These projects are meant to be interesting and enjoyable assignments, not chores, so choose your topics with care. Hence most primes are not twin primes. Only 527 places were correct, however! In fact there are some theorems for which only representation theoretic proofs are known. Mathematics flourished in particular in Iran, Syria and India. It is an interesting non-Euclidean geometry in its own right, a link with classical projective geometry and the mechanism for proof of many otherwise difficult Euclidean theorems including Feuerbach's Theorem on the 9-point circle.
Caution: you may experience delays in connecting to this site. A separate article, , focuses on the early history of mathematics in the Indian subcontinent and the development there of the modern decimal place-value numeral system. The application of mathematics to astronomy, however, flourished during the Persian and Greek periods. A senior thesis project could include a presentation of several different types of proof and a search for an algebraic one. These sources do not list project topics! It is a human activity which impinges upon and is impacted by the culture which surrounds it. For further information, see Mike Olinick. Albert Einstein was the first to suggest that rivers have a tendency towards an ever more loopy path because the slightest curve will lead to faster currents on the outer side, which in turn will result in more erosion and a sharper bend.
Junior high students use the Internet to learn more about famous mathematicians in this four day lesson plan. Scholars are still debating of the construction and the intended use of this table, but no one questions the high level of expertise implied by it. Such solutions are sometimes called. Ross, Introduction to Probability Models Academic Press, 1993 , Chapter 9. Existing specimens of mathematics represent all the major eras—the kingdoms of the 3rd millennium bce, the and regimes 2nd millennium , and the empires of the early 1st millennium , 6th through 4th century bce , and Greeks 3rd century bce to 1st century ce. Special Project for Graduate Students All the graduate those registered for Math 5010 students and anyone else who may be interested will work as a team for this project.
Only when some record of the counting was kept and, therefore, some representation of numbers occurred can mathematics be said to have started. In geometry produced fundamental work on analytic geometry and in synthetic geometry. These social groupings are often formalized in various ways and they permit complex interactions to be played out. Additional sources may be presented. In recent years, new and simpler existence proofs of the fixed point theorem have been discovered. The level of competence was already high as early as the , the time of the lawgiver-king c. Iterated Function Systems Roughly speaking, a contraction of the plane is a transformation f: R 2 ¨ R 2 such that if P and Q are any two points in the plane then the distance from f P to f Q is strictly less than the distance from P to Q -- i.
But Arabic, chine, and Indian mathematicians continued their practices and increased their understanding towards its principles and concepts. References: Hardy, Littlewood, and P—lya, Inequalities, Cambridge, 1952. In fact there is no real reason why negative numbers should be introduced at all. If the successive choices are made by tossing a coin, what is the expected number of moves until the rook has visited each square on the board? This investigation would examine models and their assumptions for three-way and higher-way tables. This could be a very interesting and challenging topic with either a mathematical or computational focus. Specifically, in order to be Riemann integrable, a function must be continuous almost everywhere.
The development of the theory was carried on at the turn of the century by Frobenius as well as Shur and Burnside. For example, a difference of a single atom in the length of a 10-centimeter needle would show up around the 9th digit of the result. A project on Euclid and the Pythagorean theorem will be much more manageable that one on the theorem from Pythagoras to the present. For further information, see Mike Olinick. Brun's proof is rather difficult but does not depend too heavily on a strong number theory background. However, in 1919 Viggo Brun proved the following: if q runs through the series of twin primes, then S converges. Statistical mechanics was developed by , and.
Everything you ever wanted to know about this topic. However, Hilbert's proof did not determine the numerical value of g k for any k. Starting with characterizations of the Poisson process, a thesis might develop some of its important properties and applications. Interviews with current staff and possibly some recent retirees would be useful Roxanne Byrne would be a particularly good person to interview. An interesting tablet in the collection of shows a with its diagonals. Further, the Babylonian rule for estimating square roots was widely used in Greek geometric computations, and there may also have been some shared nuances of technical terminology.
For instance, in how many ways can we write an integer as the sum of two squares? There still remain many open questions, for example, do there exist any odd perfect numbers? That is, they should meet early in the term and break up the assignment into tasks for each team member I will help facilitate this meeting if desired. » Optional History of Mathematics Project History of Mathematics Project The main objective of this project is to perhaps spark your interest in the amazing ways that Mathematics has changed the world. The only prerequisites for this topic are calculus, linear and abstract algebra. A type of problem that occurs frequently in the Babylonian tablets seeks the base and height of a rectangle, where their product and sum have specified values. You will graded on creativity, knowledge of the topic and presentation. That is, we want a set of sets from F such that any two sets have a non-empty intersection.