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I've grouped the class meetings into seven blocks of two weeks each. Usually homework (HW) is due on the last Thursday of the block. The HW lists are intended to be the minimal required to get by. Most students should do at least 50 per cent more (your choice), to master the material and do well on the exams. I will probably have to adjust some dates and content from time to time. I will make those changes as early as I can, and will announce any major ones in class.

How to read the tables: As you can see from the table below, I expect to cover at least 1 section of our book per lecture. The last column says you should do the exercises from Ch 1.1 asap after my first lecture. But you will not hand this in until Jan 22, along with the rest of HW 1 (Chs 1.1 thru 1.5). Exam 1 will be Thursday, Jan 29, mainly covering the topics in HW 1 (Chs 1.1 thru 1.5). It might also include some fairly easy questions on recent topics from my lectures up to one week before the exam - in this case this means Ch.1.6. These recent topics may re-appear on Exam 2. The other blocks, HW and Exams follow the same pattern, except that most other exams will cover two HWs, plus new "recent topics".

I may abbreviate, for example, "problems 1, 3, 5 and 7" by "odds to 7". Contact me if you don't understand anything, or you see a conflict with a religious holiday, or some other mistake.

Weeks 1-2

Read Chs 1.1-1.6. I may go through 1.5-1.6 rather quickly, unless there are questions about these topics. I suggest scanning each section before the lecture, then reading it carefully afterwards, and then doing the exercises, but this is up to you. Many students learn 1.1 through 1.6 quickly, but need more time with 1.7 and 1.8. I'd suggest starting those asap and doing ALL the exercises in Ch.1.7 if you have time. This is great preparation for the rest of this course, and future mathematics courses. Since that's probably too much for some students, I won't require you to do them all, but can give some extra credit for that (see me, if interested). Recently, a few people bought textbooks online which did not quite match ours. Check in your book that HW problem 50 from Ch.1.1 is about a barber. If not, you may have a problem.

Look over my website, so that you know my policies, abbreviations, and the resources it may offer you this term. I once wrote some web pages to help students in another class with logic and proofs. I have also posted all of that for you - and you can start practicing with Proofwriting Part I now, if you like (this is not required, but past students said it helps).  I have created other "Help" pages for many of my classes, and will do so for Discrete Math, if I get many common questions. Meet our Learning Assistant, John Williams, by attending one of his LA sessions (TRs, from 11:00 AM - 1:00 PM in room 409A.). Attendance is not required, but this may help your grade a little if you are on a borderline at the end.

If you don't want your HW graded, you need to write me a note or email in the first week.

I may update this page at any time - for example, to add advice about an exam, or adjust a HW list. So, even if you print this out, it would be a good idea to re-visit this page every week and pay close attention to announcements in class.

Weeks 3-4

John's LA hours - Tuesdays and Thursdays from 11:00 AM - 1:00 PM in room 409A. I strongly encourage you to attend regularly, and bring questions.

For Exam I, I mainly expect you to do HW 1, and to read through Ch 1.6 or 1.7 until you feel you have mastered those topics. There may also be easier questions based on the lectures through 1/22 [eg Ch.1.7]. I've posted some old exams and quizzes on my exam page which you can use for practice or feedback. The division of topics will vary a bit by semester. Your Exam I topics might resemble Quiz 1 + Quiz 2 topics from previous years. I will post answers there for the 2015 exams, often with updated grading scales, a few days after each exam. I may include True-False or an easy proof (though proofs will be more likely on Exam 2, etc). If you feel lost on proof-writing, try my online drills, or come by my office hours for help. There are also a few good books on proofs (eg Velleman's) which you can buy at local bookstores if you need to spend more time on this.

Some links and remarks from my 2012 course, possibly still interesting, but not required - - - Logic gates were built from mechanical devices in the 1800's (see the textbook, page 31 - Augusta Ada), and then with transistors in the 1900's. Scientists are now experimenting with DNA or bacteria based gates. Apparently, they can now calculate the square root of 2 with these - see DNA computer. If you are interested in AI, check out Cleverbot talks to itself. These links are mainly for fun, though I may use them for extra credit questions.

I give a little extra credit for finding mistakes on the website, so let me know if you spot any. Also, some students have helped out by providing links to other useful sites. If people express interest, or ask similar questions, I will create a Help Page.

When practicing proofs, imagine your reader is very skeptical of all your ideas, but not so well-educated as yourself, and needs your help. (this link may be amusing, but is NOT required). It may be useful to show your first proofs to a skeptical friend, or to John our LA, or to me. Get some feedback!

As usual, HW will be due on Thursday, and it starts where HW 1 stopped, at Ch. 1.6.

Here is an interesting article about our future and artificial intelligence. Perhaps Discrete Math will play a role in this ?

Weeks 5-6

Learn how to use words and phrases like "even", "rational", "f(S)", "onto" etc, etc, in proofs. Definitions are major proofwriting tools and the HW should help build your skills with these, but I also recommend memorizing these definitions as needed. Hopefully, we can get a little ahead of the schedule below, to spend more time on harder topics later on.

Weeks 7-8

John expects to finish grading HW 3 by Thursday morning. You can come by my office Thursday from approx 10:15am to 10:45am or 1pm to 1:45pm to pick it up. You can ask a friend to pick it up for you, but in that case send me an email including your student ID and giving me your permission. If you like, you can email John for an update, and/or possibly pick it up from him.

Exam 2 will mainly cover topics from HW2 and HW3, Chs 1.6 to 2.6. You should be able to write induction proofs about sums, powers, divisibility, postage stamps, triominoes, etc, as in the HW and lectures. Study Cantor's diagonal argument and other "standard proofs" such as the square root of 2 one. I may also ask relatively simple questions related to my recent lectures (eg 2/19), thru Ch. 5.1. Be able to do basic calculations involving infinite intersections or unions of sets, [Boolean] products of matrices, sums and double sums.

I am assigning more problems than usual this week, because counting is a new skill that takes practice. Once you get it, most of these problems should seem fairly quick and easy [maybe even fun]. Feel free to ask me or your LA for tips. 

This is the Sierpiski Gasket, an example of a two dimensional fractal set. I created this image using PhotoShop and a recursive method of cutting, pasting and shrinking. Perhaps it is not very important, but you can view it as a rotated Pascal's Triangle [see Ch 6.4], with the even numbers blanked out (many details omitted, see me if interested).

Spring Break, Mar 9-14

Weeks 9-10

Some people develop counting skills over time. If it is coming slowly to you, I'd suggest practicing lots of easy problems (Ch 6.1) until you have totally mastered those before going on. But the next exam may include medium-hard counting problems similar to those on the HW, lectures or reading. Go as deep as you can.

I think 3/23 is the Spring term drop date, but you should check this, and handle it yourself. I am not usually involved unless you ask my advice. The grading scales on the answer keys should tell you where you stand (not including the effects of HW, extra credit, etc).

*In the HW problems, 9.1.35 and 9.1.37 below, just do parts a, c, e and g.

Weeks 11-12

Exam 3 will mainly cover topics from HWs 4 and 5, but also recent lectures through 3/26 (approx Ch 10.1). Understand and memorize the Binomial Theorem in Ch.6.4 (this kind of thing may go without saying, but the exam answers were not always good in the past). Know the combinatorial proof of it from my lecture and the proof in Ch. 6.2 that r(3,3)=6. Know the proof of Thm 1 in 9.1 (about transitive relations).

I wrote this for anoher class, which had trouble with counting problems the first time ... I want you to practice more with easy counting problems, and may ask about the number of edges in various graphs from 10.2 or 10.3 (such as Wheels, nCubes, etc). Also, there are many good counting questions from Ch 9. I am planning to put at least one counting problem on the final, and also one basic proof (about sets and subsets, for example). So, practice your proofwriting style, and feel free to ask for help, or to check your answers.

The Last Weeks

Extra Credit projects are due Thursday 4/16/15, unless I give you an extension in writing, for choosing an especially difficult topic for example. I may accept late projects until 4/21/15.

The final will NOT be based on the exams, except that it might review any weak spots identified in the answer keys. It is more likely to be based on the homework, lectures and reading. It counts 30 points. At least one third of it, perhaps half, will be on topics from the last 4-5 weeks, starting around Ch.10.3, like an "Exam 4". The rest will be about earlier topics. You don't have to hand-in the problems after Ch 11.2. They are really practice problems for the final exam.

I assume you'll spend most of your final exam study time on the recent material. If you have some time for review, I'd suggest reading over Chs 1.6 and 1.7 (on basic proof-writing) and practicing those ideas in Ch 2. [For example, you could work through problems similar to 2.1 - 17, 23 and 2.3 - 29, 36]. That should remind you of vocabulary such as "onto", etc. In fact, I'd suggest a quick review of the vocabulary for the whole course. Practice more with counting problems, too. Know the same proofs as for Exam 3 (since that exam did not contain a proof). Upon request, I am posting review sheet 1 and review sheet 2 for the final. I hope they help you study, but using them is completely optional. I repeat my suggestion that mastering the HW lists is the best strategy.

April 21 is the final deadline for providing medical excuses, late HW 6 or late projects, regrading requests, etc (but for better responses, do not wait until then). I may be harder to reach after that.

Final Exam : Thurs, 4/30/15, 12pm to 2pm, in our usual room, it covers the entire course.

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