# Mathematics (2020)

Mathematics is a language of fundamental importance which underpins many activities of society. It plays a crucial role, both theoretically and practically, in many areas such as science, computing, economics and finance.

Mathematics is available as a major for the Bachelor of Computing and Mathematical Sciences with Honours and the Bachelor of Science. Mathematics may also be included as a second major or minor in other undergraduate degrees, subject to the approval of the Faculty in which the student is enrolled.

To complete Mathematics as a single major for the BCMS(Hons) or the BSc, students must gain 135 points from papers listed for Mathematics, including 105 points above 100 level, and 60 points above 200 level. Students must complete MATHS101, MATHS102, MATHS201, MATHS202, and at least one of MATHS301 and MATHS302. Students may include up to 30 points of STATS-coded papers as part of their Mathematics major. Students in the BCMS(Hons) will also need to take at least 60 points in the subject of Mathematics at 500 level, including MATHS520.

To complete Mathematics as part of a double major for the BCMS(Hons), BSc or other undergraduate degree, students must gain 120 points from papers listed for Mathematics, including 90 points above 100 level, and 45 points above 200 level. Students must complete MATHS101, MATHS102, MATHS201, MATHS202, and at least one of MATHS301 and MATHS302. Students may include up to 30 points of STATS-coded papers as part of their Mathematics major. Students in the BCMS(Hons) will also need to take at least 60 points in the subject of their first major at 500 level including MATHS520 if Mathematics is the first major.

To complete a minor in Mathematics, students must complete 60 points from the papers listed for the Mathematics major, including at least 30 points above 100 level.

**Note:** Students who commenced a major in Mathematics in 2017 or prior are encouraged to contact the Faculty of Computing and Mathematical Sciences for programme advice.

**Note on Assessment:** To be eligible to pass these papers students should normally achieve a minimum grade of D in the internal assessment and the final examination, and an overall grade of C. Because of the technical nature of the terminology and accepted international protocol, the Department of Mathematics requires that all assessment for all papers be presented in English. Payment for translation will not be available from the Department.

## On this page

- Prescriptions for the GradCert(Math) and GradDip(Math)
- Prescriptions for the PGCert(Math), PGDip(Math), BA(Hons), BSc(Hons), MA, MSc and MSc (Research)
- Prescriptions for the MPhil
- Prescriptions for the PhD
- 100 Level
- 200 Level
- 300 Level
- 500 Level
- 800 Level
- 900 Level

### Prescriptions for the GradCert(Math) and GradDip(Math)

A Graduate Certificate and Graduate Diploma are available to graduates who have not included Mathematics at an advanced level in their first degree.

For further details, contact the Faculty of Computing and Mathematical Sciences Office.

### Prescriptions for the PGCert(Math), PGDip(Math), BA(Hons), BSc(Hons), MA, MSc and MSc (Research)

The paper MATHS520 is normally available for only the BCMS(Hons) degree.

To complete a PGCert(Math), students must complete 60 points at 500 level consisting of 60 points from papers listed for Mathematics.

To complete a PGDip(Math), students must complete 120 points at 500 level including at least 90 points from papers listed for Mathematics.

To complete a BA(Hons) in Mathematics, students must complete 120 points at 500 level, including at least 60 points from the papers listed for Mathematics, of which at least 30 points must be in research (normally MATHS591).

Enrolment in papers towards the BSc(Hons) is only by invitation of the Chairperson. To complete a BSc(Hons) in Mathematics, students must complete 120 points at 500 level, including at least 60 points from the papers listed for Mathematics, of which at least 30 points must be in research (normally MATHS591).

To complete an MA in Mathematics, students admitted under section 2(b) of the MA regulations must take a 120 point thesis, or a 90 point thesis and 30 points from approved 500 level papers, or a 60 point dissertation and 60 points from approved 500 level papers.

To complete an MSc in Mathematics, students admitted under section 2(a) of the MSc regulations must complete 180 points at 500 level including MATHS592 and at least 60 points from papers listed for Mathematics.

To complete an MSc (Research) in Mathematics, students admitted under section 2(a) of the MSc (Research) regulations must complete 180 points at 500 level consisting of MATHS594 and 60 points from papers listed for Mathematics.

Candidates for graduate qualifications should select their papers in consultation with the Graduate Adviser in Mathematics of the Department of Mathematics and Statistics.

### Prescriptions for the MPhil

The Master of Philosophy is an 18 month research-based degree in which students undertake a programme of approved and supervised research that leads to a thesis which critically investigates an approved topic of substance and significance, demonstrates expertise in the methods of research and scholarship, displays intellectual independence and makes a substantial original contribution to the subject area concerned, and is of publishable quality.

### Prescriptions for the PhD

The Doctor of Philosophy is a three year research-based degree in which students undertake a programme of approved and supervised research that leads to a thesis which critically investigates an approved topic of substance and significance, demonstrates expertise in the methods of research and scholarship, displays intellectual independence and makes a substantial original contribution to the subject area concerned, and is of publishable quality.

### 100 Level

Code Paper Title Occurrence / Location CSMAX170 Foundations in Computing and Mathematical Sciences 20A (Hamilton), 20A (Tauranga) & 20B (Hamilton) The objective of this paper is to provide students with the academic foundations for computing and mathematical sciences. The paper will cover the following areas: -Effective academic reasoning and communication -Information literacy and research skills -Academic integrity -Techniques and tools in the computing and mathematical sci... ENGEN101 Engineering Mathematics 1A 20A (Hamilton), 20A (Tauranga) & 20B (Hamilton) A study of the fundamental techniques of algebra and calculus with engineering applications. ENGEN102 Engineering Mathematics 1B 20B (Hamilton), 20B (Tauranga) & 20C (Hamilton) A further study of the fundamental techniques of algebra and calculus with engineering applications. Includes an introduction to relevant statistical methods. ENGEN184 Calculus for Engineers 20S (Hamilton) A study of the fundamental techniques of calculus, including differentiation and integration for functions of one real variable, with engineering applications. MATHS101 Introduction to Calculus 20A (Hamilton) A study of the fundamental techniques of calculus, including differentiation and integration for functions of one real variable, with applications to rate problems, graph sketching, areas and volumes. MATHS102 Introduction to Algebra 20B (Hamilton) A study of the fundamental techniques and applications of algebra including Gaussian elimination, vector and matrix algebra, complex numbers, induction and recursion. MATHS135 Discrete Structures 20B (Hamilton) & 20B (Tauranga) An introduction to a number of the structures of discrete mathematics with wide applicability in areas such as: computer logic, analysis of algorithms, telecommunications, networks and public key cryptography. In addition it introduces a number of fundamental concepts which are useful in Statistics, Computer Science and further stu... MATHS165 General Mathematics 20A (Hamilton) An introduction to algebra, calculus and applications for students without NCEA Level 3 Mathematics. Students who meet the prerequisites of MATH101 and/or MATH102 should take these papers instead. MATHS166 Management Mathematics 20A (Hamilton) & 20X (Zhejiang University City College, Hangzhou China) An introduction to algebra and calculus for students in Management or Social Sciences. Students who meet the prerequisites of MATH101 and/or MATH102 may wish to take these paper(s) instead. MATHS168 Preparatory Mathematics 20A (Hamilton), 20B (Hamilton) & 20X (Hamilton) Basic algebraic concepts and an introduction to Calculus and Statistics. This paper provides a last chance for students to correct a weak background in mathematics. Students who meet the prerequisites of MATH165 or MATH166 should take one of those papers instead. RPLCR103 Recognition of Prior Learning - Introduction to Calculus 20A (Hamilton) & 20S (Hamilton) A study of the fundamental techniques of calculus, including differentiation and integration for functions of one real variable, with applications to rate problems, graph sketching, areas and volumes. RPLCR104 Recognition of Prior Learning - Introduction to Algebra 20A (Hamilton) & 20S (Hamilton) A study of the fundamental techniques and applications of algebra including Gaussian elimination, vector and matrix algebra, complex numbers, induction and recursion. ### 200 Level

Code Paper Title Occurrence / Location CSMAX270 Cultural Perspectives for Computing and Mathematical Sciences 20B (Hamilton) The paper provides students with an understanding of scientific and culture-specific perspectives on computing and mathematical science issues and the ability to apply these in diverse contexts. ENGEN201 Engineering Mathematics 2 20B (Hamilton) Calculus of Several Variables and its Applications. Vector calculus (Green's, Gauss' and Stokes' theorems). Taylor's Theorem in n dimensions. Introduction to ordinary differential equations and methods to solve them. MATHS201 Continuing Calculus 20B (Hamilton) Calculus of Several Variables and its Applications. Vector calculus (Green's, Gauss' and Stokes' theorems). Taylor's Theorem in n dimensions. The gamma and beta functions. MATHS202 Linear Algebra 20A (Hamilton) A formal approach to linear algebra, with applications. Topics include: axioms of a vector space, linear independence, spanning sets and bases. Linear transformations, the Gram-Schmidt process. MATHS203 Differential Equations and Modelling 20A (Hamilton) Systems of ordinary differential equations and their applications, including phase plane methods. Introduction to partial differential equations. Fourier series. STATS221 Statistical Data Analysis 20A (Hamilton) This paper introduces students to the R programming language which is used to investigate a collection of real data sets. Analysis of variance, multiple regression, non parametric methods and time series are covered. STATS226 Bayesian Statistics 20B (Hamilton) This paper introduces statistical methods from a Bayesian perspective, which gives a coherent approach to the problem of revising beliefs given relevant data. It is particularly relevant for data analytics, statistics, mathematics and computer science. ### 300 Level

Code Paper Title Occurrence / Location COMPX361 Logic and Computation 20B (Hamilton) The syllabus includes: further development of predicate logic with application to program verification; mathematical induction including structural induction; finite state automata and regular languages; Kleene's Theorem; Turing machines, the Church-Turing thesis, universal Turing machines and the Halting problem; formal grammars a... ENGEN301 Engineering Mathematics 3 20A (Hamilton) Introduces numerical methods and statistical ideas relevant to Engineering. MATHS301 Real and Complex Analysis 20A (Hamilton) Further real analysis, including a formal approach to continuity, differentiability and power series. An introduction to the calculus of complex functions and its applications. MATHS302 Abstract Algebra 20B (Hamilton) An introduction to abstract algebra via the theory of groups and rings. MATHS303 Applied Mathematics 20B (Hamilton) Develops the most widely used methods for solving ordinary and partial differential equations, especially those arising in physical applications. MATHS304 Computational Mathematics 20A (Hamilton) Introduces numerical methods for solving various mathematical problems. MATHS314 Number Theory and Cryptography 20A (Hamilton) An introduction to number theoretic ideas with emphasis on their applications in cryptography. MATHS390 Directed Study 20A (Hamilton) & 20B (Hamilton) Students carry out an independent research project on an approved topic under staff supervision. MATHS397 Work-Integrated Learning Directed Study 20A (Hamilton), 20B (Hamilton) & 20X (Hamilton) Students carry out an independent work-related project on an approved topic under staff supervision. ### 500 Level

Code Paper Title Occurrence / Location COMPX502 Cryptography 20A (Hamilton) An introduction to cryptographic methods. MATHS501 Metric Spaces 20A (Hamilton) Axioms of a metric space, open and closed sets, limit points etc. Completeness, continuity, connectedness and compactness in metric spaces. Fixed-point theorems. Generalisation to topological spaces. MATHS505 Advanced Topics in Pure Mathematics 20A (Hamilton) & 20B (Hamilton) A study at an advanced level of one or more topics in pure mathematics. MATHS513 Finite Groups 20A (Hamilton) & 20B (Hamilton) An in-depth study of the theory of finite groups. MATHS516 Topics in Discrete Mathematics 20B (Hamilton) An introduction to graph theory and combinatorics, including network optimisation algorithms. MATHS517 Stochastic Differential Equations with Applications to Finance 20B (Hamilton) A study of stochastic differential equations and their applications in the physical sciences and finance. MATHS520 Dissertation 20X (Hamilton) A directed investigation and report on an approved project or study topic. MATHS543 Nonlinear Dynamics and Chaos 20A (Hamilton) Systems of first order differential equations and their phase plane analysis, limit cycles and bifurcations. MATHS553 Fluid Dynamics 20B (Hamilton) Basic principles of fluid dynamics with applications. MATHS555 Advanced Classical Mechanics 20A (Hamilton) The theory of classical mechanics from a variational point of view. MATHS581 Special Topic in Mathematics 1 20A (Hamilton) & 20B (Hamilton) One or more special topics in mathematics, at an advanced level. MATHS582 Special Topic in Mathematics 2 20A (Hamilton) & 20B (Hamilton) One or more special topics in mathematics, at an advanced level. MATHS591 Dissertation 20X (Hamilton) A report on the findings of a theoretical or empirical investigation. MATHS592 Dissertation 20X (Hamilton) A report on the findings of a theoretical or empirical investigation. MATHS593 Mathematics Thesis 20X (Hamilton) An externally examined piece of written work that reports on the findings of supervised research. MATHS594 Mathematics Thesis 20X (Hamilton) An externally examined piece of written work that reports on the findings of supervised research. ### 800 Level

Code Paper Title Occurrence / Location MATHS800 Mathematics MPhil Thesis 20X (Hamilton) *No description available.*### 900 Level

Code Paper Title Occurrence / Location MATHS900 Mathematics PhD Thesis 20X (Hamilton) *No description available.*

** 2020 Catalogue of Papers information current as of : ** 16 October 2019 10:03am