Math 40970 and 60970 Special Topics - Advanced Real Analysis I
Spring 2015, section 040, MWF 12-12:50 in TUC 352
Instructor: Dr. Igor Prokhorenkov. Office: TTC 311.
Office Hours (I am also available at other times as needed.)
| My Phone | Office: 817-257-6342 (I have voice mail) Home: 817-423-9030. Feel free to call me at home at reasonable times (9:00 am - 9:00 pm). |
Class web page:
Class web page is available at the address
http://faculty.tcu.edu/prokhor/real.html , it contains links to the
syllabus and homework assignments.
Textbook:
Stephen Abbott Understanding Analysis, 1st ed.,
Springer 2001 and Karen Saxe Beginning Functional Analysis, 1st ed.,
Springer 2002.
Prerequisites:
MATH 50503.
Course Description and Goals:
the goal of Real Analysis is to provide insights into logical foundations
and inner workings of Calculus. We will spend a lot of time
practicing understanding and writing precise mathematical arguments and proofs.
The following topics will be covered: power series, Riemann integration,
metric, normed, and inner product spaces, Lebesgue measure and
integration, Fourier analysis in Hilbert spaces .
Calculator/Computer:
You do not need a calculator in this class.
Grading:
The final grade for this course will be determined as follows.
| Homework and Quizzes | 25% | |
| Test #1 | 20% | Mon, Feb. 23 |
| Test #2 | 20% | Wed, April 1 |
| Cumulative Final Exam | 35% | Mon, May 4, 11:30 - 2 p.m. |
Your weighted course average x determined by your scores and the percentages above will be used to determine the final grade as specified in the table.
|
Note that only undergraduates have the possibility of
the "D" grade. Example of grading calculation:
|
- Homework: will be assigned on the web site, and it is due at the beginning of class period. No late homework will be accepted. I will grade all or part of your homework. Your homework should be neat, legibly written, and problems should be clearly labeled. You should leave some space on each page for comments. You can work together on assignments, but the work you turn in should reflect your personal effort and understanding, i.e. direct copying from any source is not permitted. In some cases, the homework may include material that is not covered in the lectures.
- Additional homework problems: Graduate students will be assigned additional homework problems.
- Quizzes: the quizzes will be given as necessary. They may cover definitions, statements, and typical problems that are needed to understand the material. If you miss a quiz due to absence, it will count as a zero, except in cases of excused absence (these require a note from Campus Life or documented participation in university activities).
- I will drop one lowest homework score and one lowest quiz score.
- The last day to withdraw from the class is Thursday, April 2. The last day to select P/NC is Monday, April 6.
- Please turn off your cell phones and other electronic devices in class.
Disabilities Statement: Texas Christian University complies with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973 regarding students with disabilities. Eligible students seeking accommodations should contact the Coordinator of Student Disabilities Services in the Center for Academic Services located in Sadler Hall, 1010. Accommodations are not retroactive, therefore, students should contact the Coordinator as soon as possible in the term for which they are seeking accommodations. Further information can be obtained from the Center for Academic Services, TCU Box 297710, Fort Worth, TX 76129, or at (817) 257-6567.
Attendance Policy: The university attendance policy states that regular and punctual class attendance is essential and that no assigned work is excused because of absence, no matter what the cause.
Academic Misconduct: Any act that violates the academic integrity of the institution is considered academic misconduct. The procedures used to resolve suspected acts of academic misconduct are available in the offices of Academic Deans and the Office of Campus Life. Specific examples and more details are in the Student Handbook.