# 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