As a full time student, you will study a total of 120 credits each year. Credits are made up of mandatory modules and you may have a list of optional modules to choose from. Not every programme offers optional modules and when an optional module is available it will be clearly marked. All modules are listed below and you may not be required to complete all of these modules. Most modules are 20 credits and dissertations are 40 credits. Please note that not all optional modules run every year. For further information please email admissions@newman.ac.uk.
Year 1 modules
MATHEMATICAL THINKING
MODULE TITLE : MATHEMATICAL THINKING
MODULE CODE : MAU401
MODULE 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  :  200.00 
MODULE 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)
MATHEMATICAL METHODS
MODULE TITLE : MATHEMATICAL METHODS
MODULE CODE : MAU403
MODULE 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  :  200.00 
MODULE 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
MODULE TITLE : MATHEMATICAL MODELLING
MODULE CODE : MAU404
MODULE 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  :  200.00 
MODULE 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
MODULE TITLE : LINEAR ALGEBRA AND APPLICATIONS
MODULE CODE : MAU405
MODULE 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  :  200.00 
MODULE 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
MODULE TITLE : PROBABILITY AND STATISTICS
MODULE CODE : MAU406
MODULE 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  :  200.00 
MODULE 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
MODULE TITLE : INTRODUCTION TO WORK RELATED LEARNING
MODULE CODE : PLU404
MODULE 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  :  100.00 
MODULE 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
THE MATHEMATICAL PROFESSIONAL
MODULE TITLE : THE MATHEMATICAL PROFESSIONAL
MODULE CODE : MAU402
MODULE 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  :  100.00 
MODULE 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)
Year 2 modules
RESEARCH METHODS FOR MATHEMATICIANS I
MODULE TITLE : RESEARCH SKILLS FOR MATHEMATICIANS I
MODULE CODE : MAU500
MODULE SUMMARY :
Mathematics graduates at Newman are expected to have a good exposure to the formalities and rigour of mathematics, as well as having the ability to explain, communicate and illustrate such formalities using appropriate tools. The formalities will be illustrated with student developed geometric simulation, which will be the main key to penetrate important research skills of mathematicians. MAU500 develops an approach to the study and practice of formal mathematics, its rigour and the importance of proof and clarity. Building on both MAU401 and MAU403, this module goes deeper into levels of rigour and revisits in a much stronger way the epsilondelta definition of limits, continuity and differentiability. Such formal aspects will be reinforced via the student development of simulation models. Appropriate computer programming languages and/or software will also be exploited to support simulation of concepts.
CONTACT HOURS :
Scheduled  :  18.00 
Independent  :  82.00 
Placement  :  
Total  :  100.00 
MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Demonstrate some formal proofs involving epsilon – delta definitions.

Construct formal proofs of theorems related to differential calculus.

Appraise a proof or argument.

Value the importance of neatness and clarity in mathematics.

Demonstrate formal aspects of mathematics using simulation.

Criticise simulation as a proof of some aspects of mathematics.

Apply deeper understandings of mathematics and its proofs.

Review an accessible research paper.

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

Apply epsilondelta definitions to formal proofs.

Apply analysis to some situations.

Recognise and apply advanced key ideas related to proofs.

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

Solve a number of problem sets within strict deadlines.

Use software and/or programming to illustrate concepts and proofs.
METHOD OF ASSESSMENT :
Component 1  60% Small Group Project (1000 Words)
Component 2  40% Group Presentation (10 Mins  1000 Word Equivalent)
RESEARCH METHODS FOR MATHEMATICIANS II
MODULE TITLE : RESEARCH SKILLS FOR MATHEMATICIANS II
MODULE CODE : MAU520
MODULE SUMMARY :
Mathematics graduates at Newman are expected to have a good exposure to the formalities and rigour of mathematics, as well as having the ability to explain, communicate and illustrate such formalities using appropriate tools. The formalities will be illustrated with student developed geometric simulation, which will be the main key to penetrate important research skills of mathematicians. MAU520 develops an appreciation of the value and importance of study and practice of formal mathematics, its rigour and the importance of proof and clarity. Building on MAU500, this module develops Riemann integration and the fundamental theorem of calculus is formally established. Such formal aspects will be reinforced via the development of simulation models together with a discussion on the formal differences between simulation and proof. Appropriate computer software and/or programming languages will also be exploited to support simulation models.
CONTACT HOURS :
Scheduled  :  18.00 
Independent  :  82.00 
Placement  :  
Total  :  100.00 
MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Demonstrate some formal proofs involving epsilon – delta definitions.

Construct formal proofs of theorems related to calculus.

Appraise a proof or argument.

Value the importance of neatness and clarity in mathematics.

Demonstrate a formal aspect of mathematics using simulation.

Criticise simulation as a proof of some aspects of mathematics.

Promote a better understanding of mathematics and its proofs.

Review an accessible research paper.

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

Apply epsilondelta definitions to formal proofs.

Recognise and apply advanced key ideas related to proofs.

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

Solve a number of problem sets within strict deadlines.

Use software and/or programming to illustrate concepts and proofs.
METHOD OF ASSESSMENT :
Component 1  60% Project (1000 Words)
Component 2  40% Group Presentation (1000 Words Equivalent)
ADVANCED CALCULUS
MODULE TITLE : ADVANCED CALCULUS
MODULE CODE : MAU502
MODULE SUMMARY :
MAU502 introduces multivariable calculus, vector calculus and various differential equations The course begins with a discussion of functions of severable variables, partial derivatives, directional derivatives and “The Derivative” for a function from to , classifying stationary points, classifying stationary points using eigenvalues, equilibrium theory, vector calculus, polar and spherical coordinate systems and multiple integrals. Detailed applications are also carefully illustrated. More complicated differential equations compared to previous modules are motivated and discussed, including various series solutions of differential equations and SturmLiouville problems if time permits. The focus of MAU502 is to apply advanced calculus techniques to solve applied problems.
CONTACT HOURS :
Scheduled  :  36.00 
Independent  :  164.00 
Placement  :  
Total  :  200.00 
MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Use and apply functions of several variables.

Solve optimization problems involving functions of several variables.

Determine and classify stationary points of functions of several variables.

Formulate vector calculus.

Demonstrate properties of differential equations.
Solve and simulate solutions of differential equations, including series solutions.
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have the opportunity to:

Apply a range of mathematical techniques to solve a wide range of applied problems.

Recognise and apply advanced key ideas of advanced calculus and differential equations.

Apply optimization problems.

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

Solve a number of problem sets within strict deadlines.

Use software and/or programming to solve problems related to functions of many variables and differential equations.

Discuss employability skills associated with the module.
METHOD OF ASSESSMENT :
Component 1  50% Electronically Marked Assignment (5 EMAs) (5 Hours Equivalent)
Component 2  50% Final Examination (3 Hours)
STATISTICAL METHODS AND MODELLING
MODULE TITLE : STATISTICAL METHODS AND MODELLING
MODULE CODE : MAU503
MODULE SUMMARY :
Understanding and modelling data and its variation is an important application of statistics and is vitally important with applications in the sciences, technology sector, engineering, business and the social sciences. Statistics that has already been studied will be extended and applied to analyse applied linear and multilinear regression models together with an emphasis on the clear communication and interpretation of results and conclusions. Data transformations will also be exploited together with variable screening to optimize the fit of regressions models, including the general testing and verification of models and their applications and limitations.
CONTACT HOURS :
Scheduled  :  36.00 
Independent  :  164.00 
Placement  :  
Total  :  200.00 
MODULE CURRICULUM LED OUTCOMES :

Set up linear and multilinear regression models

Estimate regression model parameters and interpret their meaning, mean and variance

Examine the relationship between model parameters and data

Construct and analyse variables and their correlation

Use and interpret variable screening

Apply data transformations to better fit regression models

Formulate statistical tests and apply to residue analysis

Apply and interpret regression models to various forms of data types
Discuss employability skills associated with the module.
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have the opportunity to:

Apply a range of statistical techniques to solve a wide range of applied statistical problems

Recognise and apply advanced key ideas of statistics and regression models

Solve problems individually and/or as part of a group

Solve a number of problem sets within strict deadlines

Use software and/or programming to solve problems related to linear and multilinear regression models
METHOD OF ASSESSMENT :
Component 1  60% Project (1500 Words)
Component 2  40% Final Examination (3 hours)
MATHEMATICAL MODELLING AND NUMERICAL METHODS
MODULE TITLE : MATHEMATICAL MODELLING AND NUMERICAL METHODS
MODULE CODE : MAU504
MODULE SUMMARY :
The focus of MAU504 will be mathematical modelling of a wide range of applications using difference equations and ordinary differential equations. Both discrete and continuous dynamical systems are also considered, including situations exhibiting the onset of chaos. Numerical methods are motivated that begin with simple numerical solution techniques such as Taylor series and truncation methods. Euler’s and associated methods are then introduced including RungeeKutta methods. Stability and error analysis are considered and the numerical analysis of nonlinear systems is formulated. Simulation is a key approach of the module together with practical and robust solution methods. A strong understanding and control of errors and error analysis is also developed and applied.
CONTACT HOURS :
Scheduled  :  36.00 
Independent  :  164.00 
Placement  :  
Total  :  200.00 
MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Demonstrate the mathematical modelling process

Apply force problems using potential fields

Formulate appropriate equations, especially differential equations, to model various real world situations.

Identify appropriate numerical methods to solve a class of differential equations.

Design numerical solutions to minimise errors, including appropriate classification of errors and error analysis

Appraise, test, and evaluate mathematical models
Discuss employability skills associated with the module
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have the opportunity to:

Apply a range of mathematical techniques to solve a wide range of applied problems

Recognise and apply advanced key ideas of mathematical modelling and numerical methods.

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

Solve a number of problem sets within strict deadlines.

Use software and/or programming to solve and simulate problems related to mathematical modelling and numerical methods.
METHOD OF ASSESSMENT :
Component 1  50% Electronically Marked Assignment (5 EMAs) (5 Hours Equivalent)
Component 2  50% Simulation Model/Digital Resource (2000 Word Equivalent)
OPTIMIZATION
MODULE TITLE : OPTIMATIZATION
MODULE CODE : MAU505
MODULE SUMMARY :
Optimization is a key and important mathematical theme as many applied mathematical problems are concerned with maximizing or minimizing some expression or quantity. MAU505 will begin with linear optimization methods and applications. After a review of matrix and matrix iterative methods, simplex methods and linear programming techniques are introduced and for large scale problems the more modern interior point method is reviewed and applied. The course goes on to discuss nonlinear optimization, including topics such as gradient and nongradient search methods, efficiency methods, constraints including inequality constraints. An important approach to the course is an emphasis on applications and the use of computers and/or computer algebra to solve problems that could not be solved otherwise.
CONTACT HOURS :
Scheduled  :  36.00 
Independent  :  164.00 
Placement  :  
Total  :  200.00 
MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Set up and apply the LU decomposition technique to systems of linear equations, including conditions of convergence,

Construct graphical and mathematical linear models of linear optimization problems, including their solution.

Use various simplex methods to solve linear optimization problems.

Formulate and apply integer and linear programming methods and models, including the interior point method.

Apply iterative solution techniques to nonlinear equations.

Analyse stability issues related to model parameter changes.

Prepare and solve gradient and nongradient search techniques to optimize nonlinear models.

Formulate and solve optimization problems with constraints, including inequality constraints.

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

Apply a range of mathematical techniques to solve a wide range of applied optimization problems.

Recognise and apply advanced key ideas of optimization

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

Solve a number of problem sets within strict deadlines.

Use software and/or programming to solve problems related to linear and nonlinear optimization problems and models.
METHOD OF ASSESSMENT :
Component 1  50% Electronically Marked Assignment (5 EMAs) (5 Hours Equivalent)
Component 2  50% Final Examination (3 hours)
WORK PLACEMENT
MODULE TITLE : WORK PLACEMENT
MODULE CODE : PLU502
MODULE SUMMARY :
This yearlong module offers learners the opportunity to apply and explore knowledge within a workbased context, through the mode of work place learning. The placement supervisor in the work place will negotiate the focus for the learner’s role on placement, with the learner. Students complete 100 hours in the work setting. The learner will reflect critically on different dimensions of the work place setting.
CONTACT HOURS :
Scheduled  :  10.00 
Independent  :  90.00 
Placement  :  100.00 
Total  :  200.00 
MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Encourage students to take responsibility for initiating, directing and managing their own placement in a workplace setting.

Encourage students to work constructively with their workplace supervisor and university placement tutor, taking ownership of the placement and of their independent learning throughout the experience.

Enable students to negotiate the relationship between academic theory and their understanding of workplace settings and their roles within those settings.

Encourage students to reflect critically on their experiences.

Encourage students to produce a reflective digital resource aimed at an external audience, to contribute towards work and study transitions.
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have had the opportunity to:

Secure, negotiate and undertake a specific role in a workplace setting.

Evaluate features of the workplace setting and their role within it.

Critically evaluate the learning opportunities provided by the workplace experience and understand that learning will benefit current and lifelong learning, values and future employability.

Present a creatively engaging argument within an appropriate digital medium for an external audience, which critically reflects upon an issue or interrelating issues affecting the workplace setting.
METHOD OF ASSESSMENT :
Component 1  % PLACEMENT REGISTRATION FORM
Component 2  60% WORK PLACEMENT REFLECTION (2500 WORDS)
Component 3  40% WORK PLACEMENT EVALUATION: DIGITAL RESOURCE (1500 WORDS EQUIVALENT)
Year 3 modules
DISSERTATION (CAPSTONE)  optional module
Dissertation (Capstone)
Module Title: Dissertation (Capstone)
Module Code: MAU601
Module Summary:
The module builds on prior learning and offers students the opportunity for further development of skills and knowledge learnt throughout the course with the opportunity to further develop a mathematical topic of particular interest. The dissertation involves the development of an independent research project. The project must include the analysis of related literature and the application of applied or theoretical principles.
CATS Value: 40
ECTS Value: 20
Contact Hours:
Scheduled: 30
Independent: 370
Placement: 0
Total Hours: 400
Programmes for which this Module is Mandatory: None
Programmes where this Module may be taken as an Option:
BSc (Honours) Single Honours Mathematics
Module Curriculum Led Outcomes:
This module aims to:
• Provide students with an opportunity for personal development in applying prior mathematical learning to a selected topic, and to demonstrate ability to carry out a sustained piece of independent work
• Encourage individual thought, initiative, time management, goods level of written and communication skills and indepth knowledge and understanding of a particular mathematical topic
• Equip students with the skills to complete a full written report
Learning Opportunities:
Students will, by the end of the module, have the opportunity to:
• Undertake a substantial piece of independent research relevant to the degree programme
• Critically interpret data of different kinds and appraise the strengths and weakness of approaches used
• Research and assess paradigms, theories, principles, concepts and factual information and apply such skills in explaining and solving problems
• Complete a sustained period of independent study, which includes: critical evaluation of literature and study design, application or appropriate methodology, theoretical framework and analysis
• Produce a report
Assessment:
Component 1: 20% Research proposal (equivalent to 2000 words)
Component 2: 80% Report (equivalent to 6000 words)
COMPLEX ANALYSIS AND APPLICATIONS
Complex Analysis and Applications
Module Title: Complex Analysis and Applications
Module Code: MAU602
Module Summary:
Complex analysis is firstly considered including topics such as the complex number field, complex functions, sequences and subsets, limits, continuity, differentiation, Cauchy Riemann equations, integration, the Cauchy integral theory, Taylor and Laurent series, singularities, the residue theorem and applications to the evaluation of real integrals and series. The module then considers some applications of complex analysis, in particular integral transforms together with their application, including Laplace transformations and Fourier transforms. If time permits, applications of complex analysis to two dimensional fluids will be discussed.
CATS Value: 20
ECTS Value: 10
Contact Hours:
Scheduled: 24
Independent: 176
Placement: 0
Total Hours: 200
Programmes for which this Module is Mandatory: BSc (Honours) Single Honours Mathematics
Programmes where this Module may be taken as an Option: None
Module Curriculum Led Outcomes:
This module aims to:
• Demonstrate properties of complex numbers and complex valued functions
• Examine limits, continuity and differentiability of complex valued functions
• Compute integrals of complex valued functions and apply to the evaluation of real integrals and series
• Formulate and apply integral transforms
• Evaluate Laplace and Fourier transforms
• Interpret Laplace and Fourier transforms
• Discuss employability skills associated with the module.
Learning Opportunities:
Students will, by the end of the module, have the opportunity to:
• Apply a range of mathematical techniques to solve a wide range of applied problems related to functions of a complex variables and integral transforms
• Recognise and apply advanced key ideas of complex variable methods and integral transforms
• Solve problems individually and/or as part of a group.
• Solve a number of problem sets within strict deadlines.
• Use software and/or programming to solve problems related to complex valued functions and integral transforms
Assessment:
Component 1: 50% Electronically Marked Assignment (5 EMAs) (5 hours equivalent) (50%)
Component 2: 50% Final Examination (3 hours)
GRAPH THEORY AND NETWORKS
Graph Theory and Networks
Module Title: Graph Theory and Networks
Module Code: MAU603
Module Summary:
Graph theory and networks is a detailed study of the mathematics associated with connected systems. It is a branch of discrete mathematics with strong links to combinatorics. After formalising basic graph theory such as graphs, digraphs, tress, connectivity, network flow, matching, planer graphs, vertex and edge colours, the important role and connection with algorithmic graph theory is established. Applications are then developed to diverse areas such as scheduling, circuit analysis, geometric design, kinetic design and block design.
CATS Value: 20
ECTS Value: 10
Contact Hours:
Scheduled: 24
Independent: 176
Placement: 0
Total Hours: 200
Programmes for which this Module is Mandatory: BSc (Honours) Single Honours Mathematics
Programmes where this Module may be taken as an Option: None
Module Curriculum Led Outcomes:
This module aims to:
• Verify structures as graphs and determine graph properties.
• Formulate and analyse connectivity and network flow problems.
• Set up and test graph based algorithms.
• Formulate and apply circuit equations.
• Create and solve communication code problems, including the shortening of codes.
• Appraise design blocks.
• Discuss employability skills associated with the module.
Learning Opportunities:
Students will, by the end of the module, have the opportunity to:
• Apply a range of mathematical techniques to solve a wide range of applied problems.
• Recognise and apply advanced key ideas of graph theory and networks.
• Formulate connectivity problems.
• Solve problems individually and/or as part of a group.
• Solve a number of problem sets within strict deadlines.
• Use software and/or programming to solve problems related to graphs and networks.
Assessment:
Component 1: 50% Electronically Marked Assignment (5 EMAs) (5 hours equivalent)
Component 2: 50% Final Examination (3 hours)
DATA SCIENCE
Data Science
Module Title: Data Science
Module Code: MAU604
Module Summary: Machine learning is concerned with the development of algorithms that learn to recognise patterns in data and use these to make intelligent decisions. Examples include spam detection, credit card fraud detection and product recommendation. This module aims to introduce students to the mathematical foundations for machine learning and a set of approaches to address data driven problem solving.
CATS Value: 20
ECTS Value: 10
Contact Hours:
Scheduled: 24
Independent: 176
Placement: 0
Total: 200
Programmes for which this Module is Mandatory: BSc (Honours) Single Honours Mathematics
Programmes where this Module may be taken as an Option: None
Module Curriculum Led Outcomes:
This module aims to:
• Examine the three main areas of machine learning: supervised, unsupervised and reinforcement learning
• Discuss models and algorithms for regression, classification and clustering
Learning Opportunities:
Students will, by the end of the module, have the opportunity to:
• Critically examine the issues involved in learning from data
• Apply a variety of learning algorithms to handle datasets
• Examine and apply the mathematical approaches that underpin machine learning algorithms e.g. linear regression, Bayesian statistics
Assessment:
Component 1: 60% Project (2400 words)
Component 2: 40% Presentation (1600 words equivalent)
PARTIAL DIFFERENTIAL EQUATIONS
Partial Differential Equations
Module Title: Partial Differential Equations
Module Code: MAU605
Module Summary:
MAU605 is a natural extension of both MAU502 and MAU505. The core theme is boundary value problems of partial differential equations including connections with special types of ordinary differential equations. A classification is first made of various types of partial differential equations including various methods of solution such as the method of characteristics and separation of variables. Both the heat and wave equations are explored and applied, including the associated Laplace equation. A number of solution approaches and techniques are established including relevant solutions of associated ordinary differential equations, Fourier series solutions and associated eigenvalue and eigenvector approaches. Linear operator approaches are also firmly established including related SturmLiouville problems.
CATS Value: 20
ECTS Value: 10
Contact Hours:
Scheduled: 24
Independent: 176
Placement: 0
Total Hours: 200
Programmes for which this Module is Mandatory: BSc (Honours) Single Honours Mathematics
Programmes where this Module may be taken as an Option: None
Module Curriculum Led Outcomes:
This module aims to:
• Solve first order partial differential equations.
• Formulate a number of solutions to second order partial differential equations.
• Evaluate series solutions of ordinary and partial differential equations.
• Construct and classify eigenvalue problems related to differential equations, in particular SturmLiouville theory.
• Arrange differential equations in various coordinate systems.
• Apply and demonstrate solutions to Laplace and wave equations.
• Discuss employability skills associated with the module.
Learning Opportunities:
Students will, by the end of the module, have the opportunity to:
• Apply a range of mathematical techniques to solve a wide range of applied problems.
• Recognise and apply advanced key ideas of advanced calculus and differential equations.
• Apply differential equations to solve problems.
• Model real world problems with differential equations
• Solve problems individually and/or as part of a group.
• Solve a number of problem sets within strict deadlines.
• Use software and/or programming to solve problems related to partial differential equations.
Assessment:
Component 1: 50% Electronically Marked Assignment (5 EMAs) (5 hours equivalent)
Component 2: 50% Final Examination (3 hours)
NEGOTIATED WORKBASED RESEARCH PROJECT  optional module
MODULE TITLE : NEGOTIATED WORKBASED RESEARCH PROJECT
MODULE CODE : PLU601
MODULE SUMMARY :
This module offers students the opportunity to build on their level 5 work placement through the more developed application of a negotiated workbased research project. Students will agree with their placement tutor and workplace mentor a brief for a project which addresses a need within the organisation. Learners should complete a minimum of 100 hours in the work place. It is in the spirit of this module that wherever possible, the focus will be on social or community / sustainable development.
CONTACT HOURS :
Scheduled  :  24.00 
Independent  :  276.00 
Placement  :  100.00 
Total  :  400.00 
MODULE CURRICULUM LED OUTCOMES :
This module aims to:

Enable students to take responsibility for initiating, directing and managing a negotiated workbased research project

Encourage students to use appropriate workbased research methods

Enable students to work collaboratively in a work setting, establishing continuity from their previous work placement and offering tangible evidence of building on this prior experience, where possible

Generate confidence and security in students’ employability on graduation
LEARNING OPPORTUNITIES :
Students will, by the end of the module, have the opportunity to:

Secure, negotiate and design a workbased research project

Develop an understanding of, and apply, research methods that are appropriate to workbased contexts

Interpret gathered information

Make a clear and productive contribution to the organization through the development of recommendations arising from the workbased research project

Present a creatively engaging argument
METHOD OF ASSESSMENT :
Component 1  100% NEGOTIATED WORKBASED RESEARCH PROJECT (8000 WORDS)