# Mathematics

Mathematics is a subject of vital importance that underpins many activities of our modern world. Employers recognise University of Waikato Mathematics graduates for their analytical and problem solving skills as well as their high level of numeracy, which are critical skills for a broad range of jobs.

If you are a graduate with a Mathematics degree, or even with a strong Mathematical component to your degree, you will be a valuable person in today's workforce, with a qualification that appeals to a wide range of employers including banks, insurance companies, schools and government departments.

There is strong employer demand for Mathematicians, due to a shortage of Mathematics graduates and in particular a critical shortage of Mathematics teachers.

Studying Mathematics in combination with another subject means you can work in a number of different fields, such as Chemistry, Biological Sciences, Earth Sciences, Economics, Finance, Engineering (Chemical and Biological Engineering, Civil Engineering, Electrical Engineering, Environmental Engineering, Materials and Process Engineering, Mechanical Engineering, Software Engineering), Physics, Electronics, Banking and Meteorology.

Capable students should consider the flexible double major options in Mathematics and Computer Science, or Mathematics and Data Analytics.

### Facilities at Waikato

The computing facilities at the University of Waikato are among the best in New Zealand, and you will have 24 hour access to computer labs equipped with all the latest computer software.

### Key information

Study Locations: | Hamilton, TaurangaPapers offered differ by location. The Catalogue of Papers has full location info. |
---|---|

Faculty: |

### Study Mathematics in these qualifications

- Bachelor of Arts
- Bachelor of Communication Studies
- Bachelor of Computing and Mathematical Sciences with Honours
- Bachelor of Health, Sport and Human Performance
- Bachelor of Laws
- Bachelor of Management Studies with Honours
- Bachelor of Media and Creative Technologies (China only)
- Bachelor of Music
- Bachelor of Science
- Bachelor of Science (Technology)
- Bachelor of Social Sciences
- Certificate
- Diploma
- Doctor of Philosophy
- Graduate Certificate
- Graduate Diploma
- Master of Arts
- Master of Arts (Applied)
- Master of Laws
- Master of Management Studies
- Master of Māori and Pacific Development
- Master of Philosophy
- Master of Science
- Master of Science (Research)
- Master of Science (Technology)
- Master of Social Sciences
- Postgraduate Certificate
- Postgraduate Diploma

### Study Mathematics as a specialisation of

- Bachelor of Arts
- Bachelor of Communication Studies
- Bachelor of Computing and Mathematical Sciences with Honours
- Bachelor of Health, Sport and Human Performance
- Bachelor of Laws
- Bachelor of Management Studies with Honours
- Bachelor of Media and Creative Technologies (China only)
- Bachelor of Music
- Bachelor of Science
- Bachelor of Science (Technology)
- Bachelor of Social Sciences
- Certificate
- Diploma
- Doctor of Philosophy
- Graduate Certificate
- Graduate Diploma
- Master of Arts
- Master of Arts (Applied)
- Master of Laws
- Master of Management Studies
- Master of Māori and Pacific Development
- Master of Philosophy
- Master of Science
- Master of Science (Research)
- Master of Science (Technology)
- Master of Social Sciences
- Postgraduate Certificate
- Postgraduate Diploma

### Career opportunities

- Data Analyst
- Financial Analyst
- IT or Computing Analyst
- Mathematical Modeller
- Meteorologist
- Research Scientist
- Secondary School Teacher

### Papers

Available Mathematics papers

### 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 | 19A (Hamilton) & 19B (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... | ||

ENGEN183 | Linear Algebra and Statistics for Engineers | 19A (Hamilton), 19A (Tauranga), 19B (Hamilton) & 19B (Tauranga) |

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 | 19A (Hamilton), 19A (Tauranga), 19B (Hamilton), 19B (Tauranga), 19S (Hamilton) & 19S (Tauranga) |

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 | 19A (Hamilton) & 19B (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 | 19A (Hamilton) & 19B (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 | 19A (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 | 19A (Hamilton) & 19B (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 | 19A (Hamilton), 19B (Hamilton) & 19C (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 | 19A (Hamilton), 19B (Hamilton) & 19C (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 | 19A (Hamilton) & 19S (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 | 19A (Hamilton) & 19S (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 | 19B (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 | 19B (Hamilton) & 19S (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 | 19B (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 | 19A (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 | 19B (Hamilton) |

Systems of ordinary differential equations and their applications, including phase plane methods. Introduction to partial differential equations. Fourier series. | ||

STATS221 | Statistical Data Analysis | 19A (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 | 19B (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 | 19B (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 | 19C (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. | ||

MATHS301 | Real and Complex Analysis | 19A (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 | 19A (Hamilton) |

An introduction to abstract algebra via the theory of groups and rings. | ||

MATHS303 | Applied Mathematics | 19B (Hamilton) |

Develops the most widely used methods for solving ordinary and partial differential equations, especially those arising in physical applications. | ||

MATHS304 | Computational Mathematics | 19A (Hamilton) |

Introduces numerical methods for solving various mathematical problems. | ||

MATHS314 | Number Theory and Cryptography | 19B (Hamilton) |

An introduction to number theoretic ideas with emphasis on their applications in cryptography. | ||

MATHS390 | Directed Study | 19A (Hamilton) & 19B (Hamilton) |

Students carry out an independent research project on an approved topic under staff supervision. | ||

MATHS391 | Undergraduate Research Project | 19A (Hamilton), 19B (Hamilton), 19C (Hamilton) & 19S (Hamilton) |

Students carry out an independent research project on an approved topic under staff supervision. | ||

MATHS397 | Work-Integrated Learning Directed Study | 19A (Hamilton) & 19B (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 | 19B (Hamilton) |

An introduction to cryptographic methods. | ||

MATHS501 | Metric Spaces | 19A (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. | ||

MATHS506 | Combinatorics | 19A (Hamilton) |

No description available. | ||

MATHS511 | Semigroups and Universal Algebra | 19B (Hamilton) |

No description available. | ||

MATHS512 | Continuous Groups | 19B (Hamilton) |

No description available. | ||

MATHS517 | Stochastic Differential Equations with Applications to Finance | 19B (Hamilton) |

A study of stochastic differential equations and their applications in the physical sciences and finance. | ||

MATHS520 | Dissertation | 19C (Hamilton) |

A directed investigation and report on an approved project or study topic. | ||

MATHS541 | Classical Partial Differential Equations | 19A (Hamilton) & 19B (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 | ||

MATHS564 | Special Relativity | 19A (Hamilton) |

An introduction to the methods and theory of special relativity. | ||

MATHS565 | General Relativity | 19A (Hamilton) & 19B (Hamilton) |

The theory of gravitational fields and cosmology using the methods of general relativity. | ||

MATHS581 | Special Topic in Mathematics 1 | 19A (Hamilton) & 19B (Hamilton) |

One or more special topics in mathematics, at an advanced level. | ||

MATHS582 | Special Topic in Mathematics 2 | 19A (Hamilton) & 19B (Hamilton) |

One or more special topics in mathematics, at an advanced level. | ||

MATHS591 | Dissertation | 19C (Hamilton) |

A report on the findings of a theoretical or empirical investigation. | ||

MATHS592 | Dissertation | 19C (Hamilton) |

A report on the findings of a theoretical or empirical investigation. | ||

MATHS593 | Mathematics Thesis | 19C (Hamilton) |

An externally examined piece of written work that reports on the findings of supervised research. | ||

MATHS594 | Mathematics Thesis | 19C (Hamilton) |

An externally examined piece of written work that reports on the findings of supervised research. |

### 800 Level

Code | Paper Title | Occurrence / Location |
---|---|---|

MATH800 | Mathematics MPhil Thesis | 19C (Hamilton) |

No description available. |

### 900 Level

Code | Paper Title | Occurrence / Location |
---|---|---|

MATH900 | Mathematics PhD Thesis | 19C (Hamilton) & 19D (Hamilton) |

No description available. |

### Scholarships and Prizes

Selected scholarships for Mathematics students.

New to Waikato? The International Excellence Scholarship is worth up to $10,000.

#### CMS International Exchange Scholarship Closed

For students who have completed at least one year of study in the Faculty of Computing & Mathematical Sciences, applied for a University of Waikato exchange programme, and who will be enrolled full-time in FCMS in the year of tenure.

#### The A Zulauf Trust Scholarship Closed

For students who are enrolled or intending to enrol full-time in the research portion (i.e. a 90- or 120-point thesis) of their Masters degree in Mathematics in the year of application. It is expected that the bulk of the research will take place in the year of application. The Scholarship has a value of up to $5,000.

#### Looking for more scholarships?

### Contacts

**Faculty of Computing & Mathematical Sciences**

**Phone: **0800 924 528 ext: 4322 or +64 7 838 4322**Email:** cms@wu.ac.nz**Website:** cms.wu.ac.nz**Facebook:** facebook.com/WaikatoFCMS