MATH240-20S2 (C) Semester Two 2020

Analysis and Groups

15 points

Details:
Start Date: Monday, 13 July 2020
End Date: Sunday, 8 November 2020
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 24 July 2020
  • Without academic penalty (including no fee refund): Friday, 25 September 2020

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 2020

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Monday 10:00 - 11:00 A4 Lecture Theatre
13 Jul - 23 Aug
7 Sep - 18 Oct
Lecture B
Activity Day Time Location Weeks
01 Thursday 10:00 - 11:00 A4 Lecture Theatre
13 Jul - 23 Aug
7 Sep - 18 Oct
Lecture C
Activity Day Time Location Weeks
01 Friday 09:00 - 10:00 Jack Erskine 031 Lecture Theatre
13 Jul - 23 Aug
7 Sep - 18 Oct
Tutorial A
Activity Day Time Location Weeks
01 Tuesday 14:00 - 15:00 Ernest Rutherford 260 20 Jul - 23 Aug
7 Sep - 18 Oct
02 Tuesday 08:00 - 09:00 Rehua 429 20 Jul - 23 Aug
7 Sep - 18 Oct

Course Coordinator / Lecturer

Felipe Voloch

Indicative Fees

Domestic fee $780.00

International fee $4,250.00

* 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

  • MATH240-20S2 (C) Semester Two 2020