Real Analysis I
MATH 401-01
Margie Hale, Spring 2010

214-5 Elizabeth Hall
ext. 7551
campus box 8340
Office Hours:
Mon 10:00 - 10:50, 2:30 - 3:20
Tue 10:00 - 10:50
Wed 10:00 - 10:50
Fri 10:00 - 10:50
or by appt.

Course Overview   Real analysis is a large field of mathematics based on the properties of the real numbers and the ideas of sets, functions, and limits. It is the theory behind calculus, differential equations, and probability, and it is part of the essential foundation of graduate study in many areas of pure and applied mathematics. A study of real analysis allows for an appreciation of the many interconnections between areas of mathematics.

Course Goals:

  1. a knowledge of the real number system;
  2. familiarity with the major concepts of modern analysis;
  3. an increase in your level of mathematical maturity, including discovering and writing your own proofs.


  1. a deeper knowledge of what mathematics is and an appreciation of its power;
  2. enjoyment in learning;
  3. precision of thought;
  4. skill in communication, oral and written.
Each of these can contribute substantially to your future career, whatever it will be.

Text   The text is Bartle and Sherbert, Introduction to Real Analysis, 3rd ed.

Grading   Your grade will be based on the following:

Homework & Class Participation 30%
2 Oral Tests 15% 25%
Written Final Exam 30%

Tests will be conducted orally and in private outside of class. The final exam is written and in class: Saturday 5/1, 5-7 pm. The tests and final will contain definitions, exercises, and theorems, some of which you will have seen before, and some that are new but accessible to you. An overview and knowledge of interrelations will be stressed.

Homework should consume about 8 hours per week outside of class. Read the section and class notes, think about results, organize your knowledge, and write out proofs and answers to the exercises. Those listed on the syllabus will be collected and graded, but you should do many more. Some have hints or answers in the back of the book.

Participation means both quantity and quality. Some variation in individual style is allowed, but everyone should plan to speak every class period. In fact, if you don't speak, not much will happen! Part of every homework assignment is to read the material for the next assignment so that we can discuss it in class. Work through the book's examples and proofs, and identify the questions you need answered so that you can do the next homework assignment.

Attendance is expected. Previous students have found that loyal attendance (3 or fewer absences) is required for success in my courses.

Assistance   You are expected to talk with me outside of class and visit my office. Ask me about homework, in class, in my office, or via email. You may work with other students. For full value, re-do homework in your own words. Professional ethics require that you credit any help received. All work on tests must be your own, with no help from books, notes, or other people. I support the Honor System.

This is a 400-level course for mature learners; you are in charge of your own success. You are responsible for learning the material, reading the text, identifying your questions and difficulties, talking with me inside and outside of class, keeping up with the syllabus, reading your email, and knowing class policies. Visit my web site to find out more about me and about the course. If you have special needs, please don't hesitate to discuss them, either with me or with the Academic Success Center.

Communication   I use email and Blackboard to communicate important information and distribute course materials. To reach me, see my contact information above. You are welcome in my office, my voicemail, and my Inbox.

spring 2010 syllabus
Guidelines for Math Talks
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