## Papers

Download the flowchart for 2020

### Which 100-level Math paper?

Struggling to decide which 100-level Mathematics paper to take first? Our placement tools can help you.

The Department offers 17 Mathematics undergraduate papers at 100, 200 and 300-level (as well as a selection of 400-level postgraduate papers). This section includes short descriptions of these papers, together with links to individual illustrated paper pages which feature information about the subject, the paper and assessment procedures.

See the flowchart of available papers for 2020, their prerequisites and semesters.

Click the paper name below for complete details.

Jump to 200 level, 300 level, 400 level

## 100 level

COMO101 Modelling and Computation 18 points Second SemesterAn introduction to mathematical and computational modelling with applications in science, engineering, biomedicine and industry. Topics include the translation of observations into mathematical models, and the use of simulation and numerical methods to evaluate and apply the models.

MATH151 General Mathematics 18 points First Semester, Summer School

Topics such as basic mathematical models, operations research, introductory calculus, compound interest, exponential growth and decay, simple differentiation and integration, as well as exponential, logarithmic and trigonometric functions.

* This paper is recommended for students with NCEA Level 2 mathematics or equivalent. It provides excellent preparation for students wishing to take MATH 160.

* MATH 151 cannot be credited together with MATH 101-104, 160 or 170 passed previously or concurrently.

MATH160 Mathematics 1 18 points First Semester, Second Semester, Summer School

This paper is divided between algebra and calculus. The algebra component introduces vectors and geometric constructions fundamental to applications in mechanics and computer graphics. Matrices, polynomials, and complex numbers are introduced. The calculus component covers ideas and methods of differential and integral calculus together with key applications and extensions.

* This paper is recommended for students with MATH 151, NCEA Level 3 mathematics, or equivalent.

* MATH 160 cannot be credited together with MATH 103, MATH 104, or MATH 170 passed previously or concurrently.

MATH170 Mathematics 2 18 points First Semester, Second Semester

This paper is divided between algebra and calculus components (which can be taken as separate 9 point papers). The algebra component covers linear transformations and eigenvalues and introduces aspects of discrete mathematics. The calculus component covers sequence and series, inverse trigonometric and hyperbolic functions, advanced integration techniques, differential equations and their applications.

Note: This paper assumes material covered in MATH 160 and provides essential preparation for 200-level mathematics. Students with excellent results in Year 13 mathematics are able to enrol in MATH 170 without first taking MATH 160.

## 200 level

COMO204 Differential Equations 18 points Second SemesterThis course is an introduction to mathematical techniques useful for solving problems arising in the physical, health and life sciences, and commerce. Topics include analytical solutions of ordinary differential equations, Laplace transforms, systems of linear ordinary differential equations, and nonlinear dynamical systems.

MATH201 Real Analysis 18 points First Semester

MATH 201 is an introduction to the basic techniques of real analysis in the familiar context of single-variable calculus. This paper is compulsory for the Mathematics major.

MATH202 Linear Algebra 18 points Second Semester

MATH 202 is an introduction to the fundamental ideas and techniques of linear algebra, and the application of these ideas to computer science, the sciences and engineering. This paper is compulsory for the Mathematics major.

MATH203 Calculus of Several Variables 18 points First Semester

This paper is an introduction to the mathematics of curves, surfaces and volumes in three-dimensional space, and extends the notions of differentiation and integration to higher dimensions. It is a prerequisite for three level-300 MATH papers.

MATH272 Discrete Mathematics 18 points Second Semester

Graph theory and algorithms; combinatorial counting techniques; sets, relations, generating functions, cardinality. There is an emphasis on both proof techniques and practical algorithms.

MATS204 Treasure or Trash: Sustainability of Materials 18 points Summer School

Introduction

This paper develops understanding of the principles and complexities of sustainability of materials and their application in design, selection, processing, manufacture, use and disposal of products.

## 300 level

COMO303 Numerical Methods 18 points First SemesterThis paper develops the theory and techniques required to apply computational methods in modelling, applied mathematics and data analysis. Topics include matrix computation, data fitting, and the numerical solution of differential equations.

MATH301 Hilbert Spaces 18 points First Semester

This paper is an introduction to Hilbert spaces and linear operators on Hilbert spaces. It extends the techniques of linear algebra and real analysis to study problems of an intrinsically infinite-dimensional nature.

MATH302 Complex Analysis 18 points Second Semester

This paper develops the differential and integral calculus of functions of a complex variable, and its applications.

MATH304 Partial Differential Equations 18 points Second Semester

This paper gives an introduction to the theory of partial differential equations by discussing the main examples (Laplace's equation, Poisson's equation, transport equation, wave equation) and their applications.

MATH306 Geometry of Curves and Surfaces 18 points Second Semester

This paper is an introduction to differential geometry; its focus is the structure of two-dimensional surfaces.

MATH342 Modern Algebra 18 points First Semester

This paper introduces groups and rings. These are algebraic structures consisting of a set with one or more binary operations on that set satisfying certain conditions. These structures are ubiquitous throughout modern mathematics and this paper examines their properties and some applications.

MATH374 Mathematical Physics 18 points Second Semester

This paper presents the foundation theory for two major topics in Physics. The Classical Mechanics section introduces the formal framework of Classical Mechanics and illustrates its application to two-body problems, rotating systems, collisions, and chaos. The Special Relativity and Cosmology section covers the special theory of relativity with applications to relativistic mechanics, electrodynamics in covariant form, and cosmology.

This paper is the same as the PHSI336 paper offered by the Physics Department. It is taught jointly by staff from both Departments.