preparation

Mon 7 Sep

• Read the Preface, 1.1 and 1.2.

Wed 9 Sep

• John:
  • 1.2.3a,
  • Suppose that the US replaced all of its coins and notes with a 3 cent coin and a 5 cent coin. What values could things be priced at? Prove it.
• Numen:
  • 1.2.3b
  • Prove that \( \sum_{i=1}^n i^2 = n(n+1)(2n+1)/6 \)
• Sam:
  • 1.2.3c
  • Let \( x\) be a real number not divisible by \( \pi \). Prove that \( \sin x + \sin 3x + \sin 5x + \cdots + \sin(2n-1)x = (1-\cos 2nx) / 2 \sin x \)
• Casey:
  • 1.2.2.d (1st ed)
  • Prove that \( \sum_{i=1}^n 2i-1 = n^2 \)

• Everyone:
  • One more question from 1.2 of your own choosing.
  • Read 1.3.

Mon 14 Sep

Wed 16 Sep and Mon 21 Sep

Wed 23 Sep

Mon 28 Sep

• Read 2.2-2.4, including trying a few exercises and having either interesting ones or ones where you got stuck ready to share. It's more important that you read deeply and carefully and do some exercises than get to the end of 2.4, so concentrate on that.

Wed 30 Sep

• Exercises for 2.4 if you didn't get that far last time, and read to 2.6 (again, doing exercises).

Mon 6 Oct

• As well as the material for 30 Sep, read and do exercises from 2.7.

Wed 8 Oct

• 2.8 and 2.9.

Mon 13 Oct

• 3.1, 3.2, 3.3 up to (but not including) open covers and the Chapter 3 epilogue (just a first-pass read-through to get a sense of the ideas---you don't have to try any exercises yet).
• Assignment due today

Wed 15 Oct

• 4.1 and 4.2, including doing lots of exercises for discussion.

Wed 22 Oct

• 4.3 and 4.4, including doing lots of exercises for discussion.

Mon 27 Oct

• Quiz! (Easy questions from Chapters 1 and 2---make sure you know the definitions and can state the important theorems especially.)
• 4.5.

Wed 29 Oct

• Read 4.6 in sufficient detail to have a good sense of the overall structure, and maybe try one or two of the embedded exercises. Come to class ready to try to fill in the details.
• Read 4.7 and 5.1.

Mon 2 Nov

• 5.2, 5.3 (bring exercises to discuss).

Wed 4 Nov

• Read 5.4 in sufficient detail to have a good sense of the overall structure, and maybe try one or two of the embedded exercises. Come to class ready to try to fill in the details.
• Read 5.5.
• (Also, there's an assignment due today.)

Mon 9 Nov

• Skim through 6.1.
• Read 6.2 and 6.3 and attempt some exercises.

Wed 11 Nov

• Try to get through 6.4 and 6.5, but it's more important to do exercises than to get to the end of 6.5.

Mon 16 Nov

• Quiz! Be ready to answer questions from the material we covered in Chapters 3 and 4.
• Get to the end of Taylor Series and try to understand what's going on with the counterexample near the end of the chapter. Read the epilogue.
• Assignment is/was due on Friday 13 Nov.

Wed 18 Nov

• 7.1 to 7.3, including trying some exercises.

Mon 23 Nov

• Familiarise yourselves with 7.4 and 7.5.
• 7.6 and epilogue.
• Be ready to build your post-thanksgiving schedule.

Wed 25 Nov

• Open class: more on the details of 7.4 and 7.5, or anything else you'd like to talk about.
• Assignment due.