MAT 311 Syllabus Number Theory Spring 2011

The schedule for topics covered in lecture is as follows. Please do the assigned reading prior to lecture. This will make the lectures more effective for you.

• February 1
  Unit 1 Divisibility and Congruences
  Section 1.1 Introduction, Section 1.2 Divisibility
  
• February 3
  Section 1.3 Primes, Section 1.4 The Binomial Theorem
  
• February 8
  Section 2.1 Congruences
  
• February 10
  Section 2.2 Solutions of Congruences
  Problem Set 1 due in lecture.
  
• February 15
  Section 2.3 The Chinese Remainder Theorem
  
• February 17
  Section 2.6 Prime Power Moduli
  Problem Set 2 due in lecture.
  
• February 22
  Section 2.7 Prime Modulus
  
• February 24
  Section 2.8 Primitive Roots and Power Residues
  Problem Set 3 due in lecture.
  
• March 1
  Unit 2 Quadratic Reciprocity and Diophantine Equations
  Section 3.1 Quadratic Residues
  
• March 3
  Section 3.2 Quadratic Reciprocity
  Problem Set 4 due in lecture.
  
• March 8
  Miscellaneous
  
• March 10
  MIDTERM 1 ON UNIT 1
  
• March 15
  Section 5.1 Binary Linear Forms, Section 5.2 Simultaneous Linear Equations
  
• March 17
  Section 3.4 Binary Quadratic Forms
  Problem Set 5 due in lecture.
  
• March 22
  Section 5.3 Pythagorean Triples
  
• March 24
  Section 3.5 Equivalence and Reduction of Binary Quadratic Forms
  Problem Set 6 due in lecture.
  
• March 29
  Section 3.6 Sums of Two Squares
  
• March 31
  Section 5.5 Ternary Quadratic Forms
  Problem Set 7 due in lecture.
  
• April 5
  Unit 3 Special Cases of Fermat's Last Theorem
  Sums of Four Squares (some overlap with Chapter 6)
  
• April 7
  Section 9.1 Polynomials, Section 9.2 Algebraic Numbers, Section 9.3 Algebraic Number Fields
  Problem Set 8 due in lecture.
  
• April 12
  Miscellaneous
  
• April 14
  MIDTERM 2 ON UNIT 2
  
• April 26
  Section 9.4 Algebraic Integers, Section 9.5 Quadratic Fields, Section 9.6 Units in Quadratic Fields
  
• April 28
  Section 9.7 Primes in Quadratic Fields, Section 9.8 Unique Factorization, Section 9.9 Primes in Quadratic Fields with the UFD property
  Problem Set 9 due in lecture.
  
• May 3
  Section 9.10 The Cubic Case of Fermat's Last Theorem
  
• May 5
  Selected Topics from Chapter 7
  Problem Set 10 due in lecture.
  
• May 10
  Selected Topics from Chapter 7
  
• May 12
  Miscellaneous
  

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