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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.Have an understanding of some topics in graph theory with an emphasis on graph algorithms and proof techniques.
This course will provide students with an opportunity to develop the Graduate Attributes specified below:
Critically competent in a core academic discipline of their award
Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.
Employable, innovative and enterprising
Students will develop key skills and attributes sought by employers that can be used in a range of applications.
Globally aware
Students will comprehend the influence of global conditions on their discipline and will be competent in engaging with global and multi-cultural contexts.
MATH120 and one of MATH102, MATH103, MATH199, EMTH118, EMTH119
MATH221, MATH231
Students must attend one activity from each section.
Brendan Creutz
Jeanette McLeod
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.
Buchmann, Johannes; Introduction to cryptography ; 2nd ed; Springer, 2004.
Clark, John. , Holton, Derek Allan; A first look at graph theory ; World Scientific, 1991.
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.
General information for students Library portal LEARN
Domestic fee $847.00
International fee $4,988.00
* 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.
For further information see Mathematics and Statistics .