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Math 323, Real Analysis I, Fall 2012

Instructor

Marius Ionescu
Office: 201K MCGREG
email: mionescu at colgate.edu
Office Hours: We 1:00-2:30pm, Th 3:00-4:30pm

Classes

• MWF 11:20-12:10am 215 MCGREG

Exams

• First midterm: Friday, October 5, in class
• Second midterm: Friday, November 9, in class

Textbook

Understanding Analysis by Stephen Abbott, Springer Verlag.

Homework

I will post weekly homework on this webpage. I will post both the pdf and the latex (source) file of the homework. Recall that you need to turn in the homework typed in LaTeX starting with the fourth assignment.

Lectures

1. Half day, 08/27/12 Note the special hour: 11:00am Introduction, Syllabus
2. Lecture 1, 08/29/12 Sections 1.1, 1.5
3. Lecture 2, 09/03/12 Section 1.3;
   Homework #1, due Friday, September 7: PDF file and TEX file
4. Lecture 3, 09/05/12 Sections 1.3 (cont'd) and 1.4;
5. Lecture 4, 09/07/12 Section 1.4 (cont'd); Section 2.2
   Homework #2, due Friday, September 14: PDF file and TEX file
6. Lecture 5, 09/10/12 Section 2.2 (cont'd)
7. Lecture 6, 09/12/12 Section 2.2 (cont'd), 2.3;
   Practice Problems (not to be handed in): page 18 #1.3.5, 1.3.8; page 27 1.4.5, 1.4.7 page 32 #1.5.9; page 42 #2.2.4, 2.2.5, 2.2.8
8. Lecture 7, 09/14/12 Section 2.3 (cont'd);
   Homework #3, due Friday, September 21: PDF file and TEX file
   Practice problems (not to be handed in): page 49 #2.3.5, 2.3.7, 2.3.10, 2.3.11
9. Lecture 8, 09/17/12 Section 2.4
10. Lecture 9, 09/19/12 Section 2.5
11. Lecture 10. 09/21/12 Problems;
    Homework #4, due Monday, October 1: PDF file and TEX file
    Practice problems (not to be handed in): page 54 #2.4.3, 2.4.6; page 58 #2.5.4, 2.5.5, 2.5.6; page 62 #2.6.4, 2.6.5, 2.6.6 a) only
12. Lecture 11, 09/24/12 Section 2.5 (cont'd);
13. Lecture 12, 09/26/12 Section 2.5 (cont'd)
14. Lecture 13, 09/28/12 Section 2.6
15. Lecture 14, 10/01/12 Section 2.7
16. Lecture 15, 10/03/12 Section 2.7 (cont'd);
17. Lecture 16, 10/05/12 First midterm; you can find solutions here
18. Lecture 17, 10/10/12 Section 2.7 (cont'd)
19. Lecture 18, 10/12/12 Section 2.7 (cont'd);
    Homework #5, due > Friday, October 19: PDF file and TEX file; Practice problems: page 68 #2.7.10, 2.7.12, 2.7.13
20. Lecture 19, 10/15/12 Section 3.1
21. Lecture 20, 10/17/12 Section 3.2
22. Lecture 21, 10/19/12 Section 3.2 (cont'd)
    Homework #6, due > Friday, October 26: PDF file and TEX file;
23. Lecture 22, 10/22/12 Section 3.3
24. Lecture 23, 10/24/12 Section 4.2
25. Lecture 24, 10/26/12 Section 4.2 (cont'd), 4.3;
    Homework #7, due > Friday, November 2: PDF file and TEX file;
    Practice problems: page 83 #3.2.10, 3.2.11, 3.2.12, 3.2.13; page 88 #3.3.4, 3.3.7; page 108 #4.2.3, 4.2.4, 4.2.7, 4.2.8
26. Lecture 25, 10/29/12 Sections 4.3 (cont'd) 4.4;
27. Lecture 26, 10/31/12 Section 4.4; Contraction mapping theorem in action
28. Lecture 27, 11/2/12 Section 4.4 (cont'd)
    Homework #8, due > Friday, November 9: PDF file and TEX file;
    Practice problems page 113 #4.3.1, 4.3.4, 4.3.6 a), 4.3.8, 4.3.11, page 119 #4.4.2, 4.4.6, 4.4.7, 4.4.10, 4.4.11; page 124 #4.5.2, 4.5.4, 4.5.7
29. Lecture 28, 11/5/12 Section 4.4 (cont'd)
30. Lecture 29, 11/7/12 Section 5.2
31. Lecture 30, 11/9/12 Section 5.2 (cont'd)
32. Lecture 31, 11/12/12 Midterm Review
33. Lecture 32, 11/14/12 Sections 5.2 (cont'd), 5.3;
34. Lecture 33, 11/16/12 Sections 5.4 and 6.2
35. Lecture 35, 11/19/12 Section 6.2 (cont'd)
    Homework #9, due Friday, November 30: PDF file and TEX file;
    Practice problems page 136 #5.2.5, 5.2.8; page 143 #5.3.2, 5.3.3, 5.3.6, 5.3.7; page 160 #6.2.2, 6.2.3
36. Lecture 36, 11/26/12 Section 6.3, 6.4; You can find solutions for our second midterm here
37. Lecture 37, 11/28/12 Section 6.4 (cont'd)
38. Lecture 38, 11/30/12 Section 6.5;
    Homework #10, due Sunday, December 9: PDF file and TEX file; Stay tuned for practice problems.
39. Lecture 39, 12/03/12 Section 7.2
Practice problems page 136 #5.2.5, 5.2.8; page 143 #5.3.2, 5.3.3, 5.3.6, 5.3.7 (part b)), 5.3.8; page 160 #6.2.2, 6.2.4, 6.2.5, 6.2.6, 6.2.8, 6.2.9, 6.2.10, 6.2.11; page 166 #6.3.2, 6.3.3, 6.3.4; page 168 #6.4.1, 6.4.5, 6.4.6; page 174 #6.5.3, 6.5.9; page 190 # 7.2.1, 7.2.2, 7.2.5; page 193 #7.3.1, 7.3.3. Updated on 12/09: page 120 #4.4.13
40. Lecture 40, 12/05/12 Section 7.2 (cont'd)
41. Lecture 41, 12/07/12 Final Exam review;

LaTeX Info

Here are some websites where you can find tutorials and information about LaTeX:

• A not so short introduction to LaTeX
• http://www.math.harvard.edu/texman/
• http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/
• http://www.latex-project.org/intro.html

How to install and use LaTeX

• If you are using Linux then you should install Texlive using your favorite software manager. Suggested editors are: texmaker, kile, emacs (for the power users); you can install all these editors using your favorite software manager.
• If you are using Windows then you should install Miktex; suggested editor: texmaker; there are many other Latex editors for Windows but I am not familiar with them.
• If you are using MacOSX then you should install TexShop. It comes with its own editor. You can also use texmaker.

Beamer

Beamer is a special LaTeX package that you can use to create great presentations. You should be able to install easily beamer from Miktex or Texshop. If you use Linux you can install the beamer package using a software manager.
You can download the beamer manual here

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Marius Ionescu, 16 Sep 2012