Math 3210 - Foundations of Analysis
Fall 2015
Office hourse during exam week: Monday (12/14) 11-12 and 1-3, Tuesday (12/15) 1:30-2:30, Wednesday (12/16) 10-12 and 1-3
If you can't make it during those times please let me know and we can arrange another time.

Notes for the final.



Instructor: Ken Bromberg
Office: JWB 303
Email: [email protected]
Office hours: MWF 9:30-10:30 or by appointment (Click on the link for my schedule.)

Prerequisites: Math 2210 or consent of instructor.

Meeting place and time: MWF 8:35-9:25, LCB 222 and T 8:35-9:25, LCB 215

There will be no class on Tuesday, August 25 and Wednesday, November 25.

Text: Foundations of Analysis, by Joseph L. Taylor

Course description: The purpose of this course is the rigorous development of the calculus of one variable, starting from a rigorous development of the real numbers. This means that the emphasis of the course will be on proofs, and a lot of time will be spent on practicing how to write proofs. The real numbers will be constructed from the integers and the rational numbers. The basic completeness property of the real numbers will be derived. From the completeness we will then prove the basic theorems of one variable calculus. We will cover chapters 1 through 6 of the book.

Homework: Homework will be assigned weekly and generally due on Tuesdays. Late homework will not be accepted. A random subset of the problems will be graded.
Extra problems: The 3rd column contains extra problems from the book Principles of Mathematical Analysis by Walter Rudin. These problems are not required and will not be tested on. They are just there for students who are interested in working on some extra very challenging problems. I am happy to look over any solutions to these extra problems.

Due Date

Assignment

 Extra problems from Rudin

09/01/15

1.1: 2, 4, 5, 9, 11
1.2: 8, 10

09/08/15

1.3: 8, 9, 10, 12, 13, 14

09/15/15

1.4: 4, 7, 10, 11
1.5: 3, 4, 12

09/22/15

2.1: 2, 5, 6, 8, 10

09/29/15

2.2: 5, 6
2.3: 2, 4, 8, 9, 11
2.4: 3, 4, 14

10/06/15

2.5: 2, 3, 6, 9, 11, 12
2.6: 2, 4, 11

10/20/15

3.1: 4, 10, 11, 12
3.2: 3, 8, 10

10/27/15

3.3: 4, 5, 6, 8
3.4: 5, 12

11/03/15

4.1: 2, 11
4.2: 1, 7, 11, 12
4.3: 3, 4

Chapter 5: 3, 5, 6, 9, 13, 14

11/10/15

4.3: 12, 13
4.4: 1, 4, 5, 15
5.1: 1, 5, 8

Chapter 6: 10, 11, 12

11/17/15

5.2: 1, 9, 10
5.3: 4, 5

Chapter 6: 16

11/24/15

5.3: 6, 8
5.4: 4, 5, 12

12/01/15

6.1: 12, 14
6.2: 11, 12

12/09/15

6.3: 7, 11
6.4: 10, 11, 12
6.5: 5, 9, 11


Problem session: Tuesday's class session will be a problem session. Students will present problems on the board. For each problem you volunteer to do at the board I will add 25/25 to your homework score.

Midterms: There will be three midterms. The first is on September 16th, the second is on October 23rd and the third is on November 20th.

Date
 Test
 Solution
9/16
 Midterm 1
 Solutions
10/23
 Midterm 2
 Solutions
11/20
 Midterm 3
 Solutions

Final: The final is on December 17th from 8:00 AM - 10:00 AM. It will be cumulative although it will weighted towards material that has not been covered on one of the midterms.

Grades: There are two possible grading schemes for this course. I will calculate your grade using both schemes and give you the better of the two grades.

Scheme 1: Your final grade will be determined from the following components: homework 20%, midterms 40%, final 40%. The lowest of the 3 midterm scores is dropped and each of the other 2 counts 20% toward the final grade.

Scheme 2: Your final grade will be determined from the following components: homework 20%, midterms 60%, final 20%. In this scheme all 3 midterm scores will be counted equally towards your final grade.

I will drop your two lowest homework scores. Makeups for exams will only be given in University excused absences.

Tutoring is available from the Math Tutoring Center.

Students with disabilities may contact the instructor at the beginning of the semester to discuss special accommodations for the course.