MATH 340 Number Theory
Number theory is the mathematical theory of the integers and, in particular, the natural or counting numbers. This course covers the principles of elementary number theory beginning with mathematical induction and divisibility. Topics include the Euclidean algorithm, the fundamental theorem of arithmetic, linear congruences, theorems of Fermat and Wilson, the Chinese remainder theorem, the Moebius inversion formula, reduced residue systems, and prime numbers. The course concludes with quadratic residues, Gauss’s famous law of quadratic reciprocity, and current applications to computer data encryption. This course emphasizes the writing of mathematical proofs.