Math 3001: Analysis 1

Instructor: Sean O'Rourke
Office: Math 325
Office Hours: M: 11:00 am - 12:00 pm, F: 9:00 am - 10:00 am, and by appointment.
E-mail: -
Lectures: MWF: 12:00 pm - 12:50 pm in FLMG 154

Course Description

The goal of this course is to develop a precise understanding of the concepts that underlie calculus including the real numbers, continuous functions, sequences and their limits, the derivative, and the integral. Using this precise understanding, we will then rigorously prove many of the major results from single-variable calculus such as the Intermediate Value Theorem, the Mean Value Theorem, and the Fundamental Theorem of Calculus.

In this course, you will improve your understanding of mathematical proofs. You will also gain lots of experience constructing mathematically rigorous arguments using proof techniques both new (e.g. epsilon-delta proofs) and familiar (e.g. proof by contradiction, inductive proofs).


We will be using Analysis with an introduction to proof (4th Edition) by S. R. Lay. Some other introductory books on the subject include Principles of mathematical analysis (3rd Edition) by W. Rudin and Real Analysis and Foundations by S. Krantz.


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


Every week you will have a written homework assignment, which will give you an opportunity to practice constructing and writing proofs using the concepts, definitions, theorems and techniques we have learned. These will be posted on the course website. Late homework will not be accepted.

Homework should be legible, have your name on it, and be stapled in order to ensure that you get credit. A primary goal of this course is for you to improve your ability to write clear, precise proofs; the homework (and the exams) will be graded accordingly.

I encourage you to discuss the homework problems with your classmates, tutors, or me (or any other resources you find helpful). However, the Honor Code requires that the solution you turn in must be in your own words and reflect your own understanding.

Starred problems

Each week, (at most) one problem on the homework assignment will be starred (e.g. Chapter 6, problem 4*). These problems will usually be more challenging than the rest of the homework. The starred problem should be turned in on a separate page from the rest of the written homework. I will grade these problems myself on a credit/no credit basis (but with comments so that you know what you need to fix). If you receive a score of no credit, you can resubmit the problem the next week along with that week's homework assignment, and you can continue this process until you receive credit. The primary point of these problems is to make sure that everyone learns to write good proofs. The secondary point is to encourage you to solve problems which might require more than one week of thinking -- although not all of the starred problems will be that hard.

Homework Assignments


Course policies

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).

Student classroom and course-related 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. See policies regarding classroom behavior and student conduct.

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 Medical Conditions: Injuries, Surgeries, and Illnesses guidelines and discuss your needs with your professor.

Religious obligations

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.

If a religious observance conflicts with a scheduled exam or other course activity, please let me know during the first two weeks of the semester so that we can make alternate arrangements.

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, age, disability, creed, religion, sexual orientation, or veteran status 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, or veteran status. Individuals who believe they have been discriminated against should contact the Office of Discrimination and Harassment (ODH) at 303-492-2127 or the Office of Student Conduct (OSC) at 303-492-5550.

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