Exam 3 Review is posted

Hi everyone,

Your third exam will take place next Thursday, November 21st.  The review sheet is posted on the Exam Reviews page (solutions will be added over the next few days).  Feel free to post questions or comments here!

Best of luck with your studying,

Prof. Reitz

Homework Week 12

Homework Week 12
Written work – Chapter 10 p167: 25, 28 (problem 30 is extra credit),  Section 11.0 p176: 3,4 (Due Tues 11/19)
WeBWorK – Assignment6-Sec11.1 (Due Tuesday 11/19 at midnight)
OpenLab – (reminder: OpenLab #4, “The MIU puzzle continued,” is due Thursday 11/14. Submit your answer between Tuesday, 11/12 and Thursday, 11/14. )

Proof by Contradiction Examples

By request, I’ve done some looking around for  resources related to Proof by Contradiction.  I haven’t found a page with a good “big picture” overview yet, but I have found some decent examples – here goes:

Getting started – some basic examples.  This page has a few examples worked out completely – not too long or involved, and (I hope) not too difficult to follow.

Numberphile: Proof (by contradiction) that there are infinitely many primes.  A really good illustration of proof by contradiction.  The numberphile guys make cool math videos – if you like it, search for numberphile and check out their other stuff.

Induction Examples

Hi everyone,

I wanted to post some resources on mathematical induction — if you are having trouble with induction, I highly recommend taking a look.

Introductory Examples:  Here is a page with a bunch of examples of proofs by induction, similar to what we have done in class.  This is a good place to start.

Khan Academy: If you find video explanations helpful, here is the Khan Academy on induction:

Even More Videos: This page has a collection of Induction Example videos – I haven’t watched them all, so if you do look at them please tell me what you think:

Advanced/wacky examples: This pdf has some great examples in Section 6(page 4) — they show how induction can be applied to all kinds of different mathematical problems.  Solutions are included.  This is a good resource if you are familiar with induction, and want to take things a little farther.



Homework Week 11

Homework Week 11
Written work – Chapter 10 p167: 1, 2, 10, 15 (Due Tuesday 11/12)
WeBWorK – none
OpenLab (reminder: OpenLab #4, “The MIU puzzle continued,” is due Thursday 11/14. Submit your answer between Tuesday, 11/12 and Thursday, 11/14. )

OpenLab #4: The MIU puzzle, continued

UPDATE: See the “Assignment Version 2” added below.

This assignment is a continuation of OpenLab #3, on the MIU puzzle.  Your assignment this time is a little different.  Consider the following conjecture about the MIU puzzle:

Conjecture.  Any goal word (any word with first letter M, followed by a combination of U’s and I’s) can be obtained from the starting word MI using the rules of the MIU puzzle.

Assignment (Due Thursday 11/14.  Submit your answer between Tuesday, 11/12 and Thursday, 11/14). Is the conjecture above true?  If so, prove this fact.  If not, provide an example of a goal word that cannot be obtained, and prove that it is impossible for your word to be obtained.

IMPORTANT: Because of the nature of this assignment, DO NOT SUBMIT YOUR ANSWER BEFORE  TUESDAY 11/12. However, I strongly recommend getting started on this problem well before that date!


If you wish, you can respond to the assignment below INSTEAD of completing the assignment above.  In the assignment below, you will be writing about your experience working on the MIU puzzle above.  Be sure to respond to EACH PART – detailed answers to part 2 and 3 below will gain the MOST credit.

  1. Write down what you think the answer is – no proof necessary.
  2. Describe in as much detail as you can the process of working on the assignment.  What did you think in the beginning? What are the different things you tried in order to solve the problem?  Describe each one, in the order that you tried them.
  3. Give a detailed list of the resources you used, and how you used each one (these could include anything – your brain, pen & paper, a computer (what applications did you use), the internet, other people, and so on).
  4. What activity or resource do you feel was most effective for you in working on the assignment (what helped you the most in understanding the assignment and figuring out an answer)?

Extra Credit.  Respond to one of your classmates’ submissions.



Improve your grade on Exam #2.

You can earn additional points towards your Exam #2 grade by completing the following assignment.

Due Thursday, 11/7.  Choose TWO problems from Exam #2 (Hint: choose the two problems that you did worst on).  Re-do these problems.  Hand in all the following, STAPLED TOGETHER, on Thursday 11/7:

  1. For each of the two problems:
    1. Clearly state how many points you received on each problem.
    2. Give an explanation consisting of at least one complete sentence explaining your error, and how you fixed it.
    3. Give a complete, correct solution to the problem.
  2. Hand in your exam paper along with your corrections.

You will be able to earn up to half the points you missed on the two selected problems, to be added back into your Exam #2 score.

Example.  Suppose you received 68 on the exam.  You choose problem #3 (scored 8 points out of 20), and problem #5 (scored 4 points out of 20).  You complete the assignment perfectly.  Since you missed a total of 28 points on these two problems (12 on problem 3, and 16 on problem 5), you will have 14 points added to your exam score.

Homework Week 10

Homework Week 10
Written work – Chapter 8 p143: 3, 8, 18, 19,    Chapter 9 p150: 3, 4, 5 (Due Tuesday 11/5)
WeBWorK – none
OpenLab – OpenLab #4, The MIU puzzle continued, is due Thursday 11/14. Submit your answer between Tuesday, 11/12 and Thursday, 11/14.  (The assignment will be posted after class on Tuesday 10/29.)

Office hours today

I will be available between 2pm – 3pm today in my office N707.  My usual office hours (11:15-1:15) are canceled.


Prof. Reitz

IMPORTANT – Bring Written Work Chp 4-5 to class on Thursday

Hi everyone,

If you picked up your (graded) written work from Chapters 4 and 5 today, please bring it with you on Thursday to class — I need to record your score in my gradesheet, or you will not get credit for the assignment.  Oops!


Prof. Reitz