Math 19900

Introduction to Analysis & Linear Algebra.

University of Chicago.
Department of Mathematics.
Spring 2009.
Time and place: MWF 12:30-1:20pm at Eckhart 203.
Instructor: Antonio Montalbán
E-mail: antonio at math.uchicago.edu
Office hours: Mondays 5:30-6:30pm and Wednesdays 4:30-5:30pm in Eck 328.
Textbook: Paul Sally, Tools of the Trade. (Chapters 1,2 and 3)
Web page: www.math.uchicago.edu/~antonio/math199

Homework.


HW1  due Wednesday April 8th in class  -  Read  Sections 1, 2, 3, 4 and 5 of Chapter 1.
                                                                  - Do Exercises  1.3.9(iv), (ix), (xi), (xii) - 1.4.4 - 1.6.10 - 1.6.2.

HW2 due Wednesday April 15th in class - Read  Sections 1 through 7 of Chapter 1.
                                                                  - Do Exercises  1.7.15;   1.7.25  -  1.5.2;  1.5.6;   1.5.8.

HW3 due Wednesday April 22th in class - Read  Sections 1 through 7 of Chapter 1. Read Section 1 of Chapter 3
                                                                  - Do Exercises  1.6.14  - 1.6.17(iii) and (v)  - 1.7.19  -  3.1.3  -  3.1.5

HW4 due Friday May 1st in class - Read sections 1,2,4,6 of chapter 3.
                                                      - Do Exercises 3.1.7(w proof) - 3.1.14(i) - 3.2.9 - 3.6.3(1)(2) - 3.6.5

HW5 due Friday May 8th in class - Read sections 6 of chapter 3.
                                                       - Exercises here.

HW6 due Friday May 15th in class -  Read sections 1-7 of Chapter 1, and sections 1,2,4,6 of chapter 3.
                                                       - Exercises  3.6.21 and 3.6.24 (except for (i) and (ii)).

HW7 due Wednesday May 27th in class - Read Section 1 of Chapter 2.
                                                                  - Exercises here.

HW8 due Wednesday June 3rd in class - Read Sections 1 and 2 of Chapter  2.
                                                                - Exercises 2.1.29 - 2.1.30(i)(ii) - 2.2.2 - 2.2.3 - 2.2.6

Announcements.

General Policy.

Homework: There will be weekly homework. You may work with others, but you should write up your own solutions independently. Late homework will not be accepted. However, the lowest homework grade will not be counted.

Midterm:  There  will be two midterms: One on Wednesday April 22nd, and the other one on Friday May 15th. Both at regular class time.

Final Exam: The final exam will be on Thursday June 11th, from 4pm to 6pm.
It is the policy of the Department of Mathematics that the following rules apply to final exams in all undergraduate mathematics courses: 1. The final exam must occur at the time and place designated on the College Final Exam Schedule. In particular, no final examinations may be given during the tenth week of the quarter, except in the case of graduating seniors. 2.Any student who wishes to depart form the scheduled final exam time for the course must receive permission from Paul Sally (office: Ry 350, e-mail: sally at math.uchicago.edu). Instructors are not permitted to excuse students form the scheduled time of the final exam except in the cases of an Incomplete.


The final grade final grade will be 20% from the Homework, 20% from each midterm and 40% from the final.

Syllabus:

  1. Set Theory, Functions, and equivalnece Clases.
  2. Axioms for Fields and Ordered Fields.
  3. Topology of the Real line.
  4. Linear Algebra.

Sumplementary Reading