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 Monday May 12, 2008
