Note: If this course is being taught this semester, more information can be found at the course home page.
This course is a prerequisite or co-requisite for
The theory of numbers is a broad subject with many connections to other parts of mathematics as well as to computer science, physics, and cryptography. It is the study of the properties of the natural numbers. For example, why does the decimal expansion of 1/7 have period 6 while that of 1/11 has period 2? Why does x2 + y2 = z2 have infinitely many solutions in positive integers while x3 + y3 = z3 has none? Can every even number greater than 4 be expressed as a sum of two odd primes? A partial list of the topics we will cover are:
- divisibility theory and Euclid’s algorithm
- the theory of congruences
- the distribution of prime numbers
- primitive roots
- the law of quadratic reciprocity
- sums of squares
- factoring and primality testing
- public key cryptosystems
Divisibility, primes, congruences, quadratic residues and quadratic reciprocity, primitive roots, elementary prime number theory.