Math 311 syllabus
Introduction to Number Theory
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,
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
- 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.
- 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
- 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