Math 105A               Real Analysis               Spring 2009

Updated 6/14/09

 

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
 

TEACHING ASSISTANT

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
 

TEXT

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.
 

PSSSIBLY USEFUL WEB SITES

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

Your overall score in the course will be the best of three weighted averages of your homework, midterm, and final exam scores. Your lowest homework score will be dropped.

 
HOMEWORK POLICIES

There will be weekly homework assignments, given in class on Wednesdays and due at the beginning of class the following Wednesday. Homework assignments will be posted online, but assignments are not 'locked in' until they've been given in lecture. Please let me know ASAP if you notice a discrepancy between an online assignment and the one given in class.
Most exercises will be from the text, but some may be taken from other sources (these will be provided as hard copies and online).

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.