MATH240-23S2 (C) Semester Two 2023

Analysis and Groups

15 points

Details:
Start Date: Monday, 17 July 2023
End Date: Sunday, 12 November 2023
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 30 July 2023
  • Without academic penalty (including no fee refund): Sunday, 1 October 2023

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

Timetable 2023

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Tuesday 11:00 - 12:00 Jack Erskine 031 Lecture Theatre
17 Jul - 27 Aug
11 Sep - 22 Oct
Lecture B
Activity Day Time Location Weeks
01 Thursday 11:00 - 12:00 Ernest Rutherford 141
17 Jul - 27 Aug
11 Sep - 22 Oct
Lecture C
Activity Day Time Location Weeks
01 Monday 15:00 - 16:00 Ernest Rutherford 141
17 Jul - 27 Aug
11 Sep - 22 Oct
Tutorial A
Activity Day Time Location Weeks
01 Tuesday 15:00 - 16:00 Elsie Locke 611 Meeting Room
24 Jul - 27 Aug
11 Sep - 22 Oct
02 Thursday 10:00 - 11:00 Meremere 409
24 Jul - 27 Aug
11 Sep - 22 Oct
03 Tuesday 10:00 - 11:00 Elsie Locke 611 Meeting Room
24 Jul - 27 Aug
11 Sep - 22 Oct

Course Administrator

Felipe Voloch

Lecturer

Felipe Voloch

Indicative Fees

Domestic fee $824.00

International fee $4,750.00

* 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

  • MATH240-23S2 (C) Semester Two 2023