Real Analysis I
MS 401-01
Margie Hale, Fall 2000

214-5 Elizabeth Hall ext. 7551 campus box 8340 http://www.stetson.edu/~mhale/

Office Hours: Mon 3:00 - 5:00 Wed 11:00 - 12:00 Fri 11:00 - 12:00 or by appt.

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 more. A study of real analysis allows for an appreciation of the many interconnections with other mathematical areas.

Your major goals are these:

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.

Goal 3 is the most substantial, and the most exciting to progress toward. Most of your analysis time will be spent outside of class puzzling over and writing proofs. Some of these will be collected and graded. Because this is an independent study, we will meet once per week. Our class time will be used for presentation and analysis of proofs and examples, and for answering your questions. You should plan to spend about 6 hours per week outside of class.

As in most undergraduate courses, the material you will see in MS 401 is well-known and publicized. You are duplicating the work of others, not for the betterment of humanity, but solely for your own benefit. It is thus important to have a Rule.

The Rule: No books, journals, or people outside this class may be used.

Your grade will be based on the following:

Prove the theorems and do the exercises in the order given. Theorem 10 may be used to prove theorem 12, but not vice-versa. If theorem 10 has stumped you, consider it proved temporarily and proceed to use it when needed. Proofs will be graded for both content and form on a scale of 0-2. Some of these may be resubmitted for credit. You may work together on the numbered theorems and exercises, as long as you do not consult with anyone outside the class. There is no penalty for cooperation. Please write up submitted work in your own words and give credit to collaborators. The tests will consist of definitions and theorems you have seen and some theorems you have not seen, but that are accessible to you. An overview and knowledge of interrelations will be stressed. Oral exams are conducted in private.

My hope is that you will derive some side benefits not directly related to the content of the course:

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.

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