Math 311, Introduction to Analysis, Spring 2008

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. http://cuinfo.cornell.edu/Academic/RSS8/RSS8MATH.html

Instructor

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

TA

Andrew Marshall
Office Hours: Monday 1:30--3:00 pm, 218 MH

Syllabus


Lectures and Homework

  1. Lecture 1, 01/21/08 Introduction, Syllabus, Appendix A1,A2
  2. Lecture 2, 01/23/08 Chapter 1
    Homework 1, due 02/06/08 (Solutions and more) Exercises 1.3.1, 1.4.1, 1.6.1, Problems 1-1, 1-2.
  3. Lecture 3, 01/28/08 Sections 1.3 and 1.4
  4. Lecture 4, 01/28/08 Sections 1.5 and 1.6
  5. Lecture 5, 02/04/08Sections 2.2, 2.3, 2.4
  6. Lecture 6, 02/06/08Sections 2.5, 2.6, 3.1
    Homework 2, due 02/13/08(Solutions) Exercises 2.1.2, 2.2.1, 2.4.2, 2.6.1, 2.6.2, Problems 2-1 and 2-2.
  7. Lecture 7, 02/11/08Section 3.1, 3.2
  8. Lecture 8, 02/13/08Section 3.3-3.7
    Homework 3, due 02/20/08(Solutions) Exercuses 3.1.1 (a,d,e), 3.2.2, 3.2.4, 3.3.2, 3.6.1 and Problems 3-1 and 3-4.
  9. Lecture 9, 02/18/08Section 4.1, 5.1
  10. Lecture 10, 02/20/08Section 5.2, Section 5.3
    Homework 4, due 02/27/08(Solutions) Problem 4-1; Exercises 5.1.1, 5.1.4, 5.2.1, 5.2.3
  11. Lecture 11, 02/25/08 Section 5.3, 5.4
  12. Lecture 12, 02/27/08 Section 5.4, 6.1
    No homework assigned; I will hand in the first prelim on Wednesday; Solutions to the first prelim
  13. Lecture 13, 03/03/08 Section 6.1 (cont'd)
  14. Lecture 14, 03/05/08 Section 6.2, 6.3
    Homework 5, due 03/12/08(Solutions) Exercises 6.1.1, 6.2.2, 6.3.1, Problem 5-2
  15. Lecture 15, 03/10/08 Section 6.3 and 7.1
  16. Lecture 16, 03/12/08 Section 7.1, 7.2
    Homework 6, due 03/26/08(Solutions) Exercises 6.4.2, 7.1.1, 7.2.2, 7.2.4, Problem 6-1.
  17. Lecture 17, 03/24/08 Section 7.3, 7.4, parts of 7.5
  18. Lecture 18, 03/26/08 Section 7.4, 7.5, 8.1
    Homework 7, due 04/02/08(Solutions) Exercises 7.3.2, 7.3.3, 7.4.1( b),d),i),j) ), 7.4.2. Problem 7-3.
  19. Lecture 19, 03/31/08 Chapter 8
  20. Lecture 20, 04/02/08 Sections 9.1, 9.2, 9.3
    I will hand in the second prelim on Wednesday Solutions to the second prelim)
  21. Lecture 21, 04/07/08 Section 9.4, 10.1
  22. Lecture 22, 04/09/08Section 10.1, 10.2, 10.3
    Homework 8, due 04/16/08(Solutions)Exercises 9.4.1, 10.1.6, 10.1.8, 10.4.1, 10.4.2
    Andrew wrote a nice sum-up about pointwise, local, and global properties of functions. You can get it from here
  23. Lecture 23, 04/14/08 Section 11.1,11.2, 11.3
  24. Lecture 24, 04/16/08 Section 11.4, 11.5
    Homework 9, due 04/23/08 (Solutions) Exercises 11.2.2, 11.3.1(a), 11.4.2, 11.5.1, PRoblem 11-3.
  25. Lecture 25, 04/21/08 Chapter 12
  26. Lecture 26, 04/23/08 Sections 13.1, 13.2
    Last homework, #10 Exercises 12.1.1, 12.1.3 (ignore the part about Newton's method), 12.1.4, 13.1.1
  27. Lecture 27, 04/28/08 Sections 13.3 and 13.4
  28. Lecture 28, 04/30/08 Section 13.5
    I will hand out the final on Wednesday! Good luck
Marius Ionescu, 01 May 2008