Search Course Outline
Showing 25 course outlines from 722 matches
376
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
377
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
378
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
379
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
380
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
381
MATHS 399
: Capstone: Mathematics2021 Semester Two (1215)
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
382
MATHS 399
: Capstone: Mathematics2021 Semester One (1213)
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
383
MATHS 702
: Mathematical Processes in the Curriculum2021 Semester Two (1215)
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
384
MATHS 703
: What Can Be More Practical Than a Good Theory?2021 Summer School (1210)
An analysis of theoretical perspectives that inform research in mathematics education, with a focus on learning theories, both social and psychological, and their implications for teaching and learning in mathematics.
Prerequisite: MATHS 302 or significant teaching experience or department approval
385
MATHS 714
: Number Theory2021 Semester Two (1215)
A broad introduction to various aspects of elementary, algebraic and computational number theory and its applications, including primality testing and cryptography.
Prerequisite: B+ in MATHS 328 or 320
386
MATHS 715
: Graph Theory and Combinatorics2021 Semester One (1213)
A study of combinatorial graphs (networks), designs and codes illustrating their application and importance in other branches of mathematics and computer science.
Prerequisite: B+ pass in MATHS 326 or 320
387
MATHS 720
: Group Theory2021 Semester One (1213)
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
388
MATHS 725
: Lie Groups and Lie Algebras2021 Semester Two (1215)
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
389
MATHS 730
: Measure Theory and Integration2021 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.
Prerequisite: MATHS 332
390
MATHS 731
: Functional Analysis2021 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.
Prerequisite: MATHS 332 and 333
391
MATHS 734
: 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
Restriction: MATHS 334
Restriction: MATHS 334
392
MATHS 740
: Complex Analysis2021 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.
Prerequisite: MATHS 332
Restriction: MATHS 341
Restriction: MATHS 341
393
MATHS 761
: Dynamical Systems2021 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.
Prerequisite: B- in both MATHS 340 and 361
394
MATHS 762
: Nonlinear Partial Differential Equations2021 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.
Prerequisite: B- in both MATHS 340 and 361
395
MATHS 763
: Advanced Partial Differential Equations2021 Semester One (1213)
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
396
MATHS 765
: Mathematical Modelling2021 Semester Two (1215)
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
397
MATHS 770
: Advanced Numerical Analysis2021 Semester Two (1215)
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
398
MATHS 776
: Honours Research Project2021 Semester Two (1215)
Restriction: MATHS 791
To complete this course students must enrol in MATHS 776 A and B, or MATHS 776
399
MATHS 776
: Honours Research Project2021 Semester One (1213)
Restriction: MATHS 791
To complete this course students must enrol in MATHS 776 A and B, or MATHS 776
400
MATHS 776A
: Honours Research Project2021 Semester Two (1215)
Restriction: MATHS 791
To complete this course students must enrol in MATHS 776 A and B, or MATHS 776