Math 4111
Introduction to Analysis
Fall, 2013

Mohan Kumar

Topics. This course is the first part of a rigorous introduction to mathematical analysis. We will cover basic inequalities for real and complex numbers, basic set theory, and basic point-set topology such as limits of sequences, the least upper bound property, compactness, connectedness, and continuity. We will study absolute continuity, uniform continuity, differentiability, bounded variation, and rectifiability, all in the context of metric spaces. We will prove the mean value theorem, Taylor's theorem, L'Hopital's rule, and other theorems concerning differentiation and extrema of functions of n variables. We will finish with a rigorous development of the Riemann-Stieltjes integral, proving the second fundamental theorem of calculus and other theorems concerning differentiation of integrals, changes of variable, and interchanges of the order of multiple integrals.

Time. Classes meet Tuesdays and Thursdays, 11:30 am to 1 pm in Duncker 101.

Prerequisites. Math 310, or the permission of the instructor.

Text. The lectures will follow the first half (chapters 1-7) of the book Mathematical Analysis by Tom Apostol, second edition, published by Addison-Wesley, ISBN 0-201-00288-4 (1974). One change in the order of topics is, I will start with Set Theory, chapter 2, sections 1-10 and then go onto chapter 1.

Homework. There will be weekly homework which will be posted here on Thursdays and to be returned on next Thursday. You are encouraged to collaborate on homework, and to work additional exercises from the relevant problem sections. Solutions are due at the end of class on the due date. Late homework will not be accepted.

Tests. Midterm examination: Thursday, October 17, 2013, in class. Cumulative Final Examination: Monday December 16, 2013, 1:00 PM - 3:00 PM, in class.

Grading. One grade will be assigned for homework, one for the midterm examination, and one for the final examination. These three will contribute equally to the course grade. Letter grades, computed from the course score will be at least the following:

Course score at least:





Letter grade at least:





Students taking the Cr/NCr or P/F options will need a grade of D or better to pass. Students auditing the course will need to attend at least 25 lectures to receive a successful audit grade.

Office Hours. See the instructor in Cupples I, room 111A, on Tuesdays and Thursdays from 2-3pm, or make an appointment by telephone or email.

Questions? Return to Mohan Kumar's home page for contact information.

Last modified on August 13, 2013.