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.

We will begin with Analysis in Term 3 and follow with Group Theory in Term 4.

While the contents of this course are drawn from Analysis and Algebra, the course goals are to develop mathematical thinking, rigour and the construction of clear and precise mathematical arguments that communicate your thinking to others. You will learn about the role that axiomatic, abstract theory plays in mathematics by working with the concepts and actually doing mathematics!

We will help you to develop your mathematical thinking via

• the concepts, explanations, examples and proofs in lectures; and
• the problems that we ask you to do on your own; and
• collaboration with peers; and
• feedback on your work.

Syllabus / 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. Differentiation and Taylor’s Theorem (as time permits).

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

## Learning Outcomes

• Upon successful completion of the course, students will:

• understand a range of topics in real analysis and group theory;
• be able to formulate formal mathematical arguments and proofs;
• be able to 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. Employable, innovative and enterprising Students will develop key skills and attributes sought by employers that can be used in a range of applications.

MATH222, MATH243

## Timetable 2023

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Tuesday 11:00 - 12:00 Jack Erskine 445 17 Jul - 27 Aug 11 Sep - 22 Oct Lecture B 01 Thursday 11:00 - 12:00 Ernest Rutherford 141 17 Jul - 27 Aug 11 Sep - 22 Oct Lecture C 01 Monday 15:00 - 16:00 Ernest Rutherford 141 17 Jul - 20 Aug 11 Sep - 22 Oct Tutorial A 01 Tuesday 15:00 - 16:00 Jack Erskine 240 24 Jul - 27 Aug 11 Sep - 22 Oct 02 Tuesday 14:00 - 15:00 Jack Erskine 239 24 Jul - 27 Aug 11 Sep - 22 Oct 03 Tuesday 10:00 - 11:00 Jack Erskine 239 24 Jul - 27 Aug 11 Sep - 22 Oct

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Monday 15:00 - 16:00 Ernest Rutherford 141 21 Aug - 27 Aug

## 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