e-learning @ Divine Word University: Courses

A metric space is a set together with a good definition of the distance between each pair of points in the set. Metric spaces occur naturally in many parts of mathematics, including geometry, fractal geometry, topology, functional analysis and number theory. This unit will present the basic ideas of the theory, and illustrate them with a wealth of examples and applications.

This unit builds on Algebraic Structures 1, which is a prerequisite, and continues the strong emphasis on examples. Factorisation in polynomial rings and rings of integers of number fields will also be studied in the first part. The second part will begin by developing further properties of key examples, such as permutation groups, and will emphasise actions of groups. Then the construction of quotient objects and the connection with homomorphisms in the context of groups will be developed and illustrated by many examples.

This unit addresses the principles of programming language design and use. It introduces different models of computation and the programming languages based on them, particularly functional programming and logic programming. It then examines a range of underlying issues in programming languages, such as semantics of programming languages, type systems, and control in programming languages.

This unit provides an introduction to database concepts superseding the relational model focusing on an in-depth theoretical treatment of the topic. The students are expected to be already familiar with a database management system and basic database models. This unit offers a rigorous mathematical treatment of database theory.

This unit is an introduction to the area of computer security concerned with techniques based on a secret key for concealing or enciphering data. Only someone who has access to the key is capable of deciphering the encrypted information. In principle, this is impossible for anyone else to do.

Coding theory plays a crucial role in the transmission of information. Due to the effect of noise and interference, the received message may differ somewhat from the original message that is transmitted. The main goal of Coding Theory is the study of techniques which permit the detection of errors and which, if necessary, provide methods to reconstruct the original message. The subject involves some elegant algebra and has become an important tool in banking and commerce.

This unit continues the development of probability and statistics from the first year unit MC 171 so that all students have the basic grounding in this area that would be expected of a mathematics graduate. It provides a solid basis for a wide variety of options later in the program for students who wish to take their studies in probability and/or statistics further.