BSc (Hons) Mathematics with Secondary Education (QTS)

This course extends the analysis and calculus studied in year 1. It is designed into two streams. The first stream consists of 24 hours of lectures over 12 consecutive weeks covering Real Analysis. In real analysis we extend and reinforce the calculus and analysis studied in year 1. The second stream consists of 24 hours of lectures over 12 consecutive weeks on Complex Analysis. Complex analysis involves the analysis of functions of a complex variable. It is a rich and deep subject with applications in fluid mechanics and engineering as well as within real analysis. Real Analysis - The Real Numbers, boundedness, supremum, infimum, completeness of the reals, the Archimedean property, the density of the rationals, defining the real numbers. - Sequences, partial sums, convergence, divergence, limit of a sequence, squeeze theorem, convergence criteria, subsequences. - Series, convergence, divergence, telescoping series, geometric series, harmonic series etc. Tests for convergence, comparison test, ratio test. - Continuity & amp; Differentiability, epsilon-delta limits, continuity, intermediate value theorem, differentiability, piecewise continuous functions, mean value theorem, Rolle& rsquo;s theorem. Complex Analysis -Review of Complex numbers: definition as an ordered pair, geometry in the complex plane, polar form, Euler& rsquo;s formula, roots of unity. -Set Theory in the Complex Plane: open/closed discs, boundary points, closure, annulus, bounded/unbounded, the Riemann Sphere, Stereographic Projection. -Complex Functions: limits, continuity, differentiability, holomorphicity, Cauchy-Riemann theorem, Laplace equation, Harmonic conjugates. -Complex Integration: curves, contours and simply connected domains, integration along curves and contours (path integral), ML-Inequality, fundamental theorem of contour integration, Cauchy-Goursat and deformation theorem, Cauchy& rsquo;s Integral Formula. -Series: Taylor and Laurent series, Laurent& rsquo;s theorem, poles, removable and essential singularities. -Cauchy& #39;s Residue Theorem: residue theory, the residue theorem, evaluation of real integrals (infinite and trigonometric).

The purpose of this module is to provide a framework that will enable you to build your capacity to teach your specialist subject.  You will be required to meet those essential professional standards identified in the module as fundamental to the beginning teacher. You will be able to identify and express learning objectives appropriate to a range of different learners and be able to assess the learning outcomes.  You will engage with a range of pedagogical approaches appropriate to your specialist subject.  You will be supported to identify your professional identity as a beginning teacher. The module will support your development as a reflective practitioner in a variety of learning contexts.  This will include university-based sessions and experience within school-based environments, supported by university-based and school-based tutors.  You will make effective use of current theories and practices in education.  Reading, observation, personal practice and discussion will inform your professional development.  Your capacity for reflection is expected to impact on your classroom practice.  You are expected to build professional relationships with pupils, teachers and other professionals.

This course extends the probability and statistics studied in year 1. It will introduce you to the theory and practice of Linear Statistical Modelling and Survey Design. Linear statistical modelling statistical modelling where a response variable depends on one or more explanatory variables. Examples include, how well a patient responds to treatment, given their age and disease severity, or how different strains of corn compare when grown in various conditions. Survey design is a critical topic when determining the quality of survey based research. The potential for poor survey design is enormous whether intentional or not. Examples of poor survey design can be found in many real world spheres including political polling and readership surveys.

The purpose of this module is to provide a framework that will enable you to build your capacity to teach your specialist subject.  You will be able to identify and express learning objectives appropriate to a range of different learners.  You will be aware of a range of pedagogical approaches available in your specialist subject and know how to select approaches and strategies to meet and assess learning objectives. The module will also support your development as a reflective practitioner with an emphasis on understanding the ways in which theories of learning, teaching and assessment can inform your practice. You will develop an ability to learn from experience by engaging in learning conversations with university-based and school-based tutors, so that together you can agree well-focussed targets for your subject-specific development. Although a significant proportion of the training associated with this module is delivered through university -based sessions, the major part will take place in school, supported by university-based tutors and school-based tutors.    

This course extends the algebra and calculus studied in year 1. This module is designed in two separate streams. The first stream is on Discrete Mathematics. Discrete mathematics involves the study of structures which are discrete rather than continuous. It is often viewed as the foundation of computer science. The second stream is on Numerical Analysis. Numerical analysis is the area of mathematics that creates, analyses, and implements algorithms for solving numerically the problems of continuous mathematics.

The purpose of this module is to provide an introduction to the teaching of your specialist subject in the secondary school curriculum. You will consider educational policies and the impact of these on your own education. The module will draw upon subject specific reading to identify what you consider to be the rationale that justifies and underpins the teaching of your specialist subject. You will begin to identify and express learning objectives appropriate to a range of different learners. You will be introduced to a range of pedagogical approaches and strategies to deliver lesson objectives.

This module builds on the knowledge, skills and understanding gained in the previous modules; revising some of the content in light of experience and encouraging you to take a deeper approach to learning to become a teacher.  This will require you to: engage with theories of teaching and learning across the themes of national policies and strategies in education, subject pedagogy, assessment within the framework of national target setting and use of data, behaviour management and assessment for learning in the classroom critically relate these theories to your practice in the context of the classroom and in the wider context, showing how deep knowledge and understanding had helped you in the development of your practice continue to develop your professional identity as a developing teacher Although a significant proportion of the training associated with this module is delivered through university-based sessions, the major part will take place in the school-based environment supported by university tutors and school-based tutors.

The purpose of this module is to enable you to further develop your specialist skills as a teacher of your subject.  The focus will be on developing your creativity in planning, teaching and assessment.  You will be required to undertake an investigation into the teaching of your subject by applying theoretical ideas.  You will develop expertise in one aspect of subject-specific pedagogy as the basis of a classroom based investigation. Although a significant proportion of this module will be delivered through university-based sessions, your investigation will be undertaken during your school placement.

This module will help you to develop knowledge and understanding of major techniques in calculus which will either extend topics you have covered previously or will be completely new to you. For example, you will learn further methods to solve differential equations (such as Fourier Transforms, Laplace Transforms, Reduction of Order, Variation of Parameters, Power Series, the Frobenius method…etc). You will also extend your knowledge of functions of multiple variables and/or integral calculus by studying a selection of topics which might include: multiple integration, absolute extrema, Lagrange Multipliers, surface integrals or complex integrals.

This module extends the algebra you have learned in previous modules in the shape of the two applied areas of Coding Theory and Cryptography. Coding Theory is concerned with error detection and correction in transmitted data. It utilises tools from linear algebra and field theory to do this. Cryptography is concerned with securing digital communications. You may already be familiar with Diffie-Hellmann Key Exchange and the RSA algortihm from first year. Here we build on this material from an applied standpoint.

Multivariate statistics is a branch of statistics involving the observation and analysis of more than one outcome variable at the same time. There are various forms of multivariate analysis and in this module you will be learn about several. Cybermetrics aims to measure aspects of the World Wide Web to gain information about hyperlinks between pages. It encompasses many techniques including network visualisation and content analysis. In this module you will learn about these and more.