Math 3592H Honors Mathematics I Fall Semester 2003

Assignment 1 - Due Thursday 9/11/2002

Read: Hubbard and Hubbard Sections 1.1 and 1.2. The authors make some distinctions which I would not make myself and which I think add unnecessarily to the complication of the material being presented. They distinguish between a point in Euclidean space and a vector, the latter being something with magnitude and direction, and use round or square brackets to indicate a difference. I would use the same notation myself in both cases (probably round brackets), and not make the distinction. In the text they do indicate how it is that a point can be regarded as a vector, once the origin of the coordinate system has been chosen.

We are starting with vectors and matrices, although the emphasis of the course is on advanced calculus, in part because the book starts there, but also because I am not sure of your background in analysis (sequences and series etc.). With vectors and matrices I assume you know nothing about them, and that makes it easier for me! The point of the exercise you did on Tuesday was to give me some idea of what you already know about analysis, and if necessary I can supplement what is in the book to bring you up to speed in that area.

Exercises:
Hand in only the exercises which have stars by them. The remaining questions are listed because you should get practice multiplying matrices etc. if you have not already had practice doing this. On Thursday next week there will be a quiz, and it will be based on the homework questions listed below, including the ones you are not asked to hand in.

Section 1.1 (pages 42-43): 1, 2, 4b*, 5ab, 6bcfg, 7b*, 8*

Section 1.2 (pages 55-58): 2abde, 3ab, 4, 5, 6bcgh, 7, 8*, 10, 11, 13, 15, 16, 17*, 20, 21*