MAT2313 - Revision history

Jose.iovino: /* Catalog entry */

2025-01-21T21:52:57Z

Catalog entry

Jose.iovino: /* Combinatorics and Probability - MAT2313 */

2025-01-21T21:51:46Z

Combinatorics and Probability - MAT2313

Jose.iovino: /* Combinatorics and Probability - MAT2313 */

2025-01-21T21:49:48Z

Combinatorics and Probability - MAT2313

Jose.iovino: /* Combinatorics and Probability - MAT2313 */

2025-01-21T21:28:35Z

Combinatorics and Probability - MAT2313

Eduardo.duenez: /* Topics List */

2023-08-14T22:49:38Z

Topics List

Juan.gutierrez3 at 03:48, 26 April 2023

2023-04-26T03:48:43Z

Juan.gutierrez3: Changed content from Probability to combinatorics

2023-04-26T03:41:28Z

Changed content from Probability to combinatorics

Jose.iovino: /* Sample textbooks */

2023-03-26T03:02:29Z

Sample textbooks

Jose.iovino: /* Topics List */

2023-03-26T03:01:35Z

Topics List

Jose.iovino: /* Topics List */

2023-03-26T02:52:48Z

Topics List

@@ Line 4: / Line 4: @@
 ''Prerequisite'': Algebra and Number Systems [[MAT1313]], or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
-''Corequisite'': [[MAT1224]].
+''Corequisite'': [[MAT1224]]. (3-0) 3 Credit Hours.
 ''Content'': Basic counting principles. Permutations and combinations. Binomial and multinomial coefficients. Pigeonhole and inclusion-exclusion principles. Graphs, colorings, planarity. Eulerian and Hamiltonian graphs. Recurrence relations. Generating functions.  3 Credit Hours
 ''Sample textbooks'': Alan Tucker, Applied Combinatorics (6th ed). Wiley (2012).
 ==Topics List==

@@ Line 6: / Line 6: @@
 ''Corequisite'': [[MAT1224]].
-''Content'': Basic counting principles. Permutations and combinations. Binomial and multinomial coefficients. Pigeonhole and inclusion-exclusion principles. Graphs, colorings, planarity. Eulerian and Hamiltonian graphs. Recurrence relations. Generating functions. Prerequisites: MAT1224 Calculus II and MAT 1313 Algebra and Number Systems. 3 Credit Hours
+''Content'': Basic counting principles. Permutations and combinations. Binomial and multinomial coefficients. Pigeonhole and inclusion-exclusion principles. Graphs, colorings, planarity. Eulerian and Hamiltonian graphs. Recurrence relations. Generating functions.  3 Credit Hours
 ''Sample textbooks'': Alan Tucker, Applied Combinatorics (6th ed). Wiley (2012).

@@ Line 3: / Line 3: @@
 == Catalog entry ==
-''Prerequisite'': Algebra and Number Systems [[MAT 1313]], or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
+''Prerequisite'': Algebra and Number Systems [[MAT1313]], or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
 ''Corequisite'': [[MAT1224]].

← Older revision		Revision as of 21:28, 21 January 2025
Line 1:		Line 1:
	= Combinatorics and Probability - MAT2313=		= Combinatorics and Probability - MAT2313=
		+
		+	== Catalog entry ==
		+
		+	''Prerequisite'': Algebra and Number Systems [[MAT 1313]], or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
	''Corequisite'': [[MAT1224]].		''Corequisite'': [[MAT1224]].

@@ Line 25: / Line 25: @@
 Week 8: Trees. Colorings. Planarity.
-Week 9: Review. First midterm exam.
+Week 9: Review. Second midterm exam.
 Week 10: Generating functions. The Binomial Theorem. Partitions.

@@ Line 1: / Line 1: @@
-Foundations of Mathematics (3-0) 3 Credit Hours
+= Combinatorics and Probability=
 ==Course Catalog==
 ''Corequisite'': [[MAT1224]].
-''Content'': Permutations, combinations, multinational coefficients, inclusion/exclusion principle, axioms of probability, conditional probability, Bayes formula, independent events, discrete random variables, expected value,m variance, discrete random variables (Bernoulli, Binomial, Poisson, geometric, hypergeometric and Zeta random variables), continuous random variables (uniform, normal and other distributions), joint distributions, properties of expectations, limit theorems (Chebyshev's inequality, Central Limit Theorem, Law of Large Numbers)) Generally offered: Fall, Spring, Summer.
+''Content'': Basic counting principles. Permutations and combinations. Binomial and multinomial coefficients. Pigeonhole and inclusion-exclusion principles. Graphs, colorings, planarity. Eulerian and Hamiltonian graphs. Recurrence relations. Generating functions. Prerequisites: MAT1224 Calculus II and MAT 1313 Algebra and Number Systems.
 ==Description==
 Introduction to the theory of probability, through the study of discrete and continuous random variables.
 ==Sample textbooks==
-* A ''Probability Course for the Actuaries: A Preparation for Exam P/1'', by Marcel B. Finan. Freely available [https://people.cas.uab.edu/~pjung/teaching_files/ProbabilityForActuaries.pdf online].
+Week 6: Graphs and multigraphs.
-==Topics List==
+Week 7: Eulerian and Hamiltonian graphs.
-{| class="wikitable sortable"
-! Week !! Topic !! Sections from Finan's book !! Subtopics
+Week 8: Trees. Colorings. Planarity.
-|-
-|  1-2
+Week 9: Review. First midterm exam.
-|| [[Populations and Samples]]
-|| Chapters 1-2
+Week 10: Generating functions. The Binomial Theorem. Partitions.
-|-
+Week 11: Recurrence relations. Linear recurrences.
-|}
+Week 12: Solving recurrences by generating functions.
-==See also==
+Week 13: Exponential generating functions. Nonlinear recurrences.
-* [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/ UTSA Undergraduate Mathematics Course Descriptions]
+Week 15: Review.

@@ Line 52: / Line 52: @@
 * Expected Value of a Discrete Random Variable
 * Expected Value of a Function of a Discrete Random Variable
 * Variance and Standard Deviation
 |-
-|  5
+|  9-10
-||
+|| [[Continuous Random Variables]]
-||
+|| Chapter 6
 ||
-|-
+* Distribution Functions
-|  6
+* Expectation, Variance and Standard Deviation
-||
+* The Uniform Distribution Function
-||
+* Normal Random Variables
-||
+* Exponential Random Variables
-|-
+* Gamma and Beta Distributions
-|  7
+* The Distribution of a Function of a Random Variable
-||
 |-
 |  11
-||
+|| [[Joint Distributions]]
-||
+|| Chapter 7
 ||
 |-
 |  12
-||
+|| [[Properties of Expectation]]
-||
+|| Chapter 8
 ||
-|-
+* Expected Value of a Function of Two Random Variables . . . . . 351
-|  13
+* Covariance, Variance of Sums, and Correlations . . . . . . . . . 362
-||
+* Conditional Expectation . . . . . . . . . . . . . . . . . . . . . . 376
-||
+* Moment Generating Functions
 |-
-|  33
+|  13-14
-||
+|| [[Limit Theorems]]
-||
+|| Chapter 9
 ||
 |}

@@ Line 35: / Line 35: @@
 * Probability and Counting Techniques
 |-
-|  5-6
+|  5
 || [[Conditional Probability and Independence]]
 || Chapter 4
@@ Line 44: / Line 44: @@
 * Odds and Conditional Probability
 |-
-|  4
+|  6-8
-||
+|| [[Discrete Random Variables]]
-||
+|| Chapter 5
 ||
 |-
 |  5