Course 311: Michaelmas Term 2005 Part I: Topics in Number Theory
نویسندگان
چکیده
1 Topics in Number Theory 2 1.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 2 1.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 2 1.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 3 1.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . 5 1.6 The Infinitude of Primes . . . . . . . . . . . . . . . . . . . . . 6 1.7 Congruences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.8 The Chinese Remainder Theorem . . . . . . . . . . . . . . . . 8 1.9 The Euler Totient Function . . . . . . . . . . . . . . . . . . . 9 1.10 The Theorems of Fermat, Wilson and Euler . . . . . . . . . . 11 1.11 Solutions of Polynomial Congruences . . . . . . . . . . . . . . 13 1.12 Primitive Roots . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.13 Quadratic Residues . . . . . . . . . . . . . . . . . . . . . . . . 16 1.14 Quadratic Reciprocity . . . . . . . . . . . . . . . . . . . . . . 21 1.15 The Jacobi Symbol . . . . . . . . . . . . . . . . . . . . . . . . 22
منابع مشابه
Course 311: Michaelmas Term 2005 Part II: Topics in Group Theory
2 Topics in Group Theory 2 2.1 Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Examples of Groups . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Elementary Properties of Groups . . . . . . . . . . . . . . . . 4 2.4 Subgroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.5 Cyclic Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.6 Co...
متن کاملCourse 311: Michaelmas Term 2005 Part III: Topics in Commutative Algebra
3 Topics in Commutative Algebra 2 3.1 Rings and Fields . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.3 Quotient Rings and Homomorphisms . . . . . . . . . . . . . . 5 3.4 The Characteristic of a Ring . . . . . . . . . . . . . . . . . . . 7 3.5 Polynomial Rings in Several Variables . . . . . . . . . . . . . . 7 3.6...
متن کاملMSc in CRIMINOLOGY and CRIMINAL JUSTICE
• Option Essays In each of Michaelmas and Hilary Terms, students were required to take two optional seminar courses (out of a choice of three in Michaelmas and four in Hilary). These were examined by essays, the titles of which were posted on Friday of 6 week, to be submitted by noon on Friday of ninth week. Each essay was to be no less than 3,500 and no more than 5,000 words, including footnot...
متن کاملCos 594d: a Theorist’s Toolkit
These are edited lecture notes from a graduate course at the Computer Science department of Princeton University in Fall 2002. The course was my attempt to teach first year graduate students students many mathematical tools useful in theoretical computer science. Of course, the goal was too ambitious for a course with 12 three hour lectures. I had to relegate some topics to homework; these incl...
متن کاملCourse 2BA1: Michaelmas Term 2005 Section 2: Sets and Functions
2 Sets and Functions 1 2.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 Unions, Intersections and Complements of Sets . . . . . . . . . 2 2.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 4 2.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 6 2.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.6 Congr...
متن کامل