Foundations of Analysis

Foundations of Analysis
MAT 3213 Section 003
Fall, 2001
Instructor: Prof. J. Iovino

A course outline and a general description of the policies of the course is available here

News

December 3

The take-home final exercises are as follows.
Chapter 5: #8, #41; Chapter 6: #7, Chapter8: #2, #12, #17. Due no later than December 14 at noon. Enjoy!

November 21

We will skip Chapter 7, and start Chapter 8 immediately after the Thanksgiving break. This is a very important chapter, so don't get behind. See the assigment below.

October 16

Here are the take-home exercises: Chapter 1, #17; Chapter 2, #4, #20; Chapter 3, #12, Chapter 4, #18.

September 24

Homework 2 has been postponed until September 24. The revision of Homework 1 is due October 2.

Homework 1: Study for for 8/29: pp. 3-10.; Prepare for 8/29: Chapter 1, Exercises 1(i), 1(ii), 1(iii), 1(iv), 2, 3(iii).
Homework 2: Study for for 9/5: Finish Chapter 1.; Prepare for 9/5: 5(i), 5(ii), 5(iii), Theorem 1 (p. 11).; Hand-in on 9/12: 7, 9.
Homework 3: Prepare for 9/10: 12, 14.
Homework 4: Prepare for 9/12: 12(iii)-12(vii) (without using cases), 14, 18.; Study for 9/12: pp. 21-26.
Homework 5: Prepare for 9/19: Exercises 1-3, p. 27.; Hand-in on 9/24: Exercise 18, p. 17.
Homework 6: Prepare for 10/1: 8, 10, p. 30.; Prepare for 10/3: 12, 13, 14.
Homework 7: Study for 10/8: Pages 39-48 (Chapter 3). Study these carefully.
Homework 8: Prepare for 10/10: Exercises 1,3, p. 69.
Homework 9: Hand-in on 10/17: Exercise 4, p. 69.
Homework 10: Study for 10/17: Pages 90-101. Study these pages carefully. They are fundamental.; Prepare for 10/17: Theorem 1, p. 98 and Lemma on p. 101.
Homework 11: Prepare for 10/26: Theorem 2 on p. 102, and pages 103-105.
Homework 12: Prepare for 10/29: Exercises 3(i) and 3(ii), p. 106.
Homework 13: Prepare for 10/31: Exercises 3(iv) and 3(v), p. 106.
Homework 14:: Prepare for 11/5: Exercises 7 and 12, p. 107.
Homework 15:: Prepare for 11/7 and 11/12: Exercises 13, 17, 37, 38, Chapter 5.; Hand-in on 11/21: Exercises 21 and 22, Chapter 5.
Homework 16:: Study for 11/14: Pages 113-117.; Prepare for 11/14: Exercise 3, p.117.
Homework 17:: Prepare for 11/19: Exercise 16, p. 119, parts (a)-(c), and Theorem 3, p. 117.
Homework 18:: Prepare for 11/21: Exercise 10 (all parts)
Homework 19:: Prepare for 11/26: Pages 131-136. Study these pages carefully.
Homework 20:: Prepare for 11/28: Exercise 1, p. 137 (all parts, except (i) and (ii), which were done in class.).
Homework 21:: Prepare for 12/3 and 12/6: All the proofs in Chapter 8.

Material covered

8/27: Chapter 1 (axioms of field).
8/29: Chapter 1 (axioms of order).
9/10: Chapter 1 (absolute value).
9/12: Chapter 1 (exercises).
9/17: Chapter 1 (exercises).
9/19: Chapter 2 (axiom of induction).
9/24: Basic combinatorics: permutations and combinations.
9/26: Binomial coefficients and more combinatorics.
10/1: The Binomial Theorem.
10/3: Rational an irrational numbers.
10/8: Chapter 2 (exercises).
10/10: Chapter 4 (exercises).
10/15: Chapter 4 (exercises).
10/17: Started Chapter 5.
10/22: Chapter 5.
10/24: Chapter 5.
10/24: Chapter 5 (more examples and exercises).
10/24: Chapter 5 (exercises).
11/5: Chapter 5 (exercises).
11/7: Chapter 5 (exercises).
11/12: Chapter 5 (exercises).
11/14: Chapter 6 (exercises and various counterexamples).
11/19: Chapter 6 (exercises).
11/21: Chapter 6 (exercises).
11/26: Chapter 8 (introduction and examples)
11/28: Course survey. Remarks about Chapter 8.
12/3: Detailed proof of Theorem 7-1 (page 133).

Exam Dates

Midterm: Wednesday, October 17.
Final: Friday, December 14, 1:30 - 4:15 PM.