Difference between revisions of "MAT3233"

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Prerequisites: [[MAT2233]] and [[MAT3003]].
 
Prerequisites: [[MAT2233]] and [[MAT3003]].
  
An introduction to the theory of groups, rings, and fields:  Basic examples of groups. Cyclic groups. Permutation groups and cycle decompositions. Group homomorphisms. Normal subgroups, factor groups, and direct products of groups. Definitions and basic examples of rings, integral domains and fields. Ring homomorphisms. Ideals, factor rings, and direct products of rings. Unique factorization of integers and polynomials. Generally offered: Fall, Spring, Summer. Differential Tuition: $150.
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An introduction to modern algebra building up from concrete examples in elementary algebra and number theory which lead to the abstract theory of groups, rings, and fields. Topics include:  Basic examples of groups. Cyclic groups. Permutation groups and cycle decompositions. Group homomorphisms. Normal subgroups, factor groups, and direct products of groups. Definitions and basic examples of rings, integral domains and fields. Ring homomorphisms. Ideals, factor rings, and direct products of rings. Unique factorization of integers and polynomials. Generally offered: Fall, Spring, Summer. Differential Tuition: $150.
  
 
==Textbook==
 
==Textbook==

Revision as of 15:55, 24 March 2023

Modern Algebra

MAT 3233 Modern Algebra. (3-0) 3 Credit Hours.

Prerequisites: MAT2233 and MAT3003.

An introduction to modern algebra building up from concrete examples in elementary algebra and number theory which lead to the abstract theory of groups, rings, and fields. Topics include: Basic examples of groups. Cyclic groups. Permutation groups and cycle decompositions. Group homomorphisms. Normal subgroups, factor groups, and direct products of groups. Definitions and basic examples of rings, integral domains and fields. Ring homomorphisms. Ideals, factor rings, and direct products of rings. Unique factorization of integers and polynomials. Generally offered: Fall, Spring, Summer. Differential Tuition: $150.

Textbook

Lindsay N. Childs, A Concrete Introduction to Higher Algebra (3rd. ed.) Springer-Verlag (2009). ISBN: 978-0-387-74527-5

Week Sections Topics Student learning outcomes
Example

Chapter 1

Preliminaries

Example

Example

Chapter 2

The Integers Example Example
Example Chapter 3 Groups Example Example
Example Chapter 4 Cyclic Groups Example Example
Example Chapter 5 Permutation Groups Example Example
Example Chapter 6 Cosets and Lagrange’s Theorem Example Example
Example Chapter 9 Isomorphisms Example Example
Example Chapter 10 Normal Subgroups and Factor Groups Example Example
Example Chapter 11 Homomorphisms Example Example
Example Chapter 13 The Structure of Groups Example Example
Example Chapter 16 Rings Example Example
Example Chapter 17 Polynomials Example Example
Example Chapter 18 Integral Domains Example Example