Math 352-10          Analysis          Spring 2008
Instructor	Office	Phone	Hours
Jimmie Lee Johnson	Auditorium Campus Chicago, Illinois Room 416	(312) 341-3552 Voice Mail	Tu 5:00-6:30pm and by appointment.
Tu 6:00-8:30pm 907
	E-mail:  jjohnson@roosevelt.edu Web Page:  http://faculty.roosevelt.edu/jjohnson/

Text: Understanding Analysis, by Stephen Abbott, Springer, 2001 ISBN 0-387-95060-5.

Prerequisite: Grades of C or better in Math 233 Calculus III and either in Math 245 Discrete Structures or Math 290 Mathematical Reasoning. It is also recommended that you have a C or better in Math 300 Linear Algebra.

Class will consist of oral reports, quizzes, examples, theorem proving and the answering of questions. Prior to each class, you must do the assigned reading or you will be lost; make notes of topics you feel need elaboration in class. For each class, be prepared to give a short explanation of a definition or proof of a theorem orally, at the chalkboard. You are responsible for all assigned reading even if it is not discussed in class.  Class will usually include
     1. a short quiz each week;
     2. now and then, a short oral presentation of current material by selected students;
     3. discussion of new material via examples and the proof of new theorems.

Quizzes will be given each week beginning February 5th, except for the weeks of the exams. The quizzes will be closed book, and will count for 15% of your grade. The two lowest quiz grades will be dropped. No make-ups; a missed quiz will count as one of the dropped grades.

Homework will be collected, discussed, graded and returned; Homework, along with oral presentation scores, will count for 15% of your grade. Late homework may be downgraded, if it is later than a week, but it is still worth more than no credit at all. I recommend the use of the software Maple 11 to help with examples involving much of the homework.

Exams will be given on March 11th and April 15th. The first will be closed book but the second will be a take home exam, due the following week. I expect to give the Major Field Test for mathematics during class time on April 15th. The average of the March exam and the take home exam will count for 30% of your grade. If you miss the March exam, your score on the Final Exam will be used for both. No make-ups except for excused absences with advance notice. Your performance on the Field Test will be noted for assessment but will not be used for your grade in this class as the results will not be known until the summer. If you fail to take the Field Test the take home exam will not be available to you, but your score on the final exam will be used for the take home score.

Final Examination will be given on Tuesday, May 13th, closed book and comprehensive. It will normally count for 40% of your grade.

Grades: Regulations covering grades (especially I and W) are on pages 254-256 of the 2006-2008 Undergraduate Catalog or on pages 203-205of the 2005-2007 Graduate Catalog. Incompletes will not be given, except to a student who has done passing work up to the Final Examination (including most of the homework) but misses the final exam because of an excused absence with advanced notice. The last day to drop a class (with a grade of "W") is Friday, March 28th, and the drop form must be submitted to the Registrar's Office. Anyone registered after that must be graded solely on academic performance.

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Objectives: The student is expected to learn the rudiments of the theory of real analysis, including the following ideas: 1.) Complete ordered field. 2.) Sequences, series, and their limits, including the Bolzano-Weierstrass Theorem. 3.) Limits of a function of a real variable, both at a real number and at infinity. 4.) Continuity of a function, including the Intermediate Value Theorem. 5.) Differentiability of a function, including Rolle's Theorem and the Mean Value Theorem. 6.) Integrability of a function, including the Fundamental Theorem of Calculus. To this end, the completion of a variety of homework problems and the occasional oral presentation are expected of each student. For assessment purposes, copies of some graded homework assignments and exams of each student will be placed in a file in the school office. Further review of these materials for assessment purposes will not affect the student's standing.

Syllabus

Date	Sections	Topics -  changeable
January 29	1.1 1.2	Irrationality of the square root of 2 Some Preliminaries
February 5	1.3 1.4 1.5	Axiom of Completeness Consequences of Completeness Cantor's Theorem.
February 12	2.1 2.2 2.3	Rearrangements of Infinite Series Limit of a Sequence Algebraic and Order Limit Theorems
February 19	2.4 2.5 2.6	Monotone Convergence and Infinite Series Subsequences and Bolzano Weierstrass Theorem Cauchy Criterion
February 26	2.7 2.8 3.1	Properties of Infinite Series Double Summations and Products of Infinite Series The Cantor Set
March 4	3.2 3.3 3.4	Open and Closed Sets Compact Sets Perfect and Connected Sets; Review
March 11	Exam #1	Chapters 1, 2, Sections 3.1-3.2 -- Lecture Afterward.
(March 18)	No Class!	Spring Break.
March 25	3.5 4.1 4.2 4.3	Baire's Theorem Examples of Dirichlet and Thomae Functional Limits Combinations of Continuous Functions
April 1	4.4 4.5 4.6	Continuous Functions on Compact Sets Intermediate Value Theorem Sets of Discontinuity
April 8	5.1 5.2 5.3 5.4	Are Derivatives Continuous? Derivatives and the Intermediate Value Property Mean Value Theorem A Continuous Nowhere Differentiable Function
April 15	Exam #2	Major Field Test (in class) Take Home Exam:
April 22	6.1 6.2 6.3 6.4	Branching Processes Uniform Convergence of a Sequence of Functions Uniform Convergence and Differentiation Series of Functions
April 29	7.1 7.2 7.3 7.4	How Should Integration be Defined? Definition of the Riemann Integral Integrating Functions with Discontinuities Properties of the Integral
May 6	7.5 7.6 6.5 6.6	Fundamental Theorem of Calculus Lebesgue's Criterion for Riemann Integrability Power Series Taylor Series; Review
May 13	Final	Comprehensive.

This page is at http://faculty.roosevelt.edu/jjohnson/Spring2008/M352S08.htm and was last revised April 22 2008.