MATH 406 (Number Theory)
| DESCRIPTION |
Integers, divisibility, prime numbers, unique factorization,
congruences,
quadratic reciprocity, Diophantine equations and arithmetic functions. |
| PREREQUISITES |
MATH 141 |
| TOPICS |
The integers
Divisibility
Prime numbers
Greatest common divisor
Euclidean algorithm
Unique factorization
Congruences
Basic properties
Modular arithmetic
Euler's phi function
Fermat's, Euler's and Wilson's theorems
Chinese remainder theorem
Quadratic Reciprocity
Quadratic residues
Legendre and Jacobi symbols
Law of quadratic reciprocity (possibility skip proof
to allow time for other topics)
Additional Topics, (as time allows)
Diophantine equations: Pythagoras, Fermat,
Pell
Primitive roots: Lagrange's Theorem
Primality testing
Factoring
RSA Algorithm
Arithmetic functions, Moebius inversion formula,
Mersenne primes
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| TEXT |
Text(s)
typically used in this course. |
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