MATH103 to MATH515
MATH103 Discrete Mathematics
10 cp
Prerequisites Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed
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 Calculus
10 cp
Prerequisites Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed
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 Geometry
10 cp
Prerequisites Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed
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 Fundamentals of Mathematics
10 cp
Prerequisites Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed
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 Number Theory
10 cp
Prerequisites MATH108 Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed
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 Advanced Calculus
10 cp
Prerequisites MATH104 Calculus and Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed
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 Applications of Mathematics
10 cp
Prerequisites Mathematics (not General Mathematics) (NSW), Further Mathematics or Mathematical Methods (Vic) assumed
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.
MATH200 Calculus
10 cp
Prerequisites 1 100-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.
MATH203 Advanced Calculus
10 cp
Prerequisites 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.
MATH205 Geometry
10 cp
Prerequisites 1 100-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.
MATH208 Number Theory
10 cp
Prerequisites 1 100-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.
MATH211 Fundamentals of Mathematics
10 cp
Prerequisites 1 100-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.
MATH214 Discrete Mathematics
10 cp
Prerequisites 1 100-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.
MATH215 Applications of Mathematics
10 cp
Prerequisites 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 2 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.
Page last updated: 2017-06-29
Short url: https://handbook.acu.edu.au/61511
Page last updated: 2017-06-29
Short url: https://handbook.acu.edu.au/61511