MATH220-19S1 (C) Semester One 2019

Discrete Mathematics and Cryptography

15 points
18 Feb 2019 - 23 Jun 2019

Description

Discrete mathematics underpins many areas of modern-day science. This course is an introduction to graph theory and cryptography, two central topics in discrete mathematics.

Discrete mathematics underpins many areas of modern-day science. This course is an introduction to graph theory and cryptography, two central topics in discrete mathematics, each having fundamental links to many branches of science. Graph theory underlies the solution to many problems in a variety of disciplines including operations research and computational biology. Cryptography has applications to all communications security, from state security to online banking and mobile phone conversations. This course is designed for mathematics and computer science students.

Topics covered:

Cryptography: Basic ideas and terminology of cryptography. Shift and affine ciphers. One-time pads. Basic properties of the integers. Euclid’s algorithm. Modular arithmetic. Public key ciphers. The RSA, Rabin and ElGamal ciphers. Diffie-Hellman key exchange. Arithmetic of polynomials over finite fields. Constructing finite fields. Linear and non-linear shift registers.

Graph theory: Concepts and terminology of graphs. Eulerian and Hamiltonian graphs. Complexity, polynomial-time and exponential-time algorithms. Chromatic polynomials. Matchings and Hall’s Marriage Theorem. The Greedy Algorithm. Directed graphs. Network flows.

Learning Outcomes

  • At the end of the course, students will:

  • be familiar with  some of the old and modern cryptographic schemes and have developed the necessary mathematics to understand and analyse them.
  • be familiar with some of the basic techniques of decipherment.
  • have an understanding the field of graph theory with an emphasis on graph algorithms and proof techniques.

Pre-requisites

Restrictions

MATH221, MATH231

Timetable 2019

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Tuesday 16:00 - 17:00 E9 Lecture Theatre 18 Feb - 7 Apr
29 Apr - 2 Jun
Lecture B
Activity Day Time Location Weeks
01 Monday 12:00 - 13:00 E9 Lecture Theatre 18 Feb - 7 Apr
29 Apr - 2 Jun
Lecture C
Activity Day Time Location Weeks
01 Wednesday 17:00 - 18:00 Meremere 108 Lecture Theatre 18 Feb - 7 Apr
29 Apr - 2 Jun
Tutorial A
Activity Day Time Location Weeks
01 Wednesday 15:00 - 16:00 Jack Erskine 240 25 Feb - 7 Apr
29 Apr - 2 Jun
02 Wednesday 14:00 - 15:00 Ernest Rutherford 260 25 Feb - 7 Apr
29 Apr - 2 Jun
03 Monday 15:00 - 16:00 Jack Erskine 121 25 Feb - 7 Apr
29 Apr - 2 Jun
04 Tuesday 12:00 - 13:00 Jack Erskine 240 25 Feb - 7 Apr
29 Apr - 2 Jun
05 Wednesday 16:00 - 17:00 E13 25 Feb - 7 Apr
29 Apr - 2 Jun
06 Monday 10:00 - 11:00 Jack Erskine 242 25 Feb - 7 Apr
29 Apr - 2 Jun
07 Monday 16:00 - 17:00 Jack Erskine 121 25 Feb - 7 Apr
29 Apr - 2 Jun

Examination and Formal Tests

Test A
Activity Day Time Location Weeks
01 Friday 18:30 - 19:30 K1 Lecture Theatre 25 Mar - 31 Mar

Course Coordinator / Lecturer

Charles Semple

Lecturer

Jeanette McLeod

Assessment

Assessment Due Date Percentage 
Assignments 25%
Test 25%
Final Examination 50%


To obtain a passing grade in this course you must pass the course as a whole (which requires an overall mark of 50% or more) and score at least 40% in the final exam.

Textbooks

There is no set text for the course. But there are several books that are recommended reading:
1. Buchmann, Introduction to Cryptography (2nd Edition)
2. Clark and Holton, A First Look at Graph Theory

Copies of these books will be on reserve in the Engineering and Physical Sciences Library. Also, there are a number of other good books on cryptography and graph theory in the library.

Indicative Fees

Domestic fee $764.00

International fee $4,000.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

All MATH220 Occurrences

  • MATH220-19S1 (C) Semester One 2019