Math 311, Introduction to Analysis, Fall 2007

Overview

This course is a bridge from introductory calculus to higher-level analysis. The main focus will be on developing the logical skills required to analyze and construct mathematical proofs. This will be done in the setting of familiar ideas from basic calculus, which will be revisited in rigorous detail.

Textbook

Introduction to Analysis, by Arthur Mattuck.

Instructor

Marius Ionescu
Office: 588 Malott Hall
email: mionescu@math.cornell.edu
Office Hours: Monday 11:00--12:30pm, Tuesday 3:30--4:30pm

TA

Ri-Xiang Chen
Office Hours: Malott 218 Thursday 11:30--12:30pm, Friday 10:30--11:30.
email: rxc@math.cornell.edu

Syllabus


Lectures and Homework

  1. Lecture 1, 08/23/07 Introduction, Syllabus, Appendix A1,A2
  2. Lecture 2, 08/28/07 Chapter 1
    Homework 1, due 09/04/2007 Exercises 1.3.1, 1.4.1, 1.6.1, Problems 1-1.
  3. Lecture 3, 08/30/07 Chapter 1 (cont'd) Chapter 2
    Homework 1 (cont'd), due 09/04/07; Solutions Exercises 2.1.1, 2.2.1 Problem 2-1
  4. Lecture 4, 09/04/07 Chapter 2 (cont'd)
  5. Lecture 5, 09/06/07 Chapter 3
    Homework 2, due 09/11/07; Solutions Chapter 2 Exercises 2.4.2, 2.6.2, 2.6.3 and Problem 2-2; Chapter 3 Exercises 3.1.1, 3.2.2, and Problem 3-1
  6. Lecture 6, 09/11/07 Chapter 3 (cont'd), Chapter 4
  7. Lecture 7, 09/13/07 Chapter 5
    Homework 3, due 09/18/07 Solutions Chapter 3 Exercises 3.3.1, 3.4.1; Chapter 4 Exercises 4.1, 4.2.1, and 4.2.2; Chapter 5 Exercises 5.1.1
  8. Lecture 8, 09/18/07 Chapter 5 (cont'd)
  9. Lecture 9, 09/20/07 Chapter 6
    Homework 4, due 09/25/07 Solutions Chapter 5 Exercises 5.2.3, 5.3.3, Problem 5-2; Chapter 7 Exercises 7.1.1
  10. Lecture 10, 09/25/07 Chapter 7; prepare questions 7.2.1, 7.2.5, and 7.3.1.
  11. Lecture 11, 09/27/07 Chapter 7; prepare questions 7.4, 7.5, 7.6.1
    Homnework 5, due 10/02/07 Solutions Chapter 7 Exercises 7.2.1, 7.3.2, 7.4-7.5 1 a),b), d), f), h), j), 7.6.1
  12. Lecture 12, 10/02/07 Chapter 8; prepare question 8.1;
    Some notes on infinite series.
  13. Lecture 13, 10/04/07 Chapter 8; prepare question 8.2 and 8.3
    Homework 6, due 10/11/07 SolutionsChapter 8, 8.1 a), c), f), g), 8.2.1, 8.3.1
  14. Lecture 14 Chapter 9, 9.1, 9.2, 9.3;
    Homework 7, due 10/23/07 Chapter 9 Exercises 9.2.1, 9.2.3, 9.3.1;
  15. Lecture 15 Chapter 9;
    First prelim solutions
  16. Lecture 16 Chapter 9 and Chapter 10
    Homework 7 (cont'd), due 10/23/07 Solutions Chapter 9 Problem 9-1; Chapter 10 Exercises 10.1.1, 10.1.2, 10.4.1
  17. Lecture 17 Chapter 10 and Chapter 11
  18. Lecture 18 Chapter 11
    Homework 8 Solutions Chapter 11 Exercises 11.1.2, 11.1.6, 11.2.1, 11.3.1
  19. Lecture 19 Chapter 11 (cont'd)
  20. Lecture 20 Chapter 11 (cont'd), Chapter 12
    No homework assigned. On Thursday I will hand out the second prelim! Good luck Solutions of the second prelim.
  21. Lecture 21Chapter 12
  22. Lecture 22 Chapter 12 (cont'd), Chapter 13
    Homework 9, due Tuesday, 11/13/07 Solutions Chapter 12 Exercises 12.1.2, 12.1.4, 12.2.4, Problem 12-2.
  23. Lecture 23 Chapter 13 (cont'd)
  24. Lecture 24 Chapter 13 (cont'd)
    Homework 10, due Tuesday, 11/20/07 Solutions Chapter 13 Exercises 13.1.1, 13.3.1, 13.4.1; Problem 13-4.
  25. Lecture 25 Chapter 14
  26. Lecture 26 Chapter 15
  27. Lecture 27 Chapter 15
    I will hand in the final on Thursday; our last day of class; the final is due Thursday, December 6 by 5:00 pm. Good luck!
Marius Ionescu, 27 Nov 2007