MATH 213 - Basic Discrete Mathematics

Office hours: 3:00-4:00 PM MF or by appointment in 222A Illini Hall

Syllabus (exam dates are subject to change)

Announcements

• The extra final review will be Thursday, Dec. 8 from 5 p.m. in 141 Altgeld Hall.
• The extra review for exam 3 will be on Thursday, Dec. 1 from 5 p.m. in 141 Altgeld Hall.
• Exam 3 is on Friday, Dec. 2nd!
• Office hours are now WF 3:00-5:00.
• The extra review for exam 2 will be on Thursday, Oct. 27 from 5 p.m. in 141 Altgeld Hall.
• Exam 2 is on Friday, October 28th! (Ignore the date on the syllabus.)
• The big-O problem on exam 1 asked you to prove a false statement! All students will be awarded full points on this problem. Come see me if you haven't already had your grade fixed.

Homeworks

• homework 9:
  • 9.5: # 9, 26, 46, 65
  • 9.7: # 5, 6, 17, 26, 29
  • 9.8: # 8, 14, 36
• homework 8:
  • 9.2: # 18, 36adegh, 44, 53, 58
  • 9.3: # 10, 28, 38
  • 9.4: # 20, 26, 28, 41
• homework 7:
  • 7.1: # 6abeh, 8dfg, 24, 26, 28, 44
  • 7.2: # 4(ad), 7, 11, 12, 30
• homework 6:
  • 6.1: # 4, 6, 16, 29, 41
  • 6.2: # 8, 11, 23, 24, 34
  • 6.4: # 4, 7, 13, 19, 22
• homework 5:
  • 5.3: # 2, 14, 16, 24, 29, 34, 40
  • 5.4: # 10, 14, 20, 28, 32, 38
• homework 4:
  • 5.1: # 1, 4, 12, 26, 35, 38, 44
  • 5.2: # 2, 4, 16, 17, 29, 42
• homework 3:
  • 4.1: # 4, 6, 25, 35, 50, 54
  • 4.2: # 4, 8, 12, 23, 30, 38
• homework 2:
  • 3.1: # 24, 32, 60
  • 3.2: # 12, 20, 30, 36, 51
  • 3.3: # 24, 25
• homework 1:
  • 2.1: # 2, 18, 20, 24
  • 2.2: # 12, 20, 26, 30, 32
  • 2.3: # 2, 12, 16, 36, 70 (bc)

Class Schedule

• Thu, 12/8: (5 p.m.) Optional review for final.
• Wed, 12/7: Review for final exam.
• Mon, 12/5: Return and discuss exam 3. Begin review for final exam.
• Fri, 12/2: Exam 3.
• Thu, 12/1: (5 p.m.) Optional reivew for exam 3.
• Wed, 11/30: Review for exam 3.
• Mon, 11/28: Minimum-weight paths and Hamiltonian cycles. (Section 9.6)
• Fri, 11/18: Minimum-weight spanning trees: Prim's and Kruskal's algorithim. (Section 10.4 and 10.5)
• Wed, 11/16: Trees: spanning trees. Minimum-weight spanning trees. (Section 10.4 and 10.5)
• Mon, 11/14: Planar graphs: Kuratowski and Wagner Theorems. Graph colorings: Four Color Theorem. (Section 9.7 and 9.8)
• Fri, 11/11: Graph theory: Planar graphs: Euler characteristic, number of edges in a planar graph. (Section 9.7)
• Wed, 11/9: Graph theory: Hamiltonian cycles and paths: Dirac's Theorem, Ore's Theorem. Proof of Dirac's. (Section 9.5)
• Mon, 11/7: Graph theory: adjacency matrix, incidence matrix, isomorphic graphs, Euler circuits (Section 9.3 and 9.5)
• Fri, 11/4: More graph theory: degree sequence, subgraphs, complement, connectivity. (Section 9.4)
• Wed, 11/2: Introduction to graph theory. It's Greek to me graph. (Section 9.1 and 9.2)
• Mon, 10/31: Return exam 1 and go over solutions.
• Fri, 10/28: Exam 2.
• Wed, 10/26: Review for exam 2. Discuss some problems from homework 7.
• Mon, 10/24: Inclusion-exclusion: Proof of equation and examples. (Section 7.5 and 7.6)
• Fri, 10/21: Solving recurrence relations: linear homogeneous recurrence relations with constant coefficients (Section 7.2)
• Wed, 10/19: Recurrence relations: classic examples. (Section 7.1)
• Mon, 10/17: Class canceled.
• Fri, 10/14: Proof of R(3,3)=6 and continue lower bound on R(k,k). (Section 6.2)
• Wed, 10/12: Probabilistic method: lower bound on R(k,k). (Section 6.2)
• Mon, 10/10: Probability: expectation, linearity of expectation, expectation of successes in n Bernoulli trials (Section 6.4)
• Fri, 10/7: Probability: distributions, uniform distribution, complement, conditional probability, Bernoulli trials, binomial distribution. (Section 6.2)
• Wed, 10/5: Probability: basics and Monty Hall problem. (Section 6.1)
• Mon, 10/3: Return Exam 1 and go over solutions.
• Fri, 9/30: Generalized permutations and combinations. How do we count things with repetition? (Section 5.5)
• Wed, 9/28: Exam 1
• Tue, 9/27: Optional review in 141 Altgeld from 5:00 PM
• Mon, 9/26: In-class review for exam 1.
• Fri, 9/23: More on the binomial theorem. (Section 5.4)
• Wed, 9/21: The binomial theorem. (Section 5.4)
• Mon, 9/19: Permutations and combinations. (Section 5.3)
• Fri, 9/16: The pigeonhole principle. (Section 5.2)
• Wed, 9/14: Basic counting: sum and product rule, simple inclusion-exclusion. (Section 5.1)
• Mon, 9/12: Strong induction. (Section 4.2)
• Fri, 9/9: More on induction. (Section 4.1)
• Wed, 9/7: Induction. (Section 4.1)
• Mon, 9/5: LABOR DAY - NO CLASS
• Fri, 9/2: More on the growth of functions (Section 3.2)
• Wed, 8/31: The growth of functions (Section 3.2)
• Mon, 8/29: Algorithms. (Section 3.1)
• Fri, 8/26: Function basics. (Section 2.3)
• Wed, 8/24: Set operations. (Section 2.2)
• Mon, 8/22: Syllabus. Introduction to sets. (Section 2.1)