Math 6310: Intro to Real Analysis 1

Instructor: Sean O'Rourke
Office: Math 325
Office Hours: MW: 4:00 - 5:00 pm, and by appointment.
E-mail: -
Lectures: MWF: 3:00 pm - 3:50 pm in MUEN E131


We will be using Real Analysis: Modern Techniques and Their Applications, 2nd Edition by Gerald B. Folland. An errata is available from the author's website.

Course Description

This course is meant to familiarize students with the analysis of functions of a single real variable; an emphasis will be placed on Lebesgue measure and Lebesgue integration on the real line, together with their relationship to differentiation. Topics to be covered include: Lebesgue measurable subsets, Lebesgue measure, measurable functions, definition of the Lebesgue integral, convergence theorems, functions defined by integrals and convolution, differentiation, functions of bounded variation, absolute continuity, metric space theory, and if time permits, the Stone-Weierstrass Theorem.


Your grade in this course will be based on the following:

Homework Assignments


Course policies

Students with disabilities

If you qualify for accommodations because of a disability, please submit to your professor a letter from Disability Services in a timely manner (for exam accommodations provide your letter at least one week prior to the exam) so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities. Contact Disability Services at 303-492-8671 or by e-mail at If you have a temporary medical condition or injury, see Temporary Injuries guidelines under the Quick Links at the Disability Services website and discuss your needs with your professor.

Religious holidays

Campus policy regarding religious observances requires that faculty make every effort to deal reasonably and fairly with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance. In this class, you should contact me as soon as possible (preferably one week in advance) to establish a reasonable accommodation.

Classroom behavior

Students and faculty each have responsibility for maintaining an appropriate learning environment. Those who fail to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, color, culture, religion, creed, politics, veteran's status, sexual orientation, gender, gender identity and gender expression, age, disability, 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. For more information, see the policies on classroom behavior and the student code.

Discrimination and harassment

The University of Colorado Boulder (CU-Boulder) is committed to maintaining a positive learning, working, and living environment. 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. The full policy on discrimination and harassment contains additional information.

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 (; 303-735-2273). 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). Additional information regarding the Honor Code policy can be found online and at the Honor Code Office.

Valid XHTML 1.0 Strict.
Copyright © 2015, Sean O'Rourke
All rights reserved.