## 100-level

MATH101
Methods of Mathematics
Description
Introduction to calculus, trigonometry and algebra. Emphasis on setting up mathematical models of problems, solving them and interpreting the solutions. Applications to the physical, life and earth sciences as well as to commerce and the humanities.
Occurrences
Semester One 2023
Semester Two 2023
Whole Year 2023
Points
15 points
Restrictions

MATH102
Mathematics 1A
Description
An introductory course in calculus and linear algebra that is designed primarily for students who have done well in Level 3 NCEA Mathematics, covering single variable calculus and basic ideas in linear algebra. The mathematics in this course has applications in many areas of science and commerce.
Occurrences
Semester One 2023
Semester Two 2023
Points
15 points
Prerequisites
1. MATH101, or 2. NCEA 14 Credits at level 3 Mathematics, or 3. Cambridge: D at A level or an A at AS level in Mathematics, or 4. IB: 4 at HL or 5 at SL in Mathematics, or 5. Approval of the Head of School based on alternative prior learning.
Restrictions
MATH108, MATH199, EMTH118

MATH103
Mathematics 1B
Description
A consolidation of concepts from MATH102 and introduction to more advanced ideas in calculus and linear algebra. It is a prerequisite for many courses in mathematics and other subjects at 200-level.
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
Restrictions
MATH109, MATH199, EMTH119

MATH110
Foundations of Applied Mathematics
Description
Introduction to trigonometry and algebra. Emphasis on solving problems relevant to design, physical, life and earth sciences as well as to commerce and the humanities. An introduction to the ideas, techniques and applications of statistics and probability.
Occurrences
Semester One 2023
Points
15 points
Restrictions

MATH120
Discrete Mathematics
Description
Discrete mathematics is that part of mathematics not involving limit processes. It includes logic, the integers, finite structures, sets and networks.
Occurrences
Semester Two 2023
Summer Nov 2023
Points
15 points
Prerequisites
1. MATH101 or MATH102 or EMTH118, or 2. NCEA 14 Credits (18 strongly recommended) at level 3 Mathematics, or 3. Cambridge: D at A level or an A at AS level in Mathematics, or 4. IB: 4 at HL or 5 at SL in Mathematics, or 5. approval of the Head of School based on alternative prior learning.
Restrictions
MATH115

MATH199
AIMS - Advancing in Mathematical Sciences
Description
MATH199 is a course in calculus and linear algebra. This STAR course is designed for bright secondary school students who have excelled in level 3 NCEA Mathematics (or equivalent) and wish to take level 100 mathematics while still at school.
Occurrences
Whole Year 2023
Whole Year 2023 (Distance)
Points
30 points
Prerequisites
Subject to approval of the Head of School.
Restrictions

## 200-level

MATH201
Multivariable Calculus
Description
This course deals with techniques in multivariable calculus and vector calculus which have applications in many areas of science, commerce and engineering. It is also preparation for many courses in advanced mathematics.
Occurrences
Semester One 2023
Points
15 points
Prerequisites
Restrictions
MATH261, MATH264, EMTH202, EMTH204, EMTH210

MATH202
Differential Equations
Description
This course deals with analytical, numerical, and geometric techniques for differential equations, including applications.
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
One of MATH103, MATH199 or EMTH119; and one of COSC121, COSC131 or other relevant experience as approved by the HOS
Restrictions
MATH262, MATH264, EMTH202, EMTH204

MATH203
Linear Algebra
Description
Linear algebra is a key part of the mathematician's toolkit and has applications to many areas in science, commerce and engineering. This course develops the fundamental concepts of linear algebra, including vector spaces, linear transformations, eigenvalues, and orthogonality. Emphasis is placed on understanding both abstract mathematical structures and their concrete applications.
Occurrences
Semester One 2023
Points
15 points
Prerequisites
Restrictions
MATH252, MATH254, EMTH203, EMTH204, EMTH211, DATA203

MATH220
Discrete Mathematics and Cryptography
Description
Discrete mathematics underpins many areas of modern-day science. This course is an introduction to graph theory and cryptography, two central topics in discrete mathematics.
Occurrences
Semester One 2023
Points
15 points
Prerequisites
Restrictions
MATH221, MATH231

MATH230
Logic, Automata, and Computability
Description
An introduction to various formal logics, the theory of automata, and the theoretical limitations of the computer.
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
15 points from MATH102-199, and a further 15 points from 100 level COSC, EMTH, MATH, PHIL or STAT courses, excluding COSC110 and MATH101.
Restrictions
MATH208, MATH308, PHIL208 (prior to 2014), PHIL210, PHIL308 (prior to 2014).

MATH240
Analysis and Groups
Description
The course comprises two very different subjects, analysis and groups, both fundamental to mathematics and requiring mathematically rigorous thinking. It gives a deeper understanding of the real number system and limits, and an introduction to the methods of abstract algebra via the study of symmetries and permutations.
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
Restrictions
MATH222, MATH243

MATH270
Mathematical Modelling and Computation 2
Description
Use of the Python language for numerical methods, including solutions of systems of linear equations, solution of ordinary differential equations and systems of differential equations, boundary value problems, approximation techniques, area integration, statistics, random number generation, and Monte Carlo integration. Modelling projects and applications.
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
Both COSC121 and MATH103; or one of EMTH171, MATH170, or MATH171; or approval of the Dean of Engineering and Forestry. COSC121 can be replaced by COSC131, and MATH103 can be replaced by EMTH119 or MATH199.
Restrictions
EMTH271, MATH271

## 300-level

MATH302
Partial Differential Equations
Description
An introduction to the methods of solution for partial differential equations and to their applications.
Occurrences
Semester One 2023
Points
15 points
Prerequisites
Restrictions
MATH361, EMTH391, EMTH413

MATH303
Applied Matrix Algebra
Description
A continuation of 200-level linear algebra with computational and theoretical aspects and applications.
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
One of MATH203, EMTH211, or DATA203
Restrictions
MATH352, EMTH412

MATH320
Discrete Mathematics
Description
Discrete mathematics underpins many areas of modern-day science. In MATH320, we explore selected topics in discrete mathematics in greater depth and detail. In particular, we investigate some technical methods that allow for elegant solutions to more advanced enumeration questions, and explore the structural properties of directed graphs and partially-ordered sets (posets). Topics covered: Term 1: Combinatorial enumeration: Binomial identities and direct enumeration. Principle of Inclusion and Exclusion; Generating functions (ordinary and exponential). Lagrange inversion and applications. Term 2: Directed graphs and posets: Basic Ramsey theory, theory of directed graphs (structural results, algorithms, algebraic methods, phase transitions) and partially-ordered sets (Möbius inversion, Dilworth Theorem).
Occurrences
Semester One 2023
Points
15 points
Prerequisites

MATH321
Rings and Fields
Description
An introduction to fields and rings, including applications to coding theory and the impossibility of constructions such as ‘squaring the circle’.
Occurrences
Semester One 2023
Points
15 points
Prerequisites
One of MATH203, MATH220, MATH240, or EMTH211, and a further 15 points from MATH201-294.
Restrictions
MATH439, MATH311

MATH324
Cryptography and Coding Theory
Description
This course deals with the mathematical ideas underlying modern cryptography, including algebra, number theory and probability theory.
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
ONE of MATH203, DATA203 or EMTH211, and ONE of MATH120, MATH220, MATH240
Restrictions

MATH343
Metric, Normed and Hilbert Spaces
Description
An introduction to those parts of modern analysis essential for many aspects of pure and applied mathematics, physics, economics and finance.
Occurrences
Semester One 2023
Points
15 points
Prerequisites

MATH353
Computational Mathematics and Applications
Description
This course looks at a variety of methods for solving important computational problems that arise in science, engineering and commerce. In addition to applications, we will look at the methods' basic theoretical properties (stability, accuracy, computational complexity, convergence). During the course, you will learn about the performance of the methods through examples and counterexamples that highlight their pros and cons.
Occurrences
Semester One 2023
Points
15 points
Prerequisites
1) Either MATH201 or EMTH210; AND 2) One of MATH202, MATH203, MATH240, MATH270, EMTH211 or EMTH271. With the permission of the Head of School a high grade in either MATH201 or EMTH210 will suffice.
Restrictions

MATH363
Dynamical Systems
Description
An introduction to nonlinear systems, the use of linearisation techniques and bifurcation theory.
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
MATH201 or EMTH210 and a further 15 points from (EMTH211, EMTH271, MATH202, MATH203, MATH240, MATH270).
Restrictions

MATH365
Applications of Complex Variables
Description
Applications of complex variable theory in the physical and engineering sciences. Contour integration. Conformal mappings.
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
MATH201 or MATH240; or, a high level of achievement in EMTH210 with Head of School approval
Restrictions
MATH342

MATH380
Mathematics in Perspective
Description
Topics in the history, philosophy, directions and culture of mathematics including significant results from the past and an outline of some major areas of progress in the 20th century.
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
30 points in Mathematics or Statistics or Engineering Mathematics at 100 level. 45 points from the BA or BSc Schedule at 200 level in Mathematics, Statistics, Engineering Mathematics, related subjects, or other subjects with good grades, as approved by the Head of School.
Restrictions
MATH301, MATH433, HAPS405

MATH391
Special Topic
Description
This special topic will allow flexibility to offer new or one-off courses of strategic importance to the Department. Its potential uses include: new staff developing a course in their areas of research specialisation; visiting Erskine fellows offering courses covering exciting new developments.
Occurrences
Semester One 2023
Points
15 points
Prerequisites
Subject to the approval of the Head of School.

MATH392
Special Topic
Description
This special topic will allow flexibility to offer new or one-off courses of strategic importance to the Department. Its potential uses include: new staff developing a course in their areas of research specialisation; visiting Erskine fellows offering courses covering exciting new developments.
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
Subject to the approval of the Head of School.

MATH393
Independent Course of Study
Occurrences
Semester One 2023
Points
15 points
Prerequisites
Subject to approval of the Head of School.

MATH394
Independent Course of Study
Occurrences
Semester Two 2023
Points
15 points
Prerequisites
Subject to the approval of the Head of School.

MATH395
Mathematics Project
Description
This 150 hour course provides students with an opportunity to develop mathematical research skills to extend and strengthen their understanding of an area of mathematics. Note: This course cannot be included as part of the 300 level requirement for a Mathematics or Statistics major.
Occurrences
Summer Nov 2023
Points
15 points
Prerequisites
Subject to approval of the Head of School
Restrictions
MATH305

## 100-level

MATH101
Methods of Mathematics
Description
Introduction to calculus, trigonometry and algebra. Emphasis on setting up mathematical models of problems, solving them and interpreting the solutions. Applications to the physical, life and earth sciences as well as to commerce and the humanities.
Occurrences
MATH101-23S1 (D)
Semester One 2023 (Distance) - Not offered - see department for alternatives
For further information see MATH101 course details
MATH101-23S2 (D)
Semester Two 2023 (Distance) - Not offered - see department for alternatives
For further information see MATH101 course details
Points
15 points
Restrictions

MATH102
Mathematics 1A
Description
An introductory course in calculus and linear algebra that is designed primarily for students who have done well in Level 3 NCEA Mathematics, covering single variable calculus and basic ideas in linear algebra. The mathematics in this course has applications in many areas of science and commerce.
Occurrences
MATH102-23S1 (D)
Semester One 2023 (Distance) - Not offered
For further information see MATH102 course details
MATH102-23S2 (D)
Semester Two 2023 (Distance) - Not offered
For further information see MATH102 course details
Points
15 points
Prerequisites
1. MATH101, or 2. NCEA 14 Credits at level 3 Mathematics, or 3. Cambridge: D at A level or an A at AS level in Mathematics, or 4. IB: 4 at HL or 5 at SL in Mathematics, or 5. Approval of the Head of School based on alternative prior learning.
Restrictions
MATH108, MATH199, EMTH118

MATH103
Mathematics 1B
Description
A consolidation of concepts from MATH102 and introduction to more advanced ideas in calculus and linear algebra. It is a prerequisite for many courses in mathematics and other subjects at 200-level.
Occurrences
MATH103-23S2 (D)
Semester Two 2023 (Distance) - Not offered - see department for alternatives
For further information see MATH103 course details
Points
15 points
Prerequisites
Restrictions
MATH109, MATH199, EMTH119

MATH120
Discrete Mathematics
Description
Discrete mathematics is that part of mathematics not involving limit processes. It includes logic, the integers, finite structures, sets and networks.
Occurrences
MATH120-23S2 (D)
Semester Two 2023 (Distance) - Not offered - see department for alternatives
For further information see MATH120 course details
Points
15 points
Prerequisites
1. MATH101 or MATH102 or EMTH118, or 2. NCEA 14 Credits (18 strongly recommended) at level 3 Mathematics, or 3. Cambridge: D at A level or an A at AS level in Mathematics, or 4. IB: 4 at HL or 5 at SL in Mathematics, or 5. approval of the Head of School based on alternative prior learning.
Restrictions
MATH115

MATH130
Introduction to Logic and Computability
Description
An introduction to logic and computability.
Occurrences
Not offered 2023, offered in 2011 , 2012 , 2013 , 2014 , 2015
For further information see MATH130 course details
Points
15 points

MATH170
Mathematical Modelling and Computation
Description
An introduction to mathematical modelling and simulation via case studies using standard computer packages. Structured programming for mathematical problem solving.
Occurrences
Not offered 2023, offered in 2012 , 2013 , 2014 , 2015 , 2016
For further information see MATH170 course details
Points
15 points

## 200-level

MATH201
Multivariable Calculus
Description
This course deals with techniques in multivariable calculus and vector calculus which have applications in many areas of science, commerce and engineering. It is also preparation for many courses in advanced mathematics.
Occurrences
MATH201-23S1 (D)
Semester One 2023 (Distance) - Not offered - see department for alternatives
For further information see MATH201 course details
Points
15 points
Prerequisites
Restrictions
MATH261, MATH264, EMTH202, EMTH204, EMTH210

MATH202
Differential Equations
Description
This course deals with analytical, numerical, and geometric techniques for differential equations, including applications.
Occurrences
MATH202-23S2 (D)
Semester Two 2023 (Distance) - Not offered - see department for alternatives
For further information see MATH202 course details
Points
15 points
Prerequisites
One of MATH103, MATH199 or EMTH119; and one of COSC121, COSC131 or other relevant experience as approved by the HOS
Restrictions
MATH262, MATH264, EMTH202, EMTH204

MATH203
Linear Algebra
Description
Linear algebra is a key part of the mathematician's toolkit and has applications to many areas in science, commerce and engineering. This course develops the fundamental concepts of linear algebra, including vector spaces, linear transformations, eigenvalues, and orthogonality. Emphasis is placed on understanding both abstract mathematical structures and their concrete applications.
Occurrences
MATH203-23S1 (D)
Semester One 2023 (Distance) - Not offered - see department for alternatives
For further information see MATH203 course details
Points
15 points
Prerequisites
Restrictions
MATH252, MATH254, EMTH203, EMTH204, EMTH211, DATA203

PHIL210
Logic, Automata, and Computability
Description
An introduction to various formal logics, the theory of automata, and the theoretical limitations of the computer.
Occurrences
Not offered 2023
For further information see PHIL210 course details
Points
15 points

MATH280
Introduction to Scientific Computation
Description
Introduction to the mathematical software package, MATLAB, that integrates technical computation, graphics, visualisation, and programming
Occurrences
Not offered 2023
For further information see MATH280 course details
Points
15 points

## 300-level

MATH335
Computability Theory
Description
Mathematical models of computation. Computability and non-computability. Abstract complexity theory.
Occurrences
Not offered 2023
For further information see MATH335 course details
Points
15 points

MATH336
Foundations of Mathematics
Description
An introduction to the philosophy of mathematics, classical and intuitionistic logic, set theory, and Gödel's theorems.
Occurrences
Not offered 2023, offered in 2012 , 2013 , 2014 , 2015 , 2016
For further information see MATH336 course details
Points
15 points