Mathematics 444

Section F13/14 Fall 2011
Lecture: MWF 2-2:50 PM
Classroom: 141 Altgeld Hall

• Home
• Class Schedule
• Assignments
• Exam Info
• Handouts

Instructor Isidora Milin Office: 337 Illini Hall Email: imilin [at] illinois [dot] edu Office Hours Wednesdays 3-4:30 PM 337 Illini Hall / Espresso Royale Course Information Syllabus Class Schedule Assignments Exam Information Fourth Credit Assignments Handouts Official Course Listing from the course catalog

Math 444 - Elementary Real Analysis

This course covers basic concepts in real analysis. Our main goal will be to set a firm foundation for calculus of one variable using rigorous proofs. Calculus has provided you with a set of tools without telling you why exactly these tools work and why the theorems behind them are true. To use (or teach) mathematics effectively, it is not enough to just know what is true, you must (and should want to!) know why. In practice, this means we’ll be looking at inequalities, error estimation and limiting processes from a proof-oriented viewpoint, while striving to gain a better understanding of the concept of a limit, the derivative and the integral. The topics we will cover are:

• Preliminaries: finite and infinite sets, functions, induction
• The real numbers: ℝ is complete
• Limits: of sequences, of infinite series, and of functions at a point
• Continuity of functions
• Derivative and differentiability of functions
• Riemann integral, integrability of functions and the fundamental theorem of calculus
• Sequences of functions: pointwise and uniform convergence

Department of Mathematics College of Liberal Arts and Sciences University of Illinois at Urbana-Champaign 273 Altgeld Hall, MC-382 1409 W. Green Street, Urbana, IL 61801 USA Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576

© 2011 Isidora Milin.