Syllabus, SM462, Spring 2015-2016
Text: Abstract Algebra, 2015 edition, Thmas Judson
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§
16.1
16.1
16.1
16.2
16.2
16.3
16.3
16.3
16.4
16.5
17.1
17.1
17.2
17.3
17.3
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18.1
18.1
18.2
18.2
18.2
18.2
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21.1
21.1
21.1
21.1
21.1
21.2
21.2
quiz
22.1
22.1
Topic
Intro to rings, 1
Intro to rings, 2
Intro to rings, 3
Intro to int. domains and fields, 1
Intro to int. domains and fields, 2
Ring homs and ideals, 1
Ring homs and ideals, 2
Ring homs and ideals, 3
Maximal and prine ideals
xgcd and crt?
quiz
Intro to poly. rings, 1
Intro to poly. rings, 2
Division algorithm
Irreducible polys., 1
Irreducible polys., 2
Sage examples
quiz
Field of fractions, 1
Field of fractions, 2
Factorization in int. domains, 1
Factorization in int. domains, 2
Factorization in int. domains, 3
Factorization in int. domains, 4
Sage examples
quiz
Extension fields, 1
Extension fields, 2
Extension fields, 3
Extension fields, 4
Extension fields, 5
Splitting fields, 1
Splitting fields, 2
Finite fields, 1
Finite fields, 2
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Text Assignment
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44
22.2
22.2
22.2
23.1
23.1
23.2
23.2
review
Polynomial codes, 1
Polynomial codes, 2
Polynomial codes, 3
Field automorphisms, 1
Field automorphisms, 2
The fund. thrm of Galois theory, 1
The fund. thrm of Galois theory, 1
Upon successful completion of this course, students are able to do the
following:
• work with various tools in ring theory on specific examples and in the
abstract setting
• read, understand, devise, and communicate basic algebraic arguments
• understand the basic structure ofintegral domains, Euclideans domains
and PIDs
• understand the basic structure of polynomial rings in one variable,
• understand the basic structure of simple field extensions,
• understand the basic structure of finite fields,
• understand the basic construction and properties of cyclic and BCH
codes,
• have a basic familiariety with Galois theory.
coordinator: Prof. David Joyner, wdj@usna.edu
webpage: http://www.usna.edu/Users/math/wdj/
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