MATH320-22S1 (C) Semester One 2022

Discrete Mathematics

15 points

Details:
Start Date: Monday, 21 February 2022
End Date: Sunday, 26 June 2022
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 6 March 2022
  • Without academic penalty (including no fee refund): Sunday, 15 May 2022

Description

An introduction to various topics including combinatorial optimisation, enumeration, and set systems.

Discrete mathematics underpins many areas of modern-day science. In MATH320, we explore selected topics in discrete mathematics in greater depth and detail. In particular, we investigate some technical methods that allow for elegant solutions to more advanced enumeration questions, and explore the structural properties of directed graphs and partially-ordered sets (posets).

Topics covered:

Term 1: Combinatorial enumeration:
Binomial identities and direct enumeration. Principle of Inclusion and Exclusion; Generating functions (ordinary and exponential). Lagrange inversion and applications.

Term 2: Directed graphs and posets:
Basic Ramsey theory, theory of directed graphs (structural results, algorithms, algebraic methods, phase transitions) and partially-ordered sets (Möbius inversion, Dilworth Theorem).

Learning Outcomes

  • Understanding of a range of concepts in combinatorics and the ability to express this clearly in your own words.
  • Ability to devise and write up rigorous mathematical proofs of combinatorial results.
  • Ability to apply general theory to particular examples and problems.
    • University Graduate Attributes

      This course will provide students with an opportunity to develop the Graduate Attributes specified below:

      Employable, innovative and enterprising

      Students will develop key skills and attributes sought by employers that can be used in a range of applications.

      Engaged with the community

      Students will have observed and understood a culture within a community by reflecting on their own performance and experiences within that community.

Prerequisites

Restrictions

MATH333, MATH334

Timetable 2022

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Wednesday 09:00 - 10:00 Jack Erskine 111
21 Feb - 10 Apr
2 May - 5 Jun
Lecture B
Activity Day Time Location Weeks
01 Thursday 09:00 - 10:00 Jack Erskine 446
21 Feb - 10 Apr
2 May - 5 Jun
Tutorial A
Activity Day Time Location Weeks
01 Friday 13:00 - 14:00 Ernest Rutherford 225
28 Feb - 10 Apr
2 May - 5 Jun

Examination and Formal Tests

Test A
Activity Day Time Location Weeks
01 Wednesday 18:30 - 20:00 Online Delivery
4 Apr - 10 Apr
Test B
Activity Day Time Location Weeks
01 Friday 17:30 - 19:00 Online Delivery
30 May - 5 Jun

Course Coordinator / Lecturer

Mike Steel

Lecturer

Charles Semple

Assessment

Assessment Due Date Percentage 
Assignments 50%
Tests 50%

Indicative Fees

Domestic fee $802.00

International fee $4,563.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

Minimum enrolments

This course will not be offered if fewer than 15 people apply to enrol.

For further information see Mathematics and Statistics .

All MATH320 Occurrences

  • MATH320-22S1 (C) Semester One 2022