MATH240-19S2 (C) Semester Two 2019

Analysis and Groups

15 points

Details:
Start Date: Monday, 15 July 2019
End Date: Sunday, 10 November 2019
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 26 July 2019
  • Without academic penalty (including no fee refund): Friday, 27 September 2019

Description

The course comprises two very different subjects, analysis and groups, both fundamental to mathematics and requiring mathematically rigorous thinking. It gives a deeper understanding of the real number system and limits, and an introduction to the methods of abstract algebra via the study of symmetries and permutations.

This is a course in real analysis and group theory. These are fundamental topics and tools needed for a deeper understanding of almost all mathematics. The course comprises two somewhat different subjects, analysis and groups, both  requiring mathematically rigorous thinking. It provides a deeper understanding of the real number system and limits, as well as an introduction to the methods of abstract algebra via the study of symmetries and permutations.

Topics covered:

Analysis: Properties of the real numbers; Convergence and divergence of sequences; Limits and continuity; The Intermediate and Extreme Value Theorems; Series and power series.

Group theory: Groups and symmetry; Subgroups; Permutations; Cyclic, Dihedral and Matrix groups; Isomorphisms; Lagrange's Theorem; Fermat's Little Theorem.

Learning Outcomes

  • By the end of the course, students will be able to:
  • understand a range of topics in real analysis and group theory
  • formulate formal mathematical arguments and proofs
  • work with both concrete examples and more abstract, axiomatic theory
  • appreciate the wider relevance of the topics covered

Prerequisites

Restrictions

MATH222, MATH243

Course Coordinator / Lecturer

Mike Steel

Lecturer

Felipe Voloch

Indicative Fees

Domestic fee $764.00

International fee $4,000.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH240 Occurrences

  • MATH240-19S2 (C) Semester Two 2019
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