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 be updated most Mondays and Fridays.

• 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.

UNIT 1: Fundamentals of sets, logic, and proof structure

Week 0:

• Friday Jan 5: Section 1.1. Intro to course, basics of set notation

Extra handout of the week: None for the first day of class

HW 1, due Friday, January 12

• Most assignments will be due on Mondays, but this assignment is different. (Monday January 15 is a holiday!)
• ​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.
• Partial solutions are put on eLC one class day after the due date, after any late homework submissions are dealt with. (See the syllabus policy on makeups.)

Week 1:

• Monday Jan 8: Section 1.2. Subsets, power set.
• Wednesday Jan 10: Sections 1.3 and 1.6. Venn diagrams, set operations, Cartesian product.
• Groupwork for this class
• You can look over the problems on the first page before class, but I recommend you save the answers for after class.
• Friday Jan 12: Sections 2.1 through 2.3. Basic statements, truth tables, the connectives "not", "and", "or".

Extra handout of the week: Practice with sets, and a fun paradox

HW 2, due Monday January 22 (the week after the Martin Luther King Jr. holiday)

Week 2:

• No class Monday Jan 15 (holiday)
• Wednesday Jan 17: Sections 2.4 through 2.7. Implication, a bit about equivalent statements.
• Friday Jan 19: Sections 2.8 through 2.10. Quantified statements, more practice with equivalences, negating complicated statements.

Extra handout of the week: Practice with logical words and symbols

HW 2 is listed above. HW 3 will be released next Monday (due the Monday after).

Week 3:

• Monday Jan 22: Finish Section 2.10, go over parts of Section 7.2. Discussing and proving statements with multiple quantifiers.
• Wednesday Jan 24: Section 3.2 (skim 3.1 too). Direct proof of P => Q, introduction to proofs with parity (even/odd).
• Friday Jan 26: Sections 3.2 and 3.3. More proofs of P => Q with parity, contrapositive method with ~Q => ~P, proofs of P <=> Q

Extra handout of the week: Quantifier practice, and diagnosing flaws in a parity proof

HW 3, due Monday January 29, 2018

• This assignment is a little longer, and it may be more subtle. Try to visit office hours at least once to check up on your understanding.

Week 4:

• Monday Jan 29: Finish Section 3.3, start Section 3.4. Proofs of P <=> Q, proof by cases.
• Wednesday Jan 31: Finish Section 3.4 (and maybe skim 3.5). Proof by cases.
• Friday Feb 2: Section 4.1. Proof practice involving divisibility d | m

Extra handout of the week: The Factoring Theorem for R

HW 4, due Monday February 5, 2018

• This is the first assignment with (optional) extra credit at the end.

TEST 1 IS NEXT FRIDAY FEBRUARY 9.

• This test covers all of the material from the first day up through HW 4 (ending at Section 4.1).
• Expect 5 or 6 problems, with a 55-minute time limit.
• The first problem of my tests is always about repeating definitions. (You do not have to explain anything else.)
• Here's a topic list for review.
• Practice questions for Test 1
• We will go over some of these practice problems in class next Wednesday.

Week 5:

• Monday Feb 5: Section 4.4, practice with some set proofs.
• Wednesday Feb 7: Review for Test 1
• We can go over practice questions found in the links for the previous week.
• Friday Feb 9TEST 1 (55 minutes, not 50)

UNIT 2: Indirect proof tactics, proof by mathematical induction

Week 6:

• Monday Feb 12: Sections 5.1 and 5.2, counterexamples, basic setup of proof by contradiction.
• Wednesday Feb 14: Sections 5.2 and 5.3, contradiction proofs involving irrational numbers
• Friday Feb 16: Sections 5.2 and 5.4 (skim 5.5), contradiction proofs involving remainders, non-constructive existence proofs from calculus
• A fair bit of the material for this class is not covered much in the textbook!

Extra handout for the week: Contradiction / contrapositive with square roots, and more remainder practice

HW 5, due Monday February 19, 2018

Week 7:

• Monday Feb 19: Section 6.1, introduction to Principle of Mathematical Induction (PMI), summation problems.
• Wednesday Feb 21: Section 6.2, induction with different base cases, induction with divisibility or inequalities.
• Friday Feb 23: Section 6.2, more induction practice, induction used to "repeatedly apply" a theorem

Extra handout for the week: Using induction to explore basic parity and a tricky inequality

HW 6, due Monday February 26, 2018

Week 8:

• Monday Feb 26: Sections 6.2 and 6.4, repeatedly applying implications via induction, well-ordering of N and Strong Induction
• Wednesday Feb 28: Section 6.4, proofs with recursive sequences, part 1
• Friday Mar 2: Section 6.4, proofs with recursive sequences, part 2

Extra handout of the week: The Fundamental Theorem of Arithmetic (factoring into primes)

HW 7, due Monday March 5, 2018

TEST 2 IS NEXT FRIDAY, MARCH 9 (right before Spring Break).

• This test covers Chapters 5 and 6 (except for the sections we skipped).
• You will not have to redo all parity proofs from definition.
• You won't be tested specifically on Test 1 material, but some of those skills are still necessary! (For instance, you need to know how to negate statements to do proof by contradiction correctly.)
• Again, expect 5 or 6 problems, with a 55-minute time limit.
• Again, the first question involves quick repetition of definitions.
• Here's a topic list, with some concept questions.
• Here are some practice problems.
• Solutions for some problems can be found on eLC.
• We will review some practice problems in class next Wednesday.

Week 9:

• Monday Mar 5: Miscellaneous induction practice with Fibonacci, a game, and a puzzle
• Wednesday Mar 7: Review for Test 2
• Take a look at the practice questions above, but also bring more open-ended questions to class.
• Friday Mar 9: TEST 2 (55 minutes)
• If you cannot make Friday's class due to Spring Break, you need to message me to make alternate arrangements ASAP.

UNIT 3: Relations, equivalence classes (and some basic modular arithmetic), functions

Week 10:

• Monday Mar 19: Sections 8.1 and 8.2. Relations, domain and range, the "RST" properties (reflexive, symmetric, transitive).
• Wednesday Mar 21: Sections 8.2 and 8.3. Equivalence relations, more practice with the RST properties.
• Friday Mar 23: Section 8.3. More equivalence relations, start discussing equivalence classes.

Extra handout of the week: Generating relation examples, and a relation involving divisibility

HW 8, due Monday March 26, 2018

Week 11:

• Monday Mar 26. Section 8.4, bits of 4.2 and 8.5: more equivalence classes with level sets, equivalence class structure, introduce modular congruence.
• Wednesday Mar 28: Section 8.5. Simplifying sums and products in modular arithmetic
• A fair bit of today's coverage is not directly found in the textbook.
• Friday Mar 30: Section 8.5, 9.1. A last bit about modular arithmetc, definition of function, drawing finite functions with "arrow diagrams"

Extra handout of the week: An equivalence relation defined by mods, and its equivalence classes

• This will probably make more sense after Wednesday's class: it uses the definition of modular congruence in Section 8.5.

HW 9, due Monday April 2, 2018

• You should be able to do most of this (shorter) HW after Wednesday's class.
• Start early, in case you run into questions near the beginning!

Week 12:

• Monday Apr 2: Sections 9.2 and 9.3. The set A^B, one-to-one (aka 1-1 or injective) and onto (surjective) definitions, basic examples
• Wednesday Apr 4: Section 9.3. More examples of one-to-one and onto functions, well-defined functions (especially with Z_m)
• Friday Apr 6: Sections 9.4 and 9.5 (start): Bijection examples, definition of composite g o f

HW 10, due Monday April 9, 2018

• Most of this assignment only depends on material up through Wednesday's class, plus the weekly handout.

Week 13:

• Monday Apr 9: Section 9.5. Some basic composite proofs for one-to-one and onto-functions.
• See the weekly handout below!
• Wednesday Apr 11: Sections 9.5 and 9.6. More advanced composite proofs for one-to-one and onto functions, definition of inverse f^(-1).
• Friday Apr 13: Miscellaneous results of Section 9.6 related to inverses (not testable on Test 3).
• I can address some questions related to HW 11 to start class on this day! (Bring them up ahead of time if necessary.)

Extra handout of the week: A couple more difficult examples of proofs involving composites of one-to-one or onto functions

HW 11 is due on FRIDAY April 13 by 5:30pm.

• You may turn in the assignment in class, or you may turn it in at my extra office hours on Friday Apr 13 from 4:30-5:30pm.
• This assignment is due on Friday in order to give adequate grading time before Test 3.
• This is the last assignment.
• We will briefly explore a bit of Chapter 11 in the text (on infinite cardinality) to end the course. I will provide practice problems for it.

TEST 3 IS NEXT WEDNESDAY, APRIL 18.

Start reviewing for the final exam, if you haven't done so yet! (Schedule details at the end of this page.)

Week 14:

• Monday Apr 16: Review for Test 4.
• Wednesday Apr 18: TEST 4
• Friday Apr 20: Cardinality (from Sections 10.1 to 10.4). The definition of |A| = |B|, exploring some sets with cardinality |R|.

No extra handout this week

No more HW

• Some practice problems, with solutions, should be released next week.

Cardinality introduction

Week 15:

• Monday Apr 23: Section 10.2. Countable sets, such as Z, N x N, and Q.
• For interesting side material, do a search for "Hilbert Hotel" and see what you get. There are some good YouTube videos for sure.
• Wednesday Apr 25: Sections 10.2 and 10.3. A few more countable sets, Cantor's famous "diagonalization" proof for R
• We won't do much final exam review; there's no extra topic lists needed for the final exam.
• We'll spend some class time trying to do a summary of the purpose of the course and the key skills we need.

Extra handout of the week: Two famous cardinality arguments (primes and power sets)

Some cardinality practice problems, including solutions

• There is no graded HW on this material. These problems are meant to show possible expectations for a cardinality question on the final exam.

Final exam details

Wednesday May 2, 2018

12:00pm to 3:00pm (try to show up a bit early to get yourself settled)

Boyd 304 (our usual classroom)

• This exam will cover all the material from the three in-class exams. It might also have one short question about cardinality (covered after Test 3).
• Expect somewhere on the order of 11 to 13 questions, fairly similar to previous test questions.
• This should be around twice the length of an in-class test.
• No bathroom breaks once the test starts. Talk to me if this is an issue.
• You'll have to leave your backpack (or similar containers) at the side of the room during the test. Turn phones and smart watches off.

Last updated: 4/23/2018