Syllabus

This is a course in real analysis, that is to say the study of the calculus of real valued functions of a real variable. Questions of convergence will be prominent as we study the convergence of sequences and series of constants and functions by studying and devising proofs of classical theorems. New ideas include the notion of Cauchy sequences and completeness, use of supremum and infimum concepts, uniform convergence and its consequences, and generalizations to metric and normed linear spaces. In Stephen Abbott's book, Understanding Analysis, I tentatively plan to cover sections 1.1-1.4, 2.1-2.7, 3.1-3.4, 4.1-4.5, 5.1-5.3, 6.1-6.5, 7.1-7.5, and 8.2. Some topics may be skipped and others added as the semester evolves. The use of Maple 9 to complete some of your assignments will be expected. The course will be challenging, and require your best effort applied consistently throughout the semester. The topics to be covered are fundamental for anyone planning to go to graduate school in mathematics or interested in studying applied areas which use mathematics.

Requirements

Your grade in the course will be based on 600 possible points. There will be three one-hour exams given during the semester, each covering about four weeks of work. Tentative dates for the exams are September 26th, October 24th, and November 21st. Each one-hour exam will be worth 100 points. Homework will be collected and graded regularly. The total of all graded homework will be worth 100 points. The comprehensive final exam given at the end of the course will be worth 200 points. Clarity of thought and expression are important both on homework assignments and on exam solutions. This course will be challenging, but rewarding because hard work, perserverance, and attention to detail will usually be rewarded with success. Working in teams is valuable, but independent thinking is essential.

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Created 07/01/2003. Last modified 08/01/2003. Email to ekh@wfu.edu