# Search Course Outline

### Showing 25 course outlines from 3708 matches

1501

#### MATHS 333

: Analysis in Higher Dimensions2020 Semester One (1203)

By selecting the important properties of distance many different mathematical contexts are studied simultaneously in the framework of metric and normed spaces. Examines carefully the ways in which the derivative generalises to higher dimensional situations. These concepts lead to precise studies of continuity, fixed points and the solution of differential equations. A recommended course for all students planning to advance in pure mathematics.

Prerequisite: MATHS 332

1502

#### MATHS 334

: 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 and Departmental approval

Restriction: MATHS 734

Restriction: MATHS 734

1503

#### MATHS 334

: 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 and Departmental approval

Restriction: MATHS 734

Restriction: MATHS 734

1504

#### MATHS 340

: Real and Complex Calculus2023 Semester Two (1235)

Calculus plays a fundamental role in mathematics, answering deep theoretical problems and allowing us to solve very practical problems. Extends the ideas of calculus to two and higher dimensions, showing how to calculate integrals and derivatives in higher dimensions and exploring special relationships between integrals of different dimensions. It also extends calculus to complex variables. Recommended preparation: MATHS 253.

Prerequisite: MATHS 250

1505

#### MATHS 340

: Real and Complex Calculus2022 Semester Two (1225)

Calculus plays a fundamental role in mathematics, answering deep theoretical problems and allowing us to solve very practical problems. Extends the ideas of calculus to two and higher dimensions, showing how to calculate integrals and derivatives in higher dimensions and exploring special relationships between integrals of different dimensions. It also extends calculus to complex variables. Recommended preparation: MATHS 253.

Prerequisite: MATHS 250

1506

#### MATHS 340

: Real and Complex Calculus2021 Semester Two (1215)

Calculus plays a fundamental role in mathematics, answering deep theoretical problems and allowing us to solve very practical problems. Extends the ideas of calculus to two and higher dimensions, showing how to calculate integrals and derivatives in higher dimensions and exploring special relationships between integrals of different dimensions. It also extends calculus to complex variables. Recommended preparation: MATHS 253.

Prerequisite: MATHS 250

1507

#### MATHS 340

: Real and Complex Calculus2020 Semester Two (1205)

Prerequisite: MATHS 250

1508

#### MATHS 341

: Complex Analysis2023 Semester One (1233)

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 and Departmental approval

Restriction: MATHS 740

Restriction: MATHS 740

1509

#### MATHS 341

: Complex Analysis2021 Semester One (1213)

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 and Departmental approval

Restriction: MATHS 740

Restriction: MATHS 740

1510

#### MATHS 350

: 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, metrisation, covering spaces, the fundamental group and homology theory. Recommended preparation: MATHS 333.

Prerequisite: MATHS 332 and Departmental approval

Restriction: MATHS 750

Restriction: MATHS 750

1511

#### MATHS 350

: 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, metrisation, covering spaces, the fundamental group and homology theory. Recommended preparation: MATHS 333.

Prerequisite: MATHS 332 and Departmental approval

Restriction: MATHS 750

Restriction: MATHS 750

1512

#### MATHS 361

: Partial Differential Equations2023 Semester One (1233)

Partial differential equations (PDEs) are used to model many important applications of phenomena in the real world such as electric fields, diffusion and wave propagation. Covers: linear PDEs and analytical methods for their solution, weak solutions. Recommended preparation: MATHS 253.

Prerequisite: MATHS 250, 260

1513

#### MATHS 361

: Partial Differential Equations2022 Semester One (1223)

Partial differential equations (PDEs) are used to model many important applications of phenomena in the real world such as electric fields, diffusion and wave propagation. Covers: linear PDEs and analytical methods for their solution, weak solutions. Recommended preparation: MATHS 253.

Prerequisite: MATHS 250, 260

1514

#### MATHS 361

: Partial Differential Equations2021 Semester One (1213)

Partial differential equations (PDEs) are used to model many important applications of phenomena in the real world such as electric fields, diffusion and wave propagation. Covers: linear PDEs and analytical methods for their solution, weak solutions. Recommended preparation: MATHS 253.

Prerequisite: MATHS 250, 260

1515

#### MATHS 361

: Partial Differential Equations2020 Semester One (1203)

Prerequisite: MATHS 250, 260

1516

#### MATHS 362

: Methods in Applied Mathematics2023 Semester Two (1235)

Covers a selection of techniques including the calculus of variations, asymptotic methods and models based on conservation laws. These methods are fundamental in the analysis of traffic flow, shocks, fluid flow, as well as in control theory, and the course is recommended for students intending to advance in Applied Mathematics. Recommended preparation: MATHS 253, 361.

Prerequisite:MATHS 250, 260

1517

#### MATHS 362

: Methods in Applied Mathematics2022 Semester Two (1225)

Covers a selection of techniques including the calculus of variations, asymptotic methods and models based on conservation laws. These methods are fundamental in the analysis of traffic flow, shocks, fluid flow, as well as in control theory, and the course is recommended for students intending to advance in Applied Mathematics. Recommended preparation: MATHS 253, 361.

Prerequisite:MATHS 250, 260

1518

#### MATHS 362

: Methods in Applied Mathematics2021 Semester Two (1215)

Covers a selection of techniques including the calculus of variations, asymptotic methods and models based on conservation laws. These methods are fundamental in the analysis of traffic flow, shocks, fluid flow, as well as in control theory, and the course is recommended for students intending to advance in Applied Mathematics. Recommended preparation: MATHS 253, 361.

Prerequisite:MATHS 250, 260

1519

#### MATHS 362

: Methods in Applied Mathematics2020 Semester Two (1205)

Prerequisite:MATHS 250, 260

1520

#### MATHS 363

: Advanced Modelling and Computation2023 Semester One (1233)

In real-world situations, the interesting and important variables are often not directly observable. To address this problem, mathematical models and quantities that are observable are usually employed to carry out inference on the variables of interest. This course is an introduction to fitting of models to (noisy) observational data and how to compute estimates for the interesting variables. Numerical methods for partial differential equations, which are commonly used as models for the observations, will also be covered.

Prerequisite: MATHS 260 and 270

1521

#### MATHS 363

: Advanced Modelling and Computation2022 Semester One (1223)

In real-world situations, the interesting and important variables are often not directly observable. To address this problem, mathematical models and quantities that are observable are usually employed to carry out inference on the variables of interest. This course is an introduction to fitting of models to (noisy) observational data and how to compute estimates for the interesting variables. Numerical methods for partial differential equations, which are commonly used as models for the observations, will also be covered.

Prerequisite: MATHS 260 and 270

1522

#### MATHS 363

: Advanced Modelling and Computation2021 Semester One (1213)

In real-world situations, the interesting and important variables are often not directly observable. To address this problem, mathematical models and quantities that are observable are usually employed to carry out inference on the variables of interest. This course is an introduction to fitting of models to (noisy) observational data and how to compute estimates for the interesting variables. Numerical methods for partial differential equations, which are commonly used as models for the observations, will also be covered.

Prerequisite: MATHS 260 and 270

1523

#### MATHS 363

: Advanced Modelling and Computation2020 Semester One (1203)

Prerequisite: MATHS 260 and 270

1524

#### MATHS 399

: Capstone: Mathematics2023 Semester Two (1235)

An exploration of the role of mathematics in society and culture, and the activities performed by mathematicians as teachers, critics, and innovators. Students will develop their skills in communication, critical thinking, teaching, and creative problem solving.

Prerequisite: MATHS 250 and 30 points at Stage III in Mathematics

1525

#### MATHS 399

: Capstone: Mathematics2023 Semester One (1233)

An exploration of the role of mathematics in society and culture, and the activities performed by mathematicians as teachers, critics, and innovators. Students will develop their skills in communication, critical thinking, teaching, and creative problem solving.

Prerequisite: MATHS 250 and 30 points at Stage III in Mathematics

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