1/8: These exercises are due on 1/9. (Yes, they are due tomorrow at the beginning of class, before I take questions over the assignment. Have them ready to turn in when you enter the classroom!) FINALIZED

* DO THIS BEFORE OUR NEXT CLASS: Read Chapter 0 in the text (the syllabus). This is an important part of your assignment. Highlight items that you believe could be useful in the future. You are responsible for knowing the information contained in Chapter 0.
* DO THIS BEFORE OUR NEXT CLASS: Read Section 1.1 in the text.
* DO THIS BEFORE OUR NEXT CLASS: Re-read your class notes from the worksheet.
* DO THIS BEFORE OUR NEXT CLASS: Do exercises 2acd, 4, 7 from Section 1.1 in the notes. These exercises will be collected at the beginning of our next class on Thursday. They should be written neatly or typed on a piece of paper that can be turned in, not in your notes.
* DO THIS BEFOER OUR NEXT CLASS: To the best of your ability, determine the number of different train track layouts involving two two-way switches.Think a bit about why you think two layouts are different. This exercise will be collected at the beginning of our next class on Thursday. It can be on the same piece of paper as the exercises from Section 1.1.
* DO THIS BEFORE OUR NEXT CLASS: If you haven't done this already for another class, create your account on user.wolfram.com using your Carthage email address. If you already have an account, make sure that you remember your password. If you don't have a user.wolfram account, you can create one here with your Carthage e-mail address.
* Check the blog for new entries. Even if I fail to put this in your assignment, it would be a good idea to check the blog at least every other day. As I read your homework or think about how class went, I will post insights and hints in the blog.

* Watch these videos before class on Thursday. Take notes while watching the videos, either in the handout or in a notebook that you can bring to class. They will prepare you for class.
(1) Factorials
(2) Properties of Functions
(3) The Word "Graph"
(4) Important Graphs

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, probably to 0. This will count as an online quiz. You should also receive an email confirmation so you can check your answers.

The exercises below are due on 1/10. They are due at the beginning of class, before I take questions over the assignment. Have them ready to turn in when you enter the classroom!

* Do exercises 2bef, 3, 5, 6 from Section 1.1 in the text. For 6, don't use a computer, but a hand-held calculator may be helpful. Explain your reasoning! These exercises will be collected at the beginning of our class on Friday. They should be written neatly on a piece of paper that can be turned in, not in your notes. Turn them in as you enter the classroom or shortly thereafter. Don't wait for me to ask! Please do not put these on the same piece of paper that you turn in on Thursday!

Optional Material

* If you wish, you can download copies of the following two Discrete Structures texts which I will reference from time to time. Both are available for no cost over the internet, or for a very reasonable price in hard copy.
- The Book of Proof by Hammack
- Discrete Structures in Five Chapters by Witno

* If you want to keep going, try finding the number of layouts involving two three-way switches.

VQ for in-class use - you cannot take the quiz at this link! Use the link above.

Map for me to use in class

1/9: These exercises are due on 1/10. They will prepare you for our next class. FINALIZED

* Fill out this Google form!

* Watch these videos before our next class. Take notes while watching the videos, either in the handout or in a notebook that you can bring to class.
(1) Sets
(2) Important Sets
(3) Matrix Operations

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, perhaps to 0. This will count as a quiz. You should also receive an email confirmation so you can check your answers.

The exercises assigned below are due on 1/14. They are due at the beginning of class, before I take questions over the assignment. Turn them in when you enter the classroom!

* Read Section 1.2 in the text.
* Re-read the in-class worksheet for Section 1.2.
* Do exercises 1, 3, 5, 6 from Section 1.2 in the notes. NOTE THAT PROBLEM 4 WAS REMOVED!
* Read Section 5.1 in the text.
* Re-read the in class handout and your notes from Section 5.1.
* Do exercises 1, 3, 8aceg, 9aceg at the end Section 5.1 in the notes.

Optional Material

* How can we construct a graph from a train track layout in a way that "different" layouts (layouts we think are different) will have different graphs?

VQ for in-class use - you cannot take the quiz at this link!

1/10: These exercises are due on 1/14. These will prepare you for our next class. - FINALIZED

* Complete this Google form that appeared Saturday afternoon!

* Watch these videos before our next class. Take notes while watching the videos, either in the handout or in a notebook that you can bring to class.
(1) Propositions
(2) Compound Propositions
(3) Basic Set Operations
(4) Two More Definitions
(5) Equivalent Graphs

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, perhaps to 0. This will count as a quiz. You should also receive an email confirmation so you can check your answers.

The exercises below are due on 1/15. They are due at the beginning of class, before I take questions over the assignment. Turn them in when you enter the classroom!

* Do Exercises 7, 8 from Section 1.2 in the notes.
* Do exercises 4, 7, 8bdf, 9bdf at the end Section 5.1 in the notes.
* Read Section 1.3 in the text.
* Re-read the in-class worksheet for Section 1.3.
* Do exercises 1, 2, 4, 8, 11 from Section 1.3.
* Read Section 1.11 in the text.
* Re-read the in-class worksheet for Section 1.11.
* Do exercises 1abcf and 2abc from Section 1.11 in the text. You should be able to add and multiply small (two-by-two) matrices by hand, but you are welcome to check your work or do larger problems using Mathematica or another matrix multiplication utility.

Optional Material

* Matrix Mathematica File - Mathematica Online Version - Mathematica File For Making Graphs

VQ for in-class use

1/13: These exercises are due on 1/14. These will prepare you for our next class. - FINALIZED

No additional assignment - class cancelled due to instructor illness.

The exercises assigned today are due on 1/15.

No additional assignment - class cancelled due to instructor Illness.

Optional Material

* None.

1/14: These exercises are due on 1/15. These will prepare you for our next class. - FINALIZED

* Watch these videos before our next class.

(1) Truth Table Proofs
(2) Using a Spreadsheet
(3) Proofs of Argument Forms
(4) Quantifiers and Propositional Functions

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, perhaps to 0. This will count as a quiz. You should also receive an email confirmation so you can check your answers.

The exercises assigned today are due on 1/16.

* Do exercise 4 from Section 1.2 in the text.
* Do Exercises 5, 10, 12 from 1.3 in the text.
* Read Section 1.5 in the text.
* Re-read the in-class worksheet from Section 1.5.
* Do exercises 7ace and 8ab from Section 1.5.
* Read Section 1.6 in the text.
* Re-read the in-class worksheet from Section 1.6.
* Do exercises 1, 3abdh, 6 from Section 1.6. You do not need to prove your results in this section, particularly 3h.

Optional Material

* Explore the problem solving exercise we did in class today. Is there anything special about seven solutions? What other interesting questions arise?

1/15: These exercises are due on 1/16. These will prepare you for our next class. FINALIZED

* Watch these videos before our next class.
(1) Making a Bijection
(2) The Set \(\mathbb N\) is Not Finite

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, perhaps to 0. This will count as a quiz. You should also receive an email confirmation so you can check your answers.

The exercises below are due on 1/17.

* Do exercises 3, 6 and 13 from Section 1.3.
* Do exercises 4 from Section 1.6.
* Read Section 1.7 in the text.
* Re-read the in-class worksheet from Section 1.7.
* Do exercises 1ace, 2ace from Section 1.7.
* Read Section 2.1 in the text.
* Re-read the in-class handout over Section 2.1.
* Do exercise 1 from Section 2.1 as follows. If your last name begins with the letters A-K, prove logic rules Disjunctive Syllogism, Constructive Dilemma, Conjunction, and Double Negation. If your last name begins with the letters L-Z, prove logic rules Destructive Dilemma, Simplification, Addition, and Tautology (both parts).

Optional Material

* No additional material today.

1/16: Exam 1 will be given today. It will cover the material we covered in class from the beginning of the course up to 1/14 - that does not include the material in the videos assigned on 1/14. That includes Sections 1.1, 1.2, 1.3, 1,5, 1.6, 5.1, and all in-class work. Expect to work for around 30-40 minutes, maybe less. All of you are expected to be in class to take the exam. I will provide a calculator for you to use.

You are not permitted to communicate with any human being by any means, including but not limited to, talking, phone conversations, text messages, email messages, hand signals, smoke signals, semaphore, Morse code, Norse code (used to communicate with Vikings), social media, antisocial media, or any other means that I've omitted. You are not permitted to use any internet resource whatsoever. You are not permitted to use your phone in any way, any app on your phone, any app that's not on your phone, Google, WolframAlpha, ChapGPT or any other AI resource, or any other print or internet resource that I've omitted.

These exercises are due on 1/17. These will prepare you for our next class. - FINALIZED

* Watch these videos before our next class.
(1) The Multiplication Principle
(2) The Addition Principle
(3) The Inclusion-Exclusion Principle
(4) The First Nine Rules
(5) Which Rule Was Used?
(6) Filling in the Rules
(7) Writing a Proof

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, perhaps to 0. This will count as a quiz. You should also receive an email confirmation so you can check your answers.

The exercises assigned today are due on 1/20.

* Do exercise 7 from Section 1.3.
* Do exercise 11 from Section 1.6.
* Do exercises 1bd, 2bd from Section 1.7.
* Do exercise 2 from Section 2.1.
* Read Section 1.9 in the text.
* Re-read the in-class handout over Section 1.9.
* Do exercises 1abg from Section 1.9.

Optional Material

*

1/17: These exercises are due on 1/20. These will prepare you for our next class. - FINALIZED

* Watch these videos before our next class.
(1) Rules of Replacement
(2) Applying the Rules
(3) Definition of Divides
(4) Types of Proofs

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, perhaps to 0. This will count as a quiz. You should also receive an email confirmation so you can check your answers.

The exercises below are due on 1/21.

* Read Section 1.8 in the text.
* Re-read the in-class worksheet from Section 1.8
* Do exercises 1bcd, 3, 5, 6, 8, from Section 1.8.
* Read Section 2.2 in the text.
* Re-read the in-class handout from Section 2.2.
* Do exercises 1, 2, 3abcd from Section 2.2. (If you have trouble with problem 1, don't try problem 2! Ask for help in office hours or on the blog. If you have a lot of trouble with problem 2 (having a few problems isn't a big deal), don't move on to problem 3! Ask for help.)

Optional Material

*

1/20: These exercises are due on 1/21. These will prepare you for our next class. - FINALIZED

(1) Induction, Part I
(2) Induction, Part II
(3) An Example of an Induction Proof

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, perhaps to 0. This will count as a quiz. You should also receive an email confirmation so you can check your answers.

The exercises below are due on 1/22.

* Do exercises 3efghi from Section 2.2 in the text. (If you can't finish the proof, take a few legal steps!)
* Read Section 2.3 in the text.
* Re-read the in class handout and your notes from Section 2.3.
* Do exercises 1 and 2 from Section 2.3 in the text. (If you have trouble with problem 1, don't try problem 2! Ask for help in office hours or on the blog. If you have a lot of trouble with problem 2 (having a few problems isn't a big deal), don't move on to problem 3! Ask for help.)
* Do exercises 3a-d from Section 2.3 in the text. (If you can't finish the proof, take a few legal steps!)
* Read Section 3.1 in the text.
* Re-read the in class handout and your notes from Section 3.1.
* Do exercises 1, 3, 7, 9, and 10 from Section 3.1 in the text. TYPE YOUR PROOFS FOR EXERCISES 1 AND 3! Your proofs for Exercises 7, 9 and 10 should also be written using complete sentences with correct punctuation. (You could type them all...) See the blog for some hints!

Optional Material

Today's VQ for In-Class Use

1/21: These exercises are due on 1/22. These will prepare you for our next class. FINALIZED

* Watch these videos before our next class.
(1) The Division Algorithm
(2) Addition Modulo \(p\)
(3) Conditional Proof

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, perhaps to 0. This will count as a quiz. You should also receive an email confirmation so you can check your answers.

The exercises below are due on 1/23.

* Do exercises 3efg from Section 2.3 in the notes. (If you can't finish the proof, take a few legal steps!)
* Read Section 3.2 in the text.
* Re-read the in class handout and your notes from Section 3.2.
* Do exercises 1adfj from Section 3.2 in the text. TYPE at least one of these problems, maybe all of them. Cut and paste is a wonderful tool!
* Prove or disprove: (we *really* hope this is true!) The number of layouts using two n-way switches and no rainbows is always 2, at least of n is greater than 2.

Optional Material

* None today

1/22: These exercises are due on 1/23. These will prepare you for our next class. FINALIZED

* No pre-class assignment!

The exercises assigned today are due on 1/24.

* Do exercises 3jm from Section 2.3 in the notes. (If you can't finish the proof, take a few legal steps!)
* Do exercises 1ch, 6 and 7 from Section 3.2 in the notes. TYPE at least one part of question 1, and either 6 or 7. Any problems that are not typed should be written very neatly using complete sentences.
* Read this proof of how a contradiction can imply anything!
* Read Section 2.4 in the text.
* Do exercises 1-9 from Section 2.4.
* Read Section 3.3 in the text.
* Re-read your in-class worksheet from Section 3.3.
* Do exercises 1, 2, 4, 6 from Section 3.3.

Optional Material

* You may use the Mathematica code for constructing the zero-divisor graphs. Here is the Mathematica Online code. Explore these! Can you find patterns? Can you determine when a zero-divisor graph will be bipartite?

* Multiplication Tables

* Code for graphs in general.

1/23: Exam 2 will be given today. It will cover the material from in-class work on 1/15-1/21. That includes Sections 1.3, 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 3.1, and 3.2. Expect to work for around 45 minutes, but no more than 60 minutes. (The quiz isn't any longer, but some of you may get stuck on the logic proof(s).)

You are not permitted to communicate with any human being by any means, including but not limited to, talking, phone conversations, text messages, email messages, hand signals, smoke signals, semaphore, Morse code, Force code (used to communicate with Jedi knights), social media, antisocial media, or any other means that I've omitted. You are not permitted to use any internet resource whatsoever. You are not permitted to use any text, any app on your phone, any app that's not on your phone, Google, WolframAlpha, or any other print or internet resource that I've omitted.

These exercises are due on 1/24. These will prepare you for our next class. FINALIZED

* Watch these videos before our next class.
(1) Permutations
(2) Combinations

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, perhaps to 0. This will count as a quiz. You should also receive an email confirmation so you can check your answers.

The exercises assigned today are due on 1/27.

* Do exercises 9 and 10 from Section 3.2 in the notes. TYPE at least one of these exercises.
* Do problems 10-13 from Section 2.4.
* Read pages 255-266 (up to but not including Spanning Trees) in the text.
* Do exercises 1, 2, and 3 from Section 5.4 of the text.
* Construct adjacency matrices for all 5 of the two-switch layouts. Enter them into a Mathematica file if possible.

Optional Material

* Code for graphs in general.

* Layout Graphs

1/24: These exercises are due on 1/27. These will prepare you for our next class. FINALIZED

* No pre-class videos required for Monday!

The exercises assigned today are due on 1/28.

* Type a proof of Exercise 1k from Section 3.2. Make it look really good. This is your only written assignment today. Hopefully those of you who are little behind can use this weekend to catch up!
* Read Section 6.1 in the text.
* Re-read your class notes for Section 6.1.
* Do exercises 1-9, 12, 13, 14, 15 from Section 6.1.
* Read Section 2.5 in the text.
* Do exercises 1-4 from Section 2.5 in the text.

Optional Material

*

1/27: These exercises are due on 1/28. These will prepare you for our next class. - FINALIZED

* Watch these videos before our next class.

(1) The Euclidean Algorithm
(2) The Chart Method

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, perhaps to 0. This will count as a quiz. You should also receive an email confirmation so you can check your answers.

The exercises assigned today are due on 1/29.

* Read Section 7.1 in the text.
* Do exercises 1 from Section 7.1.
* Read Sections 6.3-6.4 in the text.
* Do exercises 4 from Section 6.3.

Optional Material

* Why 73 is Sheldon's Number. and why 42 was nominated for number of the year. The integer 1729 is known as the Hardy-Ramanujan number. Why was 12 nominated?

For more information on the Sheldon Conjecture, click here or check out this article in the November 2015 issue of Math Horizons, available in the MathLab or from me.

* Markov Graphs

* Transition Matrices for Layouts - Onine Version

1/28: These exercises are due on 1/29. These will prepare you for our next class.

* Watch these videos before our next class.
(1) Set Proofs
(2) An Example Proof

* While you are watching the videos or immediately after watching the videos, take this short quiz. You should take this quiz before our next class starts! If I don't have your response by 9:00 am, your quiz will be counted as late, and your score will be reduced, perhaps to 0. This will count as a quiz. You should also receive an email confirmation so you can check your answers.

No new exercises assigned today.

* No additional exercises to turn in. Be able to do exercises 1, 2, 7, 8 from Section 3.4 using the Euclidean Algorithm. Solutions will be posted immediately.
* No additional exercises to turn in. Be able to do exercises 1abc, 2abc by hand.
* Not on the exam: Use a computer to do 1d and 2d. You will be given this graph on the exam. Be able to LABEL \(q_0\) and \(q_1\).
* No additional exercises to turn in. Be able to do exercises 1e and 2e.

Optional Material

Voting Triangle 1 - Voting Triangle 2

Voting Triangle Code - Online Version

A Spreadsheet to Check Your Work in 3.4

1/29: No new exercises are due on 1/30.

* Study for the final exam, which will cover the entire course.

Optional Material

* Don't Panic.

* More reading on the train track problem

1/30: Our final exam is from 9:00-12:00 on Thursday, January 30. This exam covers the following sections: 1.3, 1.8, Chapter 2 (2.2, 2.3, 2.4, 2.5), Chapter 3 (sections 3.1, 3.2, 3.3, 3.4), Section 5.4, Section 6.1, Section 6.3, Sections 7.1 and 7.2, and everything we did in class since the second exam (like the train track problem). Expect more from the material that was not on the first two exams. You may start as early as 8:00 if you wish.