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Showing 25 course outlines from 4473 matches

2326

MATHS 730

: Measure Theory and Integration
2025 Semester One (1253)
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
Subject: Mathematics
Prerequisite: MATHS 332
2327

MATHS 730

: Measure Theory and Integration
2024 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
Subject: Mathematics
Prerequisite: MATHS 332
2328

MATHS 730

: Measure Theory and Integration
2023 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.
Subject: Mathematics
Prerequisite: MATHS 332
2329

MATHS 730

: Measure Theory and Integration
2022 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.
Subject: Mathematics
Prerequisite: MATHS 332
2330

MATHS 730

: Measure Theory and Integration
2021 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.
Subject: Mathematics
Prerequisite: MATHS 332
2331

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
2332

MATHS 731

: Functional Analysis
2025 Semester Two (1255)
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
2333

MATHS 731

: Functional Analysis
2024 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.
Subject: Mathematics
Prerequisite: MATHS 332 and 333
2334

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
2335

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
2336

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
2337

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
2338

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
2339

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
2340

MATHS 735

: Analysis on Manifolds and Differential Geometry
2024 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.
Subject: Mathematics
Prerequisite: MATHS 332
2341

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
2342

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
2343

MATHS 740

: Complex Analysis
2025 Semester One (1253)
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
2344

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
2345

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
2346

MATHS 750

: Topology
2024 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.
Subject: Mathematics
Prerequisite: MATHS 332
Restriction: MATHS 350
2347

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
2348

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
2349

MATHS 761

: Dynamical Systems
2025 Semester One (1253)
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
2350

MATHS 761

: Dynamical Systems
2024 Semester One (1243)
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