Difference between revisions of "MAT5183"

From Department of Mathematics at UTSA
Jump to navigation Jump to search
Line 13: Line 13:
  
 
''Contents''
 
''Contents''
−
(1) Basic counting principles: Permutations, combinations, binomial coefficients, arrangements with repetitions.
+
Vector space codes, introduction to rings, ring codes, introduction to algebraic geometry, algebraic geometry codes.  
−
(2) The Inclusion-Exclusion principle.
 
−
(3) Graph models: Isomorphisms, edge counting, planar graphs.
 
−
(4) Covering circuits and graph colorings: Euler circuits, Hamilton circuits, graph colorings, Ramsey's theorem
 
−
(5) Network algorithms: Shortest path, minimum spanning trees, matching algorithms, transportation problems.
 
−
(6) Order relations: Partially ordered sets, totally ordered sets, extreme elements (maximum, minimum, maximal and minimal elements), well-ordered sets, maximality principles.  
 
  
  
Line 28: Line 23:
 
==Topics List==
 
==Topics List==
 
{| class="wikitable sortable"
 
{| class="wikitable sortable"
−
! Week !! Topic !! Sections from Moh's book !! Subtopics !! Prerequisite
+
! Week !! Topic !! Sections from Moh's book !! Prerequisite
 
|-
 
|-
 
|  1-2   
 
|  1-2   
−
|| [[Basic counting principles]]
+
|| [[Vector space codes]]
−
|| 5.1-5.5
+
|| 1
−
|| Permutations, combinations, binomial coefficients, arrangements with repetitions
 
 
|| MAT1313, CS2233/2231, or instructor consent.
 
|| MAT1313, CS2233/2231, or instructor consent.
 
|-
 
|-
−
|  3   
+
|  3-4    
−
|| [[Inclusion-Exclusion Principle]]
+
|| [[Introduction to ring theory]]
−
|| 8.1-8.2
+
|| 2
−
|| Counting with Venn diagrams.
+
||  
 
|-
 
|-
−
|  4-6   
+
|  5-6   
−
|| [[Graph models]]
+
|| [[Ring codes]]
−
|| 12.1-12.3
+
|| 3
−
|| Isomorphism, edge counting, planar graphs.
+
||
 
|-
 
|-
 
|  7-8   
 
|  7-8   
−
|| [[Covering circuits]]
+
|| [[Introduction to algebraic geometry]]
−
|| 2.1-2.4
+
|| 4
−
|| Euler circuits, Hamilton circuits, graph colorings, coloring theorems.
 
 
|-
 
|-
 
|  9-10   
 
|  9-10   
−
|| [[Trees]]  
+
|| [[Algebraic curve Goppa  codes]]  
−
|| 3.1-3.4
+
|| 5
−
|| Search trees, spanning trees, the Traveling Salesman Problem
+
||  
 
|-
 
|-
 
|  11-13   
 
|  11-13   
−
|| [[Network algorithms]]  
+
|| [[Decoding the geometric Goppa codes]]  
−
|| 4.1-4.5
+
|| 6
−
|| Shortest path , minimum spanning trees, matching algorithms, transportation problems.
+
||  
 
|}
 
|}

Revision as of 14:19, 19 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
Retrieved from "https://mathresearch.utsa.edu/wiki/index.php?title=MAT5183&oldid=4849"