Syllabus for Math 4310 (Introduction to Real Analysis), Fall 2015
TuTh 2-3:15 pm, Dell 2 103.
- Instructor: Mikhail Ershov
- Office: Kerchof 302
- e-mail: ershov at virginia dot edu
- Office hours: 2 hrs 30 min TBA and by APPOINTMENT
- Course webpage: http://people.virginia.edu/~mve2x/4310_Fall2015
- Main text (required): Principles of Mathematical Analysis, Walter Rudin,
- Additional text (strongly recommended to buy): Introductory Real Analysis , A.N. Kolmogorov and S.V.Fomin,
revised English edition.
- 1. You should have taken MATH 3310 (Basic Real Analysis) or equivalent. The most essential
skill from 3310 that is crucial in 4310 is being able to work with the epsilon-delta
definition of the limit and related notions like convergence and continuity (just formally
understanding the definition of the limit is not enough).
- 2. As with most 4000 level math classes, you are expected to have substantial prior exposure to proofs.
You should be completely comfortable with basic proof techniques and have experience in both reading (and understanding) proofs and writing your own proofs.
The main goal of the course is to develop basic notions of mathematical analysis (convergence,
continuity, compactness etc.) in the setting of metric spaces. The material in the first half of the course
will have some overlap with that of 3310; however, almost everything will be done in greater
depth and generality. The second half will cover topics that you most
likely have not studied before, including convergence in function spaces, fixed point theorems and
Lebesgue integration. Our main textbook will be `Principles of Mathematical Analysis' by Rudin; however,
we will not be following it too closely. The tentative plan is to cover chapters 1,2,4,7,11 from Rudin's book
and some parts of other chapters. The book `Introductory Real Analysis' by Kolmogorov and Fomin will be the main
reference for Lebesque integration (roughly the last three weeks of the semester).
Evaluation The course grade will be based on homework, two midterms and the final,
with weights distributed as follows:
- homework: 30%
- midterms: 20% each
- final: 30%
The format of the exams has not been finalized at this point, but most likely the final and the first midterm
will be in-class while the second midterm will be take-home.
The midterm dates given below are tentative and may be changed later. The date and time of the final
exam is determined by the registrar and cannot be changed (in the case of a take-home final
it will be due on that date).
- First midterm exam: Thu, Oct 1st
- Second midterm exam: Thu, Nov 5th
- Final exam: Tue, Dec 15th, 9am-12pm
- Make-ups or extensions (for take-home exams) will be given only under extreme circumstances (such as
serious illness). Except for emergencies, you must obtain my permission
for a make-up (resp. extension) before the exam (resp. due date).
- If you miss an in-class exam or fail to submit a take-home exam
by the due date without a compelling reason, you will
be assigned the score of 0 on that exam.
- University regulations specifically prohibit early make-ups.
- Homework will be assigned weekly and will usually be due on Thursday.
- Please STAPLE your homework.
- No late homework will be accepted. However, two lowest
homework scores will be dropped.
- GRADING: it will not be possible to grade all homework problems. In each assignment 3-4 selected (but not announced in advance) problems will be graded for credit.
- On homework: you are welcome (and even encouraged)
to work on homework together, but you must write
up solutions independently, in your own words. In particular,
you should not be consulting others during the process of
writing down your solution.
- On take-home exams: you MAY NOT discuss problems with other people
or use any resources (including web) except for the class textbook and your
class notes. You may ask me questions about the exam problems, but normally
I will only provide very brief hints.
Major announcements will be made in class and also posted on the course
Some other announcements may only be made by e-mail, so check your
- Tuesday, September 8 -- Last day to ADD a course, elect the audit
change the grading option (grade or CR/NC), or establish an independent
- Wednesday, September 9 -- Last day to DROP a course (deletion
from the transcript)
- Tuesday, October 20 -- Last day to withdraw from a course
All students with special needs requiring accommodations should present the appropriate paperwork from
the Student Disability Access Center (SDAC). It is the student's responsibility to present this paperwork in a
timely fashion and follow up with the instructor about the accommodations being offered. Accommodations
for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.