Mathematics (2021)

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 first major for the Bachelor of Computing and Mathematical Sciences with Honours (BCMS(Hons)) and the Bachelor of Science (BSc). Mathematics may also be included as a second major or minor in other undergraduate degrees, subject to approval of the Division 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 Division of Health, Engineering, Computing and Science 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.


On this page


  • 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 Division of Health, Engineering, Computing and Science Office.

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

    The paper MATHS520 is normally available only for 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 Head of School. 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 Points Occurrence / Location
    CSMAX170Foundations in Computing and Mathematical Sciences15.021A (Hamilton), 21A (Tauranga), 21A (Waikato Pathways College), 21B (Hamilton) & 21B (Waikato Pathways College)
    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...
    ENGEN101Engineering Maths and Modelling 1A15.021A (Hamilton), 21A (Tauranga) & 21B (Hamilton)
    A study of the fundamental techniques of algebra and calculus with engineering applications.
    ENGEN102Engineering Maths and Modelling 1B15.021B (Hamilton), 21B (Tauranga) & 21G (Hamilton)
    A further study of the fundamental techniques of algebra and calculus with engineering applications. Includes an introduction to relevant statistical methods.
    MATHS101Introduction to Calculus15.021A (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.
    MATHS102Introduction to Algebra15.021B (Hamilton)
    A study of the fundamental techniques and applications of algebra including Gaussian elimination, vector and matrix algebra, complex numbers, induction and recursion.
    MATHS135Discrete Structures15.021B (Hamilton), 21B (Tauranga) & 21C (Waikato Pathways College)
    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...
    MATHS165General Mathematics15.021A (Hamilton)
    An introduction to algebra, calculus and applications for students without NCEA Level 3 Mathematics. Students who meet the prerequisites of MATHS101 and/or MATHS102, should take these papers instead.
    MATHS166Management Mathematics15.021A (Hamilton) & 21X (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.
    MATHS168Preparatory Mathematics15.021A (Hamilton), 21B (Hamilton), 21B (Waikato Pathways College) & 21C (Waikato Pathways College)
    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.
    RPLCR103Recognition of Prior Learning - Introduction to Calculus15.021A (Hamilton) & 21H (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.
    RPLCR104Recognition of Prior Learning - Introduction to Algebra15.021A (Hamilton) & 21H (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 Points Occurrence / Location
    CSMAX270Cultural Perspectives for Computing and Mathematical Sciences15.021B (Hamilton) & 21B (Tauranga)
    The paper provides students with an understanding of scientific and culture-specific perspectives on issues in computing and mathematical sciences. Students will learn how these perspectives can be applied in diverse cultural, international, ethical, and professional contexts.
    ENGEN201Engineering Maths and Modelling 215.021A (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.
    MATHS201Continuing Calculus15.021A (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.
    MATHS202Linear Algebra15.021A (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.
    MATHS203Differential Equations and Modelling15.021B (Hamilton)
    Systems of ordinary differential equations and their applications, including phase plane methods. Introduction to partial differential equations. Fourier series.
    STATS221Statistical Data Analysis15.021A (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.
    STATS226Bayesian Statistics15.021B (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 Points Occurrence / Location
    COMPX361Logic and Computation15.021B (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...
    COMPX364Cryptography and Number Theory15.021A (Hamilton)
    An introduction to number theoretic ideas with emphasis on their applications in cryptography.
    ENGEN301Engineering Maths and Modelling 315.021A (Hamilton)
    Introduces numerical methods and statistical ideas relevant to Engineering.
    MATHS301Real and Complex Analysis15.021A (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.
    MATHS302Abstract Algebra15.021B (Hamilton)
    An introduction to abstract algebra via the theory of groups and rings.
    MATHS303Applied Mathematics15.021B (Hamilton)
    Develops the most widely used methods for solving ordinary and partial differential equations, especially those arising in physical applications.
    MATHS304Computational Mathematics15.021A (Hamilton)
    Introduces numerical methods for solving various mathematical problems.
    MATHS390Directed Study15.021A (Hamilton) & 21B (Hamilton)
    Students carry out an independent research project on an approved topic under staff supervision.
    MATHS397Work-Integrated Learning Directed Study15.021A (Hamilton), 21B (Hamilton) & 21X (Hamilton)
    Students carry out an independent work-related project on an approved topic under staff supervision.
  • 500 Level

    Code Paper Title Points Occurrence / Location
    COMPX502Cryptography15.021A (Hamilton)
    An introduction to cryptographic methods.
    COMPX544Applied Computational Methods15.021A (Hamilton)
    This paper explores numerical methods with applications to real world problems. A variety of classes of problems will be introduced, and appropriate numerical methods for each will be explored. Each problem will be solved by writing code from scratch. Aspects of parallel methods will also be introduced.
    MATHS501Metric Spaces15.021B (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.
    MATHS506Combinatorics15.021A (Hamilton)
    No description available.
    MATHS511Semigroups and Universal Algebra15.021B (Hamilton)
    No description available.
    MATHS512Continuous Groups15.021A (Hamilton)
    No description available.
    MATHS517Stochastic Differential Equations with Applications to Finance15.021B (Hamilton)
    A study of stochastic differential equations and their applications in the physical sciences and finance.
    MATHS520Dissertation45.021X (Hamilton)
    A directed investigation and report on an approved project or study topic.
    MATHS541Classical Partial Differential Equations15.021B (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
    MATHS565General Relativity15.021A (Hamilton)
    The theory of gravitational fields and cosmology using the methods of general relativity.
    MATHS581Special Topic in Mathematics 115.021A (Hamilton) & 21B (Hamilton)
    One or more special topics in mathematics, at an advanced level.
    MATHS582Special Topic in Mathematics 215.021A (Hamilton) & 21B (Hamilton)
    One or more special topics in mathematics, at an advanced level.
    MATHS591Dissertation30.021X (Hamilton)
    A report on the findings of a theoretical or empirical investigation.
    MATHS592Dissertation60.021X (Hamilton)
    A report on the findings of a theoretical or empirical investigation.
    MATHS593Mathematics Thesis90.021X (Hamilton)
    An externally examined piece of written work that reports on the findings of supervised research.
    MATHS594Mathematics Thesis120.021X (Hamilton)
    An externally examined piece of written work that reports on the findings of supervised research.
  • 800 Level

    Code Paper Title Points Occurrence / Location
    MATHS800Mathematics MPhil Thesis120.021X (Hamilton)
    No description available.
  • 900 Level

    Code Paper Title Points Occurrence / Location
    MATHS900Mathematics PhD Thesis120.021I (Hamilton) & 21X (Hamilton)
    No description available.

2021 Catalogue of Papers information current as of : 23 October 2020 11:20am

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