Difference between revisions of "MAT5183"

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Introduction to algebraic codes.  
 
Introduction to algebraic codes.  
  
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'''Sample textbook''':
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== Sample textbook ==
  
 
[1] Tzuong-Tsien Moh, ''Introduction to Algebraic Codes'', 2008. Freely available to UTSA students.
 
[1] Tzuong-Tsien Moh, ''Introduction to Algebraic Codes'', 2008. Freely available to UTSA students.
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'''Catalog entry'''
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== Catalog entry ==
  
 
''Prerequisite'': Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
 
''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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''Contents'':
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(1) Basic counting principles: Permutations, combinations, binomial coefficients, arrangements with repetitions.
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Vector space codes, introduction to rings, ring codes, introduction to algebraic geometry, algebraic geometry codes.
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(2) The Inclusion-Exclusion principle.
 
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(3) Graph models: Isomorphisms, edge counting, planar graphs.
 
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(4) Covering circuits and graph colorings: Euler circuits, Hamilton circuits, graph colorings, Ramsey's theorem
 
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(5) Network algorithms: Shortest path, minimum spanning trees, matching algorithms, transportation problems.
 
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(6) Order relations: Partially ordered sets, totally ordered sets, extreme elements (maximum, minimum, maximal and minimal elements), well-ordered sets, maximality principles.  
 
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==Topics List==
 
==Topics List==
 
{| class="wikitable sortable"
 
{| class="wikitable sortable"
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! Week !! Topic !! Sections from Moh's book !! Subtopics !! Prerequisite
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! Week !! Topic !! Sections from Moh's book !! Prerequisite
 
|-
 
|-
 
|  1-2   
 
|  1-2   
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|| [[Basic counting principles]]
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|| [[Vector space codes]]
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|| 5.1-5.5
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|| 1
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|| Permutations, combinations, binomial coefficients, arrangements with repetitions
 
 
|| MAT1313, CS2233/2231, or instructor consent.
 
|| MAT1313, CS2233/2231, or instructor consent.
 
|-
 
|-
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|  3   
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|  3-4    
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|| [[Inclusion-Exclusion Principle]]
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|| [[Introduction to ring theory]]
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|| 8.1-8.2
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|| 2
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|| Counting with Venn diagrams.
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||  
 
|-
 
|-
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|  4-6   
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|  5-6   
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|| [[Graph models]]
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|| [[Ring codes]]
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|| 12.1-12.3
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|| 3
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|| Isomorphism, edge counting, planar graphs.
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||
 
|-
 
|-
 
|  7-8   
 
|  7-8   
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|| [[Covering circuits]]
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|| [[Introduction to algebraic geometry]]
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|| 2.1-2.4
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|| 4
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|| Euler circuits, Hamilton circuits, graph colorings, coloring theorems.
 
 
|-
 
|-
 
|  9-10   
 
|  9-10   
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|| [[Trees]]  
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|| [[Algebraic curve Goppa  codes]]  
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|| 3.1-3.4
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|| 5
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|| Search trees, spanning trees, the Traveling Salesman Problem
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||  
 
|-
 
|-
 
|  11-13   
 
|  11-13   
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|| [[Network algorithms]]  
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|| [[Decoding the geometric Goppa codes]]  
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|| 4.1-4.5
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|| 6
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|| Shortest path , minimum spanning trees, matching algorithms, transportation problems.
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||  
 
|}
 
|}

Latest revision as of 22:03, 25 March 2023

Introduction to algebraic codes.

Sample textbook

[1] Tzuong-Tsien Moh, Introduction to Algebraic Codes, 2008. Freely available to UTSA students.



Catalog entry

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

Contents: Vector space codes, introduction to rings, ring codes, introduction to algebraic geometry, algebraic geometry codes.

Topics List

Week Topic Sections from Moh's book Prerequisite
1-2 Vector space codes 1 MAT1313, CS2233/2231, or instructor consent.
3-4 Introduction to ring theory 2
5-6 Ring codes 3
7-8 Introduction to algebraic geometry 4
9-10 Algebraic curve Goppa codes 5
11-13 Decoding the geometric Goppa codes 6
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