0+1=1, 1+1=2, and 1+0=1 making this row 1 2 1. This rule can continue on into infinity making the triangle infinitely long. Pascal’s Triangle falls into many areas of mathematics, such as number theory, combinatorics and algebra. Throughout this paper, I will mostly be discussing how combinatorics are related to Pascal’s Triangle. Yang Hui has been found to be the oldest user of Pascal’s Triangle. But it is Blaise Pascal who around the year 1654 was credited for his extensive work on the many patterns
would teach him at home.... ... middle of paper ... ...of primes. Therefore, Paul Erdös has been a great influence in the math community today because of his discoveries. Some of his discoveries were in the number theory, graph theory, and in combinatorics. His theory's are still being taught today, many students of mathematics actually have picked too write about him because his life was so interesting. He learned math while at home and from his parents. He said that he fell in love with numbers
Pascal's Triangle Pascal's Triangle Blasé Pacal was born in France in 1623. He was a child prodigy and was fascinated by mathematics. When Pascal was 19 he invented the first calculating machine that actually worked. Many other people had tried to do the same but did not succeed. One of the topics that deeply interested him was the likelihood of an event happening (probability). This interest came to Pascal from a gambler who asked him to help him make a better guess so he could make an educated
I understand you are taking a college course in mathematics and studying permutations and combinations. Permutations and Combinations date back through the ages. According to Thomas & Pirnot (2014), there is evidence of these mathematical concepts as early as AD 200. As we solve some problems you will see why understanding these concepts is important especially when dealing with large values. I also understand you are having problems understanding their subtle differences, corresponding formulas
Blaise Pascal Blaise Pascal was born at Clermont, Auvergne, France on June 19, 1628. He was the son of Étienne Pascal, his father, and Antoinette Bégone, his mother who died when Blaise was only four years old. After her death, his only family was his father and his two sisters, Gilberte, and Jacqueline, both of whom played key roles in Pascal's life. When Blaise was seven he moved from Clermont with his father and sisters to Paris. It was at this time that his father began to school his son
Words are a powerful tool of communication ,if used well words can build a relationship but also if they are not used well they can lead into misunderstandings and sometimes cause harm to the relationships. The use of language in communication allows people to relate to each other or argue about a matter that could have been brought and this can happened unexpectedly or unexpectedly .It is important to be aware of the effect of language so that we can use it the best way we can to the best effect
and its basis within the broad subject of mathematics. Graph theory, a smaller branch in a large class of mathematics known as combinatorics, which defined by Jacob Fox as, “is the study of finite or countable discrete structures.” Areas of study in combinatorics include enumerative combinatorics, combinatorial design, extremal combinatorics, and algebraic combinatorics. These subfields consist of the counting of mathematical structures, the constructing and analyzing structures, the discovering
of the pattern in blue would force it to pop up in red. This doesn't happen in three, four, or even five dimensions. The number of dimensions required to guarantee this pattern turns out to be Graham's number. This part of mathematics is called Combinatorics, and Graham started looking into a more specific field of it, called Ramsey’s Theory. This theory could be explained the following way; this is an example of where complete disorder is impossible. In any large system, you've got to have a smaller
In the movie 21 directed by Robert Luketic, a bright student from Massachusetts Institute of Technology (MIT) gets accepted to Harvard Med a lifelong dream of his. He wants a to get a scholarship for a free ride and is asked why he should get the scholarship. He starts to tell his story when the movie starts. He earns over the amount he needs in order to get through Harvard and keeps playing. He gets caught and in return takes a beating. He goes to Las Vegas seventeen times and earns hundreds of
When I was applying for colleges my senior year of high school, my mother told me that no matter what I majored in, I should minor in mathematics. She believed that employers know that nobody can go to college for math and be stupid. Following her advice, I began at James Madison University (JMU) with a math minor. It took just one semester of Calculus III for me to reconsider my major. Before the end of my freshman year of college, I changed my major to mathematics. In the spring of my sophomore
in doubt and if a certain topic interests me, I will read up and explore beyond the syllabus independently. My curiosity motivated me to take up Raffles Academy Mathematics, H3 Mathematics and SMU H3 Game Theory as I was extremely interested in combinatorics and strategic decision making. I thoroughly enjoyed reading up on the course materials and I believe that my interest and quest to learn helped me to attain distinctions in these subjects. In my free time, I enjoy reading non-fiction books and
For several years, I have known I wanted a career involving higher-level mathematics. However, it was not until recently did I discover an interest to become a mathematician, who collaborates with other mathematicians, contributes to the math community, and has the opportunity to teach and excite students about mathematical topics. After spending two years studying at Weatherford Community College, in Weatherford TX, I chose to continue my undergraduate education at the University of Houston, in
expanding eld (pun intended). To illustrate this point, this paper will explore the relatively recent, burgeoning topic-within-a-topic of Ramsey Theory, giving an entry level mathematical introduction to the subject. Ramsey Theory is a branch of combinatorics, which is the eld of math involving the study of nite, discrete objects. In a general sense, Ramsey Theory is concerned with the preservation of certain properties of graphs under various circumstances. In more speci c terms, Ramsey Theory asks
How math is used in animation There a few different types of animation, the first one, and hand-drawn 2D aka traditional animation. When using this technique, animators need to make at least 12 drawings on paper to get 1 second length of film. The pages together basically make a flip book to show the movements. Then they get scanned and put into the computer. The next kind is Digital 2D animation, which is just drawing the frames directly onto the computer using a pen tablet. This is commonly used
Introduction Mathematical reasoning that to nowadays represents more essential to said verbal reasoning, plays a fundamental role in the development of our life and the progress of humanity. Areas such as, physics, social sciences, management and computer science. But in computing, we need more of a particular branch of the so-called mathematics: discrete mathematics. Discrete mathematics has become popular thanks to their applications in computer science. Notations and concepts of discrete mathematics
States and southern Canada to earn points as well as completing routes designated on the destination tickets. The game itself is not only a fun way to spend hours playing but it is also a good tool to showcase various concepts in graph theory and combinatorics. Graph theory may also be useful in creating or enhancing game play strategies. Set Up and Game Play The original version of the game has a map of the United States and southern Canada with 30 destination tickets. An expansion to the original
game of dice. (Witchita, 2014) Since then, interest has tended toward the methods and applications of the triangle. The methods of use are essentially number theoretical and the applications are wide. Many fields such as algebra, probability, and combinatorics may find use in Pascal’s Triangle, and additional applications include identifying number sequences such as triangular and tetrahedral numbers. Each application of Pascal’s Triangle can be solved using all methods available. The convenience of
After spending two years studying at Weatherford Community College in my hometown, Weatherford TX, I chose to continue my undergraduate education at the University of Houston, in Houston TX, to study mathematics. At the time, I was aware of the joy I found in mathematics, however only soon would I truly understand this pleasure. The transition from a community college to a research university was challenging, however by managing my capabilities and quickly adjusting to the different methods of learning
Graph Theory: The Four Coloring Theorem "Every planar map is four colorable," seems like a pretty basic and easily provable statement. However, this simple concept took over one hundred years and involved more than a dozen mathematicians to finally prove it. Throughout the century that many men pondered this idea, many other problems, solutions, and mathematical concepts were created. I find the Four Coloring Theorem to be very interesting because of it's apparent simplicity paired with it's
teaching twenty-seven hours a year in selected math courses from 0 level to 4000 level. Her teaching responsibilities include planning, grading, maintaining office hours, advising on limited bases, and other possible tasks assigned. She has a PhD in Combinatorics and Optimization. Her current position does not require that she has an education degree, only that there is at least eighteen hours of graduate level math. Dr. Riegel has strictly a math background. The most important day-to-day decisions for