Math 447: Real Variables

Fall 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.


  • Introduction
  • Sequences
  • Continuity (including metric spaces)
  • Sequences and Series of Functions
  • Differentiation
  • Integration

  • Lectures: TR 9:30-10:50, 143 Altgeld Hall

    Office hours: Monday 2-3, Wednesday 4-5

    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 Oct 1, Midterm 2: Thursday Oct 31, Midterm 3: Tuesday Dec 3.

    Final exam: 1:30-4:30 pm, Tuesday, December 17, 143 Altgeld Hall.

    Illinois Student Code

    Last modified: October 14, 2019