### Fall 2012, Math 414/514

Class: MWF 9:00-10:15, MG 124

Instructor: Dr. Zach Teitler
Office: MG 233A
Phone: 208-426-1086
E-mail: zteitler@boisestate.edu
Office hours: TuTh 10:00-11:30 (subject to change) and by appointment

Syllabus: pdf, html

Important dates:

• Mon, Aug 27: Start of term, first day of class
• Mon, Sept 3: Labor Day Holiday (no classes, university offices closed)
• Fri, Oct 5: Last day to drop classes with a W
• Mon-Sun, Nov 19-25: Thanksgiving Holiday (no classes, university offices closed)
• Fri, Dec 14: Last day of class

Textbook: Elementary Real Analysis, Second Edition (2008), by Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner.
This text is available for sale in the campus bookstore. Also available online.
See the errata page.

Weekly schedule:
Dates Topics (planned) What we actually did
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Oct 22   Cantor set
Oct 24   Cantor set, Borel sets
Oct 26   Borel sets, Oscillation
Week 10
Oct 29 Set of discontinuity points
Oct 31 Sets of measure zero
Nov 2 Sequences of functions
Week 11
Nov 5 Uniform limits
Nov 7
Nov 9

Homeworks 6-10 (show/hide)
Assigned date Assignment Assigned problems Due date
Wed, 10/10/12 6 Do the following: 4.5.9, 4.5.18, 4.6.9, 4.7.9, 4.7.11, 4.7.15, 5.2.5
Mark the two best ones, that you want me to grade.
Arguments using Heine-Borel are preferable, whenever possible; arguments using other equivalent definitions of compactness are also fine.
If that's not already too much homework, then do one additional problem chosen from 5.10.1, 5.10.6, 5.10.7.
Wed, 10/17/12
Wed, 10/17/12 7 Do the following: 4.7.17, 5.4.32, 5.5.4, two of 5.9.16-20, 6.2.9, 6.3.7
Mark the two best ones, that you want me to grade.
Students in 414: do any one additional problem from 5.10.3 (without logarithms), 5.10.5-7, 5.10.12-13; students in 514, do two.
Fri, 10/26/12
Fri, 10/26/12 8 Do the following: 5.10.11, 6.2.10, 6.3.8, either 6.4.6 or 6.4.7, 6.5.3-4, 6.6.7.
Mark the two best ones, that you want me to grade.
Students in 514: please try 6.5.6 if possible.
Wed, 11/7/12
Wed, 11/7/12 9 Do the following: 6.7.6, one of 6.8.2-4, one of 6.8.{6-8,10-12}, 6.8.14, 6.9.2.
9.2.7.
Mark the two best ones, that you want me to grade.
Students in 414: do one additional problem from 9.3.{2,4-8,11,23,24}; students in 514, do two.
Fri, 11/16/12
Mon, 11/26/12 10 Do the following: 9.3.16, 9.9.3
10.2.7, 10.2.13, 10.4.2
13.2.4 (reducing the number of assumptions!), 13.2.7
Mark the two best ones, that you want me to grade.
Also do one additional problem from: 13.3.9-10.
Wed, 12/5/12
Wed, 12/5/12 11 Do as many of the following, as you wish to do: 10.4.7
13.4.(3,4,15), 13.5.15, 13.6.7, 13.8.4, 13.8.7
(Difficult/long? 13.6.11, 13.6.42, 13.7.3, 13.8.13)
Any interesting problems from later sections in Chapter 13 are fine too.
Fri, 12/14/12

Construction of real numbers: Numerous books explain the construction of real numbers. For a description presented as a series of exercises, starting from basic logic and going through set theory, natural numbers, integers, rational numbers, and real numbers (by Cauchy sequences), see these notes (pdf, 44 pages). Please let me know if you see any mistakes (typos, wrong statements, an exercise depends on a later one, etc), or if you have any suggestions.

Selected resources:

zteitler@boisestate.edu

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