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Unit of study_

MATH1064: Discrete Mathematics for Computation

This unit introduces students to the language and key methods of the area of Discrete Mathematics. The focus is on mathematical concepts in discrete mathematics and their applications, with an emphasis on computation. For instance, to specify a computational problem precisely one needs to give an abstract formulation using mathematical objects such as sets, functions, relations, orders, and sequences. In order to prove that a proposed solution is correct, one needs to apply the principles of mathematical logic, and to use proof techniques such as induction. To reason about the efficiency of an algorithm, one often needs to estimate the growth of functions or count the size of complex mathematical objects. This unit provides the necessary mathematical background for such applications of discrete mathematics. Students will be introduced to mathematical logic and proof techniques; sets, functions, relations, orders, and sequences; counting and discrete probability; asymptotic growth; and basic graph theory.

Code MATH1064
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
MATH1004 or MATH1904
Assumed knowledge:
Coordinate geometry, basic integral and differential calculus, polynomial equations and algebraic manipulations, equivalent to HSC Mathematics

At the completion of this unit, you should be able to:

  • LO1. construct logically correct and mathematically sound proofs
  • LO2. apply concepts of logic, set theory, relations, induction, principles of counting, probability, algebraic structures, elementary number theory and asymptotic growth to mathematical and computational problems in more advanced courses
  • LO3. demonstrate an understanding and well-founded knowledge of the mathematics presented in this course and thus be able to apply techniques from this course to solve both familiar and novel problems
  • LO4. understand some applications of mathematics to relevant fields, such as computer programming and logic.