Office hours and address

Office location: Boyd 603C

Office hours for Summer 2018

  • Every day: 2:00-3:30pm
  • Tuesdays and Thursdays additional hours: 4:30-6:00pm

or by appointment. You can stop by if my door is open.

Mailing address

Dr. Michael Klipper
(706) 542-2588
Boyd GSRC 603C
The University of Georgia
Athens, GA 30602

Basic Course Information / Links

Course Sections (click on the section number for syllabus)

Section 25124: MWF 1:25pm-2:15pm in Boyd 304


Useful Website Links


Tutoring resources (includes some paid tutor options)

Math 3200, Spring 2018

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.



  • 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


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.




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