*6 points *

*Semester 1*

This unit is essential for students intending to major in Mathematical Statistics, Mathematical Sciences, or Pure or Applied Mathematics, some students in the physical sciences and all students in the combined Science/Engineering course. It is also suitable for other students wanting a strong mathematics component in their courses.

Topics include methods of proof, logic and mathematical induction; the intermediate value theorem and the mean value theorem, curve sketching, maxima and minima; integration, integrals over infinite intervals, techniques of integration; inverse functions, indeterminate forms; first-order differential equations; probability, independence, Bayes' theorem; the binomial, Poisson and normal distributions; sampling, confidence intervals, hypothesis testing and t-tests. Students make extensive use of the MiniTab statistical package.

**Lectures/workshops:**- 5 hrs per week
**Computer labs:**- 1 hr per week
**Unit Co-ordinator:**- to be advised
**Prerequisites:**- TEE Calculus and Applicable Mathematics

*6 points*

*Semester 2*

This unit is essential for students intending to major in Mathematical Statistics, Mathematical Sciences, or Pure or Applied Mathematics, some students in the physical sciences and all students in the combined Science/Engineering course. It is also suitable for other students wanting a strong mathematics component in their courses.

Topics include second-order differential equations; Taylor polynomials; parametric equations, curves,
polar co-ordinates; functions of several variables, partial derivatives, tangent planes, gradient vectors, maxima and
minima of functions of two variables; vector geometry; systems of linear equations and Gaussian elimination;
matrix algebra; subspaces, linear independence, bases and dimension in R^{n}, the rank-nullity theorem for matrices and linear transformations from R^{n} to R^{m}.

**Lectures/workshops:**- 5 hrs per week
**Computer labs:**- 1 hr per week
**Unit Co-ordinator:**- to be advised
**Prerequisite:**- Mathematics 101

*6 points*

*Semester 1*

**Outcomes: **Students are
able to extend their knowledge of mathematical techniques to include the basic
concepts of calculus and appreciate their use in problem solving; communicate
effectively with others; present mathematical results in a logical and coherent
fashion; and undertake continuous learning, and realise that an understanding
of fundamentals is necessary for effective application.

**Content: **This unit is available to students who
have passed TEE Applicable Mathematics. It emphasises the modelling and
applications aspects of mathematics. It may be taken as part of a major in
Applied Statistics or in Discrete Mathematics. It is also suitable for students
in the biological or social sciences or in computing science.

Topics are chosen from functions, limits, derivatives, curve sketching, bisection and Newton's method; maxima and minima; exponential, logarithmic and trigonometric functions; integrals and techniques of integration; first-order differential equations with applications to modelling.

**Assessment: **The assessment comprises an
examination at the end of the semester, in-semester tests, and assignments
using a computer tutorial package. All assessment tasks require students to
apply their knowledge of the unit content to solve previously unseen problems.
In written work, credit is given for clarity and correctness of presentation as
well as for actual results.

*Contact hours*: 65 (*lectures*: 52 hrs;
*labs/practice classes*: 13 hrs)

*Prerequisite*: TEE Applicable Mathematics

*Incompatible*: scaled mark above 54 per cent in
TEE Calculus

*6 points*

*Semester 2*

**Outcomes: **Students are
able to appreciate the power of statistical concepts in the interpretation of
data; develop knowledge of fundamental statistical tools and computer packages
for applying these tools; recognise the appropriate statistical techniques for use
in particular real-world settings, and to correctly apply these techniques for
data analysis; communicate effectively the results of these analyses; and
undertake continuous learning, and realise that understanding of fundamentals
is necessary for effective application.

**Content: **Topics include data exploration and
display, modelling univariate data, multivariate data; probability concepts and
probability distributions; inference including point estimation, confidence
intervals and hypothesis testing; design of experiments; chi-squared tests,
contingency tables; linear regression; analysis of variance. Students make use
of the statistical computer package MINITAB. Particular emphasis is placed on
application of statistical methods to problems in areas such as the physical,
biological, environmental and social sciences. The unit may be taken as part of
a major in Applied Statistics, Discrete Mathematics or Operations Research.

**Assessment: **This comprises an examination at the
end of the semester and in-semester tests or assignments. All assessment tasks
require students to apply their knowledge of the unit content to solve
previously unseen problems. Credit is given for clarity and correctness of
presentation as well as for actual results.

*Contact hours*: 65 (*lectures*: 52 hrs;
*labs/practice classes*: 13 hrs)

*Prerequisite*: Mathematics 155 *or*
Mathematics 165 *or* TEE Applicable Mathematics

*Incompatible*: Mathematics 101

*6 points*

*Semester 1*

This unit is suitable for non-Mathematics majors in the biological sciences, as well as students wishing to major in Operations Research, Applied Statistics or Discrete Mathematics.

Approximately half the unit comprises calculus and half probability and statistics. Topics in Calculus include limits, continuity, derivatives, curve sketching, maxima and minima, integration including integration by substitution, numerical approximation of integrals, integrals over infinite intervals, techniques of integration; first-order differential equations; functions of two variables, partial derivatives, maxima and minima of functions of two variables. Topics in Probability and Statistics include probability distributions and random variables; the binomial and normal distributions; confidence intervals, hypothesis testing. Students will make extensive use of the MiniTab statistical package.

**Lectures/workshops:**- 5 hrs per week
**Computer labs:**- 1 hr per week
**Unit Co-ordinator:**- to be advised
**Prerequisites:**- TEE Calculus and Applicable Mathematics

*6 points*

*Semester 2*

This unit is suitable for non-Mathematics majors in the biological sciences, as well as for students wishing to major in Operations Research, Applied Statistics or Discrete Mathematics.

The aim of this unit is to demonstrate the range of applications of mathematics, e.g. to problems in finance, biology, chemistry, social sciences, economics and psychology. Approximately half the unit is on deterministic modelling and half on statistical modelling. Topics in deterministic modelling include matrix games, zero sum games and dilemmas; modelling with difference and differential equations, equilibrium and stability. Topics in statistical modelling include the Poisson distribution; linear regression; analysis of variance; design of experiments; goodness-of-fit, chi-squared tests and contingency tables. Students will make extensive use of the MiniTab statistical package.

**Lectures/workshops:**- 5 hrs per week
**Computer labs:**- 1 hr per week
**Unit Co-ordinator:**- to be advised
**Prerequisite:**-
Mathematics 101
*or*175