Difference between revisions of "MAT2313"

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Foundations of Mathematics (3-0) 3 Credit Hours
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= Combinatorics and Probability - MAT2313=
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==Course Catalog==
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''Corequisite'': [[MAT1224]].
  
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3 Credit Hours. Corequisite: [[MAT1224]]. 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.  
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''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
  
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==Description==
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''Sample textbooks'': Alan Tucker, Applied Combinatorics (6th ed). Wiley (2012).
  
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Introduction to the theory of probability, through the study of discrete and continuous random variables.
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==Topics List==
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Course outline:
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Week 1: Finite sets, strings, enumeration, the addition and product rules.
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Week 2: Combinations, permutations.
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Week 3: Binomial and multinomial coefficients.
  
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==Text==
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Week 4: The Pigeonhole Principle. The Inclusion-Exclusion Formula, derangements, the Euler ɸ function (totient).
  
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* Modern Mathematical Statistics with Applications (Springer Texts in Statistics). Jay L. Devore and Kenneth N. Berk. Second Edition.
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Week 5: Review. First midterm exam.
  
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==Topics List==
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Week 6: Graphs and multigraphs.
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! Lecture !! Section !! Prerequisite Skills !! Student Learning Outcomes
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Week 7: Eulerian and Hamiltonian graphs.  
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Week 8: Trees. Colorings. Planarity.
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|| [[Populations and Samples]]
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Week 9: Review. Second midterm exam.
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Week 10: Generating functions. The Binomial Theorem. Partitions.
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Week 11: Recurrence relations. Linear recurrences.
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Week 12: Solving recurrences by generating functions.
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==See also==
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Week 13: Exponential generating functions. Nonlinear recurrences.
  
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* [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/ UTSA Undergraduate Mathematics Course Descriptions]
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Week 15: Review.

Latest revision as of 16:49, 14 August 2023

Combinatorics and Probability - MAT2313

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

Sample textbooks: Alan Tucker, Applied Combinatorics (6th ed). Wiley (2012).

Topics List

Course outline:

Week 1: Finite sets, strings, enumeration, the addition and product rules.

Week 2: Combinations, permutations.

Week 3: Binomial and multinomial coefficients.

Week 4: The Pigeonhole Principle. The Inclusion-Exclusion Formula, derangements, the Euler ɸ function (totient).

Week 5: Review. First midterm exam.

Week 6: Graphs and multigraphs.

Week 7: Eulerian and Hamiltonian graphs.

Week 8: Trees. Colorings. Planarity.

Week 9: Review. Second midterm exam.

Week 10: Generating functions. The Binomial Theorem. Partitions.

Week 11: Recurrence relations. Linear recurrences.

Week 12: Solving recurrences by generating functions.

Week 13: Exponential generating functions. Nonlinear recurrences.

Week 15: Review.

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