Date Summary Assignments and Handouts
2017/5/17, Wed. Introduction to the course. Sec. 1.1 Variables.
2017/5/18, Thu.

Sec. 2.1--compound statements, logical operators (not, and, or), truth table, logical equivalent, tautology and contradiction, properties of operators.

Sec. 2.2--conditional statements, if-then operator.
2017/5/19, Fri.

Sec. 2.2--converse, inverse, contrapositive, only if, biconditional (if and only if, iff), necessary and sufficient conditions.

Sec. 2.3--argument forms, checking an argument form is valid or invalid, rules of inference
  • Slides used in class: Sec. 2.3
  • Checklist notes: Notes 2
  • Optional self-check exercises: pp. 37, Exercise Set 2.1, exercises 6,8,15,20,31,46,53; pp. 49, Exercise Set 2.2, exercises 9,10,14,19,29,34,45,49; pp. 61, Exercise Set 2.3, exercises 7,12,37(similar to Example 2.3.8). Solution in addition to the appendix of the textbook.
2017/5/22, Mon.

Extra--examples for "if," "only if," and "if and only if"; example for "or v.s. exclusive or"; example for negation of mathematicaly inequalities.

Sec. 2.3 (continued)--contradiction rules, fallacies, converse error, inverse error.

Sec. 2.4--From truth tables to statement forms, digital logic circuits and gates, Boolean variables and expressions, DNF and CNF, NAND and NOR gates.

  • Slides used in class: Extra 1, Sec. 2.4
  • The solution for Quiz 1
  • Homework 1 is released: HW1, which is due on Thursday, 5/25, 1:15 PM in class.
  • Optional self-check exercises: pp. 61, Exercise Set 2.3, exercises 27,36; pp. 76, Exercise Set 2.4, exercises 12,17,18,26,33,34. Solution in addition to the appendix of the textbook.
2017/5/23, Tue.

Sec. 3.1--predicates, quantified statements, universal and existential quantifiers, truth and falsity of quantified statements.

Sec. 3.2--negations of quantified statements, relation among the universal/existential quantifiers and the and/or logic operators, universal conditional statements.

Sec. 3.3--multiple quantifiers, order of multiple quantifiers.
  • Slides used in class: Sec. 3.1, Sec. 3.2, Sec. 3.3
  • Checklist notes: Notes 3
  • Optional self-check exercises: pp. 106, Exercise Set 3.1, exercises 4,10,14,19,32; pp. 116, Exercise Set 3.2, exercises 3,4,17,27,42; pp. 129, Exercise Set 3.3, exercises 5,7,14,22. Solution in addition to the appendix of the textbook.
2017/5/24, Wed.

Sec. 3.3 (continued)--negations of statements with multiple quantifiers, formal logical notation.

Sec. 3.4--arguments with quantified statements.

Extra--puzzles solved by truth table, reasoning by argument forms
  • Slides used in class: Sec. 3.4, Extra 2
  • Homework 2 is released: HW2, which is due on Tuesday, 5/30, 1:15 PM in class.
  • Optional self-check exercises: pp. 129, Exercise Set 3.3, exercises 13,14,21,55,56,57,58; pp. 142, Exercise Set 3.4, exercises 8,9,23,25,33.Solution in addition to the appendix of the textbook.
2017/5/25, Thu.

Extra (continued)--transforming "unless" and "No" (or "None").

Sec 4.1--introduction to proof, direct proofs: construct an example (prove "there exists"), counterexample (disprove "for all"), exhaustion (prove "for all"), generalizing from the generic particular (prove "for all"), disproving "there exists" equivalent to proving its negation which is a "for all," proof writing directions, common mistakes.

Sec. 4.2--rational numbers.
  • Slides used in class: Sec. 4.1, Sec. 4.2
  • Homework 1 solution released.
  • Optional self-check exercises: pp. 161, Exercise Set 4.1, exercises 6,11,19,37,38,39,41. Solution in addition to the appendix of the textbook.
2017/5/26, Fri.

Sec. 4.2 (continued)--direct proofs: properties of rational numbers.

Sec. 4.3--direct proofs: properties of divisibilities, the Unique Factorization of Integers Theorem.

Sec. 4.4--direct proofs: division into cases and the Quotient-Remainder Theorem.
  • Slides used in class: Sec. 4.3, Sec. 4.4
  • Optional self-check exercises: pp. 168, Exercise Set 4.2, exercises 6,31; pp. 178, Exercise Set 4.3, exercises 15,38,41,47; pp. 189, Exercise Set 4.4, exercises 5,23,29,49. Solution in addition to the appendix of the textbook.
2017/5/29, Mon. No classes held, holiday.
2017/5/30, Tue.

Sec. 4.6--indirect proofs: proof by contradiction, proof by contraposition.

Sec. 4.7--examples for proof by contradiction: the irrationality of sqrt(2), there are infinitely many prime numbers, the uniqueness part of the Quotient-Remainder Theorem.

Sec. 5.1--sequence, explicit formulas, summation notation, product notation.
  • Slides used in class: Sec. 4.6, Sec. 4.7, Sec. 5.1
  • Homework 3 is released: HW3, which is due on Friday, 6/2, 1:15 PM in class.
  • Optional self-check exercises: pp. 206, Exercise Set 4.6, exercises 23,26,30; pp. 242, Exercise Set 5.1, exercises 19,20,40,43.
2017/5/31, Wed.

Sec. 5.1 (continued)--telescope sum, factorial, n choose r notation.

Sec. 5.2--mathematical induction.
  • Slides used in class: Sec. 5.2
  • Homework 2 solution released.
  • Optional self-check exercises: pp. 256, Exercise Set 5.2, exercises 3,5,13,33.
2017/6/1, Thu.

Sec. 5.2 (continued)--mathematical induction, examples on proof by induction.

Sec. 5.4--strong mathematical induction.
  • Slides used in class: Sec. 5.4
  • The solution for Quiz 2
  • Optional self-check exercises: pp. 266, Exercise Set 5.3, exercises 8,16; pp. 277, Exercise Set 5.4, exercises 4,17.
2017/6/2, Fri.

Sec. 5.4 (continued)--strong mathematical induction, more examples on proof by induction.

Secs. 5.6 and 5.7--defining sequences recursively, solving recurrence relations (guess first and then prove by induction).
  • Slides used in class: Secs. 5.6 and 5.7
  • Homework 4 is released: HW4, which is due on Monday, 6/5, 1:15 PM in class.
  • Homework 3 solution released.
  • Optional self-check exercises: pp. 302, Exercise Set 5.6, exercises 11,26,27; pp. 314, Exercise Set 5.7, exercises 3,28,5,30,43.
2017/6/5, Mon.

Secs. 1.2,6.1--sets, union, intersection, difference, complement, empty set, partitions of sets, power sets, tuples, Cartesian products.

Secs. 6.2--prove a subset relation, set identities (Thm. 6.2.2), prove set identities.
  • Slides used in class: Sec 6.1
  • Homework 4 solution released.
  • Checklist notes: Notes 4
  • Optional self-check exercises: pp. 349, Exercise Set 6.1, exercises 1,3,5,10,13,27,31,35. Solution in addition to the appendix of the textbook.
2017/6/6, Tue.

Secs. 6.2 (continued)--prove that a set is empty; relations between set properties and logical equivalences (Table 6.4.1 from Sec. 6.4).

Midterm Exam review.
  • Slides used in class: Sec 6.2
  • Homework 5 is released: HW5, which is due on Friday, 6/9, 1:15 PM in class.
  • Optional self-check exercises: pp. 365, Exercise Set 6.2, exercises 8,13,25,29.
2017/6/7, Wed. Midterm Exam, 1:15 PM - 2:45 PM. The exam covers and only covers Chapters 2,3,4,5, i.e., logics and proofs (lectures on or before 6/2). The exam is closed-book; however, one cheat sheet is allowed. The cheat sheet must be no larger than a US-letter-size paper. You can write or print anything you want on one or both sides of this cheat sheet, but stickers are not allowed.
2017/6/8, Thu.

Midterm Exam recap.

Sec. 1.3--the language of relations and functions.

Sec. 7.1--definition of functions; domain, co-domain, range, image, preimage(inverse image), equality of functions.
  • Slides used in class: Sec 1.3, Sec 7.1.
  • Checklist notes: Notes 5
  • Optional self-check exercises: pp. 393, Exercise Set 7.1, exercises 1,13,33,35,38,41,42,43,44. Solution in addition to the appendix of the textbook.
2017/6/9, Fri.

Sec. 7.2--injective (one-to-one), surjective (onto), and bijective (one-to-one correspondence) functions; inverse functions.

Extra--math review: exponential functions and logarithmic functions; composition of functions.
  • Slides used in class: Sec 7.2, Extra 3.
  • A figure to illustrate injections, surjections, and bijection.
  • Homework 5 solution released.
  • Homework 6 is released: HW6, which is due on Tuesday, 6/13, 1:15 PM in class.
  • Optional self-check exercises: pp. 413, Exercise Set 7.2, exercises 6,15,16,21,26.
2017/6/12, Mon.

Sec. 8.1--relations on sets, n-nary relation, binary relations on a set, directed graphs.

Sec. 8.2--reflexivity, symmetry, transitivity.

Sec. 8.3--equivalence relations, relations and partitions, equivalence classes.
  • Slides used in class: Sec 8.1, Sec 8.2, Sec 8.3.
  • Checklist notes: Notes 6
  • The solution for Quiz 3
  • Optional self-check exercises: pp. 448, Exercise Set 8.1, exercises 10,15; pp. 458, Exercise Set 8.2, exercises 1,3,9,11,28,31; pp475, Exercise Set 8.3, exercises 7,20,28.
2017/6/13, Tue.

Extra (partial Sec. 8.4)--modular arithmetic.

Extra (partial Sec. 8.5)--antisymmetry, partial order, total order, topological sorting.
  • Slides used in class: Extra 4.
  • Homework 6 solution released.
  • Homework 7 is released: HW7, which is due on Friday, 6/16, 1:15 PM in class.
2017/6/14, Wed.

Sec. 9.1--equally likely outcomes, sample space, event, discrete probability.

Secs. 9.2,9.3--multiplication rule, addition rule, difference rule, inclusive/exclusive rule.

Secs. 9.2,9.5--combinations; permutations.
  • Slides used in class: Sec 9.1, Secs 9.2,9.3,9.5.
  • Checklist notes: Notes 7
  • Optional self-check exercises: pp. 536, Exercise Set 9.2, exercises 8,9,19,34,41; pp. 549, Exercise Set 9.3, exercises 4,16,; pp581, Exercise Set 9.5, exercises 6,19.
2017/6/15, Thu.

Sec. 9.8--probability formulas, expected value

Sec. 9.9--conditional probability, Bayes' theorem, independent event.
  • Slides used in class: Secs 9.8 and 9.9.
  • The solution for Quiz 4
  • Homework 8 is released: HW8, which is due on Monday, 6/19, 1:15 PM in class.
  • Optional self-check exercises: pp. 610, Exercise Set 9.8, exercises 14,19; pp. 622, Exercise Set 9.9, exercises 11,14.
2017/6/16, Fri.

Sec. 9.9 (continued)--example for conditional probability and Bayes' Theorem.

Secs. 9.4, 9.7 (on whiteboard)--pigeonhole principle, Pascal's Triangle, Binomial Theorem.

Secs. 10.1, 10.2, 10.5--graphs, paths, circuits, trees.
  • Slides used in class: Sec. 10.1, 10.2, 10.5, Extra 5.
  • Homework 7 solution released.
  • Optional self-check exercises: pp. 539, Exercise Set 10.1, exercises 5,8; pp. 657, Exercise Set 10.2, exercises 1.
2017/6/19, Mon.

Final Exam review.
2017/6/20, Tue. No classes held, reading day.
2017/6/21, Wed. No classes held, exam day (for other courses).
2017/6/22, Thu. Final Exam, 11:30 AM - 2:30 PM. The Final Exam may include anything in this course (before and after the Midterm). The exam is closed-book; however, two cheat sheets are allowed. Each cheat sheet must be no larger than a US-letter-size paper. You can write or print anything you want on one or both sides of this cheat sheet, but stickers are not allowed. Calculators are allowed; however, other electronic devices, such as laptops and cellphones, are NOT allowed.
2017/6/23, Fri.

Your graded Final Exam will NOT be returned--the instructor is required to keep them on file for at least one year; your Final Exam grade and your Overall Letter grade will be sent to each of you individually via email on Thursday (6/22) night. Nonetheless, on Friday (6/23) you are welcome to drop by my office (SN 139) during 1:00 PM - 2:00 PM, or make an appointment via email by 2:00 PM, to look over your graded Final Exam and/or to appeal your grade if you believe there is any error or mistake in your grade.

If I do not hear anything by 2:00 PM on Friday, 6/23, I would assume everything is good and I will go ahead to submit the Letter grades in the system.