Engr 3422 Discrete Mathematics for Engineering. 2004 Notes and Slides.

These are also available on UNIX at ~theo/pub/dm and on the windows network at L:\courses\3422 (where L is mapped to \\Moe\local).

Exams and quizzes

• Quiz 0 solution.
• Quiz 1 solution. (Correction Oct 18. Q1, "B intersection C" should be "B union C".)
• Midterm solution.
• Quiz 2 solution
• Quiz 3 solution

Problem sets and solutions

• Problem set 0 Due Sept 16 Solution
• Problem set 1 Due Sept 20 Solution
• Problem set 2 Due Sept 27 Solution Slides
• Problem set 3. Due Oct 4. Solution.
• Problem set 4. Due Oct 13. Solution.
• Problem set 5. Due Oct 18. Solution
• Problem set 6. Due Oct. 25. Solution
• Problem set 7. Due Nov 1. Solution.
• Problem set 8. Due Nov 9. Solution Slides
• Problem set 9. Due Nov 15. Solution Slides
• Problem set 10. Due Nov 22. Solution. Slides.
  • Correction to solution: In Q0(b), graph(R^-1) should be {(0,0),(0,1)} .
• Problem set 11. Due Nov 29. Solution. Slides
  • Corection to solution. In Part 1, question 3, the answer should be 9, not 13. Fixed Nov 29.

Lecture Slides

Note that 2up versions are printed two pages to the sheet.

Slide set 0 -- Introduction (2up)

Module 0. Logic and sets.

• Slide set 1 -- Propositional Logic (2up)
  • Error: On page 33 (Duality), the example law wasn't a law! Please reprint this page. Fixed on Sept 20.
  • Error: On page 37. The definition of biconditional was incorrect. It should be the same as on page 15. Fixed Sep 23.
• Cards Results
  • Error: In the result, I said, "P only if Q." I meant, "Q only if P." Fixed on Sept 20.
• Application of propositional logic (2up)
• Slide set 2 -- Sets (2up)
• Some applications of sets (2up)
• Slide set 3 -- Predicate logic (2up)
  • On slide 5, "103" should be "102" in both places. Fixed Sept30.
• Some application of predicates (2up)

Module 1. Integers, Mathematical Reasoning, Induction, and Recurrences

• Slide set 4 -- Division and Proof techniques (2up)
  • Errors. fixed Oct 13.
    • Page 14. Fixed section from "Underlying this proof technique" to "thought".
  Page 17. Transitivity should be "If a|b and b|c then a|c."
• Slide set 5 -- Prime Numbers (2up)
• Application: Public key cryptography -- An application of modular arithmetic (2up)
• Slide set 6 -- Induction (2up)
• Application: Correctness of loops and recursive subroutines -- Applications of induction (2up)
• Slide set 7 -- Linear Homogeneous Reccurence Relations of Degree 2. (2up)
• Errors fixed Nov 3
  • Page 12. r₀ should be r₂ in two places.
  • Page 16 (1-phi)² should be (1-phi)ⁿ
• Application: The maximum height of an AVL tree (2up)

Module 2. Structures: Functions, Relations, Graphs, Automata

• Slide set 8 -- Functions and Relations (2up)
• Application -- Relations for System Specification. (2up)
• Slide set 9 -- Graphs (2up)
  • Correction: On page 17, the last panel of the last figure had the wrong labels on the vertices. Fixed Nov 29.
• Slide set 10 -- Automata (2up)

Summary

• Summary (2up)