
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.

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.

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.

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.

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.

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.

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.
Mathematics BSc (Hons)
Honours Degree, Undergraduate, September 2020
Key Details
 G100 Course Code
 34.5 Years
 104 Typical UCAS Tariff
Overview
Problem solving and mathematical modelling are fundamental themes of the course – representing real world problems in a mathematical form and then using appropriate methods and techniques to simulate and analyse, translating results back from mathematics to the actual problem together with an appropriate interpretation. You will build on the mathematics that you have already studied, further extending your knowledge of calculus and algebra. You will also be introduced to mathematical modelling and simulation, including statistics, and learn how to approach building a mathematical representation to simulate real world problems.
Practicing mathematicians make extensive use of sophisticated software to analyse complex problems. During the first year you will be introduced to software tools which handle the drudgery of calculation, allowing you to focus on the higher level mathematical issues related to the appropriateness and reliability of the model being used.
This degree also includes the option of a qualified teacher status (QTS) pathway. Please note students wishing to undertake this pathway will be unable to study abroad.
Why study Mathematics?
 An ideal first degree
 A focus on using mathematics to solve real problems
 Using industry standard software to analyse complex situations
 An extensive final year project applying mathematics in an area of your own choosing
 IMA Accreditation (Institute of Mathematics and its Applications)
 A Chance to study part of your course in the USA
 Credit bearing work placement in a mathematical environment
 Development of skills to communicate findings with both those with no advanced mathematical knowledge and specialist mathematicians
Mathematics is playing an increasingly important role in modern life in areas ranging from internet security to medical imaging, from data analytics to telecommunications. And, of course, it remains important in traditional areas such as finance and teaching. Mathematicians are in high demand.
The BSc Mathematics programme at Newman will equip you with the cognitive and practical problem solving skills to successfully apply mathematical thinking in a wide range of situations. The course has also been designed to enable you to study for a semester of second year at Newman University in Wichita, USA, adding an international dimension to the degree (additional costs apply, please see additional costs section for cost estimations). Please note students wishing to undertake the qualified teacher status (QTS) pathway will be unable to study abroad.
What does the course cover?
In your first year you will study Mathematical Thinking to develop your logic and proof skills to ensure your approach to mathematics is much more formal and rigorous as well as taking modules that will develop mathematical methods and modelling skills. This will be followed by The Mathematical Professional to develop software skills and Linear Algebra and Probability and Statistics to give you an overall firm foundation in pure mathematics, applied mathematics and statistics. The various modules will also introduce a number of useful mathematical software packages to help you solve and check problems and will also allow you to experiment with mathematical ideas.
During your second year you will build on your first year modules by taking further calculus, statistics and modelling modules as well as developing further and deeper topics into pure mathematics and research methods for mathematicians. Optimization is also extensively discussed as well as further numerical methods to aid in solving equations and problems that cannot be solved exactly.
In the final year you will develop further techniques in the areas of complex analysis, graph theory, data science and partial differential equations and you will undertake an extended capstone project to be completed over two semesters that will bring together all your accumulated mathematical knowledge and skills.
How will I be assessed?
The course is assessed using a combination of examinations, projects, presentations and continuous assignments.
What careers could I consider?
The course will prepare you for a graduate role in a rapidly changing world. Graduates with mathematical and statistical skills are highly sought after in a wide range of industries, particularly if they are able to communicate clearly with those who are not mathematicians. Typically, mathematics graduates find employment in finance, computing, manufacturing, pharmaceutical industry and teaching. However, the list of sectors employing mathematicians is continually increasing. The growing volume and importance of data means that the number and range of ‘analyst’ roles is ever increasing – and mathematicians are ideally placed to fill such roles. In addition this degree course is also a strong academic base for those interested in studying at postgraduate level.
Applications are open for September entry
Thinking of starting your studies this September? We are currently accepting new applications. Applications to fulltime courses must be made via UCAS, applications to parttime courses are made directly to Newman. For help with the application process please contact our friendly and helpful admission teams via admissions@newman.ac.uk or via 0121 476 1181 ext. 3662.
Apply NowContact Details
For Admissions Enquiries
for course specific enquiries
 Dr Andrew Toon (Senior Lecturer in Mathematics)
 maths@newman.ac.uk
 0121 476 1181 (ext. 2693)
Entry Requirements
You must achieve at least 104 UCAS points including a minimum of CC at A level or equivalent (e.g.MM at BTEC Diploma; MPP at BTEC Extended Diploma) towards the total tariff.
As it is not possible to achieve 104 UCAS points through an Access course, Access Students will need 106 UCAS points. You can reach this with the following combination of Distinction, Merit and/ or Pass grades at level 3 achieved from a completed Access course. 106 UCAS Points: D27M0P18; D124M6P15; D21M12P12; D18M18P9; D15M24P6; D12M24P3; D9M36P0.
Five GCSEs at grade 4 (or C) or above (or recognised equivalents), including English Language, and a A Level (Grade C or above) in Mathematics are also required.
Applying Direct Option
You can apply direct to Newman University for the fulltime route for this course if you have not previously applied to Newman University through UCAS and you are not applying to any other universities.
Simply click on this Direct Application link to do this.
N.B. will need to enter ‘New User’ account details when first accessing this portal.
Course Fees
Fees per academic year:
Fulltime UK/EU students: £9,250 *
Parttime UK/EU students: TBC
* Fees shown are for 2020/21 academic year. The University will review tuition fees and increase fees in line with any inflationary uplift as determined by the UK Government, if permitted by law or government policy, on enrolment and in subsequent years of your course. It is anticipated that such increases would be linked to RPI (the Retail Price Index excluding mortgage interest payments).
Additional Costs
The course has been designed to enable you to study for a semester or second year at Newman University in Wichita, USA. If you choose the option to travel to Wichita to study you will need to pay for your flights and accommodation and living expenses whilst there.
Cost: return flight from Birmingham International Airport – £750;
Accommodation costs: £1,500;
A yearlong visa – (currently £150)
Living costs – £1,200 (based on 2017/18)
Find out more about the other additional costs associated with our undergraduate degrees.
Additional Information
General Academic Regulations: Terms and Conditions for students attending our courses
Modules
Please be aware that, as with any course, there may be changes to the modules delivered, for information view our Changes to Programmes of Module Changes page.
Timetables: find out when information is available to students

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.

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. This module provides an opportunity for students wishing to attain National Professional recognition with the Teaching and Learning Academy (TLA) to complete an AMTLA project. The module will also provide the opportunity for those students interested in going on to the PGCE programme to gain support and guidance with the PGCE application process.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.