MATH103 to MATH515

MATH103 tO MATH515

MATH103/214 Discrete Mathematics                                                                                                     10 cp

Prerequisites MATH103: Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed. MATH214: One 100 level MATH or STAT unit

Teaching Organisation 4 hours per week for 12 weeks or equivalent.

This unit explores mathematical facts and proofs which involve discrete rather than continuous entities. It includes an introduction to set theory and logic, different types of proofs, basic methods of counting, graph theory, and complex numbers.

MATH104/200 Calculus                                                                                                                         10 cp

Prerequisites MATH104: Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed. MATH200: One 100 level MATH or STAT unit

Teaching Organisation 4 hours per week for 12 weeks or equivalent.

This unit contains the basic concepts of Calculus: functions, limits, continuity, differentiation and integration, in a variety of environments. Calculus is a powerful mathematical tool; not only is the underlying abstract theory worthy of study per se, it gives precise answers to real questions and problems.

A good working knowledge of the calculus content of the HSC Mathematics course (not General Mathematics) is assumed.

MATH105/205 Geometry                                                                                                                       10 cp

Pre–requisites MATH105 Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed. MATH205: One 100 level MATH or STAT unit

Teaching Organisation 4 hours per week for 12 weeks or equivalent.

This unit has two distinct sections which represent the two basic aspects of geometry: Euclidean and analytic. We study a Euclidean approach to lines, polygons and circles; and also perform Euclidean constructions, giving a rationale for each one. Major theorems on concurrence and collinearity follow. Students will use a software package such as “Geometers’ Sketchpad”.In analytic geometry we study the link between geometry and the algebraic representation of familiar curves, specifically the conic sections. This includes loci, derivation of equations, tangents and normals, and proving geometric properties using algebraic techniques.

MATH107/211 Fundamentals of Mathematics                                                                                       10 cp

Prerequisites MATH107 Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed. MATH211: One 100 level MATH or STAT unit

Teaching Organisation There will be two hours of lectures, two hours of tutorials and two hours of a “Bridge and Support” component per week.

The unit covers a selection of topics, which form a base for further mathematics: matrices, polynomials, complex numbers and polar graphs. The underlying mathematical theory, which is studied first, is extended to problem solving.

MATH108/208 Number Theory                                                                                                              10 cp

Prerequisites MATH108 Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed. MATH208: One 100 level MATH or STAT unit

Teaching Organisation 4 hours per week for 12 weeks or equivalent.

The unit covers a selection of topics from: divisibility, primes, theory of congruences, Diophantine equations, Fermat’s theorem, the work of Pythagoras, Euler’s theorem, continued fractions, conjectures: solved and unresolved. Applications of number theory will motivate the study of these topics.

MATH114/203 Advanced Calculus                                                                                                        10 cp

Prerequisites MATH104 Calculus. MATH114 Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed. MATH203 Advanced Calculus: MATH104 Calculus

Teaching Organisation 4 hours per week for 12 weeks or equivalent.

The course extends the concepts of differentiation and integration of functions of a single variable to functions of more than one variable.

MATH115/215 Applications of Mathematics                                                                                          10 cp

Prerequisites MATH115 Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed. MATH215: MATH104/200 Calculus

Teaching Organisation 4 hours per week for 12 weeks or equivalent.

This unit investigates various applications of mathematics.

Topics covered will be chosen from mechanics, projectiles, circular motion and vectors, codes, fractals, chaos, knot theory, modelling and other related topics.

MATH301 Advanced Geometry                                                                                                             10 cp

Prerequisites MATH105/205 Geometry

Teaching Organisation 4 hours per week for 12 weeks or equivalent. There will be two hours of lectures and two hours of tutorials per week. One tutorial hour per week for six weeks will be on using Geometer’s Sketchpad.

The unit has two distinct sections: Euclidean and non-Euclidean geometry. We review Euclidean geometry from a standpoint of logic and the logical processes involved in writing formal proofs. We look at the classical definition of “constructible” and study the famous three impossible constructions. A review of formal logic leads to the study of finite geometries and Euclidean geometry as a deductive system. Alternatives to Euclid’s fifth postulate give rise to hyperbolic and Riemannian geometries. Use of the software package “Geometer’s Sketchpad” is included in the unit: students will be encouraged to demonstrate heuristically theorems which are prove axiomatically.

MATH303 Abstract Algebra                                                                                                                   10 cp

Prerequisites MATH107 Fundamentals of Mathematics

Teaching Organisation 4 hours per week for 12 weeks or equivalent.

The main topics in this unit are groups, semi-groups, rings and fields. This unit is an introduction to these areas of abstract algebra, and will normally concentrate on one of them; some applications will be given. This year we will concentrate mainly on groups, and only briefly meet rings and (perhaps) fields.

MATH306 Topology                                                                                                                              10 cp

Prerequisites Two units at 200 level

Teaching Organisation 4 hours per week for 12 weeks or equivalent.

Topology is now accepted as a branch of mathematics in its own right; ideas from topology give insight into fundamental ideas of calculus. Topology is described as “rubber sheet geometry” because it is concerned with properties of figures which remain invariant under “elastic” transformations, that is, under continuous mappings. We first compare Euclidean invariants and transformations with those of topology, then increasingly generalise from Euclidean spaces to metric spaces to topological spaces; topics include open and closed sets, homeomorphisms and properties which are invariant under homeomorphisms.

MATH307 Transformation and Symmetries                                                                                          10 cp

Prerequisites MATH303 Abstract Algebra and MATH205 Geometry

Teaching Organisation 4 hours per week for 12 weeks or equivalent.

This unit provides an introduction to geometry from an algebraic viewpoint. By considering symmetries of shapes and the transformations that preserve them group theory is used to obtain some geometric insights.

MATH512 Calculus 1                                                                                                                             10 cp

Prerequisites Nil

Teaching Organisation 3 hours per week for 12 weeks or equivalent of lectures and tutorials.

This unit contains the basic concepts of calculus: functions, limits, continuity, differentiation and integration, in a variety of environments. Calculus is a powerful mathematical tool; not only is the underlying abstract theory worthy of study per se, it gives precise answers to real questions and problems.

A good working knowledge of the calculus content of the NSW HSC Mathematics course (not General Mathematics) or equivalent is assumed.

MATH513 Discrete Mathematics                                                                                                           10 cp

Prerequisites Nil

Teaching Organisation Equivalent of 36 contact hours; 24 hours on-line and remaining contact hours of tutorial and workshop based sessions.

This unit explores mathematical facts and proofs, which involve discrete rather than continuous entities. It includes an introduction to set theory and logic, different types of proofs, basic methods of counting, complex numbers, vectors and Eulerian graphs.

MATH514 Calculus 2                                                                                                                             10 cp

Prerequisites Nil

Teaching Organisation 3 hours per week for 12 weeks or equivalent of lectures and tutorials.

The course extends the concepts of differentiation and integration of functions of a single variable to functions of more than one variable.

MATH515 Geometry                                                                                                                             10 cp

Prerequisites Nil

Teaching Organisation Equivalent of 36 contact hours; 24 hours on-line and remaining contact hours of tutorial and workshop based sessions.

This unit has two distinct sections, which represent the two basic aspects of geometry: Euclidean Geometry and Analytical Geometry. We revise and explore the Euclidean approach to lines, polygons and circles; and also perform Euclidean constructions, giving a rationale for each one. Major theorems on concurrence and collinearity follow. In analytical geometry we study the link between the geometry and the algebraic representation of familiar curves, specifically the conic sections. This includes loci, derivations of equations, tangents and normals, and proving geometric properties using algebraic techniques. Students will be introduced to a computer software package such as “Geometer’s Sketchpad”.