Department of Mathematics

Pomona College

Course Outline

Math 101. Introduction to Analysis Spring 2008

Time and Place: MW 2:45 pm - 4:00 pm, Millikan 218

Instructor: Dr. Adolfo J. Rumbos

Office: Andrew 259

Phone/e-mail: ext. 18713 / arumbos@pomona.edu

Office Hours: MWF 9:15 am - 9:50 am, Tu 9:15 am – 11:10 am

or by appointment

Text: Elementary Analysis: The Theory of Calculus

by Kenneth A. Ross; Springer-Verlag.

Prerequisite: Linear Algebra

Course Description. The main goal of this course is to give a rigorous treatment to the study of continuity of real valued functions of a single real variable. This will require an in-depth study of the real numbers system and its properties since many important facts about continuous functions (eg., the intermediate-value theorem) would not be valid without some of those properties.

About two thirds of the class time will be spent on student presentations. The instructor will lecture or lead discussion the other third of the time. The content of the course is dictated by a series of assigned problems, most of which will involve the development of mathematical arguments, whose solutions will be presented by the students to the class. In addition, students will be required to give a formal presentation at the end of the semester on a special topic related to the course material (see attached list of special topics).

Assigned Readings and Problem Sets. Readings and problem sets will be assigned at every class meeting. Students are expected to do all the assigned reading and work on all the assigned problems, as they will be asked to present solutions to the class at a subsequent meeting. Each student will be required to keep a journal in which complete solutions of all problems presented in class are recorded. This journal is to be separate from notebooks in which the student takes notes during lectures and student presentations.

Grading Policy. Grades will be based on presentations and solutions to assigned problems, two 50-minute examinations, weekly assignments, and a formal presentation. The overall score will be computed as follows:

Problem solutions journal 15%

Homework assignments 20%

Problem solutions presentation 10%

Two examinations 40%

Formal presentation 15%

Math 101 Spring 2008

Tentative Schedule of Topics, Presentations and Examinations

Date Topic

W Jan. 23 Introduction to mathematical reasoning

M Jan. 28 Ways of proving mathematical statements

W Jan. 30 The real numbers system. Numbers: rational and irrational

M Feb. 4 Properties of real numbers

W Feb. 6 Properties of real numbers (continued)

M Feb. 11 Sequences of real numbers

W Feb. 13 Convergence

M Feb. 18 Completeness

W Feb. 18 Real valued functions of a real variable

M Feb. 25 Limits and continuity

W Feb. 27 Continuity

M Mar. 3 Review

W Mar. 5 Exam 1

M Mar. 10 Functional limits

W Mar. 12 Continuous functions

M Mar. 17 Spring Recess

W Mar. 19 Spring Recess

M Mar. 24 Properties of continuous functions

W Mar. 26 Properties of continuous functions (continued)

M Mar. 30 Topology of the real line

W Apr. 2 Connected sets and compact sets

M Apr. 7 The intermediate value theorem

W Apr. 9 The intermediate value theorem (continued)

M Apr. 14 Continuous functions over compact sets

W Apr. 16 The extremal value theorem

M Apr. 21 Review

W Apr. 23 Exam 2

M Apr. 28 Special Topic

W Apr. 30 Special Topic

M May 5 Special Topic

W May 7 Special Topic