MATH240-18S2 (C) Semester Two 2018

Analysis and Groups

15 points
16 Jul 2018 - 18 Nov 2018

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
    • University Graduate Attributes

      This course will provide students with an opportunity to develop the Graduate Attributes specified below:

      Critically competent in a core academic discipline of their award

      Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

Pre-requisites

Restrictions

MATH222, MATH243

Timetable 2018

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Thursday 16:00 - 17:00 Ernest Rutherford 465 16 Jul - 19 Aug
10 Sep - 21 Oct
Lecture B
Activity Day Time Location Weeks
01 Monday 13:00 - 14:00 Ernest Rutherford 465 16 Jul - 26 Aug
10 Sep - 21 Oct
Lecture C
Activity Day Time Location Weeks
01 Tuesday 14:00 - 15:00 Jack Erskine 111 16 Jul - 26 Aug
10 Sep - 21 Oct
Tutorial A
Activity Day Time Location Weeks
01 Friday 12:00 - 13:00 Jack Erskine 242 23 Jul - 26 Aug
10 Sep - 21 Oct
02 Friday 14:00 - 15:00 Jack Erskine 101 23 Jul - 26 Aug
10 Sep - 21 Oct

Examination and Formal Tests

Test A
Activity Day Time Location Weeks
01 Thursday 16:00 - 17:00 Ernest Rutherford 465 20 Aug - 26 Aug

Course Coordinator / Lecturer

Felipe Voloch

Lecturer

Ngin-Tee Koh

Indicative Fees

Domestic fee $749.00

International fee $3,788.00

* 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

  • MATH240-18S2 (C) Semester Two 2018