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
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 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
Study Levels
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