Difference between revisions of "MAT2313"
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''Prerequisite'': Algebra and Number Systems [[MAT1313]], 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]]. | + | ''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 | ''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). | + | ''Sample textbooks'': Alan Tucker, Applied Combinatorics (6th ed). Wiley (2012). |
==Topics List== | ==Topics List== | ||
Latest revision as of 15:52, 21 January 2025
Combinatorics and Probability - MAT2313
Catalog entry
Prerequisite: Algebra and Number Systems MAT1313, or Discrete Mathematical Structures (CS 2233/2231), or instructor consent. 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
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.
