Discrete Mathematics and Combinatorics explores a variety of topics within discrete mathematics. This is the branch of mathematics that deals with countable sets. The module introduces the concepts of using discrete mathematics to model and solve problems. It provides you with the opportunity to study modern topics within mathematics, gaining an appreciation and understanding of the algorithms involved in the graphs and networks used in computers and route planners such as Google Maps. You will additionally focus on combinatorics, which involves the selecting or counting of objects to satisfy certain criteria and deciding when the criteria can be met. Graph theory, flow, matchings, allocation and transportation will also be introduced, all of which have numerous applications in solving real life problems.

Differential Calculus provides a foundation in calculus, introducing the fundamental mathematical concepts which underpin mathematics at degree level. Calculus is one of the foremost branches of mathematics and its mathematical discipline has a unique legacy over the history of mathematics. This module enables you to use a mixture of numerical and analytical techniques to help achieve a deeper understanding of key concepts. It also embraces topics such as functions, limits, the fundamental theorem of calculus, differentiation from first principles, differentiating hyperbolic functions and inverse hyperbolic functions, improper integrals, numerical solutions, numerical differentiation, numerical integration and approximations to functions.

Algebraic Structure focuses on aspects of pure mathematics. The module will equip you with a deep understanding of numbers and examine the links between algebra and geometry. You will be introduced to the concepts which underpin mathematics at degree level. This includes mathematical principles such as algebraic structure, proof, matrix algebra and the extension of the number system to include complex numbers. You will also be introduced to computer algebra and mathematical word processing.

Establishing the Conditions for Studentship introduces the themes of studentship, educational research, learning environments and professional identity. You will develop an initial understanding of the four areas to construct an identity as an academic learner and student teacher. The module will build personal resilience and promote independence within a community of learners, encouraging you to connect with your own experiences to develop your practice.

Establishing Educational Values for Schools and Learners introduces you to the underlying concepts, principles and values in educational theory, policy and practice. Predominantly focused on the present day, the module will equip you with a deeper understanding of contemporary education. This will ensure that you are comprehensively prepared for practice in educational settings. You will also have the opportunity to consider your own sets of values and predispositions and begin to develop a critical understanding of how seemingly objective values may disguise highly subjective ideological concepts.

Establishing the Conditions for Learning in Mathematics combines taught sessions on campus with experiential observations in schools. The module introduces you to the practical elements of teaching mathematics and provides an insight into good teaching practice and barriers to pupils’ learning. You will participate in lessons under the direction of a mentor and steadily increase your responsibility for planning and teaching. You will initially teach parts of lessons and build to whole class lessons, teaching jointly with your mentor at first, then individually. The placement will typically equate to 30 hours of teaching across an eight-week period. While being guided in the craft of teaching mathematics, you will also be introduced to wider school issues such as behaviour management, inclusion, and child wellbeing and psychology. These combined elements will enable you to begin to gathering evidence to show that you are starting to meet the Teachers’ Standards.

Inferential Statistics develops your understanding of statistical techniques and test-structures. The module embraces essential topics such as probability distributions, sampling techniques, hypothesis testing, application of the central limit theorem, confidence intervals, chi-squared tests, goodness of fit, contingency tables, Type 1 and Type 2 errors, and the power of a hypothesis test. The module will reveal how hypothesis testing, estimation and prediction are used in a growing number of real-world fields and are central to much academic research work.

Applications of Calculus recognises that calculus is a form of mathematics which has applications deeply integrated in every branch of the physical sciences, computer science, statistics, engineering, economics, business and medicine. Applications of calculus are part of modern mathematics education, combining logic and precision with intuition and imagination. This module enhances your knowledge of calculus and introduces greater rigour into your studies. You will explore new topics such as polar coordinates, applications of higher order partial derivatives, double integrals and centres of mass in two dimensions, as well as the application of first order ordinary differential equations in real life. Although computers and graphic calculators will be used, the emphasis is on enhancing, not replacing, your mathematical skill and reasoning.

Linear Algebra is central to both pure and applied mathematics and is vital to practically every area of modern science. It is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes and subspaces but is also concerned with properties common to all vector spaces. The module explores the links between numbers, algebra and geometry, embracing topics such as linear algebra, solving linear equations, Eigenvectors, numerical techniques and Guassian elimination. You will learn how to apply algebraic results geometrically, recognise applications of linear algebra and interpret results, explain and manipulate the concepts of a vector space, and use and interpret the output of computer algebra and graphing packages to solve and present solutions to problems in algebra and geometry.

Building Research Informed Knowledge further develops the themes of studentship, educational research, learning environments and professional identity. You will progress your understanding of these four areas while continuing to develop your role as an academic learner, researcher and student teacher. Exploring the significance, implications and impact of educational research on your own practice, the module will explore a range of research perspectives and methodologies in education. You will receive a comprehensive overview of the research process and consider ethical issues related to the practical application of research.

Building Knowledge of Educational Values develops your critical engagement with the underlying concepts, principles and values of educational theory, policy, and practice. Through a central focus on the past, you will track the genealogy and evolution of values and gain insight into the mutability of these apparently fixed social concepts and principles. The module will engage you with the idea that values are not fixed, that they have not always been as they currently are, and that they will therefore continue to change and evolve in the future.

Building Knowledge of Teaching Mathematics develops the practical elements of teaching mathematics on a professional practice placement while critically engaging with the underlying concepts and principles of educational theory and policy. The placement will typically equate to 60 hours of teaching across an eight-week period. You will assume significant teaching responsibility, developing your skills in planning teaching episodes and ensuring that pupils make progress. With comprehensive support and mentoring, you will plan lessons and sessions, or parts of lessons and sessions, for up to 50% of a Newly Qualified Teacher’s typical timetable, covering small group, whole class and solo teaching as appropriate. You will reflect on your own practice and school and educational policies and gather evidence to show that you are progressing towards meeting the Teachers’ Standards.

Statistical Modelling develops and extends the use of statistics in more complex problem solving and research design. The focus on mathematical structure in the module serves a dual purpose. First, you will gain understanding of, and confidence in, the procedures that you are using. Second, the module will prepare you for the demands of statistics as an ever-growing subject area. Embracing important statistical topics such as multiple regression analysis, Markov Chains and Estimators, you will select and execute tests for averages based upon parametric and non-parametric data, analyse and calculate estimators, use probability models to solve problems, and access and make appropriate use of computer software in data analysis.

Integral Calculus develops your understanding of the techniques of differential and integral calculus in multivariate settings. The module considers applications of triple integrals in finding the volumes of three-dimensional solids and centres of mass using spherical and cylindrical coordinates. It also considers second order differential equations and their applications to real-life situations. You will learn how to find general solutions for special types of differential equations and appreciate the existence and uniqueness of solutions. You will also discover how to deploy various tests for convergent and divergent series and use 3×3 Jacobian matrices.

Number Theory is the study of the fascinating properties of the natural number system. The module is about the theory of whole numbers, deepening your knowledge of numbers and giving you the opportunity to put the study of numbers into a wider cultural and historical context. You will explore some of the fundamental properties of prime numbers and the fundamental theorem of arithmetic, as well as the properties of congruences and elementary number theories, such as Fermat’s theorem, Wilson’s theorem and Euler’s theorem. You will also discover how to manipulate continued fractions and develop your knowledge and understanding of some of the many number theoretic functions such as ‘number of divisors’ and ‘sum of divisors’.

Researching Possibilities in Secondary Education enables you to conduct a piece of self-initiated research on a relevant topic of your choice. The module draws together the themes of studentship, educational research, learning environments and professional identity from earlier in the programme. You will further enhance your knowledge and understanding of research, developing critical and analytical skills in reviewing both literature and educational research methodologies, while gaining additional expertise in presenting data in a variety of formats. The value of research for teachers and wider school communities will also be explored.

Exploring Possibilities for Schools and Learners considers a hypothetical future for education. Engaging you with the concepts and principles of educational values, the speculative nature of this module will equip you with the knowledge, understanding, critical skills and self-awareness to develop convincing and complex critiques of where education appears to be heading. You will contrast this with where you think it ought to be heading. The module will enable you to develop as a practitioner with sophisticated and robust opinions about how education ought to be practised and governed, informed by the latest insights into theory, policy and practice. This focus on the future will prepare you to become an agent of change in your future career, equipped with the knowledge, motivation and communication skills to lead movements for positive change.

Exploring Possibilities in Teaching Mathematics enables you review, consolidate, extend and apply your knowledge through a final professional practice placement. The placement will typically equate to 120 hours of teaching across a twelve-week period. Demonstrating excellence in the practice of teaching mathematics, you will take a full role in school life, from tutor work and pastoral care to extra-curricular activities, parents’ evenings, school events, professional development activities and other enhancement opportunities which may be offered by your setting. You will also reflect on your own practice, assessing your strengths and weaknesses, responding to feedback and honing your skills and abilities. The module will enable you to demonstrate that you have met the Teachers’ Standards.

Example offers updated to include the Education and Childcare T Level with an overall grade of Merit.

MAT1000 Discrete Mathematics and Combinatorics (20 credits), MAT1001 Differential Calculus (20 credits), MAT1002 Algebraic Structure (20 credits), SEC1000 Establishing the Conditions for Studentship (20 credits), SEC1001 Establishing Educational Values for Schools and Learners (20 credits) and SEC1003 Establishing the Conditions for Learning in Mathematics (20 credits) replace SUG1000 Professional Practice 1A (20 credits), SUG1001 Personal and Professional Conduct – Transition into Higher Education and the Teaching Profession (20 credits), SUG1005 Principles, Pedagogy and Planning in Mathematics (20 credits), SUG1021 Mathematical Proof and Logic (20 credits), SUG1022 Modelling Using Mechanics (20 credits), SUG1023 Understanding Continuous Functions (20 credits) and SUG1024 Exploring Algebraic and Geometric Structure (20 credits) as compulsory modules in Year 1.

MAT2000 Inferential Statistics (20 credits), MAT2001 Applications of Calculus (20 credits), MAT2002 Linear Algebra (20 credits), SEC2000 Building Research Informed Knowledge (20 credits), SEC2001 Building Knowledge of Educational Values (20 credits) and SEC2003 Building Knowledge of Teaching Mathematics (20 credits) replace SUG2000 Professional Practice 1B (20 credits), SUG2001 Personal and Professional Conduct – Legal Requirements for Professional Practice (20 credits), SUG2005 Creative Medium-Term Planning and Teaching in the Mathematics Classroom (20 credits), SUG2010 Educational Research Methods for School Improvement (20 credits), SUG2020 Statistical Inference (20 credits), SUG2021 Discrete Mathematics (20 credits) and SUG2022 Linear Algebra (20 credits) as compulsory modules in Year 2.

MAT3000 Statistical Modelling (20 credits), MAT3001 Integral Calculus (20 credits), MAT3002 Number Theory (20 credits), SEC3000 Researching Possibilities in Secondary Education (20 credits), SEC3001 Exploring Possibilities for Schools and Learners (20 credits) and SEC3003 Exploring Possibilities in Teaching Mathematics (20 credits) replace SUG3000 Professional Practice 2 (40 credits), SUG3001 Personal and Professional Conduct – Employability (20 credits), SUG3005 Classroom Assessment and Target Setting Skills in Mathematics (20 credits), SUG3012 School Improvement Study in Mathematics (20 credits), SUG3025 Mathematical Models (20 credits), SUG3026 Number Theory (20 credits) and SUG3027 Ordinary Differential Equations (20 credits) as compulsory modules in Year 3.

104-112 UCAS Tariff points are required to join the 3-year route with effect from September 2021 entry.