MATH 554 and 703-I Real Analysis I  - Fall 2001 Professor Robert Sharpley Meets: TTh  4:30 - 5:45 in LeConte 401 Instructor Information  Office:   LeConte 313 D  Office Hours:   TTh 3:30-4:30; 5:45 - 6:45

Loaded at 3:42 pm on Saturday - Dec. 15   Final Results Have a good Holidays.

Course Information

Description:   The course will cover the general topics contained in the first five chapters of the text. Several additional topics will also be covered and the presentation will not necessarily follow the text. Attendence is required and the exams will be over the lectures (outlines of which are linked to this page) and homework. The course topics include:

• Countable and uncountable sets, the real numbers, order, least upper bounds, the Archimedean property and completeness.
• Sequences of real numbers, monotone sequences, convergence, subsequences, the Bolzanno-Weierstrass property and compactness.
• Topology of the real numbers: open and closed sets, the Heine-Borel theorem and compactness, connectedness.
• Limits; Continuous functions and their properties, intermediate and extreme value theorems, uniform continuity, monotone functions and inverses.
• Differentiation, the chain rule, Rolle's theorem and the Mean Value Theorem, L'Hospital's rule.
• The Riemann integral, its properties, and the Fundamental Theorem of Calculus.

Reference Text:  Real Analysis, A First Course (2-nd ed.), by Russell A. Gordon, Addision-Wesley Higher Mathematics Series, Reading, MA, 2001.

Grading scheme: Three tests, each counting 20% of the final grade. The homework, turned in on a regular basis, counts 10%, with the comprehensive final exam counting 30%.

Attendance: Classroom attendance is required according to official university policy.

Important Course Dates:

August 23   (Thursday) August 29   (Wednesday) September 3   (Monday) September 20   (Thursday) October 4   (Thursday) October 15-16   (Mon.-Tues.) October 25   (Thursday) November 20   (Tuesday) November 21-25   (Wed.-Sun.) December 7   (Friday) Classes Begin Last Day for Withdrawal w/o penalty Labor Day - no classes Test 1 Last Day for Withdrawal w/o WF grade Fall Break - no classes Test 2 Test 3 Thanksgiving Holidays - no classes Classes End December 12   (5:30 pm, Wednesday)   Final Exam

Prerequisites: Qualification through placement, or a grade of C or better in MATH 241 or its equivalent.

  Lectures Notes

  Homework Assignments

  Tests and Samples

This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated October 28, 2001.  This page ©2001-2002, The Board of Trustees of the University of South Carolina.  URL: http://www.math.sc.edu/~sharpley/math554