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OU MATH 3513 - Foundations of Analysis -Syllabus

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Foundations of AnalysisMath 3513-001Fall 2001Instructor: Andy MillerOffice: PHSC 801Phone: 325-4986 or 325-6711e-mail: [email protected] Web Page: www.math.ou.edu/∼amiller/3513Office Hours: MW 2:30-3:00 PM, Tues 10:00-11:00, Fri 10:30-11:30 or by appointmentBrief Description: Some of the main topics which will be explored in this course are: setsand functions; axioms for the real number system; limits of sequences; limits and continuityof functions; and, the intermediate and extreme value theorems. However the central goal forthe course is for students to attain and develop skills of constructing mathematical proofs,and to gain experience working in mathematical and axiomatic frameworks. The coursedescription in the University Catalogue reads as follows:3513 Foundations of Analysis. Prerequisite: one semester of calculus; corequisite:2433. The real number system, sequences of numbers, series of numbers, limits andcontinuity of functions, topology and continuity on the real line. (F, Sp, Su)These topics and the experience of working with mathematical theoriess are basic to nearlyall areas of mathematics. For these reasons, the Foundations course serves as a prerequisitefor many of the upper division math courses.Materials: The textbook for this course is Introduction to Real Analysis (third edition)by R. Bartle and D. Sherbert (J. Wiley & Sons, New York, 2000). Portions of Chapters 1through 5 will be covered during the semester. Additional topics may be introduced as timepermits.Assignments and Quizzes: Homework will be assigned and collected at every classperiod. Each assignment will consist of one or two problems, and because of this there willbe an expectation of carefully prepared work. Credit will be deducted for poorly written orhastily prepared work. Students are encouraged to work in study groups but must prepareeach assignment on their own. The homework assignments should be submitted on regular-sized 812× 11 paper, and each problem should be preceded by a complete written statementof the problem.2Quizzes will be given regularly during class periods. During the semester the Math Clubwill be sponsoring a number of events, and attendance at some of these will be required asspecial assignments.Exams: The final exam will be the only formal exam in the course. It will be compre-hensive over topics discussed during the semester.Grading: Course grades will be based on the following scale:Homework 50 %Quizzes 20 %Special Assignments 5 %Final Exam 25 %Student Disabilities: The instructor is committed to providing an environment in whichstudents will be able to successfully complete this course. If any student has a physicaldisability that may affect their performance, they should contact the instructor so thatsteps may be taken to ensure full participation and to facilitate educational


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