Class Schedule

All textbook sections come from the course textbook. Your homework sets also use many problems from that textbook. However, the problem text will be recopied in homework assignments, so that people with old editions of the textbook can still do the problems. For more details, consult the syllabus.

Expect this calendar to update weekly. At the end of each week, we will usually have an extra handout which can either show you more examples or can go through a detailed example more thoroughly. Make sure to check this calendar at least on Mondays and Fridays.

UNIT 1

Week 1

 Day Book Sections Topics / Due Dates Monday Jan 11 1.1 Intro to course, Basics of set notation Wednesday Jan 13 1.2 Subsets and power sets Friday Jan 15 1.3, 1.6 Several operations to combine sets, Venn diagrams

Extra handout of the week: Set calculations, and a famous paradox

HW 1, due next WEDNESDAY, January 20

• ​Practice good style! Write most of your explanations in complete sentences, and lay out your work cleanly. It may be a good idea to try out a draft or two in office hours.
• Look this assignment over early, so you can figure out what questions you'll want to ask.
• Partial solutions will go up on eLC one class day after the due date.

Week 2

 Day Book Sections Topics / Due Dates Monday Jan 18 Holiday, no class Wednesday Jan 20 2.1 - 2.4 HW 1 due Basic statements, truth tables, the connectives (and, or, not, implies) Friday Jan 22 2.5 - 2.8 Implication (in detail), converse and related, equivalence Here's a handout with useful equivalences.

Extra handout of the week: Logic vs. sets, a three-variable truth table

HW 2, due Monday, January 25

• ​This is a slightly shorter assignment, since it only covers two days of class. It may help to read ahead to Section 2.5 early.
• Partial solutions will go up on eLC one class day after the due date.

Week 3

 Day Book Sections Topics / Due Dates Monday Jan 25 2.9, 2.10, start 7.2 HW 2 due Quantifiers ("for all" and "exists"), simplifying negations, mixed quantifiers Wednesday Jan 27 7.2, start 3.2 Mixed quantifiers continued, some direct proof strategies Friday Jan 29 3.2 More direct proof strategies, exercises with parity

Extra handout of the week: Multiple quantifiers, practice with parity

HW 3, due Monday, February 1

• Partial solutions will go up on eLC one class day after the due date.

Week 4

 Day Book Sections Topics / Due Dates Monday Feb 1 3.3, 3.4 HW 3 due Proof by contrapositive, start proof by cases Wednesday Feb 3 3.4 More proof by cases, with some situations other than parity Friday Feb 5 4.1 Definition of divisibility, some basic properties, cases on remainders

Extra handout of the week: Some proofs by cases dealing with real numbers

Test 1 is coming up next week! More review information will be uploaded on Monday February 8.

HW 4, due Monday, February 8

• Partial solutions will go up on eLC one class day after the due date.

Week 5

 Day Book Sections Topics / Due Dates Monday Feb 8 Misc, 4.4 HW 4 due Practice with proofs involving sets (not tested directly on Test 1) Wednesday Feb 10 In-class review for Test 1 Friday Feb 12 TEST 1 (Remember that all tests are 55 minutes, not 50.)

There is no HW due this week. Instead, see test review materials below.

TEST 1 Review Materials

UNIT 2

Week 6

 Day Book Sections Topics / Due Dates Monday Feb 15 5.1, 5.2 Counterexamples, start proof by contradiction Wednesday Feb 17 5.2 More proofs by contradiction, irrational numbers Friday Feb 19 5.4, 5.5 Disproving existence via cases, nonconstructive proof in calculus

Extra handout of the week: Contradiction vs contrapositive, and some more remainders

HW 5, due Monday, February 22

• Partial solutions will go up on eLC one class day after the due date.

Week 7

 Day Book Sections Topics / Due Dates Monday Feb 22 6.1 Intro to mathematical induction Wednesday Feb 24 6.2 Induction examples with different base cases Divisibility and inequality examples Friday Feb 26 6.2 Examples generalizing a property on one or two values, i.e. "repeated reuse of a result" proofs

Extra handout of the week: Parity with induction, along with a neat "regrouping" result

HW 6, due Monday, February 29

• Partial solutions will go up on eLC one class day after the due date.

Week 8

 Day Book Sections Topics / Due Dates Monday Feb 29 6.2, misc HW 6 due Induction with recursive sequences (part 1) Here are more examples dealing with sequences. Wednesday Mar 2 6.4 Strong induction Induction with recursive sequences (part 2) Friday Mar 4 6.4, misc More unusual strong induction examples A couple examples with pictures and games

Extra handout of the week: Strong induction used for an algorithm and a game strategy

HW 7, due Monday, March 14 (after Spring Break)

• ​This assignment has fewer problems, but it is not easy. Start early!
• Because this assignment is due around the time of Test 2, late submissions cannot be accepted. This allows me to release solutions promptly.
• Partial solutions will go up on eLC on the due date.

Test 2 is coming up the next week of classes (after Spring Break)! Review material should go up by Monday, March 14.

Week 9

 Day Book Sections Topics / Due Dates Monday Mar 14 6.4, misc HW 7 due More examples of induction and strong induction (not directly on Test 2) Wednesday Mar 16 In-class review for Test 2 Friday Mar 18 TEST 2 (Remember that all tests are 55 minutes, not 50.)

There is no HW due this week. Instead, see test review materials below.

TEST 2 Review Materials

UNIT 3

Week 10

 Day Book Sections Topics / Due Dates Monday Mar 21 8.1, start 8.2 Definition of relation, introduction to the "RST" properties: Reflexive, Symmetric, Transitive Wednesday Mar 23 8.2, start 8.3 More work with RST properties, equivalence relations Friday Mar 25 8.3 More work with equivalence relations, thinking of equivalence classes

Extra handout of the week: Practice with the RST properties with examples and proofs

HW 8, due Monday, March 28

• Partial solutions will go up on eLC one class day after the due date.

Week 11

 Day Book Sections Topics / Due Dates Monday Mar 28 1.4, 8.5 Equivalence classes on A and partitions of A Wednesday Mar 30 4.2, 8.5, 8.6 Congruence mod m, simplifying in Z_m Friday Apr 1 8.5, 8.6 More facts about Z_m, studying classes of relations using mod m

Extra handout of the week: Set operations with relations, and an example relation featuring mods

HW 9, due Monday, April 4

• Partial solutions will go up on eLC one class day after the due date.

Week 12

 Day Book Sections Topics / Due Dates Monday Apr 4 9.1, 9.2 Definition of function, domain and range, arrow diagrams Wednesday Apr 6 9.3 One-to-one (injective) and onto (surjective) functions Friday Apr 8 9.3, 9.4 Well-defined functions on equivalence classes Bijective functions

Extra handout of the week: 1-1 and onto functions in calculus, and another bijection with linear systems

HW 10, due Monday, April 11

• Partial solutions will go up on eLC one class day after the due date.

Week 13

 Day Book Sections Topics / Due Dates Monday Apr 11 9.5 HW 10 due Composite functions Proofs involving composites with 1-1 and onto (part 1) Wednesday Apr 13 9.5, 9.6 Proofs involving composites with 1-1 and onto (part 2) Inverse functions, calculating inverses Friday Apr 15 9.5, 9.6 HW 11 due by 5pm Proofs and comments involving composites (part 3) Some theoretical properties of inverses

Extra handout of the weekTwo examples of proofs involving composites

HW 11 due FRIDAY, April 15, 2016 by 5pm

• You may hand this assignment in during class on Friday, or you may bring it to my office by 5pm. (You may slide the HW under my door if needed.)
• If this will not work for you, please send me advance notice and work out alternate arrangements.
• Partial solutions will be up on eLC by Monday, April 18.

Test 3 is the WEDNESDAY of next week.

• We will have in-class review next Monday.

TEST 3 Review Materials

FINAL UNIT

Week 14

 Day Book Sections Topics / Due Dates Monday Apr 18 In-class review for Test 3 Wednesday Apr 20 TEST 3 (Remember that all tests are 55 minutes, not 50.) Friday Apr 22 10.1, 10.2 Cardinality of infinite sets (introduction)

Test 3 Review Material can be found in last week's schedule.

HW 12 due FRIDAY, April 29, 2016 in class

• Unlike HW 11, this assignment is due by class time, like most assignments.
• Partial solutions will be up on eLC on Monday, May 2.

Week 15 and the final day of class

 Day Book Sections Topics / Due Dates Monday Apr 25 10.2 Denumerable and countable sets Showing Z and N x N are countable Wednesday Apr 27 10.2, 10.3 Building more countable sets Some facts about uncountable sets Friday Apr 29 10.3 HW 12 due Two famous contradiction cardinality proofs (not covered on final exam) Final exam review (half a day) Monday May 2 Last day of class Second day of final exam review

Extra handout of the week: Showing a set is countable, and countable unions of countable sets

UNIT 4 Review Materials

• I'll provide review lists and practice questions just covering cardinality.
• However, the final exam is cumulative. You should be able to review your old exams.
• Topic list and concept-check questions
• Practice questions
• Solutions to some of these problems will be uploaded on eLC by Monday, May 2 at the latest.

Last updated: 4/29/2016