Math 6320, Introduction to Real Analysis 2

Semester 2, 2015-16

Course Lecturer:

Dr. Judith Packer, Dept. of Mathematics

Tel: (303) 492-6979
Office: Math 227
Email: packer@euclid.colorado.edu
URL: http://spot.colorado.edu/~packer

Course Information:
 This course is meant to continue the study of analysis of real-valued functions of one or several variables, with an emphasis on Lebesgue measure and Lebesgue integration on the real line and R^n. Topics to be covered include:
Locally compact Hausdorff spaces, the Stone-Weirstrass Theorem, the Arzela-Ascoli Theorem; Elements of functional analysis, including normed vector spaces, linear functionals, the Baire Category Theorem, Hilbert spaces; L^p - spaces, definitions and examples; Minkowski's inequality, Holder's inequality, interpolation of $L^p$-spaces; Radon measures: positive linear functionals on C_C(X) and the Riesz representation theorems, regularity of measures, the dual of $C_0(X),$ products of Radon measures; Elements of Fourier analysis: convolutions, the Fourier transform, summation of Fourier integrals and series and appplications of Hilbert space theory, pointwise convergence of Fourier series, Fourier analysis of measures.

Prerequisite:
 Math 6310, or instructor consent.

Course Text:
 We will use as a primary text the book "Real Analysis: Modern Techniques and their Applications", by G.B. Folland, covering most of Chapters 4 - 7, and part of Chapter 8.

Folland has an errata page for this textbook at http://www.math.washington.edu/~folland/Homepage/reals.pdf

Assessment: Lecture Hours and Venue:
MWF 1 p.m.-1:50 p.m. ECCR 118

Office Hours:
Mon, Wed., Fri. 11 a.m. -12 noon, and by appointment.

Homework:
Some Important Names associated with Real Analysis :

Various other matters :
For informations on students with disabilities, religious obligations, honor code, student classroom and course-related behavior, and discrimination and harassment issues, see the university pages on these matters at:
Students With Disabilities
www.colorado.edu/disabilityservices.

Missed Exams:
If you know that you are going to miss an exam or cannot take the final exam at the scheduled time, please notify me at least two weeks in advance. If you miss a midterm exam for any acceptable reason (e.g. religious obligation, documented illness), you will be given an average score based on your performance in the other midterm and final exam. If you miss all midterm exams for acceptable reasons, your course grade will be based entirely on your final exam score. If you miss the final exam and have not rescheduled it in advance, you will score zero on the final.

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 this class, you should notify me of any conflict at least two weeks in advance. See full details at www.colorado.edu/policies/observance-religious-holidays-and-absences-classes-andor-exams.

Student 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. Your instructor will gladly honor your request to address you by an alternate name or gender pronoun. Please advise your instructor of this preference early in the semester so that appropriate changes may be made to the records. See polices at www.colorado.edu/policies/student-classroom-and-course-related-behavior.

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 www.colorado.edu/policies/student-honor-code-policy.

Statement on Discrimination and Harassment:
The University of Colorado Boulder (CU-Boulder) is committed to maintaining a positive learning, working, and living environment. The University of Colorado does not discriminate on the basis of race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation or political philosophy in admission and access to, and treatment and employment in, its educational programs and activities. (Regent Law, Article 10, amended 11/8/2001). CU-Boulder will not tolerate acts of discrimination or harassment based upon Protected Classes or related retaliation against or by any employee or student. For purposes of this CU-Boulder policy, ``Protected Classes" refers to race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation or political philosophy. Individuals who believe they have been discriminated against should contact the Office of Institutional Equity and Compliance (OIEC) at 303-492-2127 or the Office of Student Conduct and Conflict Resolution (OSC) at 303-492-5550. Information about the OIEC, the above referenced policies, and the campus resources available to assist individuals regarding discrimination or harassment can be found at the OIEC website www.colorado.edu/institutionalequity/.

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Last modified January 5, 2016.