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.
Suggested Text: Elementary Number Theory, 7th edition, by David M. Burton. McGraw Hill.
Coverage: Chapter 1 - all sections, Chapter 2 - all sections, Chapter 3 (omit 3.3), Chapter 4 (all sections), Chapter 5 (omit 5.4), Chapter 6 (omit 6.3. and 6.4), Chapter 7 (all sections), Chapter 15 (omit 15.1 and 15.4)
Learning outcomes: Upon the successful completion of the course a student will
Understand the principle of finite induction and be able to write proofs by induction.
Write short proofs using techniques such as proof by contradiction and the contrapositive.
Understand and be able to execute the division algorithm and the Euclidean algorithm.
Understand the meaning of terms such as prime number, greatest common divisor and be able to verify the equivalence of various definitions for these terms.
Solve Diophantine equations and linear congruences.
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 be able to manipulate multiplicative functions.
Understand finite and infinite continued fractions.