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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.
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.
One of MATH102, MATH103, MATH120, MATH199, EMTH118 or EMTH119.
Students must attend one activity from each section.
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.
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 TheoryCopies 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.
General information for students
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.