MAT5183 - Revision history

Jose.iovino: /* vCatalog entryv */

2023-03-26T04:03:52Z

vCatalog entryv

Jose.iovino at 04:03, 26 March 2023

2023-03-26T04:03:36Z

Jose.iovino at 20:19, 19 March 2023

2023-03-19T20:19:23Z

Jose.iovino at 20:19, 19 March 2023

2023-03-19T20:19:02Z

Jose.iovino at 18:51, 19 March 2023

2023-03-19T18:51:35Z

Jose.iovino: Created page with "Special topics in algebra."

2023-03-09T23:25:31Z

Created page with "Special topics in algebra."

New page

Special topics in algebra.

@@ Line 8: / Line 8: @@
-==vCatalog entryv==
+== 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==

@@ Line 1: / Line 1: @@
 Introduction to algebraic codes.
-'''Sample textbook''':
+== Sample textbook ==
 [1] Tzuong-Tsien Moh, ''Introduction to Algebraic Codes'', 2008. Freely available to UTSA students.
@@ Line 8: / Line 8: @@
-'''Catalog entry'''
+==vCatalog entryv==
 ''Prerequisite'': Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.

@@ Line 12: / Line 12: @@
 ''Prerequisite'': Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
-''Contents''
+''Contents'':
 Vector space codes, introduction to rings, ring codes, introduction to algebraic geometry, algebraic geometry codes.

@@ Line 13: / Line 13: @@
 ''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.
@@ Line 28: / Line 23: @@
 ==Topics List==
 {| class="wikitable sortable"
-! Week !! Topic !! Sections from Moh's book !! Subtopics !! Prerequisite
+! Week !! Topic !! Sections from Moh's book !! Prerequisite
 |-
 |  1-2
-|| [[Basic counting principles]]
+|| [[Vector space codes]]
-|| 5.1-5.5
+|| 1
 || 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
-|| [[Covering circuits]]
+|| [[Introduction to algebraic geometry]]
-|| 2.1-2.4
+|| 4
 |-
 |  9-10
-|| [[Trees]]
+|| [[Algebraic curve Goppa  codes]]
-|| 3.1-3.4
+|| 5
-|| Search trees, spanning trees, the Traveling Salesman Problem
+||
 |-
 |  11-13
-|| [[Network algorithms]]
+|| [[Decoding the geometric Goppa codes]]
-|| 4.1-4.5
+|| 6
-|| Shortest path , minimum spanning trees, matching algorithms, transportation problems.
+||
 |}

← Older revision		Revision as of 18:51, 19 March 2023
Line 1:		Line 1:
−	~~Special topics in algebra~~.	+	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''
		+	(1) Basic counting principles: Permutations, combinations, binomial coefficients, arrangements with repetitions.
		+	(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.
		+
		+
		+
		+
		+
		+
		+
		+	==Topics List==
		+	{\| class="wikitable sortable"
		+	! Week !! Topic !! Sections from Moh's book !! Subtopics !! Prerequisite
		+	\|-
		+	\| 1-2
		+	\|\| [[Basic counting principles]]
		+	\|\| 5.1-5.5
		+	\|\| Permutations, combinations, binomial coefficients, arrangements with repetitions
		+	\|\| MAT1313, CS2233/2231, or instructor consent.
		+	\|-
		+	\| 3
		+	\|\| [[Inclusion-Exclusion Principle]]
		+	\|\| 8.1-8.2
		+	\|\| Counting with Venn diagrams.
		+	\|-
		+	\| 4-6
		+	\|\| [[Graph models]]
		+	\|\| 12.1-12.3
		+	\|\| Isomorphism, edge counting, planar graphs.
		+	\|-
		+	\| 7-8
		+	\|\| [[Covering circuits]]
		+	\|\| 2.1-2.4
		+	\|\| Euler circuits, Hamilton circuits, graph colorings, coloring theorems.
		+	\|-
		+	\| 9-10
		+	\|\| [[Trees]]
		+	\|\| 3.1-3.4
		+	\|\| Search trees, spanning trees, the Traveling Salesman Problem
		+	\|-
		+	\| 11-13
		+	\|\| [[Network algorithms]]
		+	\|\| 4.1-4.5
		+	\|\| Shortest path , minimum spanning trees, matching algorithms, transportation problems.
		+	\|}