Math 3592H Honors Mathematics I Fall Semester 2003
Assignment 10 - Due Thursday 11/13/2003
Read: Hubbard and Hubbard Section 2.3, 2.4 and maybe even 2.5. The trouble is that 2.4 is rather a long section with some important concepts in it, as is 2.5, and I find this makes it hard to judge how far we will get. However, we have already got 2.3 out of the way.
Exercises (Due Thursday 11/13/2003):
Hand in only the exercises which have stars by them.
Section 2.3 (pages 190-192): 2, 3, 3a*, 4, 5, 6, 7, 8, 9, 11
Section 2.4 (pages 204-206): 2, 2b*, 4*, 7, 8*, 9, 10, 11, 13*, 14*
1*. Express the matrices in question 2.3.2b and 2.3.2c on page 190 as products of elementary matrices.
2. Suppose that is a linear mapping between spaces of the same dimension. Prove that if f is 1-1 then f is onto. Prove conversely that if f is onto then f is 1-1.
Comments on some exercises:
Some of the exercises in Section 2.4 seem too easy, like questions 3, 5 and 6 for example, and I have left them out of the recommended list. Others seem to require the reader to understand some very specific things which do not seem to me to be that instructive. I include questions 12 and 13 from Section 2.4 in this category, even though in the margin the authors suggest that question 12 is an important exercise. Have a look, and form your own opinion.
In the exam on November 6 the material will be taken from Sections 1.5 - 1.10, starting in Section 1.5 at page 94 where limits, continuity etc. of sequences of vectors and vector-valued functions are introduced, plus the extra questions on the assignment sheets. You may not use books or notes on the exam, but you may use a calculator.
There is a question on the exam in which you are asked to choose between a pair of statements (both are true statements) and prove one of them. If you can answer questions like 1.7.14 or 1.6.7 adequately you should be able to do this question. The trouble will probably be that you do not have much experience doing this kind of question.
There were 10 copycats on a boat. One of them jumped overboard. How many were left?