George Polya
(1887-1985)
-Chronological order:
Fibonacci, Simon Stevin, Leonhard Euler, Carl Gauss, Augustus DeMorgan,
J.J. Sylvester, Charles Dodgson, John Venn, and George Polya
George Polya was born and educated in Budapest Hungry. He enrolled at the University of Budapest to study law but found it to be boring. He then switched his studies to languages and literature, which he found to be more interesting. And in an attempt to better understand philosophy he studied mathematics. He later obtained his Ph.D. in mathematics from Budapest in 1912. He later went on to teach in Switzerland and Brown, Smith, and Stanford Universities in the United States.
Solving problems is a particular art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice…if you wish to learn swimming you have to go in the water, and if you wish to become a problem solver you have to solve problems. -Mathematical Discovery
In 1914 while in Zurich Polya had a wide variety of mathematical output. By 1918 Polya published a selection of papers. These papers consisted of such subjects as number theory, combinatorics, and voting systems. While doing so he studied intently in the following years on integral functions. As time went by he was noted for many of his quotes such as the following.
-In order to solve this differential equation you look at it till a solution occurs to you.
-This principle is so perfectly general that no particular application of it is possible.
-Geometry is the science of correct reasoning on incorrect figures.
-My method to overcome a difficulty is to go round it.
-What is the difference between method and device? A method is a device which you use twice.
(www-groups.dcs.st-and.ac.uk)
One of Polya’s most noted problem solving techniques can be found in “How to Solve it”, 2nd ed., Princeton University Press, 1957.
1. Understanding the problem
2. Devising a plan
3. Carrying out the plan
4. Looking back
This can be described as See, Plan, Do, Check.
Polya continued to write many more books throughout the years and has been distinguished as one of the most dedicated mathematicians.
Teen pregnancy is surprisingly decreasing over the years. According to Farber, “the most recent studies have shown that there has been a decrease in the rate of pregnancies among all teenagers and among sexually active teenagers (16). Although this issue seems is decreasing this is still a problem faced by many teenage girls today. Each year, 7.5 percent of all 15-19 year old women become pregnant (Maynard 1). Not only does this issue affects the pregnant teen but it also affects the economy. Teen pregnancy affects graduation rates. Many teen mothers cite pregnancy as the key reason of them not finishing school. Only 40 percent of teen mothers finish high school (Teen Pregnancy Affects Graduation Rates). The 60 percent of teen mothers that do not finish high school not only influence their future, but the future of their unborn baby. The best solution to help teen pregnancy become obsolete and save many teenagers futures is abstinence. Abstinence is the best solution because this solution has four advantages such as, it has the highest effectiveness, it teaches other important life skills, it aids teens in school and it halts the spread of STDs among adolescents.
There is no doubt that recent technological advancements have changed the way humans interact with one another in the 21st century. Through email, text messages, and social networking sites, we are able to get in touch with people all over the world in a much faster and more efficient manner than in previous years. Since modern technology has become such an integral part of our everyday lives, it is certainly not uncommon for two people to meet and connect with each other via the Internet. Members of this relatively new subculture of online daters invest a great deal of time and energy into their romantic affairs. In fact, according to Robert Epstein’s “The Truth About Online Dating,” advertising materials from the largest online dating services suggest that over 50 million Americans are currently using such services, and that they are wholly satisfied with the results (34). Unfortunately, however, the controversial subject of online relationships in modern society is frequently misrepresented by the media. Many films and television shows exaggerate the risks associated with online dating, choosing to highlight extreme examples of lies and deception for the sake of maintaining their dramatic quality. Other forms of media tend to romanticize online dating, consequently giving Internet users unrealistic expectations for their own relationships. Whether it depicts the frightening or idealized side of online dating, popular culture makes a conscious effort to feature sensationalized stories in order to appeal to a target audience that relies solely on entertainment. As a result, the truth about Internet dating is not adequately conveyed, which ultimately results in the public’s distorted image of such online practices.
Mathematical Lectureship that he held for twenty-six years. “The income was good but the work
The uses of these dating sites and apps have greatly inclined. In 2008, only three percent of Americans used an online dating site now that has increased to nine percent (Ambrose and Palm). The whole concept of meeting a potential girlfriend or boyfriend at a public setting is no longer a
...Five percent of Americans who are in a marriage or a committed relationship say they met their significant other online” (2). The reality of how relationships are started is through the traditional methods of meeting people offline. People like to meet others through introductions and referrals because it provides a sense of security. Due to the direction that society is headed, we are seeing more and more technological advances. These new advances are giving people the freedom to meet and integrate with others in the society in a safe fashion. However, we know that technology is not one-hundred percent safe proof. Because technology is not completely safe and is not always accurate individuals must use common sense to determine when a situation is not being used properly. Online dating sites through the technological advances are getting lots of recognition.
In “Characteristics of Negro Expression”, Zora Neale Hurston discusses the different characteristics of African Americans and explains why they are such a complex race with intriguing qualities. Hurston talks about dancing, Negro folklore, and originality among many others. Hurston captures the complexity of African Americans by writing about all of the different characteristics that cause them to be unique, despite sometimes being mimicked by the whites. The “common folks” that she writes about are anything but common. The “common folks” had qualities that allowed them to be innovative with their music, art, and language. Hurston uses all of these different attributes to clearly set African Americans apart from whites. She shows how wonderful it was to be African American and how it could help African Americans advance as a race. However, unlike Hughes who wanted African Americans to be proud to be African American, I believe she wrote this with the intention of showing the whites how rich and beautiful the African American is culture truly is. Hurston saw how culturally diverse and rick their folk culture was and still continues to be till this day. Hurston demonstrates the richness of the folk culture through her section titled, “Negro Folklore.” She explains it not as something old, but as something that is ever changing. She says, “Negro folklore is not a thing of the past. It is still in the making. Its great variety shows the adaptability of the black man: nothing is too old or too new, domestic or foreign, high or low, for his use.” This was an excellent example of how she decided to demonstrate the richness of the African American culture to the white world. It is an attempt to show the whites that; although there folk culture may be stuck in the past African Americans are always adapting and their culture is always to be appreciated for it is one of a
June is the first character that will be analyzed. First, she was just rebounding from her mother’s death. She had thought for a long time that she had never done anything to make her
Allen, James. "Greatest Mathematicians Born Between 1800 and 1850 A.D.." Fabpedigree. N.p.. Web. 8 Dec 2013. .
Dating online has become a lot more acceptable in our generation from my observations. With a click of a few buttons, we have access to a whole pool of men and women actively seeking partners. Although, when it comes to the searching, gender differences play a huge role in finding successful relationships. The gender patterns in dating websites vary tremendously due to commitment, deceiving pictures and comments, and strictly lack of chemistry. Nonetheless, research has been conducted to prove why online dating can be so tricky sometimes. Research has stated that” Women take online dating more seriously. If men are constantly swiping, and women are hunting for their significant other, it will be a difficult journey to find a perfect match”
Leonhard was sent to school in Basel and during this time he lived with his maternal grandmother. The school was a rather poor one, and Euler learned no mathematics at all from there. However, his father’s teaching had sparked his interest in mathematics. He read mathematics books and papers on his own and took some private lessons (Leonhard Euler).
This paper will provide evidence and use of online dating, and show the effects on psychological, safety and social aspects.
Tsai and Wong (2003) acknowledged many risks factors, which is a contributor to teen pregnancy. The influence involves numerous sexual partners, drug abuse, unprotected sex, use of or lack of contraceptives, poor attendance, school performance, and lack of family support, etc. Teen pregnancy is a main issue in every health care system, and affects a young girl’s ...
Leonhard Euler was easily the best mathematician of the eighteenth century. His contributions to mathematics ranges from common notation to proving the hypothesis of Newton and Leibnitz. His discoveries cannot be limited to just one field of interest, nor just the field of mathematics. He made great strides in geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory and other areas of physics. He is also one of the most well written mathematicians whose works could be contained in 60–80 quarto volumes. Probably the most extraordinary fact about him is that the majority of the work he did was in the last twenty years of his life, when he was completely blind. Euler is arguably one of the greatest mathematicians who ever lived.
Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.
“First, many targets report feeling depressed, sad, angry, and frustrated.” (Hinduja and Patchin). These are just some of the bad effects that cyber bullying is causing for today’s teens. One of the worse effects of cyber bullying is the link between cyber bullying and suicide. “Finally, cyberbullied youth also report having suicidal thoughts, and there have been a number of examples in the United States and abroad where youth who were victimized ended up taking their own lives.” (Hinduja and Patchin). This alarming fact should be the wakeup call to the U.S. that we need to do something about this problem and fast. Cyber bullying simply does not just hurt someone’s feelings, but it is taking lives of our youth. The first step to help prevent this issue can be to have our schools inform the students of the dangers of cyber bullying. “Furthermore, school district personnel should review their harassment and bullying policies to ensure that it allows for the discipline of students who engage in cyberbullying.” (Hinduja and