# Search Course Outline

### Showing 25 course outlines from 2938 matches

1551

#### MATHS 730

: Measure Theory and Integration2020 Semester One (1203)

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

1552

#### 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

1553

#### 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

1554

#### MATHS 731

: Functional Analysis2021 Semester Two (1215)

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

1555

#### MATHS 731

: Functional Analysis2020 Semester Two (1205)

Prerequisite: MATHS 332 and 333

1556

#### 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

1557

#### 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

1558

#### 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

1559

#### 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

1560

#### 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

1561

#### 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

1562

#### 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

1563

#### MATHS 750

: Topology2020 Semester Two (1205)

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

1564

#### MATHS 761

: Dynamical Systems2023 Semester One (1233)

Mathematical models of systems that change are frequently written in the form of nonlinear differential equations, but it is usually not possible to write down explicit solutions to these equations. This course covers analytical and numerical techniques that are useful for determining the qualitative properties of solutions to nonlinear differential equations.

Prerequisite: B- in both MATHS 340 and 361

1565

#### MATHS 761

: Dynamical Systems2022 Semester One (1223)

Mathematical models of systems that change are frequently written in the form of nonlinear differential equations, but it is usually not possible to write down explicit solutions to these equations. This course covers analytical and numerical techniques that are useful for determining the qualitative properties of solutions to nonlinear differential equations.

Prerequisite: B- in both MATHS 340 and 361

1566

#### MATHS 761

: Dynamical Systems2021 Semester One (1213)

Mathematical models of systems that change are frequently written in the form of nonlinear differential equations, but it is usually not possible to write down explicit solutions to these equations. This course covers analytical and numerical techniques that are useful for determining the qualitative properties of solutions to nonlinear differential equations.

Prerequisite: B- in both MATHS 340 and 361

1567

#### MATHS 761

: Dynamical Systems2020 Semester One (1203)

Prerequisite: B- in both MATHS 340 and 361

1568

#### MATHS 762

: Nonlinear Partial Differential Equations2023 Semester Two (1235)

A study of exact and numerical methods for non-linear partial differential equations. The focus will be on the kinds of phenomena which only occur for non-linear partial differential equations, such as blow up, shock waves, solitons and special travelling wave solutions.

Prerequisite: B- in both MATHS 340 and 361

1569

#### MATHS 762

: Nonlinear Partial Differential Equations2022 Semester Two (1225)

A study of exact and numerical methods for non-linear partial differential equations. The focus will be on the kinds of phenomena which only occur for non-linear partial differential equations, such as blow up, shock waves, solitons and special travelling wave solutions.

Prerequisite: B- in both MATHS 340 and 361

1570

#### MATHS 762

: Nonlinear Partial Differential Equations2021 Semester Two (1215)

A study of exact and numerical methods for non-linear partial differential equations. The focus will be on the kinds of phenomena which only occur for non-linear partial differential equations, such as blow up, shock waves, solitons and special travelling wave solutions.

Prerequisite: B- in both MATHS 340 and 361

1571

#### MATHS 762

: Nonlinear Partial Differential Equations2020 Semester Two (1205)

Prerequisite: B- in both MATHS 340 and 361

1572

#### MATHS 763

: Advanced Partial Differential Equations2023 Semester One (1233)

A study of exact and approximate methods of solution for the linear partial differential equations that frequently arise in applications.

Prerequisite: B- in both MATHS 340 and 361

1573

#### MATHS 763

: Advanced Partial Differential Equations2022 Semester One (1223)

A study of exact and approximate methods of solution for the linear partial differential equations that frequently arise in applications.

Prerequisite: B- in both MATHS 340 and 361

1574

#### MATHS 763

: Advanced Partial Differential Equations2021 Semester One (1213)

A study of exact and approximate methods of solution for the linear partial differential equations that frequently arise in applications.

Prerequisite: B- in both MATHS 340 and 361

1575

#### MATHS 763

: Advanced Partial Differential Equations2020 Semester One (1203)

Prerequisite: B- in both MATHS 340 and 361

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