Math 3593H Honors Mathematics II Spring Semester 2006

Assignment 4 - Due Thursday 2/16/2006

On this date we will have the first mid-term exam, which will be about Sections 2.9, 3.1, 3.2 and 3.7. There will be no quiz! You may use a calculator. You may not use notes, the book, or a computer.

Read: Hubbard and Hubbard Sections 4.1 and 4.3.

Section 4.1 (pages 411-415): 3, 5, 6, 9*, 10*, 11, 14a*, 15, 16.
Section 4.3 (pages 434-435: 1*, 2, 5*.

Sections 4.1 and 4.3 are theoretical in nature, concentrating on the foundations of what can and cannot be done. There is a lot to read, and it probably looks rather complicated. However, if you could somehow instantly read everything the authors write, I think you may think that you could have guessed the highlights anyway (e.g. Theorem 4.3.7: continuous functions can be integrated). From Section 4.1 I have asked questions about the foundations of the integral, but they are the same as questions that could have been asked about one-dimensional integrals, which you may well have been able to answer anyway.

We are skipping Section 4.2.