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Revision as of 16:08, 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 | Chapters | Topics | Student learning outcomes | |
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1 |
1–2 |
Integers. Inductive proofs. |
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2 |
3–4 |
Divisibility. The Euclidean Algorithm. Unique factorization of integers. |
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Example |
Chapter 3 |
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Chapter 4 |
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Chapter 5 |
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Chapter 6 |
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Chapter 9 |
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Chapter 10 |
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Chapter 11 |
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Chapter 13 |
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Chapter 16 |
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Chapter 17 |
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Chapter 18 |
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