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Showing 25 course outlines from 2938 matches

1551

MATHS 730

: Measure Theory and Integration
2020 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.
Subject: Mathematics
Prerequisite: MATHS 332
1552

MATHS 731

: Functional Analysis
2023 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.
Subject: Mathematics
Prerequisite: MATHS 332 and 333
1553

MATHS 731

: Functional Analysis
2022 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.
Subject: Mathematics
Prerequisite: MATHS 332 and 333
1554

MATHS 731

: Functional Analysis
2021 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.
Subject: Mathematics
Prerequisite: MATHS 332 and 333
1555

MATHS 731

: Functional Analysis
2020 Semester Two (1205)
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.
Subject: Mathematics
Prerequisite: MATHS 332 and 333
1556

MATHS 734

: Algebraic Geometry
2023 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.
Subject: Mathematics
Prerequisite: MATHS 332 and at least one of MATHS 320, 328
Restriction: MATHS 334
1557

MATHS 734

: Algebraic Geometry
2021 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.
Subject: Mathematics
Prerequisite: MATHS 332 and at least one of MATHS 320, 328
Restriction: MATHS 334
1558

MATHS 735

: Analysis on Manifolds and Differential Geometry
2022 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.
Subject: Mathematics
Prerequisite: MATHS 332
1559

MATHS 735

: Analysis on Manifolds and Differential Geometry
2020 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.
Subject: Mathematics
Prerequisite: MATHS 332
1560

MATHS 740

: Complex Analysis
2023 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.
Subject: Mathematics
Prerequisite: MATHS 332
Restriction: MATHS 341
1561

MATHS 740

: Complex Analysis
2021 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.
Subject: Mathematics
Prerequisite: MATHS 332
Restriction: MATHS 341
1562

MATHS 750

: Topology
2022 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.
Subject: Mathematics
Prerequisite: MATHS 332
Restriction: MATHS 350
1563

MATHS 750

: Topology
2020 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.
Subject: Mathematics
Prerequisite: MATHS 332
Restriction: MATHS 350
1564

MATHS 761

: Dynamical Systems
2023 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.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361
1565

MATHS 761

: Dynamical Systems
2022 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.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361
1566

MATHS 761

: Dynamical Systems
2021 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.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361
1567

MATHS 761

: Dynamical Systems
2020 Semester One (1203)
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.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361
1568

MATHS 762

: Nonlinear Partial Differential Equations
2023 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.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361
1569

MATHS 762

: Nonlinear Partial Differential Equations
2022 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.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361
1570

MATHS 762

: Nonlinear Partial Differential Equations
2021 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.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361
1571

MATHS 762

: Nonlinear Partial Differential Equations
2020 Semester Two (1205)
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.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361
1572

MATHS 763

: Advanced Partial Differential Equations
2023 Semester One (1233)
A study of exact and approximate methods of solution for the linear partial differential equations that frequently arise in applications.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361
1573

MATHS 763

: Advanced Partial Differential Equations
2022 Semester One (1223)
A study of exact and approximate methods of solution for the linear partial differential equations that frequently arise in applications.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361
1574

MATHS 763

: Advanced Partial Differential Equations
2021 Semester One (1213)
A study of exact and approximate methods of solution for the linear partial differential equations that frequently arise in applications.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361
1575

MATHS 763

: Advanced Partial Differential Equations
2020 Semester One (1203)
A study of exact and approximate methods of solution for the linear partial differential equations that frequently arise in applications.
Subject: Mathematics
Prerequisite: B- in both MATHS 340 and 361