## Courses - Faculty of Science

# Mathematics

### Foundation Courses

Foundation Mathematics 1

This first mathematics course for students enrolled in the Tertiary Foundation Certificate programme aims to promote an understanding of number skills, including an introduction to algebra. Students will learn how to use simple technology and develop their problem solving abilities.

*Restriction: MATHS 91P*

Foundation Mathematics 2

This second mathematics course for students enrolled in the Tertiary Foundation Certificate programme aims to use the skills learnt in MATHS 91F to develop an understanding of functions in their tabular, algebraic and graphical representations. This course prepares students for MATHS 102. Recommended preparation: MATHS 91F or 93F.

Foundation Mathematics 3

This Extension Mathematics course for students enrolled in the Tertiary Foundation Certificate Programme aims to promote an understanding of numerical and algebraic skills at a deeper level than MATHS 91F. Students will learn how to use simple technology and develop their problem solving abilities.

*Restriction: MATHS 93P*

Foundation Mathematics 4

This second Extension Mathematics course for students enrolled in the Tertiary Foundation Certificate Programme aims to use the skills learnt in MATHS 93F to develop an understanding of functions, including differential functions, in their tabular, algebraic and graphical representations. This course prepares students for MATHS 102. Recommended preparation: MATHS 93F.

*Prerequisite: MATHS 93F*

### Preparatory Courses

Preparatory Mathematics 1

Aims to promote an understanding of number skills, including an introduction to algebra. Students will learn how to use simple technology and develop their problem solving abilities.

*Restriction: MATHS 91F*

### Stage I

Functioning in Mathematics

An introduction to calculus that builds mathematical skills and develops conceptual thinking. MATHS 102 works as a refresher course for those who haven’t studied Mathematics for some time, a confidence builder for those lacking Mathematical confidence and a preparation course for further study in Mathematics.

*Restriction: MATHS 102 may not be taken concurrently with any other Mathematics course, except MATHS 190 and may not be taken after ENGSCI 111 or any Mathematics course at Stage I or above, except MATHS 190/190G*

General Mathematics 1

A general entry to Mathematics for commerce and the social sciences, following Year 13 Mathematics. MATHS 108 covers selected topics in algebra and calculus and their applications, including: linear functions, linear equations and matrices; functions, equations and inequalities; limits and continuity; differential calculus of one and two variables; integral calculus of one variable. Recommended preparation: It is recommended that NCEA students have a rank score of at least 210 and a merit or excellence in the Differentiation Standard 91578. *Prerequisite: MATHS 102 or at least 13 credits in Mathematics at NCEA Level 3 including the Differentiation Standard 91578, or D in CIE A2 Mathematics or C in CIE AS Mathematics or 3 out of 7 in IB Mathematics*

*Restriction: MATHS 153, 208, 250, ENGGEN 150, ENGSCI 111. More than 15 points from MATHS 120 and 130. May not be taken with, or after, MATHS 110, 150*

Mathematics for Science

A general entry to Mathematics for the natural sciences, following Year 13 Mathematics. Covers selected topics in algebra and calculus and their application to chemistry, biology and other natural sciences. Recommended Preparation: It is recommended that NCEA students have a rank score of at least 210 and a merit or excellence in the Differentiation Standard 91578. *Prerequisite: MATHS 102 or 13 credits in Mathematics at NCEA Level 3, or D or better in Cambridge A2 Mathematics, C or better in AS Mathematics, pass in International Baccalaureate Mathematics, or equivalent*

*Restriction: MATHS 153, 208, 250, ENGGEN 150, ENGSCI 111. More than 15 points from MATHS 120 and 130. May not be taken with, or after, MATHS 108, 150*

Algebra

A foundation for further mathematics courses, essential for students intending to major in Mathematics, Applied Mathematics, Statistics, Physics, or who want a strong mathematical component to their degree. Develops skills and knowledge in linear algebra, together with an introduction to mathematical language and reasoning, including complex numbers, induction and combinatorics. Recommended preparation: Merit or excellence in the Differentiation Standard 91578 at NCEA Level 3. *Prerequisite: B- in MATHS 108 or 110, or A+ in MATHS 102 or at least 18 credits in Mathematics at NCEA Level 3 including at least 9 credits at merit or excellence, or B in CIE A2 Mathematics, or 5 out of 7 in IB Mathematics or equivalent*

*Restriction: ENGGEN 150, ENGSCI 111, MATHS 150, 153*

Calculus

A foundation for further mathematics courses, essential for students intending to major in Mathematics, Applied Mathematics, Statistics, Physics, or who want a strong mathematical component to their degree. Develops skills and knowledge in calculus of functions of a single variable. Recommended preparation: Merit or excellence in the Differentiation Standard 91578 at NCEA Level 3. *Prerequisite: B- in MATHS 108 or 110, or A+ in MATHS 102 or at least 18 credits in Mathematics at NCEA Level 3 including at least 9 credits at merit or excellence, or B in CIE A2 Mathematics, or 5 out of 7 in IB Mathematics or equivalent*

*Restriction: ENGGEN 150, ENGSCI 111, MATHS 150, 153*

Accelerated Mathematics

A course containing material from MATHS 120, 130 and ENGSCI 111 for high achieving students to be taken while they are enrolled in Year 13 at school. Enrolment requires permission from Department.

*Restriction: MATHS 108, 110, 120, 130, 150, ENGGEN 150, ENGSCI 111*

Computational Mathematics

An introduction to computational mathematics and programming in MATLAB. The course will introduce some basic concepts in computational mathematics and give applications that include cryptography, difference equations, stochastic modelling, graph theory and Markov chains.

*Corequisite: 15 points from MATHS 108, 110, 120, 150, 153, ENGSCI 111, ENGGEN 150*

Great Ideas Shaping our World

Mathematics contains many powerful and beautiful ideas that have shaped the way we understand our world. This course explores some of the grand successes of mathematical thinking. No formal mathematics background is required, just curiosity about topics such as infinity, paradoxes, cryptography, knots and fractals.

*Restriction: MATHS 190 may not be taken after any Mathematics course at Stage III*

### Stage II

Learning Mathematics through Teaching

The practice of teaching provides unique opportunities for developing mathematical and pedagogical knowledge. Through practical teaching sessions and discussions informed by research in Mathematics Education, students will make sense of common difficulties in mathematics learning and acquire effective ways for overcoming them.

*Prerequisite: At least 30 points from courses in Mathematics including either MATHS 208 or 250*

General Mathematics 2

This sequel to MATHS 108 features applications from the theory of multi-variable calculus, linear algebra and differential equations to real-life problems in statistics, economics, finance, computer science, and operations research. Matlab is used to develop analytical and numerical methods of solving problems.

*Prerequisite: 15 points from MATHS 108, 110, 150, 153, ENGGEN 150, ENGSCI 111, or MATHS 120 and 130* *
*

*
Restriction: MATHS 208 cannot be taken, concurrently with, or after MATHS 250, 253 or PHYSICS 211*

Advancing Mathematics 2

This preparation for advanced courses in mathematics is intended for all students who plan to progress further in mathematics. Covers topics from multivariable calculus and linear algebra that have many applications in science, engineering and commerce, including vector spaces, eigenvalues, power series, least squares and improper integrals. The emphasis is on both the results and the ideas underpinning these.

*Prerequisite: MATHS 120 and 130, or 15 points from ENGGEN 150, ENGSCI 111, MATHS 150, 153, or a B+ in MATHS 208*

Advancing Mathematics 3

The standard sequel to MATHS 250. It covers topics in linear algebra and multi-variable calculus including linear transformations, quadratic forms, double and triple integrals and constrained optimisation. It is a preparation for a large number of Stage III courses in mathematics and statistics, and for many advanced courses in physics and other applied sciences. All students intending to advance in mathematics should take this course.

*Prerequisite: MATHS 250 or an A+ in MATHS 208* *
*

*
Restriction: PHYSICS 211*

Principles of Mathematics

An introduction to mathematical thinking and communication: how to organise arguments logically and prove results. Rigorous notions are developed using topics that are central to the foundations of algebra and analysis including set theory, logic, abstract vector spaces and elementary number theory. An essential course for all students advancing in pure mathematics.

*Prequisite: MATHS 250, or an A+ in MATHS 208, or an A+ in MATHS 120, 130, 150, 153, ENGGEN 150, or ENGSCI 111 and a concurrent enrolment in ENGSCI 211 or MATHS 250*

Differential Equations

The study of differential equations is central to mathematical modelling of systems that change. Develops methods for understanding the behaviour of solutions to ordinary differential equations. Qualitative and elementary numerical methods for obtaining information about solutions are discussed, as well as some analytical techniques for finding exact solutions in certain cases. Some applications of differential equations to scientific modelling are discussed. A core course for Applied Mathematics.

*Prerequisite: MATHS 208 or 250 or ENGSCI 211 or a concurrent enrolment in MATHS 250*

Numerical Computation

Many mathematical models occurring in Science and Engineering cannot be solved exactly using algebra and calculus. Students are introduced to computer-based methods that can be used to find approximate solutions to these problems. The methods covered in the course are powerful yet simple to use. This is a core course for students who wish to advance in Applied Mathematics.

*Prerequisite: 30 points from MATHS 120 and 130, or 15 points from MATHS 108, 110, 150, 153, ENGGEN 150, ENGSCI 111, and 15 points from MATHS 162, COMPSCI 101, 105, 130, INFOSYS 110, 120 (recommended MATHS 162)*

### Stage III

Perspectives in Mathematics Education

For people interested in thinking about the social, cultural, political, economic, historical, technological and theoretical ideas that influence mathematics education, who want to understand the forces that shaped their own mathematics education, or who are interested in teaching. Students will develop their ability to communicate ideas in essay form. Recommended preparation: At least 45 points from courses in Mathematics or Statistics.

Special Topic in Mathematics Education 1

Both MATHS 307 and 308 deal with some special topic(s) of contemporary interest in mathematics education.

Special Topic in Mathematics Education 2

Both MATHS 307 and 308 deal with some special topic(s) of contemporary interest in mathematics education.

History of Mathematics

A study of some of the topics occurring in the history of mathematics which facilitate the understanding of modern mathematics. These include: concepts of number, geometry, algebra, and the differential and integral calculus.

*Corequisite: At least 30 points at Stage III in Mathematics*

Mathematical Logic

Logic addresses the foundations of mathematical reasoning. It models the process of mathematical proof by providing a setting and the rules of deduction. Builds a basic understanding of first order predicate logic, introduces model theory and demonstrates how models of a first order system relate to mathematical structures. The course is recommended for anyone studying high level computer science or mathematical logic.

*Prerequisite: COMPSCI 225 or MATHS 255 or PHIL 222*

Algebraic Structures

This is a framework for a unified treatment of many different mathematical structures. It concentrates on the fundamental notions of groups, rings and fields. The abstract descriptions are accompanied by numerous concrete examples. Applications abound: symmetries, geometry, coding theory, cryptography and many more. This course is recommended for those planning graduate study in pure mathematics.

*Prerequisite: MATHS 255 or 328, or an A– pass in MATHS 253*

Combinatorics

Combinatorics is a branch of mathematics that studies collections of objects that satisfy specified criteria. An important part of combinatorics is graph theory, which is now connected to other disciplines including bioinformatics, electrical engineering, molecular chemistry and social science. The use of combinatorics in solving counting and construction problems is covered using topics that include algorithmic graph theory, codes and incidence structures, and combinatorial complexity.

*Prerequisite: MATHS 255, or COMPSCI 225 and a B+ in MATHS 208, or COMPSCI 225 and any pass in MATHS 250*

Algebra and Applications

The goal of this course is to show the power of algebra and number theory in the real world. It concentrates on concrete objects like polynomial rings, finite fields, groups of points on elliptic curves, studies their elementary properties and shows their exceptional applicability to various problems in information technology including cryptography, secret sharing, and reliable transmission of information through an unreliable channel.

*Prerequisite: MATHS 255, or B+ pass in COMPSCI 225 and one of MATHS 208, 250, 253*

Real Analysis

A standard course for every student intending to advance in pure mathematics. It develops the foundational mathematics underlying calculus, it introduces a rigorous approach to continuous mathematics and fosters an understanding of the special thinking and arguments involved in this area. The main focus is analysis in one real variable with the topics including real fields, limits and continuity, Riemann integration and power series.

*Prerequisite: MATHS 255, or an A in both MATHS 253 and MATHS 260 or MATHS 250 and a concurrent enrolment in MATHS 255*

Analysis in Higher Dimensions

By selecting the important properties of distance many different mathematical contexts are studied simultaneously in the framework of metric and normed spaces. Examines carefully the ways in which the derivative generalises to higher dimensional situations. These concepts lead to precise studies of continuity, fixed points and the solution of differential equations. A recommended course for all students planning to advance in pure mathematics.

*Prerequisite: MATHS 332*

Algebraic Geometry

Algebraic geometry is a branch of mathematics studying zeros of polynomials. The fundamental objects in algebraic geometry are algebraic varieties i.e., solution sets of systems of polynomial equations.

*Prerequisite: MATHS 332, and at least one of MATHS 320, 328 and Departmental approval* *
*

*
Restriction: MATHS 734*

Real and Complex Calculus

Calculus plays a fundamental role in mathematics, answering deep theoretical problems and allowing us to solve very practical problems. Extends the ideas of calculus to two and higher dimensions, showing how to calculate integrals and derivatives in higher dimensions and exploring special relationships between integrals of different dimensions. It also extends calculus to complex variables.

*Prerequisite: MATHS 253*

Complex Analysis

Functions of one complex variable, including Cauchy’s integral formula, the index formula, Laurent series and the residue theorem. Many applications are given including a three line proof of the fundamental theorem of algebra. Complex analysis is used extensively in engineering, physics and mathematics. Strongly recommended: MATHS 333.

*Prerequisite: MATHS 332 and Departmental approval* *
*

*
Restriction: MATHS 740*

Geometry and Topology

A selection of topics providing an introduction to a range of concepts in geometry and general topology, with emphasis on visualisable aspects of these subjects. Topics include some or all of the following: axiom systems, affine geometry, Euclidean and non-Euclidean geometry, projective geometry, symmetry, convexity, the geometric topology of manifolds, and algebraic structures associated with topological spaces.

*Prerequisite: MATHS 255*

Partial Differential Equations

Partial differential equations (PDEs) are used to model many important applications of phenomena in the real world such as electric fields, diffusion and wave propagation. An introduction to linear PDEs and analytical methods for their solution. The course will also cover weak solutions.

*Prerequisite: MATHS 260 and 253, or PHYSICS 211*

Methods in Applied Mathematics

Covers a selection of techniques including the calculus of variations, asymptotic methods and models based on conservation laws. These methods are fundamental in the analysis of traffic flow, shocks, fluid flow, as well as in control theory, and the course is recommended for students intending to advance in Applied Mathematics. Recommended preparation: MATHS 361.

*Prerequisite: MATHS 260 and 253, or PHYSICS 211*

Advanced Modelling and Computation

In real-world situations, the interesting and important variables are often not directly observable. To address this problem, mathematical models and quantities that are observable are usually employed to carry out inference on the variables of interest. This course is an introduction to fitting of models to (noisy) observational data and how to compute estimates for the interesting variables. Numerical methods for partial differential equations, which are commonly used as models for the observations, will also be covered.

*Prerequisite: MATHS 260 and 270*

Special Topic in Mathematics 2

*To complete this course students must enrol in MATHS 382 A and B, or MATHS 382*

Special Topic in Mathematics 4

Each of these courses deals with some special topic(s) of contemporary interest in pure mathematics. Not all of them are offered every year; further information may be obtained from the Department of Mathematics.

Special Topic in Applied Mathematics 1

*To complete this course students must enrol in MATHS 386 A and B, or MATHS 386*

Special Topic in Applied Mathematics 2

Each of these courses deals with some special topic(s) of contemporary interest in pure mathematics. Not all of them are offered every year; further information may be obtained from the Department of Mathematics.

Special Topic in Applied Mathematics 3

Each of these courses deals with some special topic(s) of contemporary interest in pure mathematics. Not all of them are offered every year; further information may be obtained from the Department of Mathematics.

Special Topic in Applied Mathematics 4

Each of these courses deals with some special topic(s) of contemporary interest in applied and computational mathematics. Not all of them are offered every year; further information may be obtained from the Department of Mathematics.

Capstone: Mathematics

An exploration of the role of mathematics in society and culture, and the activities performed by mathematicians as teachers, critics, and innovators. Students will develop their skills in communication, critical thinking, teaching, and creative problem solving.

*Prerequisite: MATHS 250 and 30 points at Stage III in Mathematics*

### Postgraduate 700 Level Courses

Research Skills in Mathematics Education

Prepares students for postgraduate study in mathematics and statistics education. Its emphasis is on workshops in the key research skills required by students working at this level. It will cover a range of research issues and techniques.

*Prerequisite: MATHS 302 or significant teaching experience or department approval*

Mathematics Curriculum

A theoretical approach to mathematical curricula, broadly interpreted, with particular emphasis on cultural and linguistic perspectives, especially Māori. Additional issues will include a selection from history of mathematics curricula, influences on the development of a mathematics curriculum, and the aims and objectives of secondary and tertiary mathematics curricula.

Theoretical Issues in Mathematics Education

An analysis of theoretical perspectives that inform research in mathematics education, with a focus on learning theories, both social and psychological, and their implications for teaching and learning in mathematics.

*Prerequisite: MATHS 302 or significant teaching experience or department approval*

Socio-political Issues in Mathematics Education

Examines mathematics teaching and learning from a sociological perspective. Topics covered will include gender differences in mathematics, grouping students by ability vs. mixed ability teaching, and the performance of students from working class and ethnic minority backgrounds. Equity issues will be a central focus, and we will discuss the ways in which sociological ideas complement other approaches to research in mathematics education.

*Prerequisite: MATHS 302 or significant teaching experience or department approval*

Technology and Mathematics Education

Practical and theoretical perspectives on ways that technology, especially calculators and computers, can enhance teaching at senior secondary and university levels, with a particular focus on calculus. Identification of affordances, constraints and obstacles in the use of technology. Consideration of issues of teacher and lecturer development in implementation of technology.

*Prerequisite: MATHS 302 or significant teaching experience or department approval*

Special Topics in Mathematics Education 1

*Prerequisite: MATHS 302 or significant teaching experience or department approval*

Special Topics in Mathematics Education 2

*Prerequisite: MATHS 302 or significant teaching experience or department approval*

Special Topics in Mathematics Education 3

*Prerequisite: MATHS 302 or significant teaching experience or department approval*

Special Topics in Mathematics Education 4

*Prerequisite: MATHS 302 or significant teaching experience or department approval*

Special Topics in Mathematics Education 5

*Prerequisite: MATHS 302 or significant teaching experience or department approval* *
*

*
To complete this course students must enrol in MATHS 711 A and B, or MATHS 711*

Teaching and Learning in Algebra

Recent theoretical perspectives on the teaching and learning of school and university mathematics are linked to the learning of either calculus or algebra. The focus is on the mathematics content, applications, and effective learning at school and university. Students taking this course should normally have studied mathematics or statistics at 200 level.

*Prerequisite: MATHS 302 or significant teaching experience or department approval*

Logic and Set Theory

A study of the foundations of pure mathematics, formalising the notions of a 'mathematical proof' and 'mathematical structure' through predicate calculus and model theory. It includes a study of axiomatic set theory.

*Prerequisite: MATHS 315 or PHIL 305*

Number Theory

A broad introduction to various aspects of elementary, algebraic and computational number theory and its applications, including primality testing and cryptography.

*Prerequisite: B+ in MATHS 328 or 320*

Graph Theory and Combinatorics

A study of combinatorial graphs (networks), designs and codes illustrating their application and importance in other branches of mathematics and computer science.

*Prerequisite: B+ pass in MATHS 326 or 320*

Group Theory

A study of groups focusing on basic structural properties, presentations, automorphisms and actions on sets, illustrating their fundamental role in the study of symmetry (for example in crystal structures in chemistry and physics), topological spaces, and manifolds.

*Prerequisite: MATHS 320*

Representations and Structure of Algebras and Groups

Representation theory studies properties of abstract groups and algebras by representing their elements as linear transformations of vector spaces or matrices, thus reducing many problems about the structures to linear algebra, a well-understood theory.

*Prerequisite: MATHS 320*

Lie Groups and Lie Algebras

Symmetries and invariants play a fundamental role in mathematics. Especially important in their study are the Lie groups and the related structures called Lie algebras. These structures have played a pivotal role in many areas, from the theory of differential equations to the classification of elementary particles. Strongly recommended for students advancing in theoretical physics and pure mathematics. Recommended preparation: MATHS 333.

*Prerequisite: MATHS 320 and 332*

Measure Theory and Integration

Presenting the modern elegant theory of integration as developed by Riemann and Lebesgue, it includes powerful theorems for the interchange of integrals and limits so allowing very general functions to be integrated, and illustrates how the subject is both an essential tool for analysis and a critical foundation for the theory of probability. Strongly recommended: MATHS 333.

*Prerequisite: MATHS 332*

Functional Analysis

Provides the mathematical foundations behind some of the techniques used in applied mathematics and mathematical physics; it explores how many phenomena in physics can be described by the solution of a partial differential equation, for example the heat equation, the wave equation and Schrödinger's equation. Recommended preparation: MATHS 730 and 750.

*Prerequisite: MATHS 332 and 333*

Algebraic Geometry

Algebraic geometry is a branch of mathematics studying zeros of polynomials. The fundamental objects in algebraic geometry are algebraic varieties i.e., solution sets of systems of polynomial equations.

*Prerequisite: MATHS 332 and at least one of MATHS 320, 328* *
*

*
Restriction: MATHS 334*

Analysis on Manifolds and Differential Geometry

Studies surfaces and their generalisations, smooth manifolds, and the interaction between geometry, analysis and topology; it is a central tool in many areas of mathematics, physics and engineering. Topics include Stokes' theorem on manifolds and the celebrated Gauss Bonnet theorem. Strongly recommended: MATHS 333 and 340.

*Prerequisite: MATHS 332*

Complex Analysis

An introduction to functions of one complex variable, including Cauchy's integral formula, the index formula, Laurent series and the residue theorem. Many applications are given including a three line proof of the fundamental theorem of algebra. Complex analysis is used extensively in engineering, physics and mathematics. Strongly recommended: MATHS 333.

*Prerequisite: MATHS 332* *
*

*
Restriction: MATHS 341*

Topology

Aspects of point-set, set-theoretic and algebraic topology including: properties and construction of topological spaces, continuous functions, axioms of separation, countability, connectivity and compactness, metrization, covering spaces, the fundamental group and homology theory. Strongly recommended: MATHS 333.

*Prerequisite: MATHS 332*

Dynamical Systems

Mathematical models of systems that change are frequently written in the form of nonlinear differential equations, but it is usually not possible to write down explicit solutions to these equations. This course covers analytical and numerical techniques that are useful for determining the qualitative properties of solutions to nonlinear differential equations.

*Prerequisite: B- in both MATHS 340 and 361*

Nonlinear Partial Differential Equations

A study of exact and numerical methods for non-linear partial differential equations. The focus will be on the kinds of phenomena which only occur for non-linear partial differential equations, such as blow up, shock waves, solitons and special travelling wave solutions.

*Prerequisite: B- in both MATHS 340 and 361*

Advanced Partial Differential Equations

A study of exact and approximate methods of solution for the linear partial differential equations that frequently arise in applications.

*Prerequisite: B- in both MATHS 340 and 361*

Mathematical Biology

A course introducing central concepts in mathematical biology, with emphasis on modelling of physiological systems and gene dynamics.

*Prerequisite: B- in both MATHS 340 and 361*

Mathematical Modelling

Advanced topics in mathematical modelling, including selected topics in a range of application areas, principally taken from the physical and biological sciences.

*Prerequisite: At least B- or better in both MATHS 340 and 361*

Inverse Problems

Covers the mathematical and statistical theory and modelling of unstable problems that are commonly encountered in mathematics and applied sciences.

*Prerequisite: At least B- in both MATHS 340 and 363, or PHYSICS 701*

Stochastic Differential and Difference Equations

Differential and difference equations are often used as preliminary models for real world phenomena. The practically relevant models that can explain observations are, however, often the stochastic extensions of differential and difference equations. This course considers stochastic differential and difference equations and applications such as estimation and forecasting.

*Prerequisite: B- in both MATHS 340 and 361*

Advanced Numerical Analysis

Covers the use, implementation and analysis of efficient and reliable numerical algorithms for solving several classes of mathematical problems. The course assumes students have done an undergraduate course in numerical methods and can use Matlab or other high-level computational language.

*Prerequisite: B- in MATHS 270, 340 and 361*

Honours Dissertation in Mathematics or Applied Mathematics

*Restriction: MATHS 791* *
*

*
To complete this course students must enrol in MATHS 776 A and B, or MATHS 776*

Project in Mathematics 1

A supervised investigation or research project including seminar presentation in pure or applied mathematics.

*Restriction: MATHS 792*

Advanced Topic(s) in Mathematics 1

Each of these courses deals with some special topic(s) from pure mathematics. Not all of them are offered every year; further information may be obtained from the Department of Mathematics.

Advanced Topic(s) in Mathematics 2

Each of these courses deals with some special topic(s) from pure mathematics. Not all of them are offered every year; further information may be obtained from the Department of Mathematics.

Advanced Topic(s) in Mathematics 3

Each of these courses deals with some special topic(s) from pure mathematics. Not all of them are offered every year; further information may be obtained from the Department of Mathematics.

Advanced Topic(s) in Mathematics 4

Dissertation in Mathematics Education

*To complete this course students must enrol in MATHS 785 A and B*

Advanced Topic(s) in Applied Mathematics 1

Each of these courses deals with some special topic(s) from applied and computational mathematics. Not all of them are offered every year; further information may be obtained from the Department of Mathematics.

Advanced Topic(s) in Applied Mathematics 2

Each of these courses deals with some special topic(s) from applied and computational mathematics. Not all of them are offered every year; further information may be obtained from the Department of Mathematics.

Advanced Topic(s) in Applied Mathematics 3

Each of these courses deals with some special topic(s) from applied and computational mathematics. Not all of them are offered every year; further information may be obtained from the Department of Mathematics.

Advanced Topic(s) in Applied Mathematics 4

Research Portfolio in Mathematics Education

A portfolio of supervised research work in mathematics education drawing on personal experience in teaching mathematics.

*To complete this course students must enrol in MATHS 790 A and B*

Research in Mathematics Education

A portfolio of research work that will include a Research Case Study of a mathematics learner or teacher, a literature investigation and a research proposal for a larger study.

*Prerequisite: 30 points from Stage II courses in Mathematics or Statistics. MATHS 202 may not be taken as a prerequisite for this course.* *
*

*
To complete this course students must enrol in MATHS 792 A and B, or MATHS 792*

Project in Mathematics 2

Each of these courses involves participation in a research project or investigation in some topic from pure or applied mathematics, under the supervision of one or more staff members, and presentation, by the student, of the results in a seminar; further information may be obtained from the Department of Mathematics.

Project in Mathematics 3

Each of these courses involves participation in a research project or investigation in some topic from pure or applied mathematics, under the supervision of one or more staff members, and presentation, by the student, of the results in a seminar; further information may be obtained from the Department of Mathematics.

MSc Thesis in Applied Mathematics

*To complete this course students must enrol in MATHS 795 A and B*

Masters Thesis Mathematics

*To complete this course students must enrol in MATHS 796 A and B*

Advanced Research in Mathematics Education

A significant research project on some aspect of learning or teaching mathematics, including a substantive research report, including, or alongside other relevant documents such as Ethics applications, literature reviews, methodological surveys, papers for conference presentation or publication and presentation slides.

*To complete this course students must enrol in MATHS 797 A and B*