# Mathematics (2018)

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
- 400 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 ENGEN183 Linear Algebra and Statistics for Engineers 18A (Hamilton) & 18B (Hamilton) A study of introductory statistics and the fundamental techniques of algebra including Gaussian elimination, vector and matrix algebra, complex numbers, eigenvalues and eigenvectors, as well as basic statistical notions and tools, with engineering applications. ENGEN184 Calculus for Engineers 18A (Hamilton), 18B (Hamilton) & 18S (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 18A (Hamilton) & 18B (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 18A (Hamilton) & 18B (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 18B (Hamilton) 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 18A (Hamilton) & 18B (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 18A (Hamilton), 18A (Tauranga), 18B (Hamilton), 18B (Tauranga) & 18C (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 18A (Hamilton) & 18B (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. RPLC103 Introduction to Calculus RPL 18A (Hamilton) & 18S (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. Applications will be developed for the physical, engineering, biological and management sciences. RPLC104 Introduction to Algebra RPL 18A (Hamilton) & 18S (Hamilton) A study of the fundamental techniques of algebra including linear algebra and matrix representations, vectors, algebraic manipulation including binomial expansions, and complex numbers. STATS111 Statistics for Science 18A (Tauranga), 18B (Hamilton) & 18B (Tauranga) This paper provides a first course in statistics for students in the Faculty of Science and Engineering. Microsoft Excel is used throughout. Topics include the collection and presentation of data, basic principles of experimental design, hypothesis testing, regression and the analysis of categorical data. STATS121 Introduction to Statistical Methods 18A (Hamilton) An introduction to statistical data collection and analysis. Topics include general principles for statistical problem solving; some practical examples of statistical inference; and the study of relationships between variables using regression analysis. ### 200 Level

Code Paper Title Occurrence / Location CSMAX270 Cultural Perspectives for Computing and Mathematical Sciences 18B (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 18B (Hamilton) Calculus of Several Variables and its Applications. Vector calculus (Green's, Gauss' and Stokes' theorems). Taylor's Theorem in n dimensions. Introduction to partial differential equations. Fourier series. MATHS201 Continuing Calculus 18B (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 18A (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 18B (Hamilton) Systems of ordinary differential equations and their applications, including phase plane methods. Introduction to partial differential equations. Fourier series. STATS221 Statistical Data Analysis 18A (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 18B (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 18B (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... FCMS396 Work Placement 18C (Block) This paper enables students to undertake work placement in an area related to their major as part of their degree. Students work in a chosen field for a period of time in order to gain valuable work experience and learn from experts in their chosen field. MATH310 Modern Algebra 18B (Hamilton) An introduction to groups, rings and fields, which have applications to symmetry, physics, coding and cryptography, as well as many areas of mathematics such as number theory and geometry. MATH311 Advanced Calculus 18A (Hamilton) A study of advanced real calculus of one and many variables, real and complex analysis, complex calculus and its applications. MATH320 Discrete Mathematics and Number Theory 18A (Hamilton) Further work in discrete mathematics and number theory. MATH329 Topics in Applied Mathematics 18A (Hamilton) An introduction to advanced topics in applied mathematics, including: potential theory and its applications, tensor analysis, and the calculus of variations. MATH331 Methods of Applied Mathematics 18B (Hamilton) A study of the theory and applications of differential equations, solution methods including separation of variables, eigen-function expansions, integral transforms and complex variable methods. MATH334 Classical and Quantum Mechanics 18Y (Hamilton) The theory of classical mechanics from a variational point of view. Topics include fundamentals of quantum mechanics and the quantisation of elementary systems. MATH380 Topic in Mathematics 18A (Hamilton) & 18B (Hamilton) A topic in mathematics taught as either a reading or short lecture course. ### 400 Level

Code Paper Title Occurrence / Location COMP402 Cryptography 18A (Hamilton) An introduction to cryptographic methods. ### 500 Level

Code Paper Title Occurrence / Location COMP502 Cryptography 18A (Hamilton) An introduction to cryptographic methods. MATH501 Metric Spaces 18A (Hamilton) *No description available.*MATH505 Advanced Topics in Pure Mathematics 18B (Hamilton) *No description available.*MATH513 Finite Groups 18A (Hamilton) An in-depth study of the theory of finite groups. MATH516 Topics in Discrete Mathematics 18B (Hamilton) An introduction to graph theory and combinatorics, including network optimisation algorithms. MATH517 Stochastic Differential Equations with Applications to Finance 18A (Hamilton) A study of stochastic differential equations and their applications in the physical sciences and finance. MATH520 Report of an Investigation 18C (Hamilton) A directed investigation and report on an approved project or study topic. MATH541 Classical Partial Differential Equations 18B (Hamilton) Topics chosen from: first-order equations; the method of characteristics; second-order equations: wave, diffusion, and potential; separation of variables; initial and boundary value problems; applications: heat and mass transfer, fluid dynamics, finance MATH555 Advanced Classical Mechanics 18A (Hamilton) The theory of classical mechanics from a variational point of view. MATH556 Quantum Mechanics 18B (Hamilton) The fundamentals of quantum mechanics and quantisation for elementary systems. MATH581 Special Topic in Mathematics 1 18A (Hamilton) & 18B (Hamilton) One or more special topics in mathematics, at an advanced level. MATH582 Special Topic in Mathematics 2 18A (Hamilton) & 18B (Hamilton) One or more special topics in mathematics, at an advanced level. MATH591 Dissertation 18C (Hamilton) A report on the findings of a theoretical or empirical investigation. MATH592 Dissertation 18C (Hamilton) A report on the findings of a theoretical or empirical investigation. MATH593 Mathematics Thesis 18C (Hamilton) An externally examined piece of written work that reports on the findings of supervised research. MATH594 Mathematics Thesis 18C (Hamilton) An externally examined piece of written work that reports on the findings of supervised research. SCIE501 Research Methods in the Sciences 18B (Hamilton) This paper will enable students to develop the necessary communication skills and familiarity with research methods and practice to allow them to progress to the thesis component of a masters degree in the sciences, or to extend communication and research skills in those not taking a full research degree. ### 800 Level

Code Paper Title Occurrence / Location MATH800 Mathematics MPhil Thesis 18C (Hamilton) *No description available.*### 900 Level

Code Paper Title Occurrence / Location MATH900 Mathematics PhD Thesis 18C (Hamilton) & 18D (Hamilton) *No description available.*

** 2018 Catalogue of Papers information current as of : ** 16 October 2019 10:03am