Here is the link to the final exam survey! Please complete this asap!

1/9: These exercises are due on 1/10. (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!) Problems in red are challenging problems for you to try.

* CHANGE TO THE SYLLABUS: There will be 2 Exams, each of which will count for 15% of your grade, rather than the 3 exams listed in the syllabus.

* DO THIS BEFORE OUR NEXT CLASS: Read Chapter 0 in the notes. 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 notes; that means to re-read your class notes from the worksheet and read the Reading Assignment.

* DO THIS BEFORE OUR NEXT CLASS: Do exercises 1, 2, 3, 7, and 11 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 on a piece of paper that can be turned in, not in your notes.

* DO THIS BEFORE OUR NEXT CLASS: Create your account on user.wolfram.com using your Carthage email address. There is a link to instructions below. If you already have an account, make sure that you remember your password.

* 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.

The exercises below are due on 1/11.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! Problems in red are challenging problems for you to try.

You can generate circle graphs at this link, once you log in to your user.wolfram (Mathematica) account. If you don't have a user.wolfram account, you can create one here with your Carthage e-mail address.

In the past, the link above to the circle graph generator hasn't always worked well, or at least it doesn't give everyone access to the file. Here is a Mathematica file that you can download and run, or run in Mathematica online.

* Do exercises 4, 5, 6, 10, 12, 13 (An interesting number of components would be anything other than \(1\) or \(n\), but those are sort of interesting too!), 14 from Section 1.1 in the notes. 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.

* Consider this variation on the problem we addressed in class: The **first** digit of a five-digit number is 2 more than the units digit. The first and last digits of the five-digit number are switched, and the result is subtracted from the original five-digit number. The other digits are not moved. What is the units digit of the result? Can we predict the exact value of this difference?

* Suppose the middle digits are moved in some way in the previous exercise; perhaps the five-digit number is reversed. Can we still predict the units digit?

* Check the blog for new entries.

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

1/10: The exercises assigned today are due on 1/14. A Google Sheet for today over logic. Another Google Sheet with recursively defined functions.

* Read Section 1.2 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Read Section 1.3 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Do exercises 1, 5, 6, 7, 8abc, 11, 13 from Section 1.2 in the notes.

* Do exercises 4, 5, 6, from Section 1.3 in the notes.

* Complete the informal writing assignment at this link.

1/11: The exercises assigned today are due on 1/15, but will be accepted on 1/16 as well due to my typing error.

* Do exercises 1, 2, 7, 9 from Section 1.3 in the notes.

* Read Section 1.4 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Read this handout from the Book of Proof.

* Do exercises 1, 2, 3, 4, 5, 6, 7, 10abdej, 11, 13, 14, 20 from Section 1.4.

1/14: The exercises assigned today are due on 1/16.

* Do exercises 8 and 9 from Section 1.4.

* Be sure to do the reading before you try the homework!

* Read Section 1.5 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Read Section 2.1 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Do exercises 1, 2, 3, 4, 6, 7, 8, 9, 11, 13, 14 from Section 1.5.

* Do exercises 2abcdefgh from Section 2.1 on the notes.

1/15: The exercises assigned today are due on 1/17. Here is a Mathematica file to help you check your matrix multiplication and to raise matrices to higher powers.

* Read Section 1.6 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail. Use the Mathematica file provided above for help too.

* Read Section 2.2 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Read this interactive example of a fill-in-the-rule exercise using only the first 9 rules.

* Do exercises 1, 2 from Section 1.6 in the notes. You may use Mathematica for problems 1fg if necessary.

* Do exercises 1 and 2 from Section 2.2 in the notes. (If you have trouble with problem 1, don't try problem 2! Come in for help. If you have a lot of trouble with problem 2, don't move on to problem 3! Come in for help.)

* Do exercises 3abcd from Section 2.2 in the notes.

1/16: Exam 1 will be given today. It will cover the material from 1/9-1/14. Expect to work for around 45 minutes, maybe less.

The exercises assigned today are due on 1/18. Here is a copy of the logic sheet that you will have for the exam/quiz today.

* Do exercises 3efghi from Section 2.2 in the notes.

* Read
Section 3.1 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Do exercises 1, 2, 3, 4, 5ab, 6, 8, 10, 11, 12, 13, 16, 17 from Section 3.1 in the notes.

* Do the informal writing assignment at this link.

* For the function \(f:\mathbb Z \rightarrow \mathbb Z\), \(f(z):=x(k-x)\), determine the number of output values that are perfect squares for 3 different \(k\) values that we didn't try in class. We did \(k=20\) in detail in class. See the Think About It page for more details.

1/17: The exercises assigned today are due on 1/21.

* Read Section 3.3 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Read
Section 2.3 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Do exercises 1, 2, 3, 4, 5, 6, 9, 10, 12, and 14 from Section 3.3 in the notes.

* Not required, but recommended: use a spreadsheet to do the Euclidean algorithm. Automate as much of the process as possible.

* Read the interactive proofs to fill in the rules for the 19 rules.

* Read the interactive proofs for the 19 rules, but not the proofs using conditional proof.

* Do exercises 1 and 2 from Section 2.3 in the notes.

* Do exercises 3a-d from Section 2.3 in the notes.

1/18: The exercises assigned today are due on 1/23. Here is some Mathematica code for graphs. Images for today: bridges, dominoes, and more dominoes.

* Do exercises 3efg from Section 2.3 in the notes.

* Read Section 5.1 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Read
Section 4.2 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Do exercises 1, 3, 4, 6, 7, 8, 9 at the end Section 5.1 in the notes.

* Do exercises 1abdfg, 2 and 3 from Section 4.2 in the notes. (Exercise 3 may take a little imagination!)

1/21: The exercises assigned today are due on 1/24. Today's Mathematica File.

* Do exercises 3jm from Section 2.3 in the notes.

* Read Section 3.2 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Work through the interactive induction proofs.

* Read Section 3.4 in the notes.

* Do exercises 1adfj from Section 3.2 in the notes.

* Do exercises 1, 2, 3, 4, 5, 7 from Section 3.4 in the notes.

* Do the informal writing assignment at this link.

1/22: Class cancelled due to illness.

1/23: The exercises assigned today are due on 1/25. Today's Spreadsheet Today's zero-divisor graph generator. Here is the Mathematica file to generate zero-divisor graphs, just in case the previous link doesn't work for you.

* Do exercises 1ch, 6 and 7 from Section 3.2 in the notes.

* Read Section 2.4 in the notes.

* Read the interactive proofs for the 19 rules using conditional proof.

* Do exercises
1-5 from Section 2.4 in the notes.

* Read Section 3.5 in the notes.

* Do exercises 1, 2, 3, 4, 5, 7 from Section 3.5 in the notes.

1/24: Exam 2 will be given today. It will cover the material from 1/15-1/21. Expect to work for around 60 minutes, no more than 75 minutes. If you get stuck on a logic proof, concentrate on taking legal steps.

The exercises assigned today are due on 1/28. THESE WILL NOT BE GRADED - SOLUTIONS ARE POSTED NOW. YOU DO NOT NEED TO TURN THEM IN.

* Do exercises 9 and 11 from Section 3.2 in the notes.

* Do exercises 6-11 from Section 2.4 in the notes.

* Read Section 6.1 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Do exercises 1-9, 11, 12, 16, and 18 from Section 6.1 in the notes.

1/25: The exercises assigned today are due on 1/29. THIS HOMEWORK WILL NOT BE GRADED. SOLUTIONS ARE POSTED NOW. YOU DO NOT NEED TO TURN THEM IN. If you want to raise a matrix to a power and don't have Mathematica, you can use this site.

*
Read
Section 4.1 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail.

* Read Section 5.2 in the notes, reviewing the in-class worksheet and reading the Reading Assignment in detail. There is a lot in this section that we didn't cover in class. Concentrate on the exercises when studying for the upcoming exam.

* Do exercises 2, 11, 13, from Section 4.1. You may write 2 and11in two-column format if you wish.

* Do exercises 5-11 from Section 5.2 in the notes.

1/28: Class cancelled by the college due to weather conditions.

1/29: We will begin today's class by reviewing for the final exam on Thursday. The exercises assigned today will not be collected, and will not be on the final exam.

* We might do some of the material below. What I cover will be a class-time decision.

*
Read Section 2.5 in the notes.

* Read Section 8.1 in the notes.

* Do exercises 1ac, 2, and 3 from Section 2.5 in the notes.

* Do exercises 1, 2ab, 3, 4ac. from Section 8.1 in the notes.

1/30: No exercises will be assigned today. We will see a few examples of discrete structures in action, then review for the final exam. Come to class with questions to ask!

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

1/31: Our final exam is from 9:00-12:00 on Thursday, January 31. This exam covers the entire course, except the material covered on January 29. You may start as early as 8:00 if you wish.

* The comprehensive final exam will cover all of the material in the course.