Math 3210
 Foundations of Analysis
Fall
2015
Office hourse during exam week: Monday (12/14) 1112 and 13, Tuesday (12/15) 1:302:30, Wednesday (12/16) 1012 and 13
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:
bromberg@math.utah.edu
Office hours: MWF 9:3010:30 or
by appointment (Click on the link for my schedule.)
Prerequisites: Math 2210 or consent of
instructor.
Meeting place and time: MWF 8:359:25, LCB
222 and T 8:359:25, 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  
09/08/15 
1.3: 8, 9, 10, 12, 13, 14  
09/15/15 
1.4: 4, 7, 10, 11  
09/22/15 
2.1: 2, 5, 6, 8, 10  
09/29/15 
2.2: 5, 6  
10/06/15 
2.5: 2, 3, 6, 9, 11, 12  
10/20/15 
3.1: 4, 10, 11, 12 

10/27/15 
3.3: 4, 5, 6, 8  
11/03/15 
4.1: 2, 11  Chapter 5: 3, 5, 6, 9, 13, 14 
11/10/15 
4.3: 12, 13  Chapter 6: 10, 11, 12 
11/17/15 
5.2: 1, 9, 10  Chapter 6: 16 
11/24/15 
5.3: 6, 8  
12/01/15 
6.1: 12, 14  
12/09/15 
6.3: 7, 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.