NEW
Final exam
Practice problems for the final:
part 1 and
part 2 (version 2, including solutions of problems 1 and 7 from part 1)
Midterm solutions
Finals week office hours: F.M. Monday 11:30-2:30. D.L. Tuesday 10:30-12:00, and
by appt.
INSTRUCTOR
Instructor: Debra Lewis
Office: 359B Baskin Engineering
Phone: 459-2718
E-mail: lewis at ucsc dot edu
(checked more often than voicemail or gmail)
and/or DebraKLewis at gmail dot com
TA: Filix Maisch
Office: 3?? Baskin Engineering
E-mail: fmaisch at ucsc dot edu
TIMES AND PLACES
Lecture: MWF 12:30-1:40, Porter 144
Sections: Tu 2:00-3:10, Thimann Lab 101. W 2:00-3:10, JBE 301(A or B??)
D.L.'s office hours: M 2:30-3:30, M 4:00-6:00 in JBE 302, Tu 5:15-6:30 (may be pre-empted by colloquium obligations), W 9:30-10:30, and by appointment
F.M.'s office hours: Tu 12:00-1:30, F 11:00-12:15, and by appointment
Instant messaging group
Principles of Mathematical Analysis, Third Edition. Walter Rudin. McGraw-Hill, 1976.
SUPPLEMENTAL TEXTS
Real Mathematical Analysis. Charles Pugh. Springer Verlag, 2003.
The Way of Analysis. Steven Strichartz.
NOTES, SCANNED MATERIALS FROM TEXTS, ETC.
Some definitions and
useful advice regarding proofs, from Real Mathematical Analysis, by Charles Pugh.
An appendix on proofs and logic
(vertical format, suitable for on-line reading, or horizontal format, suitable for printing), from
Introduction to Real Analysis, by R. Bartle and D. Sherbert.
TRUTH TABLES
Wikipedia truth table entry
Truth table practice. Generates 'random' truth tables for you to fill
in. It tells you if your answer is right or wrong and lets you try again if you
get it wrong. Looks useful.
K. Koehler's course notes. Lots of examples, detailed discussion.
TENTATIVE LECTURE SCHEDULE
| Monday | Wednesday | Friday |
| March 30: Introduction, ordered sets | April 1: Fields, the real numbers | April 3: 1.1 The extended reals, complex numbers |
| April 6: Complex numbers (cont.), Euclidean space | April 8: Finite and (un)countable sets | April 10: Countable sets (cont.) |
| April 13: Metric spaces | April 15: Metric spaces (cont.), compact sets | April 17: Compact sets (cont.) |
| April 20: Perfect and connected sets | April 22: Convergent sequences | April 24: Subsequences |
| April 27: MIDTERM | April 29: Cauchy sequences | May 1: Upper and lower limits, special sequences |
| May 4: Series | May 6: Series of nonnegative terms, the number e | May 8: Root and ratio tests |
| May 11: Power series, summation by parts | May 13: Absolute convergence, operations on series | May 15: Limits of functions |
| May 18: Continuous functions | May 20: Continuity and compactness | May 22: Continuity and compactness (cont.) |
| May 25: HOLIDAY | May 27: Continuity and connectedness, discontinuities | May 29: Monotonic functions, infinity and limits |
| June 1: Derivatives | June 3: Mean Value Theorems and L'Hospital's Rule | June 5: Taylor's Theorem |
GRADING
HOMEWORK POLICIES
Late homework will be discounted and, at the discretion of the TA and/or the instructor, may not be accepted. We do not need to convince you that we are consistent with such decisions; don't count on the "well, you let him/her turn in last week's assignment late, so you have to let me turn in this week's assignment late" argument.
Your homework should be neatly written and well-organized, with the pages securely fastened together and your name on every page. Many of the exercises involve several nontrivial steps; make it clear to your readers (and yourself!) what it is you're doing at each step.
Clearly number the exercises and try to submit them in numerical order;
if any problems are out of sequence, indicate that at the beginning of
the assignment. (You don't need to solve them in order, just submit them
in order.)
We should not have to hunt through several pages to find a particular
problem.