Math 19900

Introduction to Analysis & Linear Algebra.

University of Chicago.
Department of Mathematics.
Spring 2011.
Time and place: MWF 11:30-12:20pm in Eckhart 312.
Instructor: Antonio Montalbán
E-mail: antonio@math.uchicago.edu
Office hours: Mondays 5-6pm and Wednesdays 3-4pm.
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 6th 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 13th in class - Read  Sections 1 through 7 of Chapter 1.
                                                                  - Do Exercises  1.7.15 (except for (iv));   1.7.25  -  1.5.2;  1.5.6;   1.5.8.

HW3 due Wednesday April 20th in class  - Read  Sections 1 through 7 of Chapter 1. Read Section 1 of Chapter 3.
                                                                   - Do Exercises  1.6.12  - 1.6.17(iii) and (v)  - 1.7.19  -  3.1.3  -  3.1.5

HW4 due Friday April 29th 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 6th in class - Read sections 6 of chapter 3.
                                                       - Exercises here.

HW6 due Friday May 13th 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 25th in class - Read Section 1 of Chapter 2.
                                                                 - Exercises here.

HW8 due Wednesday June 1st in class.  - Read Sections 1, 2 and 3 of Chapter  2.
                                                                - Exercises 2.1.29 (using R[x] instead of Q[x]) - 2.1.30(i)(ii) (where W(A) is the set of functions f, s.t. f(x)=0 for all x in A) - 2.2.6 - 2.3.3

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 20th, and the other one on Friday May 13th. Both at regular class time.

Final Exam: The final exam will be on Monday June 6th, from 10:30am to 12:30pm.
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