# Search Course Outline

### Showing 25 course outlines from 3697 matches

1926

#### MATHS 720

: Group Theory2021 Semester One (1213)

A study of groups focusing on basic structural properties, presentations, automorphisms and actions on sets, illustrating their fundamental role in the study of symmetry (for example in crystal structures in chemistry and physics), topological spaces, and manifolds.

Prerequisite: MATHS 320

1927

#### MATHS 720

: Group Theory2020 Semester One (1203)

A study of groups focusing on basic structural properties, presentations, automorphisms and actions on sets, illustrating their fundamental role in the study of symmetry (for example in crystal structures in chemistry and physics), topological spaces, and manifolds.

Prerequisite: MATHS 320

1928

#### MATHS 721

: Representations and Structure of Algebras and Groups2022 Semester Two (1225)

Representation theory studies properties of abstract groups and algebras by representing their elements as linear transformations of vector spaces or matrices, thus reducing many problems about the structures to linear algebra, a well-understood theory.

Prerequisite: MATHS 320

1929

#### MATHS 721

: Representations and Structure of Algebras and Groups2020 Semester Two (1205)

Representation theory studies properties of abstract groups and algebras by representing their elements as linear transformations of vector spaces or matrices, thus reducing many problems about the structures to linear algebra, a well-understood theory.

Prerequisite: MATHS 320

1930

#### MATHS 725

: Lie Groups and Lie Algebras2023 Semester Two (1235)

Symmetries and invariants play a fundamental role in mathematics. Especially important in their study are the Lie groups and the related structures called Lie algebras. These structures have played a pivotal role in many areas, from the theory of differential equations to the classification of elementary particles. Strongly recommended for students advancing in theoretical physics and pure mathematics. Recommended preparation: MATHS 333.

Prerequisite: MATHS 320 and 332

1931

#### MATHS 725

: Lie Groups and Lie Algebras2021 Semester Two (1215)

Symmetries and invariants play a fundamental role in mathematics. Especially important in their study are the Lie groups and the related structures called Lie algebras. These structures have played a pivotal role in many areas, from the theory of differential equations to the classification of elementary particles. Strongly recommended for students advancing in theoretical physics and pure mathematics. Recommended preparation: MATHS 333.

Prerequisite: MATHS 320 and 332

1932

#### MATHS 730

: Measure Theory and Integration2024 Semester One (1243)

Presents the modern elegant theory of integration as developed by Riemann and Lebesgue. This course includes powerful theorems for the interchange of integrals and limits, allowing very general functions to be integrated, and illustrates how the subject is both an essential tool for analysis and a critical foundation for the theory of probability. Strongly recommended: MATHS 333

Prerequisite: MATHS 332

1933

#### MATHS 730

: Measure Theory and Integration2023 Semester One (1233)

Presenting the modern elegant theory of integration as developed by Riemann and Lebesgue, it includes powerful theorems for the interchange of integrals and limits so allowing very general functions to be integrated, and illustrates how the subject is both an essential tool for analysis and a critical foundation for the theory of probability. Strongly recommended: MATHS 333.

Prerequisite: MATHS 332

1934

#### MATHS 730

: Measure Theory and Integration2022 Semester One (1223)

Presenting the modern elegant theory of integration as developed by Riemann and Lebesgue, it includes powerful theorems for the interchange of integrals and limits so allowing very general functions to be integrated, and illustrates how the subject is both an essential tool for analysis and a critical foundation for the theory of probability. Strongly recommended: MATHS 333.

Prerequisite: MATHS 332

1935

#### MATHS 730

: Measure Theory and Integration2021 Semester One (1213)

Presenting the modern elegant theory of integration as developed by Riemann and Lebesgue, it includes powerful theorems for the interchange of integrals and limits so allowing very general functions to be integrated, and illustrates how the subject is both an essential tool for analysis and a critical foundation for the theory of probability. Strongly recommended: MATHS 333.

Prerequisite: MATHS 332

1936

#### MATHS 730

: Measure Theory and Integration2020 Semester One (1203)

Prerequisite: MATHS 332

1937

#### MATHS 731

: Functional Analysis2024 Semester Two (1245)

Provides the mathematical foundations behind some of the techniques used in applied mathematics and mathematical physics; it explores how many phenomena in physics can be described by the solution of a partial differential equation, for example the heat equation, the wave equation and Schrödinger's equation. Recommended preparation: MATHS 730 and 750.

Prerequisite: MATHS 332 and 333

1938

#### MATHS 731

: Functional Analysis2023 Semester Two (1235)

Provides the mathematical foundations behind some of the techniques used in applied mathematics and mathematical physics; it explores how many phenomena in physics can be described by the solution of a partial differential equation, for example the heat equation, the wave equation and Schrödinger's equation. Recommended preparation: MATHS 730 and 750.

Prerequisite: MATHS 332 and 333

1939

#### MATHS 731

: Functional Analysis2022 Semester Two (1225)

Provides the mathematical foundations behind some of the techniques used in applied mathematics and mathematical physics; it explores how many phenomena in physics can be described by the solution of a partial differential equation, for example the heat equation, the wave equation and Schrödinger's equation. Recommended preparation: MATHS 730 and 750.

Prerequisite: MATHS 332 and 333

1940

#### MATHS 731

: Functional Analysis2021 Semester Two (1215)

Prerequisite: MATHS 332 and 333

1941

#### MATHS 731

: Functional Analysis2020 Semester Two (1205)

Prerequisite: MATHS 332 and 333

1942

#### MATHS 734

: Algebraic Geometry2023 Semester Two (1235)

Algebraic geometry is a branch of mathematics studying zeros of polynomials. The fundamental objects in algebraic geometry are algebraic varieties i.e., solution sets of systems of polynomial equations.

Prerequisite: MATHS 332 and at least one of MATHS 320, 328

Restriction: MATHS 334

Restriction: MATHS 334

1943

#### MATHS 734

: Algebraic Geometry2021 Semester Two (1215)

Algebraic geometry is a branch of mathematics studying zeros of polynomials. The fundamental objects in algebraic geometry are algebraic varieties i.e., solution sets of systems of polynomial equations.

Prerequisite: MATHS 332 and at least one of MATHS 320, 328

Restriction: MATHS 334

Restriction: MATHS 334

1944

#### MATHS 735

: Analysis on Manifolds and Differential Geometry2024 Semester One (1243)

Studies surfaces and their generalisations, smooth manifolds, and the interaction between geometry, analysis and topology; it is a central tool in many areas of mathematics, physics and engineering. Topics include Stokes' theorem on manifolds and the celebrated Gauss Bonnet theorem. Strongly recommended: MATHS 333 and 340.

Prerequisite: MATHS 332

1945

#### MATHS 735

: Analysis on Manifolds and Differential Geometry2022 Semester One (1223)

Studies surfaces and their generalisations, smooth manifolds, and the interaction between geometry, analysis and topology; it is a central tool in many areas of mathematics, physics and engineering. Topics include Stokes' theorem on manifolds and the celebrated Gauss Bonnet theorem. Strongly recommended: MATHS 333 and 340.

Prerequisite: MATHS 332

1946

#### MATHS 735

: Analysis on Manifolds and Differential Geometry2020 Semester One (1203)

Studies surfaces and their generalisations, smooth manifolds, and the interaction between geometry, analysis and topology; it is a central tool in many areas of mathematics, physics and engineering. Topics include Stokes' theorem on manifolds and the celebrated Gauss Bonnet theorem. Strongly recommended: MATHS 333 and 340.

Prerequisite: MATHS 332

1947

#### MATHS 740

: Complex Analysis2023 Semester One (1233)

An introduction to functions of one complex variable, including Cauchy's integral formula, the index formula, Laurent series and the residue theorem. Many applications are given including a three line proof of the fundamental theorem of algebra. Complex analysis is used extensively in engineering, physics and mathematics. Strongly recommended: MATHS 333.

Prerequisite: MATHS 332

Restriction: MATHS 341

Restriction: MATHS 341

1948

#### MATHS 740

: Complex Analysis2021 Semester One (1213)

An introduction to functions of one complex variable, including Cauchy's integral formula, the index formula, Laurent series and the residue theorem. Many applications are given including a three line proof of the fundamental theorem of algebra. Complex analysis is used extensively in engineering, physics and mathematics. Strongly recommended: MATHS 333.

Prerequisite: MATHS 332

Restriction: MATHS 341

Restriction: MATHS 341

1949

#### MATHS 750

: Topology2024 Semester Two (1245)

Aspects of point-set, set-theoretic and algebraic topology including: properties and construction of topological spaces, continuous functions, axioms of separation, countability, connectivity and compactness, metrization, covering spaces, the fundamental group and homology theory. Strongly recommended: MATHS 333.

Prerequisite: MATHS 332

Restriction: MATHS 350

Restriction: MATHS 350

1950

#### MATHS 750

: Topology2022 Semester Two (1225)

Aspects of point-set, set-theoretic and algebraic topology including: properties and construction of topological spaces, continuous functions, axioms of separation, countability, connectivity and compactness, metrization, covering spaces, the fundamental group and homology theory. Strongly recommended: MATHS 333.

Prerequisite: MATHS 332

Restriction: MATHS 350

Restriction: MATHS 350

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