Search Course Outline
Showing 25 course outlines from 747 matches
376
MATHS 332
: Real Analysis2023 Semester Two (1235)
A standard course for every student intending to advance in pure mathematics. It develops the foundational mathematics underlying calculus, it introduces a rigorous approach to continuous mathematics and fosters an understanding of the special thinking and arguments involved in this area. The main focus is analysis in one real variable with the topics including real fields, limits and continuity, Riemann integration and power series.
Prerequisite: MATHS 250, 254
377
MATHS 333
: Analysis in Higher Dimensions2023 Semester One (1233)
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 or a B or higher in MATHS 254
378
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
379
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
380
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
381
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
382
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
383
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
384
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
385
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
386
MATHS 702
: Mathematical Processes in the Curriculum2023 Semester Two (1235)
Historically, mathematics curricula have emphasised the what of mathematics (content), at the expense of considering the how. This course uses hands-on experiences and research literature to explore how to teach, learn and do mathematics through processes such as communication, modelling, problem solving, and proving.
No pre-requisites or restrictions
387
MATHS 712
: Teaching and Learning in Algebra2023 Summer School (1230)
Recent theoretical perspectives on the teaching and learning of school and university mathematics are linked to the learning of either calculus or algebra. The focus is on the mathematics content, applications, and effective learning at school and university. Students taking this course should normally have studied mathematics or statistics at 200 level.
Prerequisite: MATHS 302 or significant teaching experience or department approval
388
MATHS 715
: Graph Theory and Combinatorics2023 Semester One (1233)
A study of combinatorial graphs (networks), designs and codes illustrating their application and importance in other branches of mathematics and computer science.
Prerequisite: 15 points from MATHS 320, 326, 328 with a B or higher
389
MATHS 720
: Group Theory2023 Semester One (1233)
A study of groups focusing on basic structural properties, presentations, automorphisms and actions on sets, illustrating their fundamental role in the study of symmetry (for example in crystal structures in chemistry and physics), topological spaces, and manifolds.
Prerequisite: MATHS 320
390
MATHS 725
: Lie Groups and Lie Algebras2023 Semester Two (1235)
Symmetries and invariants play a fundamental role in mathematics. Especially important in their study are the Lie groups and the related structures called Lie algebras. These structures have played a pivotal role in many areas, from the theory of differential equations to the classification of elementary particles. Strongly recommended for students advancing in theoretical physics and pure mathematics. Recommended preparation: MATHS 333.
Prerequisite: MATHS 320 and 332
391
MATHS 730
: Measure Theory and Integration2023 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.
Prerequisite: MATHS 332
392
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
393
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
394
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
395
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
396
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
397
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
398
MATHS 765
: Mathematical Modelling2023 Semester Two (1235)
Advanced topics in mathematical modelling, including selected topics in a range of application areas, principally taken from the physical and biological sciences.
Prerequisite: At least B- or better in both MATHS 340 and 361
399
MATHS 770
: Advanced Numerical Analysis2023 Semester Two (1235)
Covers the use, implementation and analysis of efficient and reliable numerical algorithms for solving several classes of mathematical problems. The course assumes students have done an undergraduate course in numerical methods and can use Matlab or other high-level computational language.
Prerequisite: B- in MATHS 270, 340 and 361
400
MATHS 787
: Special Topic: Inverse Problems and Stochastic Differential Equations2023 Semester One (1233)
Covers deterministic inverse problems: Hilbert spaces and linear operator theory, singular value decomposition and pseudoinverses, Tikhonov regularisation, nonlinear problems and iterative methods, continuous time processes, stochastic differential equations, random walks and Wiener processes, Itô calculus, and applications of SDE's.
Prerequisite: B- or higher in MATHS 340 and 361
Restriction: MATHS 769, 766
Restriction: MATHS 769, 766