# Abstract Algebra and Fundamental Analysis - MATH2701

**Faculty:** Faculty of Science

**School:** School of Mathematics and Statistics

**Course Outline:** http://www.maths.unsw.edu.au/

**Campus:** Sydney

**Career:** Undergraduate

**Units of Credit:** 6

**EFTSL:** 0.12500 (more info)

**Indicative Contact Hours per Week:** 4

**Enrolment Requirements:**

Prerequisite: MATH1231 or MATH1241 or MATH1251 with at least a CR, enrolment in an advanced maths or advanced science program

**CSS Contribution Charge:** 2 (more info)

**Tuition Fee:** See Tuition Fee Schedule

**Further Information:** See Class Timetable

View course information for previous years.

## Description

The content is as follows:

- The interplay between algebra and geometry: an introduction to group theory through the study of transformation geometry. Groups, subgroups, order, generators. Transformation of the plane, isometries, symmetry groups. Group homomorphisms, normal subgroups, First Isomorphism Theorem.
- Inequalities and the effect of dimension. Asymptotics and order notation. Fundamental Inequalities: AM/GM and Cauchy-Schwartz. Norms for sequences and matrices. Further inequalities. Metric spaces and normed vector spaces. Construction of the real numbers, p-adic numbers