Penn State

Spring 2013


Concepts of Real Analysis (MATH 312)


Class: M W F 2:30PM – 3:20AM, 116 Osmond

Arriving late to class, leaving class early, or disrupting class in any way will not be tolerated.

Cellphones must be silenced during lectures.


Instructor: Mathieu Stienon <stienon@math.psu.edu>

Please, always include “312” in the subject of your message.

You can expect to get an answer by the end of the next business day.


Office hours: Tuesdays 3:30PM – 5:30PM, 325 McAllister


Course webpage: www.math.psu.edu/stienon/312


Textbook: David Brannan, A First Course in Mathematical Analysis, Cambridge University Press


Contents: This is a proof-based course whose purpose is to introduce rigorously the most basic concepts of mathematical analyis: real numbers, sequences and series, limits, continuity, derivatives, integrals. In your calculus courses, you acquired an intuitive understanding of these concepts and you learned how to exploit them in computations. There are lots of situations in which the tools of calculus and the intuition on which it relies fail. In this course, we will revisit the basic concepts introduced in calculus, give them sound foundations, and establish their properties rigorously. In the process, you will get to realize that many facts that were taken for granted in calculus are far from being obvious. Hopefully, by the end of the semester, you will be convinced of the paramount importance of rigorous proofs in mathematics. Developing the ability to recognize and write correct proofs is an essential and indispensable step in the education of every aspiring mathematician and is an extremely useful skill for any aspiring scientist as well.


Warning: This course is DIFFICULT and of FUNDAMENTAL IMPORTANCE in mathematics. In order to succeed, YOU MUST DEVOTE ADEQUATE TIME AND ATTENTION to the material by coming to ALL lectures, keeping up with reading and homework assignments, taking advantage of office hours. IF YOU DO NOT UNDERSTAND ONE CONCEPT, YOU WILL NOT UNDERSTAND SUBSEQUENT MATERIAL. It is imperative that you DO NOT FALL BEHIND. If you do, DO NOT WAIT. Come to office hours immediately to get extra help. Consistency in coursework will pay off at the end of the semester. I expect that you READ THE TEXTBOOK CAREFULLY AFTER (OR EVEN BEFORE) EACH CLASS PERIOD Your feedback about the course is most welcome.


Evaluation: Weekly homeworks, two mid-term exams, and a (comprehensive) final exam. All homeworks taken together, both mid-terms taken together, and the final exam will each be worth one third of your course grade.

Grade scale: A ≥ 90% > B ≥ 80% > C ≥ 70% > D ≥ 60 % > F.

Plus or minus grades will be given at the instructor's discretion.

Tentative mid-term examination dates: Friday February 8 and Wednesday March 20.

The final examination will be given during the week from April 29 to May 3, 2013. The final examination may be scheduled on any day during the final examination period. Do not plan to leave University Park until after Friday, May 3, 2013. Students who miss or cannot take the final examination due to a valid and documented reason, such as illness, may be allowed to take a makeup final examination. Personal business, such as travel, employment, weddings, graduations, or attendance at public events such as concerts, sporting events are not valid excuses. Forgetting the date, time or room of an examination is not a valid excuse. Students who have taken the original final examination are not permitted to take a makeup examination.


Academic integrity is the pursuit of scholarly activity in an open, honest and responsible manner. Academic integrity is a basic guiding principle for all academic activity at The Pennsylvania State University, and all members of the University community are expected to act in accordance with this principle. Consistent with this expectation, the University's Code of Conduct states that all students should act with personal integrity, respect other students' dignity, rights and property, and help create and maintain an environment in which all can succeed through the fruits of their efforts.

Academic integrity includes a commitment by all members of the University community not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others.

Academic dishonesty includes, but is not limited to, cheating, plagiarizing, fabricating of information or citations, facilitating acts of academic dishonesty by others, having unauthorized possession of examinations, submitting work of another person or work previously used without informing the instructor, or tampering with the academic work of other students. For any material or ideas obtained from other sources, such as the text or things you see on the web, in the library, etc., a source reference must be given. Direct quotes from any source must be identified as such.

Each student in this course is expected to work entirely on her/his own while taking any exam, to complete assignments on her/his own effort without the assistance of others unless directed otherwise by the instructor, and to abide by University and Eberly College of Science policies about academic integrity and academic dishonesty. Academic dishonesty can result in assignment of "F" by the course instructors or "XF" by Judicial Affairs as the final grade for the student.

All Penn State Policies regarding ethics and honorable behavior apply to this course.


Penn State welcomes students with disabilities into the University's educational programs. If you have a disability-related need for reasonable academic adjustments in this course, contact the Office for Disability Services (ODS) at 814-863-1807 (V/TTY). For further information regarding ODS, please visit the Office for Disability Services Web site at http://equity.psu.edu/ods/.

In order to receive consideration for course accommodations, you must contact ODS and provide documentation (see the documentation guidelines at http://equity.psu.edu/ods/guidelines/documentation-guidelines). If the documentation supports the need for academic adjustments, ODS will provide a letter identifying appropriate academic adjustments. Please share this letter and discuss the adjustments with your instructor as early in the course as possible. You must contact ODS and request academic adjustment letters at the beginning of each semester.