Syllabus

PEOPLE AND PLACES:

COURSE OBJECTIVES: Real analysis is the study of the continuum of real numbers and other structures in mathematics constructed from the continuum. In this course, we will discuss, among other things, a number of topics from calculus: sequences and series of real numbers, real valued functions, differentiation and integration of real valued functions. Although these topics are familiar to you, the aim in this course is to understand the theoretical foundation of calculus rather than how to use it as a computational tool.

PREREQUISITES: An interest in understanding calculus and the continuum from a fundamental proof based perspective, and a willingness to work and discuss challenging homework problems.

TEXTBOOK: W. Rudin, Principles of Mathematical Analysis, 3d Edition, McGraw-Hill (1976). Available in paperback and hardcover.

ADDITIONAL REFERENCE: C. Pugh, Real Mathematical Analysis, Springer (2010). Available electronically through the MSU library.

COURSE WEBSITE AND FORUM: http://sites.google.com/a/msu.edu/jeffrey-schenker/teaching/honors-analysis-327h-fs16

The course website is mandatory reading for the course. Reading assignments from the textbook, homework and supplementary reading materials will be posted there.

The website is a Piazza class page which provides a forum for asking and answering questions about the course. The system is highly catered to getting you help fast and efficiently from classmates and myself. Rather than emailing questions to myself or the TA, I encourage you to post your questions on Piazza. (If you have any problems or feedback for the developers, email team@piazza.com.)

CLASS EXPECTATIONS:

  1. You are expected to attend every lecture.

  2. You are expected to pay attention and participate in class.

  3. You are expected to own the text book and complete all reading assignments.

  4. You are expected to complete all homework assignments. Some of the homework will be very difficult and may take you a lot of time to complete. Don't procastinate!

  5. If you do not understand the subject, you are expected to reread the book and ask questions in lecture or online until you do.

  6. You are expected to write proofs. This is a writing course! It is important that you take the time to present your solutions and proofs in clear, well written, English prose. Translating mathematical thoughts into written english facilitates understanding at a deeper level. Solutions that are incompletely or poorly written will not be considered correct, even if it appears that the mathematical content is correct. You may be asked to revise and resubmit solutions that are not well written.

EVALUATION: Your course grade will be based on homework assignments, project homework, exams and class participation.

  • HOMEWORK: There will be weekly homework assignments. Selective homework problems will be graded.

  • PROJECT HOMEWORK: There will be two extended home work assignments with more difficult problems that develop subjects we haven't discussed completely in class.

  • EXAMS: Two hour midterm exams are scheduled in the evening on 10/6 and 11/10. The two hour final exam will be on 12/14. There is a possibility that the final will be a take home exam.

  • PARTICIPATION: Please ask questions and make constructive comments during lecture and make use of the forum. From time to time, roughly every two or three weeks, we may have an in class discussion in place of a lecture. These discussions will be devoted to questions you might have and further exploration of homework and exam problems. Expect to be called on to discuss math at the board.

GRADES: The components of your grade will be weighted as follows:

IMPORTANT DATES:

Further information can be found HERE.

TIPS FOR SUCCESS:

  • Understand the homework. All of it.

  • Frequent my office hours and ask questions in the online forum.

  • When your body is in class, have your mind in class. Put away your cell phone. Don't check your email. Multi-tasking doesn't work.

ACADEMIC INTEGRITY: You are expected to uphold standards of academic integrity in this class, as embodied in the Spartan Code of Honor academic pledge:

As a Spartan, I will strive to uphold values of the highest ethical standard. I will practice honesty in my work, foster honesty in my peers, and take pride in knowing that honor is worth more than grades. I will carry these values beyond my time as a student at Michigan State University, continuing the endeavor to build personal integrity in all that I do.

You are encouraged to collaborate with your peers on homework assignments. However, there is one simple rule that must be followed in any collaborative work:

Never present another's ideas or words as your own.

To do otherwise is called plagiarism — it is unethical and a basic violation of academic integrity. In particular, you are expected to

  1. Write solutions in your own words.

  2. Cite your collaborators and sources.

That is, work with other students but when you are done the time to sit by yourself and write the homework up in your own words and let me know who you worked with and what sources (if any) you looked at. You may be asked to revise and resubmit a proof that appears to be a near verbatim copy of another student's work.

CAMPUS EMERGENCIES: If an emergency arises in this classroom, building or vicinity, your instructor will inform you of actions to follow to enhance your safety. As a student in this class, you are responsible for knowing the location of the nearest emergency evacuation route or shelter. These directions appear on the maps posted on the walls throughout this building. If police or university officials order us to evacuate the classroom or building, follow the posted emergency route in an orderly manner and assist those who might need help in reaching a barrier-free exit or shelter. To receive emergency messages, set your cellular phones on silent mode when you enter this classroom. If you observe or receive an emergency alert, immediately and calmly inform your instructor. (See also www.alert.msu.edu.)