‘I love teaching new maths teachers, and I particularly enjoy working on this programme. I never cease to be amazed by the way in which our undergraduates manage to combine brilliant subject knowledge with a passion for teaching. Our alumni have gone on to make huge contributions to in their schools, both locally and nationally. Maths teachers are like gold dust, and our schools look out for the BSc students in particular.’
Carolyn Hume, Programme Director, BSc Mathematics with Secondary Education
In the first year you will study the following core modules at the University of Kent:
MA306 Statistics (15 credits)
Increasingly data are collected to inform future decisions, varying from which websites people access on a regular basis to how patients respond to new drugs, to how the stock market responds to global events, or to how animals move around their local habitat. Therefore, most professionals will need to extract useful information from data and to manage and present data in their working lives. This module explores some of the basic concepts of statistics, from data summarisation to the main methods of statistical inference. The techniques that are discussed can be used in their own right for simple statistical analyses, but serve as an important foundation for later, more advanced, modules. The statistical computing package R is used throughout the module for data analysis. The syllabus includes: an introduction to R and investigating data sets, sampling and sampling distributions, point and interval estimation, hypothesis testing, association between variables.
MA343 Algebraic Methods (15 credits)
This module serves as an introduction to algebraic methods. These methods are central in modern mathematics and have found applications in many other sciences, but also in our everyday life. In this module, students will also gain an appreciation of the concept of proof in mathematics. The mathematical package Maple will be used to support learning. The syllabus includes: logic, basic set theory, techniques of proof, functions, relations, systems of linear equations and Gaussian elimination, matrices and determinants.
MA344 Applications of Mathematics (15 credits)
This module introduces mathematical modelling and Newtonian mechanics. The mathematical package Maple will be used to support learning. The syllabus includes: the modelling cycle, using examples such as Newton’s law of cooling, population growth and simple reaction kinetics; the motion of a body, including aspects such as velocity and acceleration, Newton’s laws of motion and projectile motion; orbital motion, including Newton’s law of gravitation, planetary motion and Kepler’s laws.
MA346 Linear Algebra (15 credits)
This module is a sequel to Algebraic Methods. It considers the abstract theory of linear spaces together with applications to matrix algebra and other areas of Mathematics (and its applications). Since linear spaces are of fundamental importance in almost every area of mathematics, the ideas and techniques discussed in this module lie at the heart of mathematics. The mathematical package Maple will be used to support learning. The syllabus includes: vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization, orthogonality and applications using conics.
MA348 Mathematical Methods I (15 credits)
This module introduces widely-used mathematical methods for functions of a single variable. The emphasis is on the practical use of these methods and the mathematical package Maple will be used to support learning. The syllabus includes: complex numbers, polynomials, single variable calculus, scalar ordinary differential equations, curve sketching.
MA349 Mathematical Methods II (15 credits)
This module introduces widely-used mathematical methods for vectors and functions of two or more variables. The emphasis is on the practical use of these methods and the mathematical package Maple will be used to support learning. The syllabus includes: vectors and vector algebra, including the differentiation of vector-valued functions of a scalar variable and vector fields (with everyday examples); partial differentiation, including maxima, minima and saddle points and Lagrange multipliers; integration in two dimensions using Cartesian and plane polar coordinates.
MA351 Probability (15 credits)
This module introduces the basic concepts of probability. The techniques that are discussed can be used in their own right to solve simple problems, but also serve as an important foundation for later, more advanced, modules. The syllabus includes: concepts and axioms of probability, Bayes’ theorem, discrete and continuous random variables, expectation and variance, common distributions, probability and moment generating functions, weak law of large numbers, central limit theorem, transformation of a single continuous random variable, and joint distribution of discrete random variables.
MA352 Real Analysis I (15 credits0
This module provides an introduction to real analysis, i.e. the study of real numbers and real-valued functions of a real variable. The syllabus includes: real numbers, limits of sequences, completeness properties, continuity of functions, differentiation, Taylor’s theorem and Taylor series.
In the second year you will study the mathematics modules at the University of Kent and the mathematics education modules at Canterbury Christ Church University. You will study the following core modules:
MA5501 Applied Statistical Modelling I (15 credits)
Constructing suitable models for data is a key part of statistics. For example, we might want to model the yield of a chemical process in terms of the temperature and pressure of the process. Even if the temperature and pressure are fixed, there will be variation in the yield which motivates the use of a statistical model which includes a random component. In this module, we study how suitable models can be constructed, how to fit them to data and how suitable conclusions can be drawn. Both theoretical and practical aspects are covered, including the use of R.
MA5503 Groups and Symmetries (15 credits)
The concept of symmetry is one of the most fruitful ideas through which mankind has tried to understand order and beauty in nature and art. This module first develops the concept of symmetry in geometry. It subsequently discusses links with the fundamental notion of a group in algebra. Outline syllabus includes: Groups from geometry; Permutations; Basic group theory; Action of groups and applications to (i) isometries of regular polyhedra; (ii) counting colouring problems; Matrix groups.
MAE100 School Practice (10 credits)
This module encompasses the two placements completed during Year 2 - one in the role of Teaching Assistant and the other enabling you to teach some classes. It is assessed through a Record Of Development.
And you can choose 60 credits (four modules) from the following:
MA5504 Lagrangian and Hamiltonian Dynamics (15 credits)
This module will present a new perspective on Newton's familiar laws of motion. First we introduce variational calculus with applications such as finding the paths of shortest distance. This will lead us to the principle of least action from which we can derive Newton's law for conservative forces. We will also learn how symmetries lead to constants of motion. We then derive Hamilton's equations and discuss their underlying structures. The formalisms we introduce in this module form the basis for all of fundamental modern physics, from electromagnetism and general relativity, to the standard model of particle physics and string theory.
MA5505 Linear parial Differential Equations (15 credits)
In this module you will study linear partial differential equations, exploring their properties and discussing the physical interpretation of certain equations and their solutions. You will learn how to solve first order equations using the method of characteristics and second order equations using the method of separation of variables.
MA5507 Mathematical Statistics (15 credits)
This module is a pre-requisite for many of the other statistics modules at Stages 2, 3 and 4, but it can equally well be studied as a module in its own right, extending the ideas of probability and statistics met at Stage 1 and providing practice with the mathematical skills learned in MA348 and MA349. It starts by revising the idea of a probability distribution for one or more random variables and looks at different methods to derive the distribution of a function of random variables. These techniques are then used to prove some of the results underpinning the hypothesis test and confidence interval calculations met at Stage 1, such as for the t-test or the F-test. With these tools to hand, the module moves on to look at how to fit models (probability distributions) to sets of data. A standard technique, the method of maximum likelihood, is used to fit the model to the data to obtain point estimates of the model parameters and to construct hypothesis tests and confidence intervals for these parameters. Outline Syllabus includes: Joint, marginal and conditional distributions of discrete and continuous random variables; Transformations of random variables; Sampling distributions; Point and interval estimation; Properties of estimators; Maximum likelihood; Hypothesis testing; Neyman-Pearson lemma; Maximum likelihood ratio test.
MA5512 Ordinary Differential Equations (15 credits)
This module introduces the basic ideas to solve certain ordinary differential equations, like first order scalar equations, second order linear equations and systems of linear equations. It mainly considers their qualitative and analytical aspects. Outline syllabus includes: First-order scalar ODEs; Second-order scalar linear ODEs; Existence and Uniqueness of Solutions; Autonomous systems of two linear first-order ODEs.
MA5514 Rings and Fields (15 credits)
Can we square a circle? Can we trisect an angle? These two questions were studied by the Ancient Greeks and were only solved in the 19th century using algebraic structures such as rings, fields and polynomials. In this module, you will be introduced to these ideas and concepts and show how they generalise well-known objects such as integers, rational numbers, prime numbers, etc. The theory is then applied to solve problems in Geometry and Number Theory. This part of algebra has many applications in electronic communication, in particular in coding theory and cryptography.
MA566 Number Theory (15 credits)
The security of our phone calls, bank transfers, etc. all rely on one area of Mathematics: Number Theory. This module is an elementary introduction to this wide area and focuses on solving Diophantine equations. In particular, we discuss (without proof) Fermat's Last Theorem, arguably one of the most spectacular mathematical achievements of the twentieth century. Outline syllabus includes: Modular Arithmetic; Prime Numbers; Introduction to Cryptography; Quadratic Residues; Diophantine Equations.
During this year you will study the following core modules at Canterbury Christ Church University:
Subject Pedagogy I (20 credits) & II (20 credits)
These module equips you to teach mathematics and considers all key aspects of mathematics pedagogy. They are assessed through essays, critical reflection analysis and a presentation.
Research and Enquiry in Education (20 credits)
This module will support you in reflecting on improving practice in the secondary age phase through research. It will equip you with a range of educational theories and philosophies to develop your own identity and practice as a reflective secondary teacher. The module will be assessed through an essay or an essay and a presentation.
Professional Placement (20 credits)
This module encompasses your school placements and is assess through a collection of evidence against the Teachers’ Standards.
Preparing for Qualified Teacher Status (10 credits)
This module enables you to demonstrate your teaching and learning by developing a scheme of work, reflecting upon your decisions and collating evidence against the Teachers’ Standards.
We continually review and where appropriate, revise the range of modules on offer to reflect changes in the subject and ensure the best student experience.
And you will study the following core module at the University of Kent:
MA601 Individual Project in Mathematics (30 credits)
This module provides an opportunity for students on the Mathematics with Secondary Education programme to explore and research a topic in mathematics or statistics that is of interest to the student. Under the guidance of a supervisor, the student will engage in self-directed study to produce a dissertation. Outline syllabus: This is determined by the topic of the project. Indicative mathematics titles include the following: Knot theory; Logistic map; Totally non-negative matrices; Signed permutations and the four colour theorem; Generating functions; Latin squares; Teaching further Linear Algebra; Graph theory; Exploring mathematics with origami; Classical invariant theory; Zeta functions; Foundations of the real numbers; Euler's formula; Creative use of random numbers to teach Statistics; The National Lottery; Circular data.