MTH311 Number Theory
Level: 3
Credit Units: 5 Credit Units
Presentation Pattern: EVERY JULY
Synopsis:
Prime numbers are the "atoms" of numbers in the sense that all other integer numbers can be
constructed or made from prime numbers. MTH311 introduces and develops various theorems of
numbers and prime numbers, and introduces a number of classical theorems associated with the
integers.
Topics:
ƔThe greatest common divisor.
ƔPrime divisors.
ƔLinear, simultaneous linear and quadratic congruences.
ƔFermat's little theorem and Wilson's theorem.
ƔMultiplicative functions.
ƔEuler's theorem.
ƔThe Legendre symbol.
ƔEuler's criterion and Gauss' lemma.
ƔFinite and infinite continued fractions.
ƔRational approximations.
ƔPell's equation and Pythagorean triples.
ƔInfinite descent and sums of squares.
Learning Outcome:
ƔAnalyze prime numbers, congruences, multiplicative functions, Legendre symbol, continued
fractions and Pythagorean triples.
ƔCompute solutions to a system of linear congruences simultaneously.
ƔDemonstrate solutions of equations with positive integer solutions.
ƔSolve greatest common and prime divisors.
ƔUse various congruences and apply to problems using related theorems.
ƔConstruct multiplicative functions and apply Euler¶s theorem.
ƔImplement Legendre symbols and apply Euler¶s criteria.
ƔFormulate continued fractions and relate to rational approximations.
ƔEvaluate number theory applications.
ƔDescribe number theory applications.
ƔConstruct and formulate a range of mathematical techniques to solve a variety of quantitative
problems.
ƔFormulate solutions to problems individually and/or as part of a group.
ƔAnalyze and solve a number of problem sets within strict deadlines.
Assessment Strategies:
Continuous Assessment Component
COMPUTER MARKED ASSIGNMENT
COMPUTER MARKED ASSIGNMENT
Weightage (%)
10
10
Page 1 of 2
COMPUTER MARKED ASSIGNMENT
Sub-Total
Examinable Component
Written Exam
Sub-Total
Weightage Total
10
30
Weightage (%)
70
70
100
Page 2 of 2