MA 218: Number Theory
Credits: 3:0
- Fundamental theorem of arithmetic (divisibility, primes, Euclidean algorithm, infinitude of primes)
- Arithmetical functions and Dirichlet multiplication (Möbius function, Euler totient function, Dirichlet product of arithmetical functions, Dirichlet inverses and the Mobius inversion formula, Mangoldt function)
- Congruences (Linear congruences, Fermat’s little theorem, Chinese remainder theorem, quadratic residues, quadratic reciprocity law)
- Finite abelian groups and their characters (characters of finite abelian groups, orthogonality relations, Dirichlet characters)
- Dirichlet theorem of primes in arithmetic progression (including the complete proof of non-vanishing of L(1,
$\chi$) for non-principal$\chi$) - Binary quadratic forms (factorable and unfactorable forms, equivalence classes of forms, finiteness of class number of binary quadratic forms of a given discriminant)
- Algebraic number theory (Algebraic numbers and Algebraic integers, ring of integers of quadratic extensions, quadratic reciprocity using Gauss sums).
Suggested books and references:
- Apostol, T. M., Introduction to Analytic Number Theory, Springer International Student Edition, 1989.
- Niven, I. and Zuckerman, H. S., An Introduction to the Theory of numbers, Wiley Eastern Limited, 1989.
- Ireland, K. and Rosen, M., Classical Introduction to Modern Number Theory, Springer-Verlag (GTM), 1990.
- Edmund Landau, Elementary Number theory, AMS Chelsea Publisshing, 1958.