MAD 3104 Discrete Math I Section 3: Day by Day

Class Handout

  1. M 28 Aug: Homework 1-10 on relations handout. Defined relations, reflexivity, symmetric, anti-symmetric and transitive. Counter- examples and proofs. Venn diagrams. Vacuously true. [hmmm, the text does not define anti-symmetric. Relations and things in 2.2. Venn diagrams in 2.1. The appendix (mostly A.3) talks about proofs.]
  2. W 30 Aug: Homework 2.1 1-25 odd?, 11-17 on relations handout., and determine which of the relations on the digraph handout. Defined relations, are reflexive, transitive, symmetric and/or anti-symmetric. Equivalence relations and partial orders, Relations as Di-Graphs, Set Theory and review of the homework. [Set Theory in 2.1, Relations 2.2]
  3. W 6 Sep: Homework 2.2. Draw the di-graphs for 1 and 2. Prove or disprove 1-12 and do 13-17. Also read appendix 1 and do problems 1-12. Equivalent relations, partitions and equivalence classes all in 2.2. Quiz 1.
  4. M 11 Sep: Homework A.1 13-31 = 1 mod 2; A.2 1-17 = 1 mod 4; 2.3 = 1 mod 6; Negation, Truth Tables, Congruence. It was from the text for a change.
  5. W 13 Sep: Homework A.1 33-36, 1-16 on the Valid or Not handout. and the two mod 13 problems: 5 to the 1000, and solving [7][m]=[3]. Valid and Invalid reasoning (with Venn diagrams); Converse, Inverse, Contrapositive. Quiz 2.
  6. M 18 Sep: Review day for test 1. Homework due today will be collected next monday. Why do clocks go clockwise?
  7. W 20 Sep: Test 1.
  8. M 25 Sep: Homework 2.5 12, 13, 18, 19; 3.1 1, 5, 19-21, 48; Introduction to graphs, Induction. Test debriefing.
  9. W 27 Sep: Homework 2.5 14, 15, 20, 21; 3.1 26-31, 49, 51, 52. More Induction, more graphs. Quiz 3.
  10. M 2 Oct: Homework 2.3 39-42; 2.5 16, 17, 24, 25; 3.2 1-20; All Graphs with |V| = 5; All Trees with |V| = 6.
  11. W 4 Oct: Opal cancels class.
  12. M 9 Oct: Homework: More Proofs Handout 2, 6, 7; 4.1 1-17; All Trees with |V| = 7.
  13. W 11 Oct: Homework: 2.4 65-68; More Proofs Handout 3, 12; 4.2 1-8. BFS Trees, rooted trees, ordered trees. Quiz 4.
  14. M 16 Oct: Homework: 2.6 1-31=1 mod 4; 3.2 35, 37, 40; 3.3 1-15odd More proofs handout 4, 10; 4.3 1. Dijkstra's, Prim's
  15. W 18 Oct: Homework: 2.6 31,32; 3.2 48-50; 4.3 2-4, 22-25; 4.4 1-6 (find DFS spanning tree as well). Kruskal's, DFS. Quiz 5
  16. M 23 Oct: Review for test2; Homework due today will be collected 30 Oct.
  17. W 25 Oct: Test 2
  18. M 30 Oct: Strong Induction. Homework: Prove by Strong induction on the number of edges, a tree with n edges has n + 1 veritces; 3.2: 53, 54; 3.3 14
  19. W 1 Nov: The Almost Tree Proof Page And Quiz 6 Homework: Prove by Strong induction on the number of vertices, a tree with n vertices has n - 1 edges; Almost trees 1a iff 1b; A.3 13, 14.
  20. M 6 Nov: Binary Search Trees, Preorder, Postorder, Inorder, Infix, Postfix, Prefix. Homework: Prove by Weak induction on the number of vertices, a tree with n vertices has n - 1 edges; Almost trees 1a,b,c,d are equivalent; Prove by contradiction: a non-trivial tree with n vertices, n - 1 edges has a vertex of degree at most 1; 4.6 problems 1-25 = 1 mod 6.
  21. W 8 Nov: Graph coloring, more proofs. SIRS Homework: Almost trees problem 2; 3.4 1-25 odd; 4.6 47-57 odd, 67; 4.7 48, 51, 52.
  22. M 13 Nov: Level order numbering: Homework Almost trees problems 4-6; Find the smallest binary tree containing vertices with level order numbers 11, 103, and 106; Find the left child, level and parent of the vertex with level-order number 135.
  23. W 15 Nov: Homework Almost trees #7, 4.7 1-33 odd Quiz 7.
  24. M 20 Nov: Homework Almost trees #7, 3.5 1-39 odd
  25. W 21 Nov: Homework 4.5 1 - 31? odd Quiz 8.
  26. M 27 Nov: Review Homework
  27. W 29 Nov: Test 3.
  28. M 4 Dec: Homework psuedo code Prim's Algorithm
  29. W 6 Dec: Last Day of classes
  30. F 15 Dec: 12:30-2:30 Final
last update 4 Dec 95.