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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)
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
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)
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
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)
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
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)
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
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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