Mathematics

Math 420 Real Analysis
Fall 1999

 Instructor: Dr. Milan Lukic
Office: MC 521
Office Hours: M-F 10 - 11
Phone: (608) 796-3659 (Office); 787-5464 (Home)
e-mail: mnlukic@viterbo.edu
 

Course Description (from the catalog)
Study of selected topics from real variable theory such as: real numbers; topology of the real line; metric spaces; Euclidean spaces; continuity; differentiation; the Riemann-Stieltjes integral; series. Prerequisite: grades of C or higher in 260 and 320.

Text Victor Bryant, Yet Another Introduction to Analysis, Cambridge University Press, 1996.

Core (General Education) Skill Objectives:

1. Thinking Skills:

   (a)

   Students will use reasoned standards in solving problems and presenting arguments.

2. Communication Skills: Students will ...

   (a)

   ...read with comprehension and the ability to analyze and evaluate.

   (b)

   ...listen with an open mind and respond with respect.

   (c)

   ...access information and communicate using current technology.

3. Life Value Skills:

   (a)

   Students will analyze, evaluate and respond to ethical issues from an informed personal value system.

4. Cultural Skills: Students will ...

   (a)

   ...understand culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior.

   (b)

   ...demonstrate knowledge of the signs and symbols of another culture.

   (c)

   ...participate in activity that broadens their customary way of thinking.

5. Aesthetic Skills:

   (a)

   Students will develop an aesthetic sensitivity.

Specific Course Goals:

Students will ...

1. ...be exposed to an in-depth study of central ideas of real analysis.
2. ...continue to expand their ability to formulate conjectures, design proofs for them if true or counterexamples if false.
3. ...communicate those designs in writing and orally in class.
4. ...gain knowledge and skills to formalize their ideas and express them with a full mathematical rigour.

Content:

1. Firm foundations: The Set of Real Numbers - Existence of ; Supremum and Infimum.
2. Sequences; Limits; Infinite Series.
3. Functions; Continuity.
4. Differentiation.
5. Integration.
6. Sequences and Series of Functions; Metric Spaces (as time permits).

Course Philosophy and Procedure

Since all of you are math majors, I will skip the ``how to study mathematics'' part. However, it might be a good idea to take a look into a syllabus from some of your earlier math courses. I see my role as of one who helps you make your own discoveries. Thus, the class participation and the regular work after class are of vital importance. I encourage you to also look into at least some of the books listed below.

Grading will consist of three exams (two during the semester and the final exam) worth 100 points each. The homework, quizzes, in-class presentations will total to 200 points. My grading scale is A=90%, AB=87%, B=80%, BC=77%, C=70%, CD=67%, D=60%.

Yes, there will be in-class presentations. Our textbook has hints and/or solutions to all exercises. My idea is to have you present in class as many of those exercises as possible. I will also provide a number of supplementary problems as we go along, and am expecting from you to present solutions to some of those problems.
I am looking forward to explore this fascinating subject of real analysis with you, and for all of us to have an interesting and enjoyable semester.

Americans with Disability Act:

If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me and Wayne Wojciechowski in Murphy Center Room 320 (796-3085) within ten days to discuss your accommodation needs.

This syllabus is tentative and may be adjusted during the semester.

1999-09-09