Introduction to Real Analysis

(Course Web Page and Syllabus)

  MATH 6310

      Fall 2010               

                                                                                                            Instructor: Dr. Janos Englander

Course content:
Presents the basic notions of analysis, e.g., limits, lim sup and lim inf, continuity, and the topology of the real line; develops the  theory of Lebesgue measure and the Lebesgue integral on the line, emphasizing the various notions of convergence and the standard convergence theorems. Applications are made to the classical Lp spaces.

Prereq.: MATH 4310 and 4320. Instructor consent required for undergraduates.

  Text: "Real Analysis" by Royden (4th edition)
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Time: MWF 10:00-10:50

Room: MCOL E186


How to reach me:


Office: MATH 324.

Office hours: Monday and Friday 2-3 PM.

Phone: 303-492-4846 (with voice mail)

electronic mail


Enrollment questions: Please see the Registrar's web page, or call their office. 

If you still have problems, then see Tiffany at the Math. Dept. Office




Grading:

Grading will be based on homework and exams, as follows:


Bi-weekly homework:   25%

Midterm:  25%

Final:    50%


Exam Schedule:

Midterm:  October 15, in class     Test solutions

Final: December 11, 4:30-7:00, in the room where the lectures were  Solutions to Final


A FEW LINKS

Continuity and Fatou


Some practice questions


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Cantor

Lebesgue

Caratheodory

Borel

Lusin

Egorov

Vitali

Fatou

Hausdorff

Banach-Tarski Paradox


Homework: (Numbers refer to Royden's book, 4th edition)

NR    DATE      DUE             PROBLEMS

1    9/8/10    9/22/10       p. 16 Problems 20, 22, 23, 24, 25, 26

2    9/24/10    10/8/10       p. 20 Problem 34, p.24 Problem 46. p. 27-28 Problems 47, 48, 52, 53.

3    10/13/10   10/27/10      p. 34 Problems 6-10.   solution

4    11/8/2010 11/19/10      p. 59 Problem 9.,p. 67 Problem 27, p. 71 Problem 8, p. 79 Problem 16, p. 85 Problem 25    solution

(If you feel that you are absolutely unable to finish it by 11/19, then you can submit it after the break.)


SOME IMPORTANT CU POLICIES


STUDENTS WITH DISABILITIES


If you qualify for accommodations because of a disability, please submit to me a letter from Disability Services in a timely manner so that your needs may be addressed. Disability Services determines accommodations based on documented disabilities. Contact: 303-492-8671, Willard 322, and www.Colorado.EDU/disabilityservices.


RELIGIOUS OBLIGATIONS


Campus policy regarding religious observances requires that faculty make every effort to reasonably and fairly deal with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance. In case of conflict with a test, please let me know at least two weeks in advance. See full details at http://www.colorado.edu/policies/fac_relig.html.


CLASSROOM AND COURSE-RELATED BEHAVIOR


Students and faculty each have responsibility for maintaining an appropriate learning environment. Students who fail to adhere to such behavioral standards may be subject to discipline. Faculty have the professional responsibility to treat all students with understanding, dignity and respect, to guide classroom discussion and to set reasonable limits on the manner in which they and their students express opinions. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, culture, religion, politics, sexual orientation, gender variance, and nationalities. Class rosters are provided to the instructor with the student's legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records. See polices at http://www.colorado.edu/policies/classbehavior.html and at http://www.colorado.edu/studentaffairs/judicialaffairs/code.html#student_code.


DISCRIMINATION AND HARASSMENT


The University of Colorado at Boulder policy on Discrimination and Harassment 

http://www.colorado.edu/policies/discrimination.html, 

the University of Colorado policy on Sexual Harassment and the University of Colorado policy on Amorous Relationships applies to all students, staff and faculty. Any student, staff or faculty member who believes s/he has been the subject of discrimination or harassment based upon race, color, national origin, sex, age, disability, religion, sexual orientation, or veteran status should contact the Office of Discrimination and Harassment (ODH) at 303-492-2127 or the Office of Judicial Affairs at 303-492-5550. Information about the ODH and the campus resources available to assist individuals regarding discrimination or harassment can be obtained at http://www.colorado.edu/odh.


UNIVERSITY'S HONOR CODE


All students of the University of Colorado at Boulder are responsible for knowing and adhering to the academic integrity policy of this institution. Violations of this policy may include: cheating, plagiarism, aid of academic dishonesty, fabrication, lying, bribery, and threatening behavior. All incidents of academic misconduct shall be reported to the Honor Code Council (honor@colorado.edu; 303-725-2273). Students who are found to be in violation of the academic integrity policy will be subject to both academic sanctions from the faculty member and non-academic sanctions (including but not limited to university probation, suspension, or expulsion). Other information on the Honor Code can be found at http://www.colorado.edu/policies/honor.html and at http://www.colorado.edu/academics/honorcode.