**Math 447: Real Variables**

**Spring 2019**

**Instructor:** Florin P. Boca

**Office:** 371 Altgeld Hall

**Phone:** 244-9928

**E-mail:** fboca at illinois dot edu

**Textbook: Kenneth Ross, The Theory of Calculus, Second Edition (2013),
ISBN: 978-1461462705, Springer.**

Also recommended: **Kenneth Davidson, Allan Donsig**,
Real Analysis and Applications (2010), Springer, Math Library *electronic resource*.

**Prerequisites:** Prerequisite: MATH 241 or equivalent; junior standing; MATH 347 or MATH 348, or equivalent experience;
or consent of instructor. Credit is not given for both MATH 447 and either MATH 424 or MATH 444.

**Course Description:** Math 444 and 447 are the first theoretical courses in
real analysis offered here. Ideally, a student should leave such a course with not only a basic
understanding of the one-dimensional calculus, but an increased facility at reading and
writing mathematical sentences, the ability to produce and analyze examples, and
some skills at constructing and writing elementary proofs. Math 447 covers enough
metric topology to provide background for other courses such as Math 448.

**Syllabus:**

**Lectures:** TR 9:30-10:50, 443 Altgeld Hall

**Office hours:** Tuesday 1-2, Wednesday 2-3, or by appointment.

**Grading policy:** Comprehensive final exam: 35%;
Three midterm exams: 40%;
Homework/quizzes: 25%

**HW and quiz policy:** There will be 12 HW assignments. Assignments
⋕ 2N, N=1,2,...,6 will be collected and graded. Assignments ⋕ 2N-1,
N=1,2,...,6 will not be collected. Instead, a 15 min quiz with two problems from that
assignment will be given in class. Only the best 10 (out of 12) scores will count.
As a result HW extensions or make-up quizzes will not be normally allowed.

**Midterm exams calendar:** **Midterm 1:** Tuesday Feb 26,
**Midterm 2:** Tuesday April 2, **Midterm 3:** Tuesday April 23.

**Final exam: 1:30-4:30 pm, Thursday, May 9, 443 Altgeld Hall**.

Last modified:* January 8, 2019*