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Unit of study_

MATH2923: Analysis (Advanced)

Analysis grew out of calculus, which leads to the study of limits of functions, sequences and series. It is one of the fundamental topics underlying much of mathematics including differential equations, dynamical systems, differential geometry, topology and Fourier analysis. This advanced unit introduces the field of mathematical analysis both with a careful theoretical framework as well as selected applications. This unit will be useful to students with more mathematical maturity who study mathematics, science, or engineering. Starting off with an axiomatic description of the real numbers system, this unit concentrates on the limiting behaviour of sequences and series of real and complex numbers. This leads naturally to the study of functions defined as limits and to the notion of uniform con-vergence. Special attention is given to power series, leading into the theory of analytic functions and complex analysis. Besides a rigorous treatment of many concepts from calculus, you will learn the basic results of complex analysis such as the Cauchy integral theorem, Cauchy integral formula, the residues theorems, leading to useful techniques for evaluating real integrals. By doing this unit, you will develop solid foundations in the more formal aspects of analysis, including knowledge of abstract concepts, how to apply them and the ability to construct proofs in mathematics.

Code MATH2923
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
[(MATH1921 or MATH1931 or MATH1901 or MATH1906) or (a mark of 65 or above in MATH1021 or MATH1001)] and [MATH1902 or (a mark of 65 or above in MATH1002)] and [(MATH1923 or MATH1933 or MATH1903 or MATH1907) or (a mark of 65 or above in MATH1023 or MATH1003)]
MATH2023 or MATH2962 or MATH3068

At the completion of this unit, you should be able to:

  • LO1. Demonstrate a conceptual understanding of limit, continuity, differentiation, and integration as well as a thorough background in variety of techniques and applications of mathematical analysis.
  • LO2. assess problems in the framework of mathematical analysis, to choose among several potentially appropriate mathematical methods of solution, and persist in the face of difficulty
  • LO3. present complete and mathematically rigorous solutions for problems in mathematical analysis that include appropriate justification for their reasoning
  • LO4. recognise problems in mathematics, science, engineering and real life that are amenable to mathematical analysis, and to formulate models for such problems and apply the techniques of mathematical analysis in solving them
  • LO5. apply mathematical logic and rigor to solving problems, and express mathematical ideas coherently using precise mathematical language
  • LO6. understand new mathematical concepts beyond routine methods and calculations