Math 351 -Principles of Analysis (Section 002 Winter 2006)

Individual Homework Assignments

Instructor: Richard Kollár

For information on the course and my contact information, please visit the Math 351 homepage.

The following assignments must be done individually. Individual homework problems are mostly taken from the textbook. Assignments are posted below. Only problems listed under “Hand in” have to be handed in. The other problems are listed in parenthesis, and are only suggested (and, in fact, recommended) as warm up and preparation for the exams.

Individual Homework Assignment #1 [Due Wednesday January 11 (in class)

Hand in: Exercises 1.4, 1.6, 1.9, 1.11, 2.4, and show: The square root of 2 + the square root of 3 is irrational.

(Recommended: all remaining questions from 1.1-1.11 and 2.1-2.6.)

Individual Homework Assignment #2 [Due Monday January 23 (in class)]

Hand in: Exercises 3.1, 3.6, 4.5, 4.10, 4.12, 5.6.

(Recommended: 3.2, 3.3, 3.5, 3.7, 3.8, 4.1 - 4.4, 4.5 - 4.9, 4.14, 5.1-5.3)

Individual Homework Assignment #3 [Due Monday January 30 (in class)]

Hand in: Exercises 7.4, 7.5, 8.1d, 8.2e, 8.4, 8.7c.

(Recommended: 7.1, 7.3 and all remaining questions from §8.)

Individual Homework Assignment #4 [Due Monday February 6 (in class)]

Hand in: Exercises 9.2b, 9.4, 9.6, 9.12a, 9.15 and show:

Suppose that a sequence (s_n) of nonzero numbers converges to nonzero s.

Show that there is a positive number M > 0 such that every element of the sequence (s_n) has absolute value at least M.

[Hint: Mimic the proof of Theorem 9.1 or read §8 carefully.]

(Recommended: All remaining questions from §9 and 10.1.)

Individual Homework Assignment #5 [Due Monday February 13 (in class)]

Hand in: 10.6, 10.10, 11.1, 11.2, 11.4 and 11.6.

(Recommended: 10.8, 10.12, 11.3, 11.5, 11.7 and 11.9.)

Individual Homework Assignment #6 [Due Monday March 13 (in class)]

Hand in: 12.10, 12.11, 14.2, 14.4, 14.8.

(Recommended: All the remaining questions from §14.)

Individual Homework Assignment #7 [Due Monday March 13 (in class)]

Hand in: 17.2, 17.10, 17.12, 18.3, 18.6, 18.8.

(Recommended: 17.1, 17.6, 17.9, 18.1, 18.9, 18.11.)

Individual Homework Assignment #8 [Due Monday March 20 (in class)]

Hand in: 19.2, 19.4, 19.6, 19.9.

(Recommended: 19.1, 19.3, 19.7, 19.8.)

Individual Homework Assignment #9 [Due Monday March 27 (in class)]

Hand in: 20.2, 20.6, 20.14, 20.16., 23.2, 23.4.

(Recommended: 20.1.-20.10, 20.12, 20.13, 23.1, 23.5.)

Individual Homework Assignment #10 [Due Monday April 3 (in class)]

Hand in: 24.2, 24.8, 24.14, 25.8, 26.2, 26.4.

(Recommended: 24.1, 24.4, 25.3, 25.5, 25.6, 25.14, 26.3, 26.6, 26.7)

Individual Homework Assignment #11 [Due Monday April 10 (in class)]

Hand in: 26.8, 27.3, 28.2, 28.4, 28.8, 29.4.

(Recommended: 28.1, 28.3, 28.5, 28.6, 28.9, 29.1, 29.2.)

Page Updated: 4/3/2006