MSI First Year Courses
First Year Courses
The coordinator of First Year courses is Dr E. Ormerod, room
JD G21.
Read the Course Guide
Introduction and
consult staff members for advice on determining the course in which to
enrol. It is extremely important that students be enrolled in the
course most appropriate for their overall program and abilities.
Planning your program is important: students who intend to take Second
and Third Year courses in Mathematics, Physics, Statistics, Computer
Science or Economics should study the Faculty handbook entries for
those subjects carefully to ensure that they are enrolled in the
Mathematics course which will provide them with the appropriate
prerequisites. If you would like any further information about the
mathematics courses please contact the First Year Coordinator,
Elizabeth Ormerod.
Suitably qualified students may be allowed to do second
year courses.
Note for Engineering Students
MATH1013
and MATH1014: Mathematics and its Applications 1 & 2
, or the Honours versions of these courses, form part of the
Engineering program. Those who have the appropriate background in
mathematics are encouraged to enrol in MATH1115
and MATH1116: Mathematics and Applications 1 & 2 Honours.
Outlines of First Semester First Year Courses
Assumed knowledge: ACT Mathematical Methods or NSW HSC
Mathematics or equivalent
The course will introduce calculus and matrix theory and their
use in mathematical modelling. Emphasis will be placed on developing
facility, technique and use in applications. Modelling of processes and
phenomena which occur in economics and the physical, environmental and
life sciences will be used as a vehicle throughout. This course also
provides a pathway to higher level mathematics courses. Topics to be
covered include: Functions and graphs, the transcendental functions,
approximation, differential equations, techniques and uses of
differentiation and integration, solution of systems of linear
equations, matrix algebra.
Prerequisites: MATH1003 or a satisfactory result in ACT
Specialist Mathematics (Major- Minor) or NSW HSC Mathematics Extension
1 or equivalent. Students with a good pass in ACT Mathematical Methods
or NSW HSC Mathematics or equivalent will be considered.
The syllabus for the Calculus section of this course (approx
24 lectures) will be: Limits, including infinite limits and limits at
infinity. Continuity and global properties of continuous functions.
Differentiation, transcendental functions: exponential and logarithmic
functions and their connection with integration, growth and decay,
hyperbolic functions. Local and absolute extrema, concavity and
inflection points, Newton's method, Taylor polynomials, L'Hopital's
rules. Riemann integration and the Fundamental Theorem of Calculus.
Techniques of integration including the method of substitution and
integration by parts. For the Algebra section (approx 24 lectures) the
syllabus will be: Complex numbers. Solution of linear equations, vector
and matrix equations, linear transformations and the idea of a vector
space. Emphasis on understanding and using algorithms and applications.
The texts will be R. Adams: Calculus, a complete course, and D. Lay:
Linear Algebra and its Applications.
The prerequisite is MATH1013; incompatible with MATH1003.
The Calculus section will study integration and techniques of
integration and functions of several variables —
visualisation, continuity, partial derivatives and directional
derivatives. The Algebra section will include: theory and application
of Euclidean vector spaces, linear independence, bases and dimension,
eigenvalues and eigenvectors, orthogonality and least squares.
Applications will be discussed to processes and phenomena which occur
in economics and the physical, environmental and life sciences. The
texts will be as for MATH1013.
Prerequisites: A satisfactory pass in the ACT Specialist
Mathematics double major, NSW HSC Mathematics Extension 2 or equivalent
Lectures will cover the Calculus and Linear Algebra syllabus
of MATH1013 in somewhat more depth. In addition, several variable
calculus will be introduced. Lectures are organised so that it is
possible to move into MATH1013 at certain points during the semester,
but changes in the opposite direction are more difficult. The texts
will be as for MATH1013; further notes will be provided online.
This course is offered jointly with the Department of
Philosophy. It treats mathematics in its broadest sense. The philosophy
of mathematics and science will be discussed under four headings: the
history and philosophy of mathematics and science; shape and form; from
theology to cosmology; and self-organising systems. These will
emphasise the evolution of thought leading to current understandings.
There are no formal prerequisites.
Outlines of Second Semester First Year Courses
Entry to this course is as for MATH1003. Note that MATH1003 is
not a prerequisite for MATH1005.
This course is an introduction to finite mathematics and its
use in mathematical modelling. Emphasis will be placed on developing
facility, technique and use in applications. Topics to be covered
include: combinatorics and counting, elementary probability, graphs and
networks, induction and recurrence relations. The text is S. Epp:
Discrete Mathematics with Applications.
Prerequisites: MATH1003 or a satisfactory result in ACT
Specialist Mathematics or NSW HSC Mathematics Extension 1 orequivalent.
Students with a good pass in ACT Mathematical Methods or NSW HSC
Mathematics or equivalent will be considered.
The syllabus for the Calculus section of this course (approx
24 lectures) will be: Limits, including infinite limits and limits at
infinity. Continuity and global properties of continuous functions.
Differentiation, transcendental functions: exponential and logarithmic
functions and their connection with integration, growth and decay,
hyperbolic functions. Local and absolute extrema, concavity and
inflection points, Newton's method, Taylor polynomials, L'Hopital's
rules. Riemann integration and the Fundamental Theorem of Calculus.
Techniques of integration including the method of substitution and
integration by parts. For the Algebra section (approx 24 lectures) the
syllabus will be: Complex numbers. Solution of linear equations, vector
and matrix equations, linear transformations and the idea of a vector
space. Emphasis on understanding and using algorithms and applications.
The texts will be R. Adams: Calculus, a complete course, and D. Lay:
Linear Algebra and its Applications.
The prerequisite is MATH1013; incompatible with MATH1003.
The Calculus section will study integration and techniques of
integration and functions of several variables —
visualisation, continuity, partial derivatives and directional
derivatives. The Algebra section will include: theory and application
of Euclidean vector spaces, linear independence, bases and dimension,
eigenvalues and eigenvectors, orthogonality and least squares.
Applications will be discussed to processes and phenomena which occur
in economics and the physical, environmental and life sciences. The
texts will be as for MATH1013.
The prerequisite is MATH1115 at Credit level or better.
This course continues the development of Calculus and Linear
Algebra, including some more advanced material and with a particular
emphasis on the underlying foundations of mathematics. The texts will
be as for MATH1115.
The prerequisite is PHYS1101 and mathematics to at least the
standard of MATH1013.
This course is designed for students who wish to study modern
astrophysics at a level beyond most popular books. It covers
the
formation and evolution of the solar system, extra-solar
planets, the formation, evolution and death of stars, white dwarfs,
neutron stars and black holes, galaxies, cosmology, expanding space and
the Big Bang.
This page was updated on Wednesday June 17, 2009
