Math 4330, Number Theory

Final Project/Presentation

General Information: In lieu of a final exam, you are required to do a final project, which represents 20% of your final grade. The final project requires that you read a published article which includes a mathematical proof in the area of Number Theory from some scholarly journal, write a paper on the topic of the article (to include explaining the proof), and present your paper to the class, including an explanation of the key proof. The paper topic (article) must be approved by the instructor. Possible articles are below.

Paper: The paper must be 4-10 pages (typed) and include an appropriate proof from Number Theory not previously covered in class. You may also include background on the key mathematician involved or the problem, as well as appropriate contextual information. Suggest using the Microsoft Equation Editor (in Word), LaTex, or some other software package that accurately displays mathematics.

Presentation: Presentations must be 15-30 minutes long, and include the general information covered in the paper as well as the key proof, explained. Presentations will be the last day of class AND during the final exam period. Attendance at all presentations is mandatory.

Apostol	Irrationiality of Sqrt 2 - A Geometric Proof	Math Monthly	2000
Benkoski and Erdos	On Weird and Pseudoperfect Numbers	Math of Computation	1974
Bhargava	Factorial Function and Generalizations	Math Monthly	2004
Burger, Ed	Diophantine Olympics and World Champions, Polynomials and Primes Down Under	Math Monthly	2000
Clarkson, James A.	On the Series of Prime Reciprocals	Math Monthly	1996
Cohn	A short Proof of the Simple Cont Frac of e	Math Monthly
Hall, A.	Geneology of Pythagorean Triads	Math Gazette	1970
Nathanson	A short Proof of Cauchy Polygonal Number Theorem	Proceedings of the AMS	1987
Tanton, James	A Dozen Questions about Powers of Two	Horizons	2001
Benjamin and Quinn	Fibonacci Numbers Exposed More Discretely
Bressoud and Zeilburger	Bijecting Eulers Partition Recurrence	Math Monthly	1985
Chamberland	Collatz Chameleon	Horizons	2006
Harris, Schultz, and Sheflett	Reducing the Sum of Two Fractions	Math Teacher	2005
Hausner, Melvin	Applications of a Simple Counting Technique	Math Monthly	1983
Kalman & Mena	Fibonacci Numbers: Exposed	Math Monthly	2003
Montgomery, Hugh, and Wagon	A Heuristic for the Prime Number Theorem	Math Intelligences
Nelson, Roger	Visual Gems of Number Theory	Horizons	2008
Osler, Thomas	A Tale of Two Series	AMS Notices
Saidak, Filip	A New Proof of Euclid's Theorem	Math Monthly	2006
Sliverman	Taxicabs and Sums of 2 cubes	Math Monthly	1993
Tanton, James	A Dozen Questions about Fibonacci Numbers	Horizons	2005
Wastlund, Johan	An Elementary Proof of the Wallis Produce Formula for Pi	Math Monthly	2007
Zagien	A one sentence proof that every prime p=1mod 4 is the sum of two squares	Math Monthly (vol97)	1990