Syllabus for Real Analysis

Professor: Mark McClure

Course purpose

• To study real analysis: Real analysis is the theory of calculus, which is one of the most important intellectual developments of all time. Together with abstract algebra, it also forms much of the language of modern mathematics.
• To improve your understanding of mathematical proof: The main difference between this class and a calculus class is the point of view. In calculus, the main questions are, "How do I compute derivatives and integrals and what can I do with them?" In real analysis we will be interested in more theoretical questions. For example, "If a function is differentiable, is it necessarily continuous?" Or, "What about the converse statement?".

Materials

• Text: We will use the text Understanding Analysis by Stephen Abbott. This is an outstanding and readable text from an excellent series of texts. You can download it through our library.
• Discourse: I maintain an online forum for class discussion called Discourse at Marks Math . Note that we'll coordinate writing assignments through the forum.

Grades

• Mid-term exams: There will be two exams during the term worth about 100 points apiece. Likely dates for the exams are:
  • Wednesday, September 25 and
  • Wednesday, November 6.
• Quizzes: There will be two short quizzes, each scheduled 16 days prior to an exam. That works out to be
  • Monday, September 9 and
  • Monday, October 21.
  Each quiz could be worth anywhere from 20 to 40 points.
• Final exam: There will be a comprehensive final exam on Monday, December 9 at 11:30 AM.
• Homework: Our homework will be mostly coordinated through our forum and it will come in two types:
  • Problems, which you can respond to publicly to learn from and
  • Assignments, which you must respond to privately for points.
• Final grades: I will determine final grades using a scale not more stringent than the standard 90-80-70-60 scale. You will be apprised of your standing as the term progresses.
• Late work: In general, I don't accept late work.
• Cheating: I don't deal with cheating. If I suspect cheating strongly enough, I simply refer you to the provost and fail you for the class.

Your rights and responsibilities

It's worth understanding your rights and responsibilities as a student at UNCA. One of my responsibilities is to make sure you have the information that you need to do that. Since this is common to all classes, I've got that information on this legalese document.