**Math 3592H Honors Mathematics I Fall Semester 2003**

**Assignment 3: Modification** It was too much to get through Section 1.5 during this week. On Thursday 9/25/2003 hand in only Extra questions 2, 3, 4, 5 and from Section 1.5 questions 4, 6. See below for what happens to the rest of the questions!

**Assignment 4** - Due Thursday 10/2/2003

**Read: **The rest of Hubbard and Hubbard Section 1.5.

Exercises:

Hand in only the exercises which have stars by them.

Section 1.5 (pages 106-110): 8, 9, 10* (assume 9 without proof), 12, 13, 14, 15, 19, 21a*, 22, 23c*, 23e*

Extra questions:

1*. Consider the sequence of points in R^2 given by a_n = (1/(1+n), n/(1+n)). Find a number M so that |a_n - (0,1)| < 0.1 for every n with n > M.

2*. Consider the function f(x,y) = x^2 + y^3 - 3 which appears in question 14d of Section 1.5. Find a positive number d so that |(x,y) - (1,2)| < d implies |f(x,y) - 6| < 0.1 .

**Peter's Points:**

The first mid-term exam will be held in the recitation on Thursday October 2. In anticipation of this I have tried to restrain myself by not being overly ambitious about the material I hope to cover before then - believe it or not! The material which will appear on the exam will be taken from sections 1.1 - 1.5, together with material such as has appeared in the extra questions I have written out on this assignment sheet and the last. On this exam you may not use any book or notes. I have decided that you may use a calculator during the exam. The issue in my mind here is that some of you may have calculators which calculate determinants and inverses of matrices, and perhaps some other useful things. I will deal with this by not asking questions where it would be an advantage to have such a calculator. You may not bring a computer to the exam.