MA257 - Introduction to Number Theory

Multi

Module Info

Module Link/Module Webpage/Lecture Notes

Professor: Sam Chow
Term: 2
Status: Option List A
Assessment: 85% exam, 15% assignments

Rating

Difficulty:
Professor:
Teaching Style:
Would take again?

1—The Series of Primes (i) | 2—The Series of Primes (ii) | 3—Farey Series and a Theorem of Minkowski | 4—Irrational Numbers | 5—Congruences and Residues
6—Fermat’s Theorem and its Consequences | 7—General Properties of Congruences | 8—Congruences to Composite Moduli | 9—The Representation of Numbers by Decimals | 10—Continued Fractions
11—Approximation of Irrationals by Rationals | 12—The Fundamental Theorem of Arithmetic in k(1), k(i) and k(p) | 13—Some Diophantine Equations | 14—Quadratic Fields (i) | 15—Quadratic Fields (ii)
16—The Arithmetical Functions | 17—Generating Functions of Arithmetical Functions | 18—The Order of Magnitude of Arithmetical Functions | 19—Partitions | 20—The Representation of a Number by Two or Four Squares
21—Representation by Cubes and Higher Powers | 22—The Series of Primes (iii) | 23—Kronecker’s Theorem | 24—Geometry of Numbers | 25—Elliptical Curves

TopicRatingSummary
1.1 Euclid’s Algorithm
1.2 The Fundamental Theorem of Arithmetic
1.3 Fermat Primes, Mersenne Primes, and Perfect Numbers
1.4 Congruences
1.5 Linear Congruences
1.6 Standard Congruences
1.7 Primitive Roots
1.8 Quadratic Residues
2.1 The Geometry of Numbers
2.2 Sums of Squares
2.3 Gaussian Primes
2.4 Pythagorean Triples
2.5 Ternary Quadratic Equations
2.6 Hensel’s Lemma
2.7 Waring’s Problem
2.8 Diophantine Approximation