**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

- 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.

- Groupwork for this 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.- Here are some very important equivalences, especially negation rules like DeMorgan's Rule or the Contrapositive.
- Groupwork for this class

**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 9*:**TEST 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- (Recursion is not covered in detail in our textbook, unfortunately.)
- Here are some supplementary examples to show off proofs involving recursive sequences.

*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

**Extra handout of the week:** Some trickier examples of injections or surjections, exploring well-defined functions for modular arithmetic

**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**.

- The test covers Chapters 8 and 9, except for sections we skipped in class.
- Expect 5 or 6 questions, with a 55-minute time limit.
- Definitions are especially critical for this unit of material!

- Here's a topic list for this test.
- Here are some practice questions (with some solutions).
- There will be some in-class review on next Monday.

**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