Math 5020Fundamentals of Mathematics for Teachers 
Description:
Number Theory and Combinatorics are branches of
mathematics in which theorems and problems are usually easy to state
but often difficult to prove or resolve. This course will deal with
topics in these two fundamental mathematical fields, including modular
arithmetic, linear and quadratic diophantine equations, continued
fractions, permutations and combinations, distributions and partitions,
recurrence relations,
generating functions, formal power series. The use of computers
for mathematical exploration will
be encouraged through the computer program Maple. The course will
cover material from 'Number Theory' by George Andrews and supplementary
material on generating functions and species. 

Course presentation
topics 

Fermat's Little Theorem 
Kevin Smith 
Sept 29 
Wilson's Theorem 
Shirley Ting 
Oct 6 
card shuffling 
Pierre Lacoste 
Oct 20 
solving congruences 
Dorota Mazur 
Oct 27 
chinese remainder theorem 
Pauline Fu 
Nov 3 
multiplicative functions 
Mike Eden 
Nov 10 
Möbius inversion 
Samia Saleh  Nov 17 
primitive roots 
Jeff Irwin 
Nov 24 
distrib. primes &
Tchebychev's ineq 
Toni Katsinos & Carol Miron 
Dec 1 
quadratic reciprocity 
Melissa Giardina & Paul Attar 
Jan 5 
pseudoprimality testing Jacobi
and Legendre symbols 
Ada Tsui & Andrea Young 
Jan 12 
RSA and Digital Signatures 
Taravat Moshtagh 
Jan 19 
Sum of 4 squares theorem 
Keith Auyeung 
Jan 26 
Generating functions 
Anisoara Preda 
Feb 2 
Jacobi triple product identity 
Anna Yoon 
Feb 9 
Fermat's Last Theorem and A. Weil 
Margarita Panayotova 
Feb 16 
Ferrer's diagrams and partition
ident. 

partitions which fit in a
rectangle 
Class
presentation 
20% 
Unexams
(4 x) 
10%+10%+15%+15% 
Forum exercises  Fall
15%+Winter 15% 
Sept 12  Sect 1.1, 1.2, 2.1 
Sept 19  Sect 2.2, 2.3 
Sept 26  Sect 3.1, 3.2 
Oct 6  Sect 3.3, 3.5, 4.1, 4.2 
Oct 20  Sect 4.3 
Oct 27  Sect 5.1, 5.2 
Nov 3  Sect 5.3 
Nov 10  Sect 6.1,6.2,6.3 
Nov 17  Sect 6.4 