MAT 311 Syllabus Number Theory Fall 2019

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.

• August 26
  Unit 1 Divisibility and Congruences
  Section 1.1 Introduction, Section 1.2 Divisibility
  
• August 28
  Section 1.3 Primes, Section 1.4 The Binomial Theorem
  Diagnostic Quiz in lecture.
  
• September 2
  Labor Day
  
• September 4
  Section 2.1 Congruences, Section 2.2 Solutions of Congruences
  Problem Set 1 due in lecture.
  
• September 9
  Section 2.3 The Chinese Remainder Theorem
  
• September 11
  Section 2.6 Prime Power Moduli
  Problem Set 2 due in lecture.
  
• September 16
  Section 2.7 Prime Modulus
  
• September 18
  Section 2.8 Primitive Roots and Power Residues
  Problem Set 3 due in lecture.
  
• September 23
  Unit 2 Quadratic Reciprocity and Diophantine Equations
  Section 3.1 Quadratic Residues
  
• September 25
  Section 3.2 Quadratic Reciprocity
  
• September 30
  Miscellaneous
  Problem Set 4 due in lecture.
  
• October 1
  MIDTERM 1 ON UNIT 1
  
• October 7
  Section 5.1 Binary Linear Forms, Section 5.2 Simultaneous Linear Equations
  
• October 9
  Section 3.4 Binary Quadratic Forms
  Problem Set 5 due in lecture.
  
• October 14
  Fall Break
  
• October 16
  Section 5.3 Pythagorean Triples
  Problem Set 6 due in lecture.
  
• October 21
  Section 3.5 Equivalence and Reduction of Binary Quadratic Forms
  
• October 23
  Section 3.6 Sums of Two Squares
  
• October 28
  Section 5.5 Ternary Quadratic Forms
  Problem Set 7 due in lecture.
  
• October 30
  Unit 3 Special Cases of Fermat's Last Theorem
  Sums of Four Squares (some overlap with Chapter 6)
  
• November 4
  Miscellaneous
  Problem Set 8 due in lecture.
  
• November 6
  MIDTERM 2 ON UNIT 2
  
• November 11
  Section 9.1 Polynomials, Section 9.2 Algebraic Numbers
  
• November 13
  Section 9.3 Algebraic Number Fields, Section 9.4 Algebraic Integers
  Problem Set 9 due in lecture.
  
• November 18
  Section 9.5 Quadratic Fields, Section 9.6 Units in Quadratic Fields
  
• November 20
  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 10 due in lecture.
  
• November 25
  Section 9.10 The Cubic Case of Fermat's Last Theorem
  Problem Set 10 due in lecture.
  
• November 27
  Thanksgiving break
  
• December 2
  Selected Topics from Chapter 7
  
• December 4
  Selected Topics from Chapter 7
  Problem Set 11 due in lecture.
  
• December 9
  Miscellaneous
  

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