MATH240-21S2 (C) Semester Two 2021

Analysis and Groups

15 points

Details:
Start Date: Monday, 19 July 2021
End Date: Sunday, 14 November 2021
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 1 August 2021
  • Without academic penalty (including no fee refund): Friday, 1 October 2021

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.

Pre-requisites

Restrictions

MATH222, MATH243

Timetable 2021

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Thursday 09:00 - 10:00 A8 Lecture Theatre 19 Jul - 29 Aug
13 Sep - 24 Oct
Lecture B
Activity Day Time Location Weeks
01 Tuesday 11:00 - 12:00 A8 Lecture Theatre 19 Jul - 29 Aug
13 Sep - 24 Oct
Lecture C
Activity Day Time Location Weeks
01 Friday 09:00 - 10:00 F1 Lectorial 19 Jul - 29 Aug
13 Sep - 24 Oct
Tutorial A
Activity Day Time Location Weeks
01 Monday 16:00 - 17:00 Jack Erskine 446 26 Jul - 29 Aug
13 Sep - 24 Oct
02 Thursday 15:00 - 16:00 Jack Erskine 239 26 Jul - 29 Aug
13 Sep - 24 Oct

Course Coordinator / Lecturer

Felipe Voloch

Lecturer

Rosie Cameron

Indicative Fees

Domestic fee $788.00

International fee $4,438.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

All MATH240 Occurrences

  • MATH240-21S2 (C) Semester Two 2021