Difference between revisions of "MAT5173"

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(Created page with "The opportunity for development of basic theory of algebraic structures. Areas of study may include monoids, semigroups, groups, isomorphism theorems, free groups, group exten...")
 
 
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The opportunity for development of basic theory of algebraic structures. Areas of study may include monoids, semigroups, groups, isomorphism theorems, free groups, group extensions and group actions, Sylow theorems, group chains and composition series, nilpotent and solvable groups, cohomology of groups.
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Introduction to groups and rings.
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== Sample textbook ==
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[1] Thomas W. Judson and Robert A. Beezer, ''Abstract Algebra: Theory and Applications'', 2008. [http://abstract.ups.edu/aata/aata.html Freely available online].
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== Catalog entry ==
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''Prerequisite'': Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
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''Contents''
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(1) Groups: Cyclic groups, permutation groups and Cayley's theorem, group homomorphisms, normal subroups, quotient groups and Lagrange's theore, the theorems of Euler and Fermat.
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(2) Rings: Ring homomorphisms, integral domains and fields, maximal and prime ideals.
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(3) Rings of polynomials: The Division Algorithm and irreducible polynomials.
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==Topics List==
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{| class="wikitable sortable"
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! Week !! Topic !! Sections from the Judson-Beezer book !! Subtopics !! Prerequisite
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|-
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|  1-2 
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|| [[Groups]]
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|| 3
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||
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* Definitions and classical examples
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* Subgroups
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* Isomorphisms
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|| MAT1313, CS2233/2231, or instructor consent.
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|-
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|  4-5 
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|| [[Cyclic groups]]
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|| 4
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||
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* Classification of cyclic groups.
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|-
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|  5-6 
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|| [[Permutation groups]]
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|| 5
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||
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* Permutations
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*Cayley's Theorem
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|-
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|  7-8 
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|| [[Cosets and Lagrange's Theorem]]
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|| 10
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||
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* Normal subgroups
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* Factor Groups
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* The theorems of Euler and Fermat
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|-
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|  9 
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|| [[Homomorphisms]]
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|| 11
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|| The Isomorphism Theorem
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|
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|-
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|  10-11 
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|| [[Rings]]
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|| 16
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||
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* Ring homomorphisms
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*Integral domains and fields
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*Maximal and Prime Ideals
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|-
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|  12-end 
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|| [[Rings of Polynomials]]
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|| 17
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||
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* The Division Algorithm
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* Irreducible Polynomials
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* Solving cubic and quartic equations
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|}

Latest revision as of 22:02, 25 March 2023

Introduction to groups and rings.

Sample textbook

[1] Thomas W. Judson and Robert A. Beezer, Abstract Algebra: Theory and Applications, 2008. Freely available online.


Catalog entry

Prerequisite: Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.

Contents (1) Groups: Cyclic groups, permutation groups and Cayley's theorem, group homomorphisms, normal subroups, quotient groups and Lagrange's theore, the theorems of Euler and Fermat. (2) Rings: Ring homomorphisms, integral domains and fields, maximal and prime ideals. (3) Rings of polynomials: The Division Algorithm and irreducible polynomials.




Topics List

Week Topic Sections from the Judson-Beezer book Subtopics Prerequisite
1-2 Groups 3
  • Definitions and classical examples
  • Subgroups
  • Isomorphisms
 MAT1313, CS2233/2231, or instructor consent.
4-5 Cyclic groups 4
  • Classification of cyclic groups.
5-6 Permutation groups 5
  • Permutations
  • Cayley's Theorem
7-8 Cosets and Lagrange's Theorem 10
  • Normal subgroups
  • Factor Groups
  • The theorems of Euler and Fermat
9 Homomorphisms 11 The Isomorphism Theorem
10-11 Rings 16
  • Ring homomorphisms
  • Integral domains and fields
  • Maximal and Prime Ideals
12-end Rings of Polynomials 17
  • The Division Algorithm
  • Irreducible Polynomials
  • Solving cubic and quartic equations
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