• Work through Sections 5.4 and 5.5 (subsection 5.5.1 only). Section 5.4 is a Maple tutorial. Study throughly the theorems and proofs in Sections 5.3 and 5.5 (subsection 5.5.1 only).

• In class on Friday, November 7, turn in solutions to the following problems:

  5.4 Maple Problems: 1, 2, 3, 5.
  5.4 Pencil and Paper Problems: 3, 7, 9.
  5.5 Pencil and Paper Problems: 3, 4, 5.
  

• In class on Wednesday, November 5, and Friday, November 7, be prepared to present the proofs of the Fundamental Lemma and Theorems 3-8 from Sections 5.3 and 5.5 (subsection 5.5.1 only). (See the details below for "Proof Week.")

• The second midterm exam will be on Monday, November 10.

Explanation: In class on Wednesday and Friday, students will write these proofs on the board, give the proofs orally, and write them out on paper. They will not use the textbook or notes while giving these proofs. Of course, no individual student will be asked to give more than one or two proofs. Collectively, however, I hope we have time to go over all the proofs.

Advice: After studying the above sections, pick out two or three proofs to learn thoroughly. Pick the very hardest proofs that you think you can master. Memorization, you will discover, does not work well. Instead, once you have understood the proof, identify the key steps (there are usually only one or two of them); then, using your recollection of these key steps, practice writing out the proofs without looking at the text. At first, you might want to take notes describing the key steps; eventually, however, you should be able to write out the proofs without looking at these notes.