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.
Mathematical Lectureship that he held for twenty-six years. “The income was good but the work
...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.
It has been said that teens across the world have not been receiving enough sex education. This has led to many issues with teens becoming pregnant, which most of the time is unanticipated. Teenage pregnancy has been a social problem throughout the world for a number of decades now. Many studies have been completed in several countries that pertain to the amount of teens and the types of teens who are becoming pregnant. Rates among teens had been declining for some time, but are starting to take a turn and increase. This is still a significant social problem, though some people do not perceive it like it is.
The rise of the teen pregnancy rate has caused us to question the effectiveness of the prevention programs that are offered to adolescents. There have been several programs focused on preventing teen pregnancy from abstinence-only to more comprehensive sexual education programs. Abstinent-only advocates believe that abstaining from having intercourse is the only way to prevent unwanted teen pregnancy. While practicing abstinence is the only 100% secure method of reducing this rate, it is not a logical view. Adolescents will continue to have sexual behavior, and it is important in teaching them more precise education when it comes to sex education. With-holding important information and facts about sexual behavior can change an adolescents’ life forever. Whether it be from teen pregnancy or from a life threatening STD.
The Internet has always seemed like a completely separate world, very different from reality. There seemed to be so many endless possibilities. One is the new online dating craze, which has caught my attention a number of times. One rainy afternoon, curled up in a blanket at my computer chair, I decided to investigate it. I learned that as many of the baby-boomers start to become widowed or divorced, many are looking for mates, along with many others who are looking for companionship. With the new Internet-Age, many of these individuals turn to their computer to find someone. Online relationships are a growing phenomenon in the United States as well as internationally. After doing some research I could not develop an opinion on how I felt about this new trend. I found a group of specialists who had devoted some researching to it and I invited them over for dinner to find what their opinions were and why.
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.
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).
Teen pregnancy is a heavy topic in the United States that is now becoming the norm to most people. It has become broadcasted everywhere from TV shows, movies, and the Internet. Approximately 7% of teenage girl between ages 15-18 in the United States will become pregnant. Teen pregnancy has been down 42% since 1990 yet United States teen pregnancy rates are higher than any other first world country. Teenage pregnancy effects teenager’s physical health, social life, education, and jobs.
Teenage pregnancy is an epidemic that has been highly debated and publicized during the past few decades. Although it has been statistically proven to be on the decline since the 1950s, it is still a major discussion and topic of concern especially for the health of the unborn child and the mother. The aspect of teenage pregnancy might have been approved and a regular occurrence in the 1950s, but now with the multitude of contraceptives and preventative methods it is heavily frowned upon.
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.
According to U.S. Health and Human Services, 1 in 3 girls will get pregnant before she turns twenty. Almost 1 million teens get pregnant every year. Most of these pregnancies are unplanned, and cause turmoil for the teen mother, the baby's father, and their families. (surviving an unplanned pregnancy). As that may come as a shock, those statistics are realistic and accurate. In 2012 alone there were 29.4 live births for every 1,000 adolescent females ages 15-19. (hhs.gov). U.S. teen birth rate is slightly higher than any over developed country. U.S.A is holding the top rank in adolescent pregnancies. Of about 82% of pregnancy are found to be in teenagers having an age group between 15-20. (Teenage pregnancy: causes and facts). Childbearing at a young age impacts the adolescent parents both momentarily and in the forthcoming future. How can a child care for a child? They simply can't. “I’m still just as young as I was” she insists, “I haven’t grown up any faster.” (Wallis). Spoken by a young girl whom gave her perspective on giving birth at a young age. In society today, the uprising issue of adolescents having children, teen pregnancy, is becoming a lifetime impediment.
According to www.cdc.gov, in 2013, a total of two hundred and seventy-three thousand, one hundred and five babies were born to women fifteen to nineteen years of age. Though this is low for the typical rate of teen- child births, the U.S. teen pregnancy rate is substantially higher than in other western industrialized nations. There are many stories of teen mothers who feel like they have their lives together, and consider their stories “success stories”. What most teens don’t understand, is the difficulties of being a mother, especially at such a young age. Teen pregnancy has more negative outcomes than positive outcomes, as shown by a girl named Haley in her teen pregnancy story. The best way to prevent teen pregnancy is through information
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
Approximately one million teens get pregnant and give birth every year in the United States. Eighty percent of those births are to unmarried teens (ProQuest). There are serious consequences for teen pregnancy for the child as well as for the mother. The opportunity to a bright future dwindles down with such a high responsibility; a child. Many teens who end up pregnant do not finish high school and are less likely even consider going to college. Another effect of teen pregnancy is that both mother and child become apt to health issues. Infants are more likely to suffer from low birth weight and other health problems. Most teens do not have health insurance therefore it becomes harder to provide adequate healthcare for themselves and their babies. Not only are children of teen parents more likely to be unhealthy physically but sometimes emotionally as well. A teen cannot provide the fostering environment that a baby needs to develop. Although teen pregnancy rates declined throughout the 1990s, a 3 percent jump in births to teen mothers between 2005 and 2006 raised alarm that sex education programs and campaigns to reduce teen motherhood were failing (ProQuest). Various methods of contraceptives and the righteous yet difficult choice of abstinence are among possible solutions Preventing teen pregnancy is an issue in the United States of utmost importance and society as a whole must convince teens in a more innovative , extreme way and they must push forward now.
It is very fortunate that the number of teen birth rates and number of teen pregnancies have decreased significantly in the past years. Even though the numbers have decreased, it is still an important issue that needs to be publicized and heard. With the help of good, informative sexual health education programs and foundations that continue raising the awareness of teenage pregnancy, the numbers should continue going down. This would not only be a good thing for teenagers, but also the society as the whole, as they would no longer be contributing to other social issues like poverty, poor education, and abuse. With teenage pregnancy decreasing, the society as a whole would be improving.