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