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
Important dates:
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 | ||
Aug 27 | Hello, Properties and construction of real numbers | ← |
Aug 29 | Properties and construction of real numbers | ← |
Aug 31 | Properties and construction of real numbers | ← |
Week 2 | ||
Sept 3 | Labor Day | |
Sept 5 | Sequences | ← |
Sept 7 | Sequences | ← |
Week 3 | ||
Sept 10 | Sequences | ← |
Sept 12 | lim inf, lim sup | ← |
Sept 14 | Infinite sums | ← |
Week 4 | ||
Sept 17 | Series | ← |
Sept 19 | Absolute convergence, rearrangements, products of series | |
Sept 21 | Sets of real numbers (topology) | |
Week 5 | ||
Sept 24 | Compactness | |
Sept 26 | Limits of functions, continuity | |
Sept 28 | Continuity | |
Week 6 | ||
Oct 1 | ||
Oct 3 | ||
Oct 5 | Uniform continuity | |
Week 7 | ||
Oct 8 | Extremal properties | |
Oct 10 | Intermediate Value Property | |
Oct 12 | Discontinuities | |
Week 8 | ||
Oct 15 | Discontinuities | |
Oct 17 | Dense sets, Nowhere dense sets | |
Oct 19 | Baire category theorem | |
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 |
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: