# MATH2701 Abstract Algebra and Fundamental Analysis

MATH2701 is a Mathematics Level II course. See the course overview below.

Units of credit: 6

Prerequisites: MATH1231 or MATH1241 or MATH1251 with at least a CR, and enrolment in an Advanced Maths or Advanced Science Program.

Cycle of offering: Term 3

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: The Course Outline (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH2701, you can log into UNSW Moodle for this course.

#### Course Overview

This course, which is restricted to students in advanced mathematics or advanced science degrees, is designed to help bridge the gap between the second year core courses and the greater level of abstraction required in higher level III mathematics courses. While the course is intended for pure mathematics majors in advanced mathematics, it is designed to provide equally useful training and practice to other mathematics and statistics majors. The main themes explored will be groups, both abstractly and in applications to geometry, and inequalities, the use of which forms the foundation of analysis. The course will cover concrete examples that will prove helpful in the more advanced courses while introducing a level of rigor suited to advanced mathematical and statistical study.

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