
MATHEMATICAL THINKING
(Compulsory) mau401(Compulsory) MATHEMATICAL THINKING
mau401MODULE SUMMARY :
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, to take active ownership in properly engaging with mathematics and to 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.
CONTACT HOURS :
Scheduled : 48.00 Independent : 152.00 Placement : Total : 200.00MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Recognise the mathematical community, its standards and approaches.

Give examples of proof, and apply various methods of proof including their logic based foundations.

Define and illustrate the notion of a limit when applied to sequences, series, functions and continuity.

Give examples of from abstract algebra.

Employ and illustrate definitions and proofs and their consequences.

Review an accessible research paper.

Option: Appraise Hardy’s book “A Mathematicians Apology”.

Discuss employability skills associated with the module.
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have the opportunity to:

Define and prove a variety of mathematical structures involving limits, sequences, series and functions.

Recognise and apply some key basic ideas from analysis.

Solve problems individually and/or as part of a group.

Solve a number of problem sets within strict deadlines.

Use computer algebra and/or programming to solve and validate problems involving limits, sequences.
METHOD OF ASSESSMENT :
Component 1  60% Assignment/Project Work (1500 Word Equivalent)
Component 2  40% Presentation (10 Mins  1000 Word Equivalent)


THE MATHEMATICAL PROFESSIONAL
(Compulsory) mau402(Compulsory) THE MATHEMATICAL PROFESSIONAL
mau402MODULE SUMMARY :
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 addin) 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.
CONTACT HOURS :
Scheduled : 18.00 Independent : 82.00 Placement : Total : 100.00MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Develop a strong competence with using mathematical typesetting, involving software such as the MS Office suite and LaTeX, including the potential of using iPads and tablet PCs to write and present mathematics.

Use the MS Office suit to solve and illustrate mathematical and statistical problems.

Demonstrate the simulation of mathematics and/or statistics using various software tools and create the ability to make sophisticated multimedia postings within online social forums.

Create the beginnings of an appropriate online personal portfolio with resources that contain strong and rich mathematical content.

Propose and present a solution to a problem within a small group as a simulation of a small consultancy project using various tools introduced within the module.

Debate and criticize constructively on other student/group presentations.

Promote mathematics and its uses.

Discuss employability skills associated with the module.
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have the opportunity to:

Present mathematics professionally.

Recognise and apply many key ideas of applied mathematics and modelling.

Solve problems and to present and discuss mathematics both individually and/or as part of a group.

Develop a number presentations and postings within strict deadlines.

Use a number of mathematical type setting software

Use software to solve problems and to present and simulate mathematical applications and models.

Apply a scripted programming language.
METHOD OF ASSESSMENT :
Component 1  60% Small Group Project Work (1000 Word Equivalent)
Component 2  40% Small Group Presentation (10 Mins  1000 Word Equivalent)


MATHEMATICAL METHODS
(Compulsory) mau403(Compulsory) MATHEMATICAL METHODS
mau403MODULE SUMMARY :
MAU403 is an important and detailed review and 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.
CONTACT HOURS :
Scheduled : 36.00 Independent : 164.00 Placement : Total : 200.00MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Solve and apply inequalities and equations, especially simultaneous, quadratic, matrix and vector equations, to simple situations.

Illustrate and interpret number simplification, including numbers related to sequences, series, binomial expansion, and related number problems.

Identify and sketch appropriate functions to illustrate geometry and solutions to equations and inequalities.

Determine fixed points and their interpretation.

Identify and use rules of differential and integrals calculus, including Taylor series and Simpson’s rule.

Apply and solve simple differential equations.

Calculate and interpret simple probability problems of both a discrete and continuous nature, linking continuous models with calculus.

Describe and demonstrate the use of complex numbers and its algebra.

Discuss employability skills associated with the module.
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have the opportunity to:

Define and solve a variety of mathematical problems involving algebra, calculus and related themes.

Apply appropriate approximation techniques.

Apply a variety of essential mathematical techniques

Solve problems individually and/or as part of a group.

Solve a number of problem sets within strict deadlines.

Use computer algebra and/or programming to solve problems involving algebra, calculus and related themes.
METHOD OF ASSESSMENT :
Component 1  50% Electronically Marked Assignment (5 EMAs) (5 Hours Equivalent)
Component 2  50% Final Examination (3 hours)


MATHEMATICAL MODELLING
(Compulsory) mau404(Compulsory) MATHEMATICAL MODELLING
mau404MODULE SUMMARY :
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.
CONTACT HOURS :
Scheduled : 36.00 Independent : 164.00 Placement : Total : 200.00MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Identify and apply a variety of mathematical techniques to solve applied mathematical problems.

Solve and interpret first and second order differential equations.

Apply vectors and vector algebra to a variety of problems.

Solve static and force problems using vector methods.

Apply and simulate Newtonian mechanics.

Analyse, solve and simulate a variety of mathematics models from diverse applications.
Discuss employability skills associated with the module.
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have the opportunity to:

Develop mathematical models to describe aspects of the real world.

Recognise and apply many key ideas of applied mathematics and modelling.

Solve problems individually and/or as part of a group.

Solve a number of problem sets within strict deadlines.

Use computer algebra and/or programming to solve problems and to simulate mathematical applications and models.
METHOD OF ASSESSMENT :
Component 1  50% Electronically Marked Assignment (5 EMAs) (5 Hours Equivalent)
Component 2  50% Simulation (1000 Word Equivalent)


LINEAR ALGEBRA AND APPLICATIONS
(Compulsory) mau405(Compulsory) LINEAR ALGEBRA AND APPLICATIONS
mau405MODULE SUMMARY :
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 coupledlinear 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, to simulate solutions, and to 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
CONTACT HOURS :
Scheduled : 36.00 Independent : 164.00 Placement : Total : 200.00MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Implement matrix operations.

Describe linearly dependent and independent spaces, and vector spaces.

Explain and interpret determinants.

Calculate and employ eigenvalues and eigenvectors.

Explain and illustrate when a system can be expressed in matrix form.

Solve first order and second order couple linear differential equations.

Relate normal modes of coupled systems to initial conditions.

Discuss employability skills associated with the module.
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have the opportunity to:

Define, illustrate and prove a variety ideas related to linear systems.

Recognise and apply some key basic ideas from linear algebra.

Formulate problems in terms of linear algebra.

Solve problems individually and/or as part of a group.

Solve a number of problem sets within strict deadlines.

Use computer algebra and/or programming to solve problems related to linear algebra and its applications.
METHOD OF ASSESSMENT :
Component 1  50% Electronically Marked Assignment (5 EMAs) (5 Hours Equivalent)
Component 2  50% Final Examination (3 Hours)


PROBABILITY AND STATISTICS
(Compulsory) mau406(Compulsory) PROBABILITY AND STATISTICS
mau406MODULE SUMMARY :
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 probability and chance of both discrete and continuous systems and develops an understanding of their mean, standard deviation and other measure 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 carefully and clear interpretation of results and conclusions.
CONTACT HOURS :
Scheduled : 36.00 Independent : 164.00 Placement : Total : 200.00MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Describe the meaning of data.

Prepare and present data in various graphical forms.

Interpret data using a variety of probability and statistical models.

Identify and use both discrete and continuous probability models and functions.

Illustrate the central theme and concepts related to the normal and tdistributions.

Apply, interpret and form a conclusion of confidence intervals and hypotheses testing.

Apply and discuss themes related to nonparametric tests.

Create a sense of statistical thinking.

Discuss employability skills associated with the module.
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have the opportunity to:

Define, illustrate and interpret a variety ideas related to probability and statistics.

Recognise and apply some key ideas related to decision science.

Solve problems individually and/or as part of a group.

Solve a number of problem sets within strict deadlines.

Use software to solve problems related to probability, statistics and its applications.
METHOD OF ASSESSMENT :
Component 1  50% Electronically Marked Assignment (5 EMAs) (5 Hours Equivalent)
Component 2  50% Final Examination (3 hours)


INTRODUCTION TO WORK RELATED LEARNING
(Compulsory) plu404(Compulsory) INTRODUCTION TO WORK RELATED LEARNING
plu404MODULE SUMMARY :
This module aims to equip students with the knowledge and selfmanagement 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 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.
CONTACT HOURS :
Scheduled : 12.00 Independent : 88.00 Placement : Total : 100.00MODULE CURRICULUM LED OUTCOMES :
This module aims to:
 Support students in developing informed choices about the career pathways available to them, in relation to their subject choices.

Prepare students for workbased learning and the application / exploration of subject knowledge in the workplace.

Encourage students to make connections between their learning, placement choice, future job aspirations and contribution to society.

Enable students to build confidence in securing work placements and future employment.
 Support students in reflecting upon their preparation for their work placement and future employment.
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have had the opportunity to:

Examine how their experiences, accomplishments, and abilities relate to employer expectations.

Demonstrate engagement with, and an understanding of, graduate employment pathways and employability issues relating to their own career aspirations.

Research organisations for the purposes of securing a work placement.

Reflect upon their learning and development.
METHOD OF ASSESSMENT :
Component 1  100% Reflective Essay and Appendix, 2000 words