MATH 425a
Fall 2011

Professor  Ken Alexander                Phone:  213-740-3797

Office:  KAP 424E.  It is inside suite 424, SW corner of the building.  Normally the suite door is open but if it's locked, knock fairly loudly.

Email:  alexandr@usc.edu          Web Page:  http://www-bcf.usc.edu/~alexandr/ .  Links on this page will take you to course information and homework assignments.

Office hours:  Monday 2-3; Wednesday 11-12, 2-3; or by appointment.  Best to call or email at least 1-2 hours ahead, for an appointment outside office hours.  (No appointment necessary for office hours, of course.)

Teaching Assistant:

Text:  Principles of Mathematical Analysis (3rd Edition) by W. Rudin

Homework will be given approximately weekly.  On each assignment a few selected problems will be graded.  It is OK to help each other solve homework problems, but it's not OK to turn in essentially identical solutions--once you have discussed homework problems so that you understand better what to do, you should write the solutions on your own.  Homework will be accepted up to  2 lectures late, with a 20% penalty.  Not accepted more than 2 lectures late.  The deadline for both on-time and late homework is the end of the lecture hour (not the end of the day.)  Homework should be turned in either (i) in lecture, (ii) by sliding it under my office door, or (iii) by taking it to the Mathematics Department office where it can be time-stamped.  Do not place homework directly in my mailbox!   

Exams:  Two midterms plus final.  Tentative midterm dates are Friday September 30 and Friday November 4.  Final is Monday December 12, 8 - 10 am. The final is cumulative but with greater emphasis on material after the second midterm.  Locations to be announced.

  
     Update:  Midterm 1 will be Friday September 30 during lecture hour, in GFS 118.  Closed book.

Missed exams:  There will be no makeup exams.  In exceptional cases, with a written excuse, if you miss an exam I will base your grade on the exams you did take.

Grading:  Homework 30%, midterms 20% each, final 30%. No fixed quotas of A’s, B’s etc.  The number of points needed for a particular grade is not fixed in advance--if  the exam turns out to be difficult and scores are low, then fewer points are needed for an A, for a B, etc.

Auditing:  If you want to just sit in on the class, you must register for an audit.

Material to be covered:  Most of Chapters 1-5; parts of Chapters 6 and 7; occasional additional material not from the text.  See the approximate schedule on the next page.

Additional help:  There are TA's in the Math Center Mon. - Fri., generally 8 am - 6 pm.  Most of them can help you with Math 407. 

Approximate schedule:

Lecture 1:  Quantifiers, logic

Lectures 2-4:  Parts of Ch. 1--ordered fields, least upper bound property, the complex

numbers, Euclidean space.

Lectures 5-6:  Ch. 2--countable and uncountable sets.

Lectures 7-13:  Ch. 2--metric spaces, open sets, closed sets, compact sets, connected sets.

Lectures 14-15 and 17-24:  Ch. 3--sequences and series.  Estimation.

Lecture 16:  Exam #1

Lectures 25-30:  Ch. 4--continuity, uniform continuity.

Lectures 31, 33-36:  Ch. 5--derivatives, Taylor's theorem

Lecture 32:  Exam #2

Lectures 37-39:  Part of Ch. 6--the Riemann integral, the Riemann-Stieltjes integral

Lectures 40-42:  Part of Ch. 7--uniform convergence of functions, interchange of limits,

integration of series of functions.

Everything in this syllabus is in principle tentative; if necessary it will be

adjusted during the semester.