Math 308 1XB - Summer 2018

Course Syllabus

• Math 308 1XB Syllabus - Course syllabus. Contains grading policy, requirements, assignments and other important info.

Video Lectures

For YouTube videos of my Math 308 lectures, click here!

Selected HW Solutions

• HW 1 Selected Solutions
• HW 2 Selected Solutions
• HW 3 Selected Solutions
• HW 4 Selected Solutions
• HW 5 Selected Solutions
• HW 6 Selected Solutions
• HW 7 Selected Solutions
• HW 8 Selected Solutions

Reviews for Tests

Test 1 Review

• The test will have 5 problems and a section for bonus problems (on material not yet covered as of the last class the week before). The test will cover everything we have done up to mathematical induction. The bonus problems can cover anything from the second part of chapter 6 up to equivalence relations and equivalence classes in chapter 8.

• All problems will ask you to prove statements, so there is no problem that asks you to state a definition or fill out a truth table, etc. Though, of course, knowing all that is important!

• The test will also include a problem that define a new concept or object that we have not looked at in class and ask you to prove things about that concept or object. The material will be unfamiliar, but rest assured, you will be able to do the problems based on the skills highlighted in class thus far. Again, this isn't calculus, so problems like this are not only fair, but are important for you to be able to grapple with if you are to be successful in mathematics here and beyond.

• The best practice is to do as many problems as you can. Be sure to go over your homework and other problems in the text.

• Be aware of the fact that, at this level, no review can be considered comprehensive in the sense that the problems will look familiar to those you've studied. So study with the goal of learning, in general, why things work out the way they do, how a technique is used and what a definition means; as opposed to learning how to apply all these to a specific problem type. It is possible, for example, that I can ask you to do a proof by contradiction for a problem that looks nothing like a problem from homework or the review, but you will be able to do it by knowing what a proof by contradiction means and how to approach one. In general though, I usually won't require you to do a specific method of proof. You must examine the situation that you are given and use whatever proof technique you find appropriate or easiest to apply.

• Below I include a review from another instructor that gives practice problems that may be of a different "feel" than what we've done, but uses the same concepts. This will be good to practice grappling with unfamiliar concepts using familiar techniques.

• Test 1 Review - Courtesy of Wolfgang. You can find the solutions to this review here.

• The best way to study is to take a couple days to review and practice the homeworks and other problems in the text and LEARN definitions (*). (Reading solutions is NOT practicing. Practicing means doing problems that you don't already know the solution to on your own without getting help or using someone else's solutions!) Then, for the next couple of days, pick 6 proof type problems from the review above (or from the review and/or textbook) and do them under timed conditions without any help. You will have the entire class period to complete the test. So, practice to be able to do 6 problems that are challenging for you within 1 hour and 40 minutes. Use my solutions, the solutions above or see me during office hours to help you in assessing yourself.

• The practice problems that you pick should cover a variety of topics. For example, if picking problems from the text, you can choose, say, 1 problem from chapter 3, 2 problems from chapter 4, 1 problem from chapter 5, 1 problem from chapter 6, and 1 problem from chapter 8. These should not be problems that you already know the solution to. Sit down with them, put 1 hour and 40 minutes on a clock, and work away. Stop when an hour and 40 minutes have passed, or you've completed all problems, whichever comes first. Then assess yourself. Review the topics you're weak on and then rinse and repeat with a different set of problems. Keep doing this until you can get an A on your practice test. (If it feels easy, you're not practicing the right set of problems. You want to be challenged, you want to know what you don't know, you want to find gaps in your knowledge so that you can fix them before the test. Practice is not about feeling good and patting yourself on the back.)

Good luck on Thursday!

(*) I want you to use definitions as we defined them in class. If you'd like to use another definition for something, you can, but you would have to PROVE that your definition is equivalent to the one I gave you in class before you're allowed to use it. I think it is easier to just use the definition as given in class or the text, but this is an option available to you if you want to use a different definition from another source.

Remember, if when doing some problem you get a definition wrong or otherwise show that you don't know what a definition says, or if you use some equivalent definition without proving it is equivalent, then you will get a zero for that problem!

Test 2 Review

The same guidelines as for test 1 apply. For extra practice, refer to Test 2 Review - Courtesy of Wolfgang. This may also serves as a review for the final.

Test 2 will probably be a take home this semester, but going through this review can be beneficial anyway.

Solutions to Tests

Please see the section on how to use the blanks and solutions.

Test 1

• Test 1 Blank - For extra practice.
• Test 1 Solutions - To check your answers, perhaps with a tutor.
• Alternate solution to problem 4(b) - not using induction

Test 2

• Test 2 - Take home.
• Test 2 Solutions
• Examples that illustrate solution to test 2 problem 3(b)

How to use the tests and solutions I post

Test 1

I post blank versions of the tests as well as the solutions, here's how to use them.

If you feel you did well on the test:

• Review the solutions, to see if you roughly did well. Then forget about it.

• Later in the semester, closer to test 2, redo the exam on the blank copy and then check your answers with the solutions.

• While some of the topics might not appear on test 2, they may appear on the final which will only be a couple days after test 2. So it is worth redoing the exam close to test 2.

• For max benefit, make sure you forgot most of the test and solutions when retaking the test. If you have any suspicion that you remember the problems on the test or the solutions, do not redo the same test. Rather, go to a tutor with the textbook and the test and ask them to make up another similar test for you, and practice that.

If you feel you did NOT do well on the test:

Hopefully this isn't the case, but if it is, there are other options than just giving up. (If you're thinking of giving up, you should probably come see me first). That being said, if you feel you did not do well but you want to continue with the class, here's the best way to proceed from here.

• Do NOT look at the solutions file! Don't do it!!!

• But, do not wait long to go over the test. Do it NOW. When you're at home (or your preferred study location), open the blank test and do it. You don't have to time yourself. Give yourself as much time as you need, just get through the problems by yourself. No notes, no help. Do NOT look at the solutions!!!

• Go see a tutor on Monday and discuss what you did, and only open the solutions file when you're with the tutor.

• It is important that you show the tutor your worked out solutions, the ones you did without help. It will show the tutor where you're having trouble and help them help you more. If you fix your mistakes before seeing the tutor because you don't want to be embarrassed, you're shooting yourself in the foot. I've been a tutor for many years, I assure you, there's no need to feel embarrassed. Trying to save face is not worth failing the class, so be honest with what you show the tutor you've done. The tutor should be looking at your worst attempt, not your fixed-up attempt.

• When you see the tutor, you can view the solutions together (if the tutor needs to). This should be the FIRST time you're seeing the solutions. Only look at the solutions AFTER you've attempted the problems yourself, AND you've discussed your approaches and their merits (or drawbacks) with a tutor. You won't improve much otherwise.

• After you meet with the tutor and looked at the solutions, make an appointment to see me so we can talk about how to move forward in the future.

Best, Jhevon

Announcements

• Be sure to update your email on BlackBoard, or send me updated email contact.
• Test 1 will be on Thursday, June 28 during regular class time.
• Test 2 will be on the last day of classes.
• The final exam will be on Wednesday, July 25 from 10:30am to 12:45pm in our regular classroom.