Math 3210 - Foundations of Analysis
Spring 2018

Notes for the final exam.
Office hours this week are 12:30-1:30 on Wed. Apr. 25 and 1:00-3:00 on Thursday, Apr. 26. If you would like to come by at a different time please let me know.



Instructor:
Ken Bromberg
Office: JWB 303
Email: bromberg@math.utah.edu
Office hours: MF 1:00-2:00, W 11:45-12:45 or by appointment (Click on the link for my schedule.)

Prerequisites: Math 2210 or consent of instructor.

Meeting place and time: MWF 10:45-11:35, AEB 360 and T 10:45-11:35, AEB 306

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.

Due Date

Assignment

Solutions

01/16/18

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

Homework 1

01/23/18

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

Homework 2

01/30/18

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

Homework 3

02/06/18

2.1: 2, 5, 6, 8, 10

Homework 4

02/13/18

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

Homework 5

02/20/18

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

Homework 6

02/27/18

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

Homework 7

03/06/18

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

Homework 8

03/13/18

4.1: 2, 11
4.2: 1, 7, 11, 12

Homework 9

03/27/18

4.3: 3, 4, 12, 13
4.4: 1, 4, 5, 15
5.1: 1, 5

Homework 10

04/03/18

5.1: 8
5.2: 1, 9, 10
5.3: 4, 5

Homework 11

04/10/18

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

Homework 12

4/17/18

6.1: 12, 14
6.2: 11, 12
6.3: 7

Homework 13

04/24/18

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

Homework 14


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 February 2nd, the second is on February 28th and the third is on April 6th.

Date Test Solution
2/2 Midterm 1 Solutions
2/28
Midterm 2
Solutions
4/6
Midterm 3
Solutions

Final:
The final is on Friday, April 27th from 10:30 AM - 12:30 PM. 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.