## Math 405: Introduction to Real Analysis
### Course Description
This is an introduction to real analysis. Topics covered in the course will include,
The Logic of Mathematical Proofs,
Construction and Topology of the Real Line, Continuous Functions, Differential Calculus,
Integral Calculus, Sequences and Series of Functions. There will be 10 problem sets (20% of final grade),
two in class midterm exams (20% each) and one final exam (40%).
Lectures are Monday and Wednesday 1:30-2:45 in Krieger 302. Section meets Friday 1:30-2:20 in Krieger 302.
Problem sets will be due in section on Fridays (see below for dates).
No late homework will be accepted. The lowest grade will be dropped.
Office hours: W 3-5pm.
The syllabus is here.
### References
The course text is
- R. Strichartz, “The Way of Analysis," Rev. Ed. (Available on Amazon for ~$40)
### Exams
There will be three exams. Two in class midterms and a final.
The dates of the exames are
First Midterm: Wednesday, March 5.
Second Midterm: Wednesday, April 9.
Final Exam: Wednesday, May 14, 9am-12pm in Krieger 302
### (Tentative) Schedule
#### Week 1 (1/27 & 1/29) : Logic of Mathematical Proofs
Read 1.1, 1.2, 1.3, 1.4, 1.5; See M. Taylor's notes
No homework due.
#### Week 2 (2/3 & 2/5): Construction of the Real Numbers
I will be away M-W -- makeup office hours at same time on Thursday
Read 2.1, 2.2
Problem Set 1 due. *NB: corrected due date*.
#### Week 3 (2/10 & 2/12): Construction of the Real Numbers (cont.); Topology of the Real Number Line
Read 2.3, 3.1
Problem Set 2 due.
#### Week 4 (2/17 & 2/19): Topology of the Real Number Line (cont.)
Read 3.2, 3.3
Problem Set 3 due.
#### Week 5 (2/24 & 2/26): Continuous Functions
Time of office hours on 2/26 have been changed to 12-1:30.
Read 4.1
Problem Set 4 due.
#### Week 6 (3/3 & 3/5): Continuous Functions (cont.); *First Midterm*
Read 4.2
Practice Midterm. Practice Solutions. More Practice.
Midterm 1 Solutions
Extra Office Hours, 1:30pm-3:30pm on Tuesday 3/4.
No homework due.
#### Week 7 (3/10 & 3/12): Differential Calculus
Read 5.1, 5.2
Problem Set 5 due.
#### Week 8: Spring Break
No homework due.
#### Week 9 (3/24 & 3/26): Differential Calculus (cont.) ####
Read 5.3, 5.4
Problem Set 6 due. *NB: Corrected statement of problem 2(c). This part is now extra credit *.
#### Week 10 (3/31 & 4/2): Integral Calculus
Read 6.1, 6.2
Problem Set 7 due.
#### Week 11 (4/7 & 4/9): Integral Calculus (cont.); *Second Midterm*
No homework due.
Practice Midterm. Practice Solutions. More Practice -- with Solutions
Additional Office Hours Tuesday 3-5
Midterm 2 Solutions
#### Week 12 (4/14 & 4/16): Sequences and Series of Functions
Read 7.2
Problem Set 8 due.
#### Week 13 (4/21 & 4/23): Sequences and Series of Functions (cont.)
Read 7.3, 7.4
Problem Set 9 due.
#### Week 14 (4/28 & 4/30): Sequences and Series of Functions (cont.)
Read 7.5
Problem Set 10 due.
Practice Final (with solutions).
#### Final (5/14)
I will have office hours on Wednesday, May 7th, Monday, May 12th and Tuesday, May 13th from 3-5pm (each day).
The Solutions to the Final. Have a great summer! |