Math 31B, Lecture 6

Midterm 2 Information

Time and Place

The second midterm is Friday, February 23, from 12 noon to 12:50pm.

It will not be held in our normal classroom, but rather in
MS 5200.

Don't forget!

Extra Help

I will have extra office hours Wednesday at 5pm (until 6pm or as late as 7pm if there's interest), and also Thursday 9-11am.

Jane will hold a review session Thursday evening, time and place to be determined.

Exam Format

There will be 5 questions, and the exam will be worth 100 points.  Different questions will be worth different points, and there could be multiple parts per question.  The problems will vary in difficulty, but the difficulty does not necessarily correspond to the point value.  The exam covers sections 8.8, 9.1, 9.2, and 12.1 to 12.4.  Of course you may need to recall earlier material that is useful for solving problems in these sections.


  1. Remember first of all that the point of this class is for you to learn the material.  The exam is a way for me to get an idea of how much you've learned, but more importantly it's a chance for you to review what we've covered so far and learn it more thoroughly.  Concentrate on things that were confusing the first time around and work on them until they are clear. Of course don't hesitate to ask Jane and myself if you have questions.  It's not possible for me to test you on everything we've covered, but my hope is that merely by reviewing the material you'll have learned it better whether you are tested on it or not.  Ideally you'll be over-prepared for the exam!
  2. Test questions will be similar to homework problems.  The best way to review the material is to review your homework problems, and to work similar problems (for this test, odd problems in the sections and also chapter reviews).  Make sure you understand the concepts as well, so that you can solve different problems than just ones you've already seen.  This test will be more focused on concepts than on computation.
  3. The test is fairly long, so you'll need to work quickly.  Be well-prepared and well-rested.  You will need to think during the exam!
  4. On the test, show me what you know.  If you can't completely solve a problem at least show clearly what you tried, how much you understand, and how far you could get.  Don't write nonsense.  That is just a clear indication that you don't understand what you're doing.  It's better to know what you don't understand and be honest about it!
  5. You must be able to state precisely all definitions, theorems, and important results in Sections 12.1 to 12.4 of the text; that is, everything that has a red box around it.  If you forget one and need it for a later part of a problem, you may "buy" it for the number of points it is worth (in other words you get zero points for the part that asks for the definition or theorem statement, but you will be given it and can use it to solve other parts of that problem).
    You do not need to know the proofs of the theorems, except for Theorem 6 (page 741; know both proofs mentioned in exercise 69) and results 3 and 4 on page 751 (you need only remember the results for the case a=1).  For result 3 on page 751, you should know both the book's proof and the proof by mathematical induction (see homework 5).
  6. You must also be able to do simple proofs at the level of the assigned homework exercises, including simple proofs by induction.  Your proofs will be graded on completeness and clarity.
  7. Be sure to get your graded homework up to homework 3 back from Jane on Tuesday.  I will return homework 4 and 5 in lecture on Wednesday.  For homework 6, make a photocopy of your solutions before you hand them in if you wish to study for them.  Solutions to the assignment will be posted Wednesday afternoon.

Good luck!