Mathematical Thinking
20 Credits
(Compulsory)
Mathematical thinking is an approach to mathematics in terms of not only solving problems but in terms of constructing proofs, presenting convincing rigorous arguments and the ability to generalise with abstraction. MAU401 begins with a slow introduction to logic and a review of the various types of proof together with their logical foundations. Definitions are then discussed with detailed examples of rigorous deductions, leading to the very beginnings of analysis. Limits of sequences and functions are carefully discussed as well as continuity and convergence criteria of series will be investigated. If time permits, various notions of algebraic abstract structures are also introduced together with a highlight of their applications. An important aspect of Mathematical Thinking is students must feel part of the subject and its community, take active ownership in properly engaging with mathematics and foster an approach to mathematics and its applications that are insightful, well-planned, neat, rigorous and rewarding. The course will also highlight the strong historical heritage of mathematics and expose students to some important individuals of mathematics as well as reviewing accessible mathematical literature.
The Mathematical Professional
10 Credits
(Compulsory)
A modern graduate needs to operate in a world where there are a number of standard software tools that are expected to be used with confidence, and modern mathematics graduates need to exploit such tools much further for the solution and presentation of complex mathematical and statistical problems. MAU402 introduces the mathematical and typesetting capabilities of MS Office (Microsoft Mathematics add-in) and the mathematical and statistical capabilities of Excel. LaTeX is also introduced as well as other useful tools and hardware (such as iPad, tablet PC,…) for the professional presentation of high-quality documents containing mathematical content. There is also a brief introduction to the use of Maxima/Matlab as scripted programming languages. Using such tools, students will work in small groups to offer and argue a viable solution to a problem, and to present their findings both orally and in the form of multimedia posting within a social forum. The mathematical professional also needs to promote their subject, to explain its power, universality and beauty. The course will finish by establishing a strong commitment from students to promote mathematics and its uses.
Mathematical Methods
20 Credits
(Compulsory)
MAU403 is an important and detailed review and a reminder of essential and important foundational mathematics, especially themes related to algebra and calculus, for students who are new to higher education mathematics and who require a firm foundation and common grounding in level 4 beginning mathematical techniques. The course prepares students for further mathematical studies in higher education and introduces computer algebra as a vital and important tool that not only solves problems but also helps students learn and simulate mathematics. The course will also have a strong support aspect to identify early weak areas and to strengthen areas identified through online computer-marked assignments before an end-of-course examination.
Mathematical Modelling
20 Credits
(Compulsory)
Mathematical methods such as first-order and more detailed second-order differential equations are reviewed and applied, including vector algebra in three dimensions. Applications are considered related to a variety of situations, such as mechanics and motion, physics, finance, economics and other applied areas. The mathematical modelling process is introduced, applied and validated. An important approach of MAU404 is the use of computer algebra (and/or other tools) to simulate mathematical models and situations.
Linear Algebra and Applications
20 Credits
(Compulsory)
MAU405 introduces the notion of linear structures and their representation as matrices. Matrix algebra and manipulation will be formalised and linear transformations, matrix reduction techniques, vector spaces, orthogonality, determinants, eigenvalues and eigenvectors are developed together with a clear discussion of their relationship and meaning. Applications are then developed to coupled-linear systems, coupled first and second-order linear differential equations and their solutions in terms of eigenvectors and eigenvalues are developed and simulated, including the illustration of normal modes. Throughout the course, there will be a strong use of computer algebra and other software to check and test ideas, simulate solutions, and solve problems that are too large to solve by hand. If time permits, applications in diverse areas such as physics, business and bioinformatics will be demonstrated to illustrate the far-reaching power and applicability of linear algebra.
Probability and Statistics
20 Credits
(Compulsory)
MAU406 focus is on data, data collection, unbiased sampling, displaying data and reaching conclusions about populations based on samples and various statistical tests, and developing a clear understanding of variability and statistical thinking. The course begins with a review of the probability and chance of both discrete and continuous systems and develops an understanding of their mean, standard deviation and other measures of central tendency and variation. The modelling of variation is further developed including both discrete and continuous models. The central limit theorem is firmly established together with applications based on confidence intervals, hypothesis testing, nonparametric statistical tests, regression, and correlation analysis. MAU406 will focus on applied statistics using appropriate software with careful and clear interpretation of results and conclusions.
Introduction to Work-Related Learning
10 Credits
(Compulsory)
This module aims to equip students with the knowledge and self-management skills to make informed choices in preparing for work placement and the transition to employment or further study on graduation. Learners will be provided with the opportunities to develop an awareness of the workplace, identify different career and study options, recognise and articulate their own experience, accomplishments and talents and plan and implement career management strategies for the short and long term.