Math 471: Real Analysis (graduate-level)

Fall 2018

General Information

Instructor: Chris Staecker (Personal Homepage)

Email: cstaecker@fairfield.edu

Office: BNW 16

Office Hours: T 11-12:30, 1:30-3; W 2-3; R 5-6:30; F 11-12:30 or by appointment

Textbook: Introduction to Real Analysis by Bartle & Sherbert, 4th edition

Class Meetings: Thursday 6:30-9PM

Syllabus

Calendar

9/20: Homework #1 due
Section 2.1: 1ab (use ONLY the 9 "algebraic properties of R"), 10, 14, 17, 18 (consider a-b, then use #17), 20, 22 (use induction)
Section 2.2: 6a, 8a, 10b, 16 (see Def 2.2.7)
Section 2.3: 3, 4 (don't prove it), 7
Section 2.4: 3, 17 (you may assume 2.1.13a holds for cubes)
9/27: Quiz #1
10/4: Homework #2 due
Section 2.5: 2, 8, 9
Section 3.1: 5ac, 6a, 11, 12 (to start, use a trick like in Example 3.1.6d), 18
(In Section 3.1, prove directly using ε's, not using tricks from 3.2)
Section 3.2: 2, 3, 6acd (use Theorem 3.2.10 for c&d), 7
Section 3.3: 2, 3 (for these, use induction to show it's monotone)
Section 3.4: 1, 4, 9 (use Theorem 3.4.9), 14, 16
10/11: Quiz #2
10/18: Homework #3 due
Section 3.5: 1, 2a, 4, 7
Section 4.1: 9ad, 12ab, 15
(In Section 4.1, prove directly using ε's, not using tricks from 4.2)
Section 4.2: 1, 5, 6
Section 4.3: 5bg
Section 5.1: 5 (prove it will be continuous), 13 (prove it)
10/25: Quiz #3
11/1: Homework #4 due
Section 5.2: 3, 8 (yes- prove it)), 11
Section 5.3: 1, 5 (just do the first part), 7 (consider x - cos(x)), 13
Section 5.4: 2, 4, 7 (just do the second part), 15
Section 5.6: 8, 9
11/8: Quiz #4
11/15: Homework #5 due
Section 6.1: 2, 4, 9, 13
Section 6.2: 6 (read Example 6.2.10b), 7, 15
Section 6.4: 2, 8, 9 (for 8 & 9, the "remainder term" is Rn on pg 190)
11/29: Quiz #5
12/6: Homework #6 due
Section 7.1: 2b, 4a, 5, 10, 13, 15
Section 7.2: 2
12/13: (last day of class) Quiz #6
12/20: Homework #7 due (by email or bring to prof.)
Section 7.2: 4, 6, 7, 8, 10 (use #8), 13
Section 7.3: 10, 14
Section 8.1: 1, 4, 11, 14 (for #14, just the "not uniform" part)
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