy about this however because the shaky balance of power would then decisively shift to the North. The South needed more slave states. Because of this, the Missouri Compromise was then repealed. Popular sovereignty was then ruled in the territories. At the sound of that, abolitionists and pro-slavery citizens began to rush Kansas in spades. Fighting broke out so horrifically it was given the name Bleeding Kansas. During this, a new political party arose: the Free-Soilers. They were against slavery and fought state constitutions such as the Lecompton Constitution. After this, slavery issues began to spin out of control. Things like the Dred Scott Decision and John  Brown’s Raid and other slave revolts kept slavery at the forefront of everyone’s minds. The Free-Soilers then turned into the Republicans who firmly believed in the end slavery. Compromise was now nearly impossible. The possibility of compromise was then nailed shut when a Republican, Abraham Lincoln, won the election of 1860. North Carolina then seceded from the Union and other southern states soon followed suit. It’s possible that if the South had only picked one candidate, they could have won the election. [Document H] But because they hadn’t, the South then felt threatened. And because they felt threatened, they seceded. The reasons and events stated led to the eventual conclusion of the impossibility of compromise by 1860.

20 Sociology Essay Topics How to Write about Drug Use and Its Consequences

20 Sociology Essay Topics How to Write about Drug Use and Its Consequences If you are looking for a topic on which to write your drug abuse essay and the consequences of drugs, then review the topics below: The Size of Substance Misuse and Limitations on Data for Substance Abuse. Different Trends Relating to Drug Use and How It Has Changed Over Time. History of Psychoactive Substances in the Country of Your Choosing. Reasons Why Individuals Use Drugs. Different Categories of Drugs. Government Drug Misuse Strategy and Legislation. Attitudes and Values toward Drug Use. Key Areas of Response to Drug Use. Signs and Symptoms of Misuse. Popular Drug Use Paraphernalia. Range of Services Available for Drug Misuse and Organizations Available for Help. Issues Associated with Alcohol Misuse. Different Drinking Habits and the Effects of Alcohol Consumption. Myths about Drug and Alcohol Use and Ways to Respond to Alcohol Abuse. What Communities Can Do to Help Fight Substance Abuse. Why Community Responses Are Necessary and What Barriers Exist for Community Based Action Plans. Personality as a Factor in Drug Abuse. Importance of Knowing First Aid in Helping People Fighting Drug Misuse. Barriers in Effective Communication with Young People. The Screening Process for Drug Use and Its Effectiveness. Sample Expository Essay on the Personality as a Factor in Drug Use An article published in PsychologyToday.com in 2009 stresses personality as a powerful factor that helps answer why some are prone to abusing drugs and becoming addicted while others aren’t. According to the author, an addictive personality trait, owned by about 10-15% of people, makes them prone to becoming addicts. However, according to an article published four years earlier in MedicalNewsToday.com, among people with similar personality traits some are known to develop an addiction while others aren’t quite as prone. The article accounts for this phenomenon by claiming that favourable environmental and cultural conditions can help offset addictive personality traits. There is a complex interplay of societal, community, peer, family and individual factors accounting for negative behaviour such as substance abuse, according to the United Nations Office for Drug Control and Crime Prevention (2000). Globally, it has been observed that a member of a family with a history of drug abuse and dependence is more prone to drug abuse. This finding is corroborated in many studies, such as Wu et al. (1996), Wester-meyer and Neider (1994) and Madianos et al. (1995). In other studies, Jauhar and Watson (1995), and Curran et al have found the same pattern to occur with respect to alcohol abuse and dependence. Bierut, Dinwiddie, and Regleiter (1998) have established the significant influence of genetics in alcohol dependence, while Tsuang et al. (1996) have established the same causal link between genes and drug dependence. Thus, family environment is instrumental, both in promoting drug abuse and dependence and in providing protection from it. In this section, a few of these factors have been reviewed. The limitations concomitant with the chosen research design render a large number of these findings as purely correlative rather than causal. Below are several factors associated with family environment. Physical and sexual abuse in childhood: despite its design limitations, relating either to use of clinical samples or retrospective designs, research suggests that childhood abuse appears as a risk factor with regard to substance abuse. Thus, risk of alcohol abuse in adulthood is enhanced in women subjected to physical or sexual abuse in childhood, as delineated in studies done by Langeland and Hartgers (1998) and Rice et al. (2001). Curiously, with regard to males research points to contradictory evidence; perusal of studies done by Galaif et al. (2001) and Langeland and Hartgers (1998) shows this contrast. Jarvis, Copeland and Walton (1998) go a step further, establishing direct correlation between adolescent drug abuse among women and childhood sexual abuse, accompanied by the extrapolation that such drug use could be in the form of self-medication aimed at reducing emotional pain induced via childhood abuse. Family practices and attitudes relating to substance abuse:   Lane et al (2001) stressed the importance of peer influences leading to substance use among youth; however, one cannot neglect the significance of family practices and attitudes. The predominance of parental influence over that of peers is especially true in Hispanic/Latino youth, as established by Coombs, Paulson, and Richardson (1991). The frequency of youth substance use is greatly influenced by use of substances by family members and family members’ attitude with regard to it. For instance, Lane et al (2001) have referred to a household survey on substance use done in 1997 that revealed the lowest incidence of substance use among youth in the age group of 12-17 years. Said youth were said to perceive their parents as being very upset with binge drinking, cigarettes and marijuana. Swaim, Nemeth, and Oetting (1995) have highlighted a similar reduction in alcohol use among girls in Hungary, owing to strong family sanctions against such substance abuse. Boyle et al. (2001) have established that drug use by an older sibling is a greater influence than parental drug use in leading to youth substance abuse. Problematic relations with family members and partners:  the risk of substance abuse has been found to increase in direct proportion to problematic relations with family members and partners. Lane et al (2001) have brought attention to the fact that youth who had several weekly arguments with their parents showed a greater tendency to have used marijuana during the previous year than others who had one argument a week or month, as revealed by a national household survey done. Studies have established that the direct correlation between problematic relations with family members and drug abuse by adolescents manifests internationally. Women in Zagreb were more prone to alcoholism due to problematic relations with family members and partners. Other studies have shown how more than 75 of 100 Scottish males admitted for alcohol abuse blamed failed marriages and family neglect on their alcoholism. References: Barlow, K. (2000).  Substance misuse: A rationale for compulsion. Bourgois, P. (2008). The Mystery of Marijuana: Science and the U.S. War on Drugs.  Substance Use Misuse,  43(3), 581-583. doi: 10.1080/10826080701884853 Bretteville-Jensen, A. (2006). To Legalize or Not To Legalize? Economic Approaches to the Decriminalization of Drugs.  Substance Use Misuse,  41(4), 555-565. doi: 10.1080/10826080500521565 Cozic, C. P. (1998).  Illegal drugs. San Diego, CA: Greenhaven Press. Gorta, A. (2009). Illegal drug use by police officers: Using research and investigations to inform prevention strategies.  International Journal of Police Science and Management,  11(1), 85-96. doi: 10.1350/ijps.2009.11.1.112 Grossman, M., Chaloupka, F. J., Shim, K. (2002). Illegal Drug Use And Public Policy.  Health Affairs,  21(2), 134-145. doi: 10.1377/hlthaff.21.2.134 Harrison, L. (1993).  Substance misuse: Designing social work training. London: Central Council for Education and Training in Social Work. Miller, K., Hoffman, J., Barnes, G., Sabo, D., Melnick, M., Farrell, M. (2005). Adolescent Anabolic Steroid Use, Gender, Physical Activity, and Other Problem Behaviors*.  Substance Use Misuse,  40(11), 1637-1657. doi: 10.1080/10826080500222727 Trathen, B. (2003).  Guidelines for the best practice treatment of substance misuse. [England?]: B. Trathen. White, H. R., Tice, P. C., Loeber, R., Stouthamer-Loeber, M. (2002). Illegal Acts Committed by Adolescents Under the Influence of Alcohol and Drugs.  Journal of Research in Crime and Delinquency,  39(2), 131-152. doi: 10.1177/002242780203900201

Federalists and Anti Federalists essays

Federalists and Anti Federalists essays Soon after the end of the Revolutionary War if not before it became clear that the Articles of Confederation were not a workable arrangement. Wartime contingency measures might have papered over the most immediate problems, but with the coming of peace something more regular was needed. The defects of the Articles produced a host of disputes among states, which could not be resolved under its terms, and which times were serious enough to lead to militia skirmishing. More broadly, a fundamental issue had been left unresolved: Was the "United States" a nation in its own right, or a mere confederation of semi- autonomous states' This was not just an abstract question a great many group and individual interests were wrapped up in it. By and large, commercial interests were interested in a strong national government, creating an internal free-trade zone and consistent legal rules concerning trade. Other wealthy interests, however, had mainly local influence large landowners, for example, who in this era might still expect a quasi- feudal deference from tenants and neighbors. Their local standing would be diminished in a more unified national political structure. However, even these interests conceded that the original Articles were unworkable, while on the other hand many proponents of a stronger central government still had anxieties that it might become authoritarian, in 18th century language The Constitutional Convention was initially convened merely to patch up the Articles of Confederation, but it was dominated by proponents of stronger central government. Instead of modifying the Articles it threw them out entirely. Both Federalists and Anti-Federalists thereupon engaged in a propaganda battle. The Federalists won this in a mismatch: the Federalist has gone down as a political classic, while the Anti-Federalist writings have all but vanished f...

Unbroken by Laura Hillenbrandâ€Discussion Questions

'Unbroken' by Laura Hillenbrand- Discussion Questions   Unbroken by Laura Hillenbrand is the true story of Louis Zamparini, who was an Olympic runner that survived for more than a month on a raft in the Pacific Ocean after crashing his plane during World War II. He was then taken as a Prisoner of War by the Japanese. Hillenbrand tells his story in parts, and these book club questions are also divided by parts of the book so that groups or individuals can discuss the story over time or focus on the areas they want to discuss more deeply. Spoiler Warning: These questions contain details about the end of Unbroken. Finish each section before reading the questions for that part. Part I Were you interested in Part I, which was mostly about Louis childhood and running career?How do you think his childhood and Olympic training helped him survive what would come later? Part II Were you surprised by how many servicemen died in flight training or in planes that went down outside of combat?Superman received 594 holes in the battle over Nauru. What did you think of the descriptions of this air battle? Were you surprised by their ability to survive despite being hit so many times?Did you learn anything new about the Pacific theater during World War II through this part of the book? Part III How do you think Louie survived the crash?What were details of the mens survival on the raft most interesting to you? How they found and saved water or food? The ways they kept up their mental acuity? The lack of provisions in the life raft?What role did emotional and mental state play in Phil and Louies survival? How did they keep their minds sharp? Why was this important?Were you surprised by how ferocious the sharks  were?Louie had several religious experiences on the raft that led to a new belief in God: surviving the gunning by the Japanese bomber, the tranquil day at sea, the provision of rainwater and seeing singing in the clouds. What do you make of these experiences? How were they important to his life story? Part IV Were you aware of how severely the Japanese treated Prisoners of War during World War II? Were you surprised to learn how much worse it was for men captured in the Pacific war than for those captured by Nazis?When Louie is interviewed just after his release, he says If I knew I had to go through those experiences again, Id kill myself (321). As they were going through it, how do you think Louie and Phil survived the starvation and brutality they faced as prisoners?What were the ways the Japanese tried to break the mens spirits? Why does the author focus on how this was worse in many ways than the physical cruelty? What do you think was the hardest thing the men had to endure?Later in the narrative, we learn that the Bird and many of the other soldiers were pardoned? What do you think of this decision?How do you think the men escaped the Kill All order?Why do you think Louies family never gave up hope that he was alive? Part V Epilogue In many ways, Louies unraveling is not surprising considering all he endured. After attending the Billy Graham crusade, however, he never experienced another vision of the Bird, he saved his marriage and he was able to move on with his life. Why do you think this is? What roles did forgiveness and gratitude play in his ability to move on? How did he see God at work throughout his whole experience despite the unimaginable suffering he experienced?From the moment of their rescue through the present day publishing of this book and the movie adaptation, Louie Zamparini has received significant media attention whereas Allen Phillips was treated as a trivial footnote in what was celebrated as Louies story (385). Why do you think that was?Louie continued to have adventures well into old age? What parts of his post-war story were most notable to you?Rate Unbroken on a scale of 1 to 5. Details of the book: Unbroken by Laura Hillenbrand was published in November 2010.Publisher: Random House496 PagesThe movie adaptation of Unbroken was released in December 2014.

Abstract Essay Example | Topics and Well Written Essays - 500 words - 2

Abstract - Essay Example The authors note Lukas and others as the basis of their experimentation. Lukas and others studied the criticality of this problem, and came up with results that sought to be confirmed through numerous experiments conducted by the aforementioned three authors of this article. To enhance the outcome of the study, different camera sets were employed, and authors of previous related works were not contacted. The verification process set off by carrying an overview of a digital camera and the images captured using them. The imaging pipeline is analyzed, with all roles performed by the lens, filters and the sensor being presented. The outcome of this process is influenced by the camera or scanner’s manufacturer, as well as pixel values attributed to the camera. Color filtering is then introduced. Array patterns and color spaces that complement the imaging pipeline is highlighted. Sensor noise is another overview variable of the digital camera. A number of noise types are outlined, i ncluding shot noise, pattern noise and readout noise. Emphasis is given to pattern noise, which is used in the source-camera identification probe. Approaches that are correlation-based are not ignored in the underlying pursuit. Comparisons of original and denoised images are used to estimate the pattern noise frequencies, especially the frequencies that are high in that regard. Classifier training and the detection scheme are the employed approaches under the correlation-based aspect of source-camera identification. Choosing the source camera is an essential action towards assessing experimental results. Reference patterns are used, and matched with high correlation to identify the source camera. Experimental thresholds can also be used, where the source camera chosen should exhibit a higher than threshold correlation value. Figures of images, cameras and scanners are used as physical frameworks of the study. The experimental results provide a

Art black market (Iraq war missing art work) Term Paper

Art black market (Iraq war missing art work) - Term Paper Example however, this was later found. There was also an Assyrian headboard in the 900 BC which was specifically ivory headboard and was later recovered by the Jordanian officials in the custom department when it was stolen from the museum into the black market. The existence of the art work of in the museum of Iraq lead into more loses. Some additional missing artwork in Iraq was Bassetki statue. This statue was for a sitting nude male figure created in the period of 2300 BC.1 This sculpture was an artistic work which could be used by the Iranians to enhance the skills of art work. It was majorly suspected by the officials that these artifacts were taken out by foreigners who came into Iraq. Another lost art work in the museum was Sacred Vase of Warka. It existed from 3200 BC. The lost art work was very significant in the prehistoric artistic nature of the Iraq. Investigations by both Iraq and US investigators ensured that they brought back the lost art work in the Museum.2 With respect to the events, it facilitated siphoning of the art works outside Iraq. There are several art works that are still missing to date in the black market. One of the most prominent art works was Lagash statue, a headless limestone inscribed statue of Fanatum in the years dating to 2450 BC. The war facilitated stealing of many artistic works in nature because of the confusion during the time hence there was search for these items later after the war as hatched by the Iraq government. In 800 BC, there was also Nimrud lioness made up of ivory that was taken away from the museum.3 This was one of the pre historical art works in Iraq that had been taken away during the war by the soldiers and other foreigners. In the Babylonian empires, there were cuneiform bricks which were the nine royal bricks for inscription that originated from Sumerian. The bricks were beautifully made and they reflected the most artistic work of the Iraq. They were stolen during the war but later they

Dq-7.1-Terence Coursework Example | Topics and Well Written Essays - 1750 words

Dq-7.1-Terence - Coursework Example (1)What are the advantages? The new approach that many software developers are adapting today that entails parallel working among programmers has many advantages. Programmers that work in parallel when developing software can easily compare the algorithms they have concern the developments they are making. Making comparisons is important since it enables the programmers develop a system that is too fine enough to avoid minor breakdowns (Dingsà ¸yr, Nerur, & Moe, 2012). In the same way, this working model enables system developers to benefit from their colleagues in different ways. For example, one system developer can take advantage of his or her counterpart’s expertise. In this case, the less experienced worker is going to acquire tips and important knowledge from the colleague assigned to him/her. When programmers get to work in parallel, they save a lot of time for the organization they are serving. Instead of spending a lot of time working separately then combining their pieces of work later on, the programmers can just work together at the same time. The clients being served here are assured of being served instantly in some cases. Management of the software development program is also made easier by the approach of having parallel software developers. In this case, the supervisors of the projects are not compelled to supervise all the programmers’ work one after the other. The management of the project is always concerned about the quality of software that has been developed by the programming activity. There is little time that is spent on management of this activity when the process is done using the parallel approach (Ajimatanrareje, Shaw, & Pucci, 2014). The new approach of parallel working among software developers is important to any organization that is concerned about the software used I its operations. However, this approach may also have negative effects with the management is

Journal entry Essay Example | Topics and Well Written Essays - 250 words - 6

Journal entry - Essay Example at the solicitation of japan, was still in conversation with its government and emperor looking toward the maintenance of peace in the pacific† the speakers character of being a peaceful person trying to seek peaceful ways of solving a conflict is brought out. He tries to convince the congress that his government made all the peaceful attempts to find amicable solution and indeed it’s the government of japan that is at fault and therefore drastic action should be taken against them (Gross et al 78). â€Å"Yesterday the Japanese Government also launched an attack against Malaya. Last night Japanese forces attacked Hong Kong. Last night Japanese forces attacked Guam. Last night Japanese forces attacked the Philippine Islands. Last night the Japanese attacked Wake Island. And this morning the Japanese attacked Midway Island.Japan has, therefore, undertaken a surprise offensive extending throughout the Pacific area. The facts of yesterday and today speak for themselves† the speaker uses a lot of repetition employing the artistic style of logic, giving supportive evidences to bring out the facts that indeed japan is offensive due to the many attacks and congress should declare war with them (Gross et al 88) The other rhetorical technique employed by the speaker is the use of pathos when he says â€Å"The attack yesterday on the Hawaiian Islands has caused severe damage to American naval and military forces. I regret to tell you that very many American lives have been lost† the speaker tries to bring out the damage and loss of lives caused by the attack therefore tries to invoke emotions of sympathy and anger for the lives lost and anger about the attack hence the reason why congress should act(Gross et al 90). The speaker used evidence based arguments that he illustrated with a lot of emotions to bring out the urgency of the matter to congress and the American people. The use of artistic techniques such as logos pathos and ethos brought out the speakers character

Technical communication Essay Example | Topics and Well Written Essays - 250 words

Technical communication - Essay Example Therefore, the statement about the ease of operation should be changed, along with the drawing, so that the two agree in the assumption of this reasonable â€Å"fitness for a particular purpose† (Product, 2009). Ethical Case: In this case, the DMX-450 ® is advertised as a product that â€Å"makes downloading large email files almost instant. You’ll no longer have to wait for large file scans.† The ethical breach that has occurred here is that the content violates the reader’s assumptions of fact based and rational explanation of the product. Instead, the DMX is being advertised as operating at a speed that is impossible, or approaching impossible; it is not an objective or fact-based description of what the software is capable of (such as a specific baud rate or downloading speed). I would tell the co-worker that s/he should trust their consumer more, and stop trying to talk down to them with lofty exaggerations; I would advise them to simply tell the consumer about the product, rather than boasting, to make a better ethical impression. This way, the consumer will feel more secure and trusting about the company’s

Pricing Scheme Research Paper Example | Topics and Well Written Essays - 750 words

Pricing Scheme - Research Paper Example The United States stock market is the place where individuals buy or sell stocks. The markets’ sellers sell the companies’ products to the eager stock buyers. Similarly, the stock market sellers offer to buy the stocks sold by the stock owners. Economics plays a major role in the sale or purchase of the stocks. The sellers prefer to sell more stocks at higher prices. Similarly, the buyers prefer to buy stocks at lower prices. As the prices rise, the current and future customers’ demand for the products decline. When the prices rise, the supply of the products increases (Arnold 312). The current research delves on the pricing of the Verizon Company’s stock market prices. The stocks are sold and bought using a controlled computerized software program. The stock market includes the services offered by the stock market agents. The agents are selling the stocks of the communication services company, including Verizon (Morningstar 1). Table 1 shows the prices of the Verizon stocks sold in the digital stock market. The stock market prices show the equilibrium price. The equilibrium price is the price agreed upon by both the Verizon stock sellers and the Verizon stock buyers (Morningstar 1). There are economic interpretations of the stock market prices (Arnold 312). In terms of the January 10, 2014 equilibrium price, the sellers and buyers of 11,454,003 stock units agreed to sell (exchange) the stocks at $ 47.75 per stock. The price dropped from the prior week’s $48.42 stock market price. The price drop was instituted in order to increase the drop in the demand for the Verizon stocks. The 11,454,003 stock units sold show the decline from in the demand for the Verizon stock. The prior week’s stock market units sold (exchange) was higher at 12,045,205 units (Morningstar 1). Similarly, the January 31, 2014 stock market price of the Verizon stock was $48.02 each. At this price, there were 18,558,798 stock units sold.

Technical communication Essay Example | Topics and Well Written Essays - 250 words

Technical communication - Essay Example Therefore, the statement about the ease of operation should be changed, along with the drawing, so that the two agree in the assumption of this reasonable â€Å"fitness for a particular purpose† (Product, 2009). Ethical Case: In this case, the DMX-450 ® is advertised as a product that â€Å"makes downloading large email files almost instant. You’ll no longer have to wait for large file scans.† The ethical breach that has occurred here is that the content violates the reader’s assumptions of fact based and rational explanation of the product. Instead, the DMX is being advertised as operating at a speed that is impossible, or approaching impossible; it is not an objective or fact-based description of what the software is capable of (such as a specific baud rate or downloading speed). I would tell the co-worker that s/he should trust their consumer more, and stop trying to talk down to them with lofty exaggerations; I would advise them to simply tell the consumer about the product, rather than boasting, to make a better ethical impression. This way, the consumer will feel more secure and trusting about the company’s

Consumer bahaviour Essay Example | Topics and Well Written Essays - 2500 words

Consumer bahaviour - Essay Example The research was conducted on Thursday and Friday, in the afternoon and the evenings of the weekend. The reason for research at Gucci is simple, had we chosen a common store, we would have made numerous efforts to judge people as it is hard to find differences in people's behaviour at a lower level, but at Gucci, a particular society enters to buy the expensive items, so it is a lot of fun to measure how they look for something and what particular thing about Gucci changes their facial expressions. The place is excellent for people who prefer to stay fashionable and who have got the buying power. The store does not cater every one as its target audience but those who can really afford the high prices, further once the customer enters, the staff prefers to look at the customer from top to bottom but it has got its own charm. It is important to describe the outlook of the store first. The store seems to be transparent as there is just a glass with an entrance door, upon entering the sh elves are carrying bags straight ahead. People do complain about the staff as the staff is really rude especially if it sees that the customer does not look like an interested buyer but nevertheless the staff greets upon entrance. The atmosphere within the store is absolutely wonderful as it seems that there is no one near you due to silence. It seems that thousands have been invested in the interior of the shop but the figure could also be a million. A General View on Consumer Behaviour: Lifestyles emerge from various social influences. They are also derived from the individual's personal value system and personality. Marketers need to study the way consumers live and spend their money as well as how they make purchase decisions (Holbrook: 1999). For example, blue jeans may serve as inexpensive, functional clothing to bluecollar workers, but as fashionable, self-expressive apparel to upperclass members. Credit cards may be used as a convenience for the affluent, while others use them as a basis for installment purchases since balances are not paid off immediately. Decisions emanating from lifestyles are learned as the result of many influences such as culture, subcultures, social class, reference groups, and family (Beckman, William: 1967). Activities, interests, and opinions reflect how consumers spend their time and their beliefs on various social, economic, and political issues. When understood by marketers, these variables ca n help reduce risk in the decision-making process. At Gucci, people prefer to buy those materials that involve less risk and are long lasting, however the brand name itself is a guarantee that no matter what the customer buys would be long lasting and fashionable. So it is fair to say that perception plays a major part in the answer to perceived risk of purchasing a product or service. Perceived risk represents the anxieties felt because the buyer cannot anticipate the results of a purchase. A number of different strategies may be used to reduce risk. First, perceived risk can be reduced by a prepurchase information search, by decreasing the probability of failure. Second, the buyer can shift from one type of perceived risk to another type that is of less impact on the realisation of

Risk & Return Essay Example for Free

Risk Return Essay What are investment returns? What is the return on an investment that costs $1,000 and is sold after 1 year for $1,100? Investment returns is the expectation of earning money in the future on the amount of money invested. The return is the financial performance of the investment. The return is the difference between the amount invested and the amount you are returned after said investment. There are two ways to show return on investment. 1. By dollar return. Amount to be received – Amount invested = $1,100 $1,000 = $100 in return The problems with expressing returns in dollars, you don’t know the size of the investment for that dollar return and you don’t know the timing of the return. 2. Rate of Return or percentage returns Amount received – Amount invested / Amount invested = $100 / $1000 = . 10 = 10% The rate of return â€Å"standardizes† the dollar return by considering the timing b. (1) Why is the T-bill’s return independent of the state of the economy? Do T-bill’s promise a completely risk-free return? Beta coefficients are the weighted average of its individual securities’ betas. You will add each securities beta to find the portfolio’s beta. i. Suppose you have the following historical returns for the stock market and for the company P. Q. Unlimited. Explain how to calculate beta, and use the historical stock returns to calculate the beta for PQU. Interpret your results. See attached. Calculate betas using historical data. A regression line is fitted through the points of the market returns (x-axis) and company’s returns (y-axis) and the slope of that line provides an estimate of the stock’s beta.

Aging:The Original Human Condition Essay -- Geriatrics Health Papers

Aging:The Original Human Condition Aging is a phenomena we are all familiar with, a trait characteristic of all humankind, in fact, of all living organisms. What are the effects of aging, especially those which go beyond the biological aspects and effect the social aspects of changing roles, seniority, and treatment of the aged? What was the original human condition before high-tech medical interventions redefined death and dying, before the industrial age changed the nature of the nuclear and extended family? Going back still farther, what can the behavior of chimpanzees tell us about the origins of our responses to the aging of those around us? Having worked in the field of geriatrics, in a nursing home setting, I have had the opportunity to be involved in the direct care of the elderly. Over a period of time, I have come to accept living one's last years in a nursing home as an eventual "normal" response to the aging process. As a result of this study, I anticipate having an enlarged perspective and an enhanced sensitivity to the psychosocial aspects of aging. Aging Defined The Encyclopedia of Cultural Anthropology (1996) was a helpful source to gain a definition on aging which includes the concepts of life course, seniority, and treatment of the aged. Aging can be measured by common biological content: proportion of the maximum fife span one has lived, performance on a series of physiological tests which index biological age, and patterns of the age­specific risk of mortality. Despite this universal biological content, it is notable that aging takes on a variety of forms, many which show regular associations with aspects of culture. Rather than focusing on age, it may be more appropriate to review the life cy... ...k, NY: Harper Collins College Publishers Collier's Encyclopedia. 1983. New York, NY: Macmillan Educational Company Goodall, Jane. 1990. Through a Window: My 30 Years with Chimpanzees of Gombe. Boston, MA: Houghton Mifflin Company Handbook of North American Indians. 1984. Washington, D.C.: Smithsonian Institution Semour­Smith, Charlotte. 1986. Dictionary of Anthropology. Boston, MA: G.K. Hall and Company Encyclopedia of Cultural Anthropology. 1996. New York, NY: Henry Holt and Company Marshall, Loma. 1976. The !Kung of Nyae Nyae. Cambridge, MA: Harvard University Press Dentan, Robert Knox. 1968. The Semai: A Nonviolent People of Malaya. Orlando, FL: Holt, Rinehart and Winston, Inc. Maxwell, Robert J. and Phillip Silverman. 1989. "Geronticide". In The Content of Culture: Studies in Honor of John M. Roberts. New Haven, CN.: HRAF Press

Venezuela- The Age of Exploration :: essays research papers

Bolivarian Republic of Venezuela 1.  Ã‚  Ã‚  Ã‚  Ã‚  Venezuela 2.  Ã‚  Ã‚  Ã‚  Ã‚  Located on the continent of South America 3.  Ã‚  Ã‚  Ã‚  Ã‚  25,017,387 (estimated as of July 2004) 4.  Ã‚  Ã‚  Ã‚  Ã‚  Size- 912,050 sq km (land/water) 5.  Ã‚  Ã‚  Ã‚  Ã‚  Petroleum, natural gas, iron ore, gold, bauxite, other minerals, hydropower, diamonds 6.  Ã‚  Ã‚  Ã‚  Ã‚  96% Roman Catholic, 2% Protestant, 2% Other Religions   Ã‚  Ã‚  Ã‚  Ã‚  The Venezuelans were tracked back to about 13,000 BC. The settlers of that time came from three different directions. Present day Guyana, present day Brazil, and present day Antilles were the three directions. At the time there are about 500,000 indigenous peoples living in Venezuela. There was much diversity in the different tribes that settled there during this time. Religion has always been dominated by the Catholic faith. Some Venezuelans of the time had been farmers, hunters, and fishermen. The name â€Å"Venezuela† was given and the literal translation is â€Å"Little Venice.†   Ã‚  Ã‚  Ã‚  Ã‚  Venezuela was rich with grasslands and had six navigable rivers. There were many streams that also ran through the country. Mountainous areas also were abundant in the Venezuelan countryside. Venezuela has a very tropical climate. It is also rich in mineral resources. The country’s most important resource is petroleum. They are also known for their abundance of diamonds and gold which are found in the mountains.   Ã‚  Ã‚  Ã‚  Ã‚  Christopher Columbus first sighted the coast of Venezuela in 1498. In 1499 Spanish explorer Alonso de Ojeda followed that same coast to Lake Maracaibo. He was the one who named the region Venezuela because it reminded him of the buildings in Venice. The Spanish had started to settle in Venezuela in 1520. In 1528, Charles V of Spain gave the part of Venezuela that lied between Cape Vela and Maracapana to the Weslers, Bavarian bankers to whom he owed money to. The Weslers were to fill and develop the region as part of the arrangement with Charles V. They were also to set up establishments to live. Instead, their representatives enslaved the Native Americans of the area and so demoralized the European settlers that in 1546 the Spanish government revoked the grant and reassumed control. The first important settlement in Venezuela was that of Caracas which later the capital of this country became. It was settled in 1567.   Ã‚  Ã‚  Ã‚  Ã‚  The economy and its activities in the colonial period centered on agriculture, mainly tobacco and cacao. Some livestock were also traded amongst the people. Venezuela became the center of piracy and illegal smuggling, things both of which the English and the Dutch were the most notorious participants in. Venezuela at the time of colonization operated under a number of administrative jurisdictions.

Current Issues in United States History Essay

The article, Mentoring Experiences of Women in Graduate Education: Factors that Matter, focuses on women’s relational approaches which are affected by their gender socialization. The said article studies the various subjective experiences a woman encounters when teaching, counseling and mentoring. It also explores the different aspects that contribute to these experiences exclusive to women in graduate school, the costs and benefits of these relationships for women, and the women’s role models in the familial and professional areas. The article takes on a feminist approach as it differentiates the traditional male to male mentoring relationships from that of the women’s. It asserts that in the male to male relationships, there is an acceptance of patriarchal and hierarchal organization. On the contrary, the women employ a more relational approach, which gives value to the emotional factor involved in the female relationships. But presently, the prevailing standard employed by mentoring environments is that of a traditional patriarchal environment. It can therefore be said that women in mentoring fields are currently in struggle with the prevailing norms. The article undertook a study which aimed to investigate factors that affect women’s mentoring gender socialization. The study yielded seven key topics which suggest that female undergraduate students and their faculty members share same views about their respective mentoring experiences as well as views in the mentoring field. They all commonly voiced their desire for an empowering relationship. This, according to the surveyed collegiate students and teachers, is illustrated by the kind assistance, â€Å"CURRENT ISSUES IN UNITED STATES HISTORY† PAGE #2 inspiration, faith, pride, cooperative hand, and personal growth they gain from these student-teacher relationships. Also, the study explores the sense of obligation that both sides feel for each other, the overall mentor’s investment in the student-teacher relationship (personal/emotional, professional development, time/availability, and financial investment), the factors that affect the growth of their relationship towards each other, and their capacity to balance of their own personal and professional life, experiences in the male mentoring domain, and peer mentoring. The study’s results depict the multi-dimensionality of the women mentors’ needs in order to be successful in their personal and professional mentoring careers. The study also showed that these needs did not alter when compared with the past researches on the same subject. Also, this study suggests that women, in general, have corresponding views (and at the same time) distinct desires to their mentoring relationships in contrast to the more traditional, patriarchal setting typified by the male to male mentoring conditions. Generally speaking, the study only focused on the mentoring experiences’ good points. Unfortunately, it did not include the hardships that women encounter with regards to their being women. It did not tackle the prejudice that women are subjected to in the patriarchal education system. If only the study explored that particular downside, the study would be so much useful and practical. But all in all, the study would indeed be important for reflection on our current educational system with regards to the women in a male dominated field. REFERENCE Rayle A. D. , Bordes V. , Zapata A. , Arrendondo P. , Rutter M. , Howard C. (2006, May). Mentoring Experiences of Women in Graduate Education: Factors that Matter. Current Issues in Education [On-line], 9(6). http://cie. ed. asu. edu/volume9/number6/

Compilation of Mathematicians and Their Contributions

I. Greek Mathematicians Thales of Miletus Birthdate: 624 B. C. Died: 547-546 B. C. Nationality: Greek Title: Regarded as â€Å"Father of Science† Contributions: * He is credited with the first use of deductive reasoning applied to geometry. * Discovery that a circle is  bisected  by its diameter, that the base angles of an isosceles triangle are equal and that  vertical angles  are equal. * Accredited with foundation of the Ionian school of Mathematics that was a centre of learning and research. * Thales theorems used in Geometry: . The pairs of opposite angles formed by two intersecting lines are equal. 2. The base angles of an isosceles triangle are equal. 3. The sum of the angles in a triangle is 180 °. 4. An angle inscribed in a semicircle is a right angle. Pythagoras Birthdate: 569 B. C. Died: 475 B. C. Nationality: Greek Contributions: * Pythagorean Theorem. In a right angled triangle the square of the hypotenuse is equal to the sum of the squares on the other two sides. Note: A right triangle is a triangle that contains one right (90 °) angle.The longest side of a right triangle, called the hypotenuse, is the side opposite the right angle. The Pythagorean Theorem is important in mathematics, physics, and astronomy and has practical applications in surveying. * Developed a sophisticated numerology in which odd numbers denoted male and even female: 1 is the generator of numbers and is the number of reason 2 is the number of opinion 3 is the number of harmony 4 is the number of justice and retribution (opinion squared) 5 is the number of marriage (union of the ? rst male and the ? st female numbers) 6 is the number of creation 10 is the holiest of all, and was the number of the universe, because 1+2+3+4 = 10. * Discovery of incommensurate ratios, what we would call today irrational numbers. * Made the ? rst inroads into the branch of mathematics which would today be called Number Theory. * Setting up a secret mystical society, known as th e Pythagoreans that taught Mathematics and Physics. Anaxagoras Birthdate: 500 B. C. Died: 428 B. C. Nationality: Greek Contributions: * He was the first to explain that the moon shines due to reflected light from the sun. Theory of minute constituents of things and his emphasis on mechanical processes in the formation of order that paved the way for the atomic theory. * Advocated that matter is composed of infinite elements. * Introduced the notion of nous (Greek, â€Å"mind† or â€Å"reason†) into the philosophy of origins. The concept of nous (â€Å"mind†), an infinite and unchanging substance that enters into and controls every living object. He regarded material substance as an infinite multitude of imperishable primary elements, referring all generation and disappearance to mixture and separation, respectively.Euclid Birthdate: c. 335 B. C. E. Died: c. 270 B. C. E. Nationality: Greek Title: â€Å"Father of Geometry† Contributions: * Published a book called the â€Å"Elements† serving as the main textbook for teaching  mathematics  (especially  geometry) from the time of its publication until the late 19th or early 20th century. The Elements. One of the oldest surviving fragments of Euclid's  Elements, found at  Oxyrhynchus and dated to circa AD 100. * Wrote works on perspective,  conic sections,  spherical geometry,  number theory  and  rigor. In addition to the  Elements, at least five works of Euclid have survived to the present day. They follow the same logical structure as  Elements, with definitions and proved propositions. Those are the following: 1. Data  deals with the nature and implications of â€Å"given† information in geometrical problems; the subject matter is closely related to the first four books of the  Elements. 2. On Divisions of Figures, which survives only partially in  Arabic  translation, concerns the division of geometrical figures into two or more equal par ts or into parts in given  ratios.It is similar to a third century AD work by  Heron of Alexandria. 3. Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J O'Connor and E F Robertson who name  Theon of Alexandria  as a more likely author. 4. Phaenomena, a treatise on  spherical astronomy, survives in Greek; it is quite similar to  On the Moving Sphere  by  Autolycus of Pitane, who flourished around 310 BC. * Famous five postulates of Euclid as mentioned in his book Elements . Point is that which has no part. 2. Line is a breadthless length. 3. The extremities of lines are points. 4. A straight line lies equally with respect to the points on itself. 5. One can draw a straight line from any point to any point. * The  Elements  also include the following five â€Å"common notions†: 1. Things that are equal to the same thi ng are also equal to one another (Transitive property of equality). 2. If equals are added to equals, then the wholes are equal. 3. If equals are subtracted from equals, then the remainders are equal. 4.Things that coincide with one another equal one another (Reflexive Property). 5. The whole is greater than the part. Plato Birthdate: 424/423 B. C. Died: 348/347 B. C. Nationality: Greek Contributions: * He helped to distinguish between  pure  and  applied mathematics  by widening the gap between â€Å"arithmetic†, now called  number theory  and â€Å"logistic†, now called  arithmetic. * Founder of the  Academy  in  Athens, the first institution of higher learning in the  Western world. It provided a comprehensive curriculum, including such subjects as astronomy, biology, mathematics, political theory, and philosophy. Helped to lay the foundations of  Western philosophy  and  science. * Platonic solids Platonic solid is a regular, convex poly hedron. The faces are congruent, regular polygons, with the same number of faces meeting at each vertex. There are exactly five solids which meet those criteria; each is named according to its number of faces. * Polyhedron Vertices Edges FacesVertex configuration 1. tetrahedron4643. 3. 3 2. cube / hexahedron81264. 4. 4 3. octahedron61283. 3. 3. 3 4. dodecahedron2030125. 5. 5 5. icosahedron1230203. 3. 3. 3. 3 AristotleBirthdate: 384 B. C. Died: 322 BC (aged 61 or 62) Nationality: Greek Contributions: * Founded the Lyceum * His biggest contribution to the field of mathematics was his development of the study of logic, which he termed â€Å"analytics†, as the basis for mathematical study. He wrote extensively on this concept in his work Prior Analytics, which was published from Lyceum lecture notes several hundreds of years after his death. * Aristotle's Physics, which contains a discussion of the infinite that he believed existed in theory only, sparked much debate in later cen turies.It is believed that Aristotle may have been the first philosopher to draw the distinction between actual and potential infinity. When considering both actual and potential infinity, Aristotle states this:  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   1. A body is defined as that which is bounded by a surface, therefore there cannot be an infinite body. 2. A Number, Numbers, by definition, is countable, so there is no number called ‘infinity’. 3. Perceptible bodies exist somewhere, they have a place, so there cannot be an infinite body. But Aristotle says that we cannot say that the infinite does not exist for these reasons: 1.If no infinite, magnitudes will not be divisible into magnitudes, but magnitudes can be divisible into magnitudes (potentially infinitely), therefore an infinite in some sense exists. 2. If no infinite, number would not be infinite, but number is infinite (potentially), therefore infinity does exist in some sense. * He was the founder of  formal logic, pioneere d the study of  zoology, and left every future scientist and philosopher in his debt through his contributions to the scientific method. Erasthosthenes Birthdate: 276 B. C. Died: 194 B. C. Nationality: Greek Contributions: * Sieve of Eratosthenes Worked on  prime numbers.He is remembered for his prime number sieve, the ‘Sieve of Eratosthenes' which, in modified form, is still an important tool in  number theory  research. Sieve of Eratosthenes- It does so by iteratively marking as composite (i. e. not prime) the multiples of each prime, starting with the multiples of 2. The multiples of a given prime are generated starting from that prime, as a sequence of numbers with the same difference, equal to that prime, between consecutive numbers. This is the Sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. Made a surprisingly accurate measurement of the circumference of the Earth * He was the first per son to use the word â€Å"geography† in Greek and he invented the discipline of geography as we understand it. * He invented a system of  latitude  and  longitude. * He was the first to calculate the  tilt of the Earth's axis  (also with remarkable accuracy). * He may also have accurately calculated the  distance from the earth to the sun  and invented the  leap day. * He also created the first  map of the world  incorporating parallels and meridians within his cartographic depictions based on the available geographical knowledge of the era. Founder of scientific  chronology. Favourite Mathematician Euclid paves the way for what we known today as â€Å"Euclidian Geometry† that is considered as an indispensable for everyone and should be studied not only by students but by everyone because of its vast applications and relevance to everyone’s daily life. It is Euclid who is gifted with knowledge and therefore became the pillar of todayâ€℠¢s success in the field of geometry and mathematics as a whole. There were great mathematicians as there were numerous great mathematical knowledge that God wants us to know.In consideration however, there were several sagacious Greek mathematicians that had imparted their great contributions and therefore they deserve to be appreciated. But since my task is to declare my favourite mathematician, Euclid deserves most of my kudos for laying down the foundation of geometry. II. Mathematicians in the Medieval Ages Leonardo of Pisa Birthdate: 1170 Died: 1250 Nationality: Italian Contributions: * Best known to the modern world for the spreading of the Hindu–Arabic numeral system in Europe, primarily through the publication in 1202 of his Liber Abaci (Book of Calculation). Fibonacci introduces the so-called Modus Indorum (method of the Indians), today known as Arabic numerals. The book advocated numeration with the digits 0–9 and place value. The book showed the practical im portance of the new numeral system, using lattice multiplication and Egyptian fractions, by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interest, money-changing, and other applications. * He introduced us to the bar we use in fractions, previous to this, the numerator has quotations around it. * The square root notation is also a Fibonacci method. He wrote following books that deals Mathematics teachings: 1. Liber Abbaci (The Book of Calculation), 1202 (1228) 2. Practica Geometriae (The Practice of Geometry), 1220 3. Liber Quadratorum (The Book of Square Numbers), 1225 * Fibonacci sequence of numbers in which each number is the sum of the previous two numbers, starting with 0 and 1. This sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987†¦ The higher up in the sequence, the closer two consecutive â€Å"Fibonacci numbers† of the sequence divided by each other will approach the golden ratio (ap proximately 1: 1. 18 or 0. 618: 1). Roger Bacon Birthdate: 1214 Died: 1294 Nationality: English Contributions: * Opus Majus contains treatments of mathematics and optics, alchemy, and the positions and sizes of the celestial bodies. * Advocated the experimental method as the true foundation of scientific knowledge and who also did some work in astronomy, chemistry, optics, and machine design. Nicole Oresme Birthdate: 1323 Died: July 11, 1382 Nationality: French Contributions: * He also developed a language of ratios, to relate speed to force and resistance, and applied it to physical and cosmological questions. He made a careful study of musicology and used his findings to develop the use of irrational exponents. * First to theorise that sound and light are a transfer of energy that does not displace matter. * His most important contributions to mathematics are contained in Tractatus de configuratione qualitatum et motuum. * Developed the first use of powers with fractional exponent s, calculation with irrational proportions. * He proved the divergence of the harmonic series, using the standard method still taught in calculus classes today. Omar Khayyam Birhtdate: 18 May 1048Died: 4 December 1131 Nationality: Arabian Contibutions: * He derived solutions to cubic equations using the intersection of conic sections with circles. * He is the author of one of the most important treatises on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle. * He contributed to a calendar reform. * Created important works on geometry, specifically on the theory of proportions. Omar Khayyam's geometric solution to cubic equations. Binomial theorem and extraction of roots. * He may have been first to develop Pascal's Triangle, along with the essential Binomial Theorem which is sometimes called Al-Khayyam's Formula: (x+y)n = n! ? xkyn-k / k! (n -k)!. * Wrote a book entitled â€Å"Explanations of the difficulties in the postulates in Euclid's Elements† The treatise of Khayyam can be considered as the first treatment of parallels axiom which is not based on petitio principii but on more intuitive postulate. Khayyam refutes the previous attempts by other Greek and Persian mathematicians to prove the proposition.In a sense he made the first attempt at formulating a non-Euclidean postulate as an alternative to the parallel postulate. Favorite Mathematician As far as medieval times is concerned, people in this era were challenged with chaos, social turmoil, economic issues, and many other disputes. Part of this era is tinted with so called â€Å"Dark Ages† that marked the history with unfavourable events. Therefore, mathematicians during this era-after they undergone the untold toils-were deserving individuals for gratitude and praises for they had supplemented the following generations with mathematical ideas that is very useful and applicable.Leonardo Pisano or Leonardo Fibonacci caught my attention therefore he is my favourite mathematician in the medieval times. His desire to spread out the Hindu-Arabic numerals in other countries thus signifies that he is a person of generosity, with his noble will, he deserves to be†¦ III. Mathematicians in the Renaissance Period Johann Muller Regiomontanus Birthdate: 6 June 1436 Died: 6 July 1476 Nationality: German Contributions: * He completed De Triangulis omnimodus. De Triangulis (On Triangles) was one of the first textbooks presenting the current state of trigonometry. His work on arithmetic and algebra, Algorithmus Demonstratus, was among the first containing symbolic algebra. * De triangulis is in five books, the first of which gives the basic definitions: quantity, ratio, equality, circles, arcs, chords, and the sine function. * The crater Regiomontanus on the Moon is named after him. Scipione del Ferro Birthdate: 6 February 1465 Died: 5 N ovember 1526 Nationality: Italian Contributions: * Was the first to solve the cubic equation. * Contributions to the rationalization of fractions with denominators containing sums of cube roots. Investigated geometry problems with a compass set at a fixed angle. Niccolo Fontana Tartaglia Birthdate: 1499/1500 Died: 13 December 1557 Nationality: Italian Contributions: †¢He published many books, including the first Italian translations of Archimedes and Euclid, and an acclaimed compilation of mathematics. †¢Tartaglia was the first to apply mathematics to the investigation of the paths of cannonballs; his work was later validated by Galileo's studies on falling bodies. †¢He also published a treatise on retrieving sunken ships. †¢Ã¢â‚¬ Cardano-Tartaglia Formula†. †¢He makes solutions to cubic equations. Formula for solving all types of cubic equations, involving first real use of complex numbers (combinations of real and imaginary numbers). †¢Tartagli a’s Triangle (earlier version of Pascal’s Triangle) A triangular pattern of numbers in which each number is equal to the sum of the two numbers immediately above it. †¢He gives an expression for the volume of a tetrahedron: Girolamo Cardano Birthdate: 24 September 1501 Died: 21 September 1576 Nationality: Italian Contributions: * He wrote more than 200 works on medicine, mathematics, physics, philosophy, religion, and music. Was the first mathematician to make systematic use of numbers less than zero. * He published the solutions to the cubic and quartic equations in his 1545 book Ars Magna. * Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem. * His book about games of chance, Liber de ludo aleae (â€Å"Book on Games of Chance†), written in 1526, but not published until 1663, contains the first systematic treatment of probability. * He studied hypocycloids, published in de proportionibus 1570. The generating circl es of these hypocycloids were later named Cardano circles or cardanic ircles and were used for the construction of the first high-speed printing presses. * His book, Liber de ludo aleae (â€Å"Book on Games of Chance†), contains the first systematic treatment of probability. * Cardano's Ring Puzzle also known as Chinese Rings, still manufactured today and related to the Tower of Hanoi puzzle. * He introduced binomial coefficients and the binomial theorem, and introduced and solved the geometric hypocyloid problem, as well as other geometric theorems (e. g. the theorem underlying the 2:1 spur wheel which converts circular to reciprocal rectilinear motion).Binomial theorem-formula for multiplying two-part expression: a mathematical formula used to calculate the value of a two-part mathematical expression that is squared, cubed, or raised to another power or exponent, e. g. (x+y)n, without explicitly multiplying the parts themselves. Lodovico Ferrari Birthdate: February 2, 1522 Died: October 5, 1565 Nationality: Italian Contributions: * Was mainly responsible for the solution of quartic equations. * Ferrari aided Cardano on his solutions for quadratic equations and cubic equations, and was mainly responsible for the solution of quartic equations that Cardano published.As a result, mathematicians for the next several centuries tried to find a formula for the roots of equations of degree five and higher. Favorite Mathematician Indeed, this period is supplemented with great mathematician as it moved on from the Dark Ages and undergone a rebirth. Enumerated mathematician were all astounding with their performances and contributions. But for me, Niccolo Fontana Tartaglia is my favourite mathematician not only because of his undisputed contributions but on the way he keep himself calm despite of conflicts between him and other mathematicians in this period. IV. Mathematicians in the 16th CenturyFrancois Viete Birthdate: 1540 Died: 23 February 1603 Nationality: F rench Contributions: * He developed the first infinite-product formula for ?. * Vieta is most famous for his systematic use of decimal notation and variable letters, for which he is sometimes called the Father of Modern Algebra. (Used A,E,I,O,U for unknowns and consonants for parameters. ) * Worked on geometry and trigonometry, and in number theory. * Introduced the polar triangle into spherical trigonometry, and stated the multiple-angle formulas for sin (nq) and cos (nq) in terms of the powers of sin(q) and cos(q). * Published Francisci Viet? universalium inspectionum ad canonem mathematicum liber singularis; a book of trigonometry, in abbreviated Canonen mathematicum, where there are many formulas on the sine and cosine. It is unusual in using decimal numbers. * In 1600, numbers potestatum ad exegesim resolutioner, a work that provided the means for extracting roots and solutions of equations of degree at most 6. John Napier Birthdate: 1550 Birthplace: Merchiston Tower, Edinburgh Death: 4 April 1617 Contributions: * Responsible for advancing the notion of the decimal fraction by introducing the use of the decimal point. His suggestion that a simple point could be used to eparate whole number and fractional parts of a number soon became accepted practice throughout Great Britain. * Invention of the Napier’s Bone, a crude hand calculator which could be used for division and root extraction, as well as multiplication. * Written Works: 1. A Plain Discovery of the Whole Revelation of St. John. (1593) 2. A Description of the Wonderful Canon of Logarithms. (1614) Johannes Kepler Born: December 27, 1571 Died: November 15, 1630 (aged 58) Nationality: German Title: â€Å"Founder of Modern Optics† Contributions: * He generalized Alhazen's Billiard Problem, developing the notion of curvature. He was first to notice that the set of Platonic regular solids was incomplete if concave solids are admitted, and first to prove that there were only 13 â€Å"Archi medean solids. † * He proved theorems of solid geometry later discovered on the famous palimpsest of Archimedes. * He rediscovered the Fibonacci series, applied it to botany, and noted that the ratio of Fibonacci numbers converges to the Golden Mean. * He was a key early pioneer in calculus, and embraced the concept of continuity (which others avoided due to Zeno's paradoxes); his work was a direct inspiration for Cavalieri and others. He developed mensuration methods and anticipated Fermat's theorem (df(x)/dx = 0 at function extrema). * Kepler's Wine Barrel Problem, he used his rudimentary calculus to deduce which barrel shape would be the best bargain. * Kepler’s Conjecture- is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements.Marin Mersenn e Birthdate: 8 September 1588 Died: 1 September 1648 Nationality: French Contributions: * Mersenne primes. * Introduced several innovating concepts that can be considered as the basis of modern reflecting telescopes: 1. Instead of using an eyepiece, Mersenne introduced the revolutionary idea of a second mirror that would reflect the light coming from the first mirror. This allows one to focus the image behind the primary mirror in which a hole is drilled at the centre to unblock the rays. 2.Mersenne invented the afocal telescope and the beam compressor that is useful in many multiple-mirrors telescope designs. 3. Mersenne recognized also that he could correct the spherical aberration of the telescope by using nonspherical mirrors and that in the particular case of the afocal arrangement he could do this correction by using two parabolic mirrors. * He also performed extensive experiments to determine the acceleration of falling objects by comparing them with the swing of pendulums, r eported in his Cogitata Physico-Mathematica in 1644.He was the first to measure the length of the seconds pendulum, that is a pendulum whose swing takes one second, and the first to observe that a pendulum's swings are not isochronous as Galileo thought, but that large swings take longer than small swings. Gerard Desargues Birthdate: February 21, 1591 Died: September 1661 Nationality: French Contributions: * Founder of the theory of conic sections. Desargues offered a unified approach to the several types of conics through projection and section. * Perspective Theorem – that when two triangles are in perspective the meets of corresponding sides are collinear. * Founder of projective geometry. Desargues’s theorem The theorem states that if two triangles ABC and A? B? C? , situated in three-dimensional space, are related to each other in such a way that they can be seen perspectively from one point (i. e. , the lines AA? , BB? , and CC? all intersect in one point), then the points of intersection of corresponding sides all lie on one line provided that no two corresponding sides are†¦ * Desargues introduced the notions of the opposite ends of a straight line being regarded as coincident, parallel lines meeting at a point of infinity and regarding a straight line as circle whose center is at infinity. Desargues’ most important work Brouillon projet d’une atteinte aux evenemens des rencontres d? une cone avec un plan (Proposed Draft for an essay on the results of taking plane sections of a cone) was printed in 1639. In it Desargues presented innovations in projective geometry applied to the theory of conic sections. Favorite Mathematician Mathematicians in this period has its own distinct, and unique knowledge in the field of mathematics.They tackled the more complex world of mathematics, this complex world of Mathematics had at times stirred their lives, ignited some conflicts between them, unfolded their flaws and weaknesses but at the end, they build harmonious world through the unity of their formulas and much has benefited from it, they indeed reflected the beauty of Mathematics. They were all excellent mathematicians, and no doubt in it. But I admire John Napier for giving birth to Logarithms in the world of Mathematics. V. Mathematicians in the 17th Century Rene Descartes Birthdate: 31 March 1596 Died: 11 February 1650Nationality: French Contributions: * Accredited with the invention of co-ordinate geometry, the standard x,y co-ordinate system as the Cartesian plane. He developed the coordinate system as a â€Å"device to locate points on a plane†. The coordinate system includes two perpendicular lines. These lines are called axes. The vertical axis is designated as y axis while the horizontal axis is designated as the x axis. The intersection point of the two axes is called the origin or point zero. The position of any point on the plane can be located by locating how far perpendicularly from e ach axis the point lays.The position of the point in the coordinate system is specified by its two coordinates x and y. This is written as (x,y). * He is credited as the father of analytical geometry, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis. * Descartes was also one of the key figures in the Scientific Revolution and has been described as an example of genius. * He also â€Å"pioneered the standard notation† that uses superscripts to show the powers or exponents; for example, the 4 used in x4 to indicate squaring of squaring. He â€Å"invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c†. * He was first to assign a fundamental place for algebra in our system of knowledge, and believed that algebra was a method to automate or mechanize reasoning, particularly about abstract, unknown quantities. * Rene Descartes created analytic geometry, and discovered an early form of the law of conservation of momentum (the term momentum refers to the momentum of a force). * He developed a rule for determining the number of positive and negative roots in an equation.The Rule of Descartes as it is known states â€Å"An equation can have as many true [positive] roots as it contains changes of sign, from + to – or from – to +; and as many false [negative] roots as the number of times two + signs or two – signs are found in succession. † Bonaventura Francesco Cavalieri Birthdate: 1598 Died: November 30, 1647 Nationality: Italian Contributions: * He is known for his work on the problems of optics and motion. * Work on the precursors of infinitesimal calculus. * Introduction of logarithms to Italy. First book was Lo Specchio Ustorio, overo, Trattato delle settioni coniche, or The Burning Mirror, or a Treatise on Conic Sections. In this book he developed the theory of mirrors shaped into parabolas, hyperbolas, and ellipses, and various combinations of these mirrors. * Cavalieri developed a geometrical approach to calculus and published a treatise on the topic, Geometria indivisibilibus continuorum nova quadam ratione promota (Geometry, developed by a new method through the indivisibles of the continua, 1635).In this work, an area is considered as constituted by an indefinite number of parallel segments and a volume as constituted by an indefinite number of parallel planar areas. * Cavalieri's principle, which states that the volumes of two objects are equal if the areas of their corresponding cross-sections are in all cases equal. Two cross-sections correspond if they are intersections of the body with planes equidistant from a chosen base plane. * Published tables of logarithms, emphasizing their practical use in the fields of astronomy and geography.Pierre de Fermat Birthdate: 1601 or 1607/8 Died: 1665 Jan 12 Nationality: French Contributions: * Early developments that led to infinitesimal calculus, inc luding his technique of adequality. * He is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the differential calculus, then unknown, and his research into number theory. * He made notable contributions to analytic geometry, probability, and optics. * He is best known for Fermat's Last Theorem. Fermat was the first person known to have evaluated the integral of general power functions. Using an ingenious trick, he was able to reduce this evaluation to the sum of geometric series. * He invented a factorization method—Fermat's factorization method—as well as the proof technique of infinite descent, which he used to prove Fermat's Last Theorem for the case n = 4. * Fermat developed the two-square theorem, and the polygonal number theorem, which states that each number is a sum of three triangular numbers, four square numbers, five pentagonal numbers, and so on. With his gif t for number relations and his ability to find proofs for many of his theorems, Fermat essentially created the modern theory of numbers. Blaise Pascal Birthdate: 19 June 1623 Died: 19 August 1662 Nationality: French Contributions: * Pascal's Wager * Famous contribution of Pascal was his â€Å"Traite du triangle arithmetique† (Treatise on the Arithmetical Triangle), commonly known today as Pascal's triangle, which demonstrates many mathematical properties like binomial coefficients. Pascal’s Triangle At the age of 16, he formulated a basic theorem of projective geometry, known today as Pascal's theorem. * Pascal's law (a hydrostatics principle). * He invented the mechanical calculator. He built 20 of these machines (called Pascal’s calculator and later Pascaline) in the following ten years. * Corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. * Pascal's theorem. It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line).Christiaan Huygens Birthdate: April 14, 1629 Died: July 8, 1695 Nationality: Dutch Contributions: * His work included early telescopic studies elucidating the nature of the rings of Saturn and the discovery of its moon Titan. * The invention of the pendulum clock. Spring driven pendulum clock, designed by Huygens. * Discovery of the centrifugal force, the laws for collision of bodies, for his role in the development of modern calculus and his original observations on sound perception. Wrote the first book on probability theory, De ratiociniis in ludo aleae (â€Å"On Reasoning in Games of Chance†). * He also designed more accurate clocks than were available at the time, suitable for sea navigation. * In 1673 he published his mathematical analysis of pendulums, Horologium Oscillatorium sive de motu pendulorum, his greatest work on horology. I saac Newton Birthdate: 4 Jan 1643 Died: 31 March 1727 Nationality: English Contributions: * He laid the foundations for differential and integral calculus.Calculus-branch of mathematics concerned with the study of such concepts as the rate of change of one variable quantity with respect to another, the slope of a curve at a prescribed point, the computation of the maximum and minimum values of functions, and the calculation of the area bounded by curves. Evolved from algebra, arithmetic, and geometry, it is the basis of that part of mathematics called analysis. * Produced simple analytical methods that unified many separate techniques previously developed to solve apparently unrelated problems such as finding areas, tangents, the lengths of curves and the maxima and minima of functions. Investigated the theory of light, explained gravity and hence the motion of the planets. * He is also famed for inventing `Newtonian Mechanics' and explicating his famous three laws of motion. * The first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations * He discovered Newton's identities, Newton's method, classified cubic plane curves (polynomials of degree three in two variables) Newton's identities, also known as the Newton–Girard formulae, give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials.Evaluated at the roots of a monic polynomial P in one variable, they allow expressing the sums of the k-th powers of all roots of P (counted with their multiplicity) in terms of the coefficients of P, without actually finding those roots * Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function. Gottfried Wilhelm Von Leibniz Birthdate: July 1, 1646 Died: November 14, 1716 Nationality: GermanCont ributions: * Leibniz invented a mechanical calculating machine which would multiply as well as add, the mechanics of which were still being used as late as 1940. * Developed the infinitesimal calculus. * He became one of the most prolific inventors in the field of mechanical calculators. * He was the first to describe a pinwheel calculator in 1685[6] and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. * He also refined the binary number system, which is at the foundation of virtually all digital computers. Leibniz was the first, in 1692 and 1694, to employ it explicitly, to denote any of several geometric concepts derived from a curve, such as abscissa, ordinate, tangent, chord, and the perpendicular. * Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix, which can be manipulated to find the solution of the system. * He introduced several notations used to this day, for instance the integral sign ? representing an elongated S, from the Latin word summa and the d used for differentials, from the Latin word differentia.This cleverly suggestive notation for the calculus is probably his most enduring mathematical legacy. * He was the ? rst to use the notation f(x). * The notation used today in Calculus df/dx and ? f x dx are Leibniz notation. * He also did work in discrete mathematics and the foundations of logic. Favorite Mathematician Selecting favourite mathematician from these adept persons in mathematics is a hard task, but as I read the contributions of these Mathematicians, I found Sir Isaac Newton to be the greatest mathematician of this period.He invented the useful but difficult subject in mathematics- the calculus. I found him cooperative with different mathematician to derive useful formulas despite the fact that he is bright enough. Open-mindedness towards others opinion is what I discerned in him. VI. Mathematicians in the 18th Century Jacob Bernoulli Birthdate: 6 January 1655 Died: 16 August 1705 Nationality: Swiss Contributions: * Founded a school for mathematics and the sciences. * Best known for the work Ars Conjectandi (The Art of Conjecture), published eight years after his death in 1713 by his nephew Nicholas. Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra published in 1685, work on probability in 1685 and geometry in 1687. * Introduction of the theorem known as the law of large numbers. * By 1689 he had published important work on infinite series and published his law of large numbers in probability theory. * Published five treatises on infinite series between 1682 and 1704. * Bernoulli equation, y' = p(x)y + q(x)yn. * Jacob Bernoulli's paper of 1690 is important for the history of calculus, since the term integral appears for the first time with its integration meaning. Discovered a general method to determine evolutes of a curve as the envelope of its circles of curvature. He also investigated caustic curves and in particular he studied these associated curves of the parabola, the logarithmic spiral and epicycloids around 1692. * Theory of permutations and combinations; the so-called Bernoulli numbers, by which he derived the exponential series. * He was the first to think about the convergence of an infinite series and proved that the series   is convergent. * He was also the first to propose continuously compounded interest, which led him to investigate: Johan Bernoulli Birthdate: 27 July 1667Died: 1 January 1748 Nationality: Swiss Contributions: * He was a brilliant mathematician who made important discoveries in the field of calculus. * He is known for his contributions to infinitesimal calculus and educated Leonhard Euler in his youth. * Discovered fundamental principles of mechanics, and the laws of optics. * He discovered the Bernoulli series and made advances in theory of navigation and ship saili ng. * Johann Bernoulli proposed the brachistochrone problem, which asks what shape a wire must be for a bead to slide from one end to the other in the shortest possible time, as a challenge to other mathematicians in June 1696.For this, he is regarded as one of the founders of the calculus of variations. Daniel Bernoulli Birthdate: 8 February 1700 Died: 17 March 1782 Nationality: Swiss Contributions: * He is particularly remembered for his applications of mathematics to mechanics. * His pioneering work in probability and statistics. Nicolaus Bernoulli Birthdate: February 6, 1695 Died: July 31, 1726 Nationality: Swiss Contributions: †¢Worked mostly on curves, differential equations, and probability. †¢He also contributed to fluid dynamics. Abraham de Moivre Birthdate: 26 May 1667 Died: 27 November 1754 Nationality: French Contributions: Produced the second textbook on probability theory, The Doctrine of Chances: a method of calculating the probabilities of events in play. * Pioneered the development of analytic geometry and the theory of probability. * Gives the first statement of the formula for the normal distribution curve, the first method of finding the probability of the occurrence of an error of a given size when that error is expressed in terms of the variability of the distribution as a unit, and the first identification of the probable error calculation. Additionally, he applied these theories to gambling problems and actuarial tables. In 1733 he proposed the formula for estimating a factorial as n! = cnn+1/2e? n. * Published an article called Annuities upon Lives, in which he revealed the normal distribution of the mortality rate over a person’s age. * De Moivre’s formula: which he was able to prove for all positive integral values of n. * In 1722 he suggested it in the more well-known form of de Moivre's Formula: Colin Maclaurin Birthdate: February, 1698 Died: 14 June 1746 Nationality: Scottish Contributions: * Maclaurin used Taylor series to characterize maxima, minima, and points of inflection for infinitely differentiable functions in his Treatise of Fluxions. Made significant contributions to the gravitation attraction of ellipsoids. * Maclaurin discovered the Euler–Maclaurin formula. He used it to sum powers of arithmetic progressions, derive Stirling's formula, and to derive the Newton-Cotes numerical integration formulas which includes Simpson's rule as a special case. * Maclaurin contributed to the study of elliptic integrals, reducing many intractable integrals to problems of finding arcs for hyperbolas. * Maclaurin proved a rule for solving square linear systems in the cases of 2 and 3 unknowns, and discussed the case of 4 unknowns. Some of his important works are: Geometria Organica – 1720 * De Linearum Geometricarum Proprietatibus – 1720 * Treatise on Fluxions – 1742 (763 pages in two volumes. The first systematic exposition of Newton's methods. ) * Treatise on Al gebra – 1748 (two years after his death. ) * Account of Newton's Discoveries – Incomplete upon his death and published in 1750 or 1748 (sources disagree) * Colin Maclaurin was the name used for the new Mathematics and Actuarial Mathematics and Statistics Building at Heriot-Watt University, Edinburgh. Lenard Euler Birthdate: 15 April 1707 Died: 18 September 1783 Nationality: Swiss Contributions: He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. * He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. * He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy. * Euler introduced and popularized several notational conventions through his numerous and widely circulated textbooks. Most notably, he introduced the concept of a function [2] and was the first to write f(x) to denote the function f a pplied to the argument x. He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also known as Euler's number), the Greek letter ? for summations and the letter i to denote the imaginary unit. * The use of the Greek letter ? to denote the ratio of a circle's circumference to its diameter was also popularized by Euler. * Well known in analysis for his frequent use and development of power series, the expression of functions as sums of infinitely many terms, such as * Euler introduced the use of the exponential function and logarithms in analytic proofs. He discovered ways to express various logarithmic functions using power series, and he successfully defined logarithms for negative and complex numbers, thus greatly expanding the scope of mathematical applications of logarithms. * He also defined the exponential function for complex numbers, and discovered its relation to the trigonometric functions. * Elaborate d the theory of higher transcendental functions by introducing the gamma function and introduced a new method for solving quartic equations. He also found a way to calculate integrals with complex limits, foreshadowing the development of modern complex analysis.He also invented the calculus of variations including its best-known result, the Euler–Lagrange equation. * Pioneered the use of analytic methods to solve number theory problems. * Euler created the theory of hypergeometric series, q-series, hyperbolic trigonometric functions and the analytic theory of continued fractions. For example, he proved the infinitude of primes using the divergence of the harmonic series, and he used analytic methods to gain some understanding of the way prime numbers are distributed. Euler's work in this area led to the development of the prime number theorem. He proved that the sum of the reciprocals of the primes diverges. In doing so, he discovered the connection between the Riemann zeta f unction and the prime numbers; this is known as the Euler product formula for the Riemann zeta function. * He also invented the totient function ? (n) which is the number of positive integers less than or equal to the integer n that are coprime to n. * Euler also conjectured the law of quadratic reciprocity. The concept is regarded as a fundamental theorem of number theory, and his ideas paved the way for the work of Carl Friedrich Gauss. * Discovered the formula V ?E + F = 2 relating the number of vertices, edges, and faces of a convex polyhedron. * He made great strides in improving the numerical approximation of integrals, inventing what are now known as the Euler approximations. Jean Le Rond De Alembert Birthdate: 16 November 1717 Died: 29 October 1783 Nationality: French Contributions: * D'Alembert's formula for obtaining solutions to the wave equation is named after him. * In 1743 he published his most famous work, Traite de dynamique, in which he developed his own laws of mot ion. * He created his ratio test, a test to see if a series converges. The D'Alembert operator, which first arose in D'Alembert's analysis of vibrating strings, plays an important role in modern theoretical physics. * He made several contributions to mathematics, including a suggestion for a theory of limits. * He was one of the first to appreciate the importance of functions, and defined the derivative of a function as the limit of a quotient of increments. Joseph Louise Lagrange Birthdate: 25 January 1736 Died: 10 April 1813 Nationality: Italian French Contributions: * Published the ‘Mecanique Analytique' which is considered to be his monumental work in the pure maths. His most prominent influence was his contribution to the the metric system and his addition of a decimal base. * Some refer to Lagrange as the founder of the Metric System. * He was responsible for developing the groundwork for an alternate method of writing Newton's Equations of Motion. This is referred to as ‘Lagrangian Mechanics'. * In 1772, he described the Langrangian points, the points in the plane of two objects in orbit around their common center of gravity at which the combined gravitational forces are zero, and where a third particle of negligible mass can remain at rest. He made significant contributions to all fields of analysis, number theory, and classical and celestial mechanics. * Was one of the creators of the calculus of variations, deriving the Euler–Lagrange equations for extrema of functionals. * He also extended the method to take into account possible constraints, arriving at the method of Lagrange multipliers. * Lagrange invented the method of solving differential equations known as variation of parameters, applied differential calculus to the theory of probabilities and attained notable work on the solution of equations. * He proved that every natural number is a sum of four squares. Several of his early papers also deal with questions of number theo ry. 1. Lagrange (1766–1769) was the first to prove that Pell's equation has a nontrivial solution in the integers for any non-square natural number n. [7] 2. He proved the theorem, stated by Bachet without justification, that every positive integer is the sum of four squares, 1770. 3. He proved Wilson's theorem that n is a prime if and only if (n ? 1)! + 1 is always a multiple of n, 1771. 4. His papers of 1773, 1775, and 1777 gave demonstrations of several results enunciated by Fermat, and not previously proved. 5.His Recherches d'Arithmetique of 1775 developed a general theory of binary quadratic forms to handle the general problem of when an integer is representable by the form. Gaspard Monge Birthdate: May 9, 1746 Died: July 28, 1818 Nationality: French Contributions: * Inventor of descriptive geometry, the mathematical basis on which technical drawing is based. * Published the following books in mathematics: 1. The Art of Manufacturing Cannon (1793)[3] 2. Geometrie descri ptive. Lecons donnees aux ecoles normales (Descriptive Geometry): a transcription of Monge's lectures. (1799) Pierre Simon Laplace Birthdate: 23 March 1749Died: 5 March 1827 Nationality: French Contributions: * Formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics. * Laplacian differential operator, widely used in mathematics, is also named after him. * He restated and developed the nebular hypothesis of the origin of the solar system * Was one of the first scientists to postulate the existence of black holes and the notion of gravitational collapse. * Laplace made the non-trivial extension of the result to three dimensions to yield a more general set of functions, the spherical harmonics or Laplace coefficients. Issued his Theorie analytique des probabilites in which he laid down many fundamental results in statistics. * Laplace’s most important work was his Celestial Mechanics published in 5 volumes between 1798-1827. In it he sought to give a complete mathematical description of the solar system. * In Inductive probability, Laplace set out a mathematical system of inductive reasoning based on probability, which we would today recognise as Bayesian. He begins the text with a series of principles of probability, the first six being: 1.Probability is the ratio of the â€Å"favored events† to the total possible events. 2. The first principle assumes equal probabilities for all events. When this is not true, we must first determine the probabilities of each event. Then, the probability is the sum of the probabilities of all possible favored events. 3. For independent events, the probability of the occurrence of all is the probability of each multiplied together. 4. For events not independent, the probability of event B following event A (or event A causing B) is the probability of A multiplied by the probability that A and B both occur. 5.The probability that A will occur, given th at B has occurred, is the probability of A and B occurring divided by the probability of B. 6. Three corollaries are given for the sixth principle, which amount to Bayesian probability. Where event Ai ? {A1, A2, †¦ An} exhausts the list of possible causes for event B, Pr(B) = Pr(A1, A2, †¦ An). Then: * Amongst the other discoveries of Laplace in pure and applied mathematics are: 1. Discussion, contemporaneously with Alexandre-Theophile Vandermonde, of the general theory of determinants, (1772); 2. Proof that every equation of an even degree must have at least one real quadratic factor; 3.Solution of the linear partial differential equation of the second order; 4. He was the first to consider the difficult problems involved in equations of mixed differences, and to prove that the solution of an equation in finite differences of the first degree and the second order might always be obtained in the form of a continued fraction; and 5. In his theory of probabilities: 6. Evalua tion of several common definite integrals; and 7. General proof of the Lagrange reversion theorem. Adrian Marie Legendere Birthdate: 18 September 1752 Died: 10 January 1833 Nationality: French Contributions: Well-known and important concepts such as the Legendre polynomials. * He developed the least squares method, which has broad application in linear regression, signal processing, statistics, and curve fitting; this was published in 1806. * He made substantial contributions to statistics, number theory, abstract algebra, and mathematical analysis. * In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss; in connection to this, the Legendre symbol is named after him. * He also did pioneering work on the distribution of primes, and on the application of analysis to number theory. Best known as the author of Elements de geometrie, which was published in 1794 and was the leading elementary text on the topic for around 100 years. * He introduced wh at are now known as Legendre functions, solutions to Legendre’s differential equation, used to determine, via power series, the attraction of an ellipsoid at any exterior point. * Published books: 1. Elements de geometrie, textbook 1794 2. Essai sur la Theorie des Nombres 1798 3. Nouvelles Methodes pour la Determination des Orbites des Cometes, 1806 4. Exercices de Calcul Integral, book in three volumes 1811, 1817, and 1819 5.Traite des Fonctions Elliptiques, book in three volumes 1825, 1826, and 1830 Simon Dennis Poison Birthdate: 21 June 1781 Died: 25 April 1840 Nationality: French Contributions: * He published two memoirs, one on Etienne Bezout's method of elimination, the other on the number of integrals of a finite difference equation. * Poisson's well-known correction of Laplace's second order partial differential equation for potential: today named after him Poisson's equation or the potential theory equation, was first published in the Bulletin de la societe philomati que (1813). Poisson's equation for the divergence of the gradient of a scalar field, ? in 3-dimensional space: Charles Babbage Birthdate: 26 December 1791 Death: 18 October 1871 Nationality: English Contributions: * Mechanical engineer who originated the concept of a programmable computer. * Credited with inventing the first mechanical computer that eventually led to more complex designs. * He invented the Difference Engine that could compute simple calculations, like multiplication or addition, but its most important trait was its ability create tables of the results of up to seven-degree polynomial functions. Invented the Analytical Engine, and it was the first machine ever designed with the idea of programming: a computer that could understand commands and could be programmed much like a modern-day computer. * He produced a Table of logarithms of the natural numbers from 1 to 108000 which was a standard reference from 1827 through the end of the century. Favorite Mathematician No ticeably, Leonard Euler made a mark in the field of Mathematics as he contributed several concepts and formulas that encompasses many areas of Mathematics-Geometry, Calculus, Trigonometry and etc.He deserves to be praised for doing such great things in Mathematics, indeed, his work laid foundation to make the lives of the following generation sublime, ergo, He is my favourite mathematician. VII. Mathematicians in the 19th Century Carl Friedrich Gauss Birthdate: 30 April 1777 Died: 23 February 1855 Nationality: German Contributions: * He became the first to prove the quadratic reciprocity law. * Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae (Latin, Arithmetical Investigations), which, among things, introduced the symbol ? or congruence and used it in a clean presentation of modular arithmetic, contained the first two proofs of the law of quadratic reciprocity, developed the theories of binary and ternary quadratic forms, state d the class number problem for them, and showed that a regular heptadecagon (17-sided polygon) can be constructed with straightedge and compass. * He developed a method of measuring the horizontal intensity of the magnetic field which was in use well into the second half of the 20th century, and worked out the mathematical theory for separating the inner and outer (magnetospheric) sources of Earth's magnetic field.Agustin Cauchy Birthdate: 21 August 1789 Died: 23 May 1857 Nationality: French Contributions: * His most notable research was in the theory of residues, the question of convergence, differential equations, theory of functions, the legitimate use of imaginary numbers, operations with determinants, the theory of equations, the theory of probability, and the applications of mathematics to physics. * His writings introduced new standards of rigor in calculus from which grew the modern field of analysis.In Cours d’analyse de l’Ecole Polytechnique (1821), by develo ping the concepts of limits and continuity, he provided the foundation for calculus essentially as it is today. * He introduced the â€Å"epsilon-delta definition for limits (epsilon for â€Å"error† and delta for â€Å"difference’). * He transformed the theory of complex functions by discovering integral theorems and introducing the calculus of residues. * Cauchy founded the modern theory of elasticity by applying the notion of pressure on a plane, and assuming that this pressure was no longer perpendicular to the plane upon which it acts in an elastic body.In this way, he introduced the concept of stress into the theory of elasticity. * He also examined the possible deformations of an elastic body and introduced the notion of strain. * One of the most prolific mathematicians of all time, he produced 789 mathematics papers, including 500 after the age of fifty. * He had sixteen concepts and theorems named for him, including the Cauchy integral theorem, the Cauchy-Sc hwartz inequality, Cauchy sequence and Cauchy-Riemann equations. He defined continuity in terms of infinitesimals and gave several important theorems in complex analysis and initiated the study of permutation groups in abstract algebra. * He started the project of formulating and proving the theorems of infinitesimal calculus in a rigorous manner. * He was the first to define complex numbers as pairs of real numbers. * Most famous for his single-handed development of complex function theory.The first pivotal theorem proved by Cauchy, now known as Cauchy's integral theorem, was the following: where f(z) is a complex-valued function holomorphic on and within the non-self-intersecting closed curve C (contour) lying in the complex plane. * He was the first to prove Taylor's theorem rigorously. * His greatest contributions to mathematical science are enveloped in the rigorous methods which he introduced; these are mainly embodied in his three great treatises: 1. Cours d'analyse de l'Ecol e royale polytechnique (1821) 2. Le Calcul infinitesimal (1823) 3.Lecons sur les applications de calcul infinitesimal; La geometrie (1826–1828) Nicolai Ivanovich Lobachevsky Birthdate: December 1, 1792 Died: February 24, 1856 Nationality: Russian Contributions: * Lobachevsky's great contribution to the development of modern mathematics begins with the fifth postulate (sometimes referred to as axiom XI) in Euclid's Elements. A modern version of this postulate reads: Through a point lying outside a given line only one line can be drawn parallel to the given line. * Lobachevsky's geometry found application in the theory of complex numbers, the theory of vectors, and the theory of relativity. Lobachevskii's deductions produced a geometry, which he called â€Å"imaginary,† that was internally consistent and harmonious yet different from the traditional one of Euclid. In 1826, he presented the paper â€Å"Brief Exposition of the Principles of Geometry with Vigorous Proofs o f the Theorem of Parallels. † He refined his imaginary geometry in subsequent works, dating from 1835 to 1855, the last being Pangeometry. * He was well respected in the work he developed with the theory of infinite series especially trigonometric series, integral calculus, and probability. In 1834 he found a method for approximating the roots of an algebraic equation. * Lobachevsky also gave the definition of a function as a correspondence between two sets of real numbers. Johann Peter Gustav Le Jeune Dirichlet Birthdate: 13 February 1805 Died: 5 May 1859 Nationality: German Contributions: * German mathematician with deep contributions to number theory (including creating the field of analytic number theory) and to the theory of Fourier series and other topics in mathematical analysis. * He is credited with being one of the first mathematicians to give the modern formal definition of a function. Published important contributions to the biquadratic reciprocity law. * In 1837 h e published Dirichlet's theorem on arithmetic progressions, using mathematical analysis concepts to tackle an algebraic problem and thus creating the branch of analytic number theory. * He introduced the Dirichlet characters and L-functions. * In a couple of papers in 1838 and 1839 he proved the first class number formula, for quadratic forms. * Based on his research of the structure of the unit group of quadratic fields, he proved the Dirichlet unit theorem, a fundamental result in algebraic number theory. He first used the pigeonhole principle, a basic counting argument, in the proof of a theorem in diophantine approximation, later named after him Dirichlet's approximation theorem. * In 1826, Dirichlet proved that in any arithmetic progression with first term coprime to the difference there are infinitely many primes. * Developed significant theorems in the areas of elliptic functions and applied analytic techniques to mathematical theory that resulted in the fundamental developme nt of number theory. * His lectures on the equilibrium of systems and potential theory led to what is known as the Dirichlet problem.It involves finding solutions to differential equations for a given set of values of the boundary points of the region on which the equations are defined. The problem is also known as the first boundary-value problem of potential theorem. Evariste Galois Birthdate: 25 October 1811 Death: 31 May 1832 Nationality: French Contributions: * His work laid the foundations for Galois Theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections. * He was the first to use the word â€Å"group† (French: groupe) as a technical term in mathematics to represent a group of permutations. Galois published three papers, one of which laid the foundations for Galois Theory. The second one was about the numerical resolution of equations (root finding in modern terminology). The third was an important one in number theory, i n which the concept of a finite field was first articulated. * Galois' mathematical contributions were published in full in 1843 when Liouville reviewed his manuscript and declared it sound. It was finally published in the October–November 1846 issue of the Journal de Mathematiques Pures et Appliquees. 16] The most famous contribution of this manuscript was a novel proof that there is no quintic formula – that is, that fifth and higher degree equations are not generally solvable by radicals. * He also introduced the concept of a finite field (also known as a Galois field in his honor), in essentially the same form as it is understood today. * One of the founders of the branch of algebra known as group theory. He developed the concept that is today known as a normal subgroup. * Galois' most significant contribution to mathematics by far is his development of Galois Theory.He realized that the algebraic solution to a polynomial equation is related to the structure of a g roup of permutations associated with the roots of the polynomial, the Galois group of the polynomial. He found that an equation could be solved in radicals if one can find a series of subgroups of its Galois group, each one normal in its successor with abelian quotient, or its Galois group is solvable. This proved to be a fertile approach, which later mathematicians adapted to many other fields of mathematics besides the theory of equations to which Galois orig