Math 311 syllabus

Introduction to Number Theory 

Course Description:

An introduction to classical number theory with a balance between
theory and computation. Topics include mathematical induction, divisibility properties,
properties of prime numbers, the theory of congruences, number theoretic functions,
continued fractions. 

 

Prerequisites:   C or better in MA 126.  

 

Textbook:  Elementary Number Theory, 7th edition, by David M. Burton. Published by
McGraw Hill. ISBN 978-0-07-338314-9 

 

Topics & Time Distribution

Coverage:

  • Chapter 1 - all sections  (1.5 weeks)
  • Chapter 2 - all sections (2 weeks)
  • Chapter 3 - (omit 3.3)  (1 week)
  • Chapter 4 - all sections  (2 weeks)
  • Chapter 5 - (omit 5.4)  (1.5 weeks)
  • Chapter 6 - (omit 6.3. and 6.4)  (1.5 weeks)
  • Chapter 7 - all sections  (2.5 weeks)
  • Chapter 15 - (omit 15.1 and 15.4)  (2 weeks)

Note - time allotments are approximate and do not include exams. 

 

Learning Objectives

  • Understand the principle of finite induction and to be able to write proofs by induction.
  • Be able to write short proofs using techniques such as proof by contradiction and the

contrapositive.

  • Understand and executing the division algorithm and the Euclidean algorithm.
  • Understand the meaning of terms such as prime number, greatest common divisor and the ability to verify the equivalence of various definitions for these terms.
  • Be able to solve Diophantine equations and linear congruences.
  • Be able to use and justify divisibility properties. Familiarity with modular arithmetic.
  • Understand the theorems by Fermat, Wilson and Euler and their proofs.
  • Demonstrate a basic understanding of number theoretic functions including Euler's Ф -function and the Mobius μ-function.
  • Understand and manipulating multiplicative functions.
  • Understand finite and infinite continued fractions. 

 

Last updated October 30, 2014