Math 444 (Sections C13 and C14): Elementary Real Analysis

Fall 2007

Instructor: Florin Boca

Office: 359 Altgeld Hall

Phone: 244-9928

E-mail: fboca at math dot uiuc dot edu

Textbook: R.G. Bartle and D.R. Sherbert, Introduction to Real Analysis, John Wiley & Sons, Inc. (3rd edition)

Prerequisites: Math 241 (formerly Math 243) or Math 242; MATH 347 or MATH 348, or equivalent.

Syllabus

Lectures: MWF 10:00-10:50, 243 Altgeld Hall

Office hours: Monday and Wednesday 5-6, or by appointment.

Grading policy: Comprehensive final exam: 35%; Best two midterm scores (out of three tests): 40%; Homework and quizzes: 25%

Homework and quiz policy: There will be 14 HW assignments. Assignments # 1,3,5,...,13 will be collected and (randomly) selected problems will be graded. Assignments # 2,4,...,14 will not be collected. Instead, a 15 minutes quiz with two problems from that assignment will be given.

Only the best 10 (out of 14) scores will count towards the final score in the class. As a result HW extension or make-up quizzes will not be allowed.

Homework assignments:

HW # 1 (due Friday Aug 31): Section 1.1 (pp.11-12): 3,5,6,8,9,10,12-20.

HW # 2 (quiz on Friday Sep 7): Section 1.2 (pp.15-16): 1,2,5,14,16,20; Section 1.3 (p.21): 3,4,6,10,11,12.

HW # 3 (due Friday Sep 14): Section 2.1 (p.30): 19,23,26; Section 2.2 (p.34): 10,12; Section 2.3 (p.38): 4,5; Section 2.4 (p.43): 2,6,8,9,16.

HW # 4 (quiz on Friday Sep 21): Section 2.5 (pp.50-51): 8,9,10; Section 3.1 (p.60): 5-12,17.

HW # 5 (due Wednesday Sep 26): Section 3.2 (p.67): 1,6,8,9,11,13,14; Section 3.3 (pp.74-75): 4,6,7,10,11,13.

Additional problem: Suppose that the sequence (xn) converges to x. Prove that the sequence (an) of its averages defined by an=(1/n)(x1+x2+...+xn) also converges to x. Give a counter-example showing that the converse is not true.

HW # 6 (quiz on Monday Oct 8): Section 3.3 (pp.74-75): 2,3,5,12; Section 3.4 (p.80): 3,7,8,10,14; Section 3.5 (p.86): 4,5,10.

HW # 7 (due Friday Oct 12): Section 3.5 (p.86): 2,8,9,11,12,13; Section 4.1 (p.104): 1,2,3,6,8,9.

HW # 8 (quiz on Friday Oct 19): Section 4.2 (pp.110-111): 2,3,4,11,12,13; Section 5.1 (pp. 124-125): 4,6,7,11,12,14.

HW # 9 (due Friday Oct 26): Section 5.1 (pp.124-125): 8,10,13; Section 5.2 (pp.128-129): 1,5,7,9; Section 5.3 (p.135): 4,5,6; Section 5.4 (p.144): 1,2,7.

HW # 10 (quiz on Monday Nov 5): Section 5.4 (p.144): 9,11,13; Section 6.1 (p.167): 2,4,9,12,13,14; Section 6.2 (p.175): 2,3,4.

HW # 11 (due Monday Nov 12): Section 6.2 (pp.175-176): 5,6,7,15,16,17; Section 7.1 (pp.201-202): 8,10,12,14,16,17.

HW # 12 (quiz on Monday Nov 26): Section 7.1: 3,5,7; Section 7.2: 2,4,10,11,12,19; Section 7.3: 9,10,11.

HW # 13 (now due Wednesday Dec 5): Section 7.2 (p.209): 8,9,16,17,18; Section 7.3 (pp.217-219): 8,12,13,14,16,18,21.

HW # 14 (quiz on Friday Dec 7): Section 7.3: 18,19,20; Section 8.1: 3,4,13,14,19,21,22,23,24.

Midterm exams calendar: Midterm 1: Friday Sep.28, Midterm 2: Monday Oct 29, Midterm 3: Wednesday, Nov 28.

Final exam: 8-11 am, Tuesday, Dec 11, 243 Altgeld