MAT3233 - Revision history

Eduardo.duenez: Typo

2023-03-25T16:56:43Z

Typo

Eduardo.duenez: Week 15: wrap-up

2023-03-25T16:56:04Z

Week 15: wrap-up

Eduardo.duenez: None -> ---

2023-03-25T16:55:11Z

None -> ---

Eduardo.duenez: Topics header

2023-03-25T16:54:02Z

Topics header

Eduardo.duenez: UTSA permalink to textbook.

2023-03-25T16:51:32Z

UTSA permalink to textbook.

Eduardo.duenez: Hyperlink to catalog.

2023-03-25T15:58:45Z

Hyperlink to catalog.

Eduardo.duenez: Table formatting.

2023-03-24T23:58:18Z

Table formatting.

Eduardo.duenez at 23:56, 24 March 2023

2023-03-24T23:56:48Z

Eduardo.duenez: Typo

2023-03-24T23:55:44Z

Typo

Eduardo.duenez: New catalog entry. Old one commented out.

2023-03-24T23:50:10Z

New catalog entry. Old one commented out.

← Older revision		Revision as of 16:56, 25 March 2023
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		+	Wrap-up and review. Student Study Day.
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 Review. First midterm exam.
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 Review. Second midterm exam.

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 Lindsay N. Childs, [https://utsa.primo.exlibrisgroup.com/permalink/01UTXSANT_INST/1du13se/cdi_springer_books_10_1007_978_0_387_74725_5 ''A Concrete Introduction to Higher Algebra''] (3rd. ed.) Springer-Verlag (2009). ISBN: 978-0-387-74527-5
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 ==Textbook==
-Lindsay N. Childs, ''A Concrete Introduction to Higher Algebra'' (3rd. ed.) Springer-Verlag (2009). ISBN: 978-0-387-74527-5
+Lindsay N. Childs, [https://utsa.primo.exlibrisgroup.com/permalink/01UTXSANT_INST/1du13se/cdi_springer_books_10_1007_978_0_387_74725_5 ''A Concrete Introduction to Higher Algebra''] (3rd. ed.) Springer-Verlag (2009). ISBN: 978-0-387-74527-5
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 ==Modern Algebra==
-MAT 3233 Modern Algebra. (3-0) 3 Credit Hours.
+[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 3233 Modern Algebra]. (3-0) 3 Credit Hours.
 Prerequisites: [[MAT2233]] and [[MAT3003]].

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 Divisibility. The Euclidean Algorithm. Unique factorization of integers.
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 Polynomials: division and factorization.
 Divisibility and the Euclidean Algorithm.
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 Homomorphisms. Finite fields.
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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. -->
-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: Arithmetic congruences in the ring of integers; residue rings ℤₙ; finite fields 𝔽ₚ; the group of units 𝑈ₙ; cyclic groups; the Chinese Remainder, Fermat’s and Euler’s theorems; polynomial rings; the Fundamental Theorem of Algebra; irreducible polynomials and factorization in 𝔽[x] and ℤ[𝑥]; quotient rings and construction of the Galois fields 𝐺𝐹(𝑝ⁿ).
+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: Arithmetic congruences in the ring ℤ of integers; residue rings ℤₙ; finite fields 𝔽ₚ; the group of units 𝑈ₙ; cyclic groups; the Chinese Remainder, Fermat’s and Euler’s theorems; polynomial rings; the Fundamental Theorem of Algebra; irreducible polynomials and factorization in 𝔽[x] and ℤ[𝑥]; quotient rings and construction of the Galois fields 𝐺𝐹(𝑝ⁿ).
 <!-- 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. -->