Here is the catalog description of this course.

01:640:311. Advanced Calculus I (4) Prerequisites: CALC 4 and 01:640:300Introduction to language and fundamental concepts of analysis. The real numbers, sequences, limits, continuity, differentiation in one variable. |

**Instructor**

S. Greenfield,
e-mail: greenfie@math.rutgers.edu.

**Meeting time(s) and place(s)**

The course meets three times a week: Monday and Wednesday 1:10-2:30
(fourth period) in SEC 205, and Thursday 1:10-2:30 (fourth period) in
SEC 212 (all on Busch Campus). Students are expected to attend all
classes. The appointed date and time for the final
exam is Tuesday, May 13, from 12 to 3 PM.

**Text(s)**

The official text is *Introduction to Real Analysis*,
3^{rd} edition, by Robert G. Bartle and Donald R. Sherbert,
John Wiley & Sons (ISBN 0-471-32148-6). Please note that this book is
available today (1/8/2003) at the Rutger University Bookstore for the
price of $106.75 new and $80.00 used. New copies can be bought from
various vendors on the web for less than the price for a used copy at
the bookstore.

Several other books covering similar material can be recommended.

The book *Understanding Analysis* by Stephen Abbott was recently
(2001) published by Springer Verlag (ISBN 0-387-95060-5). It has
received enthusiastic reviews such as this
one.. The list price is $39.95.

*A Radical Approach to Real Analysis* by David Bressoud is
published by the Mathematical Association of America (ISBN
0-88385-701-4). The list price is $38.75. The author is a master of
exposition. The text carefully explains the reasons why close study of
the foundations of real analysis/calculus became historically
necessary. The examples are especially rich. The preface is available
through this
link, and reading it may reassure students who perceive the
subject as monumental and inhuman by explaining that one important
reason the subject started was because some intelligent and talented
people got *very* confused!

**Other material**

Most of the pedagogy of this course will be lectures. Listening to
mathematical lectures is difficult. T. W. Körner has written a short
essay on how to listen to a mathematical lecture which may be
useful.

Students likely believe (and the instructor *surely* does!) that
abstraction can be difficult to understand. Edsger W. Dijkstra was a
mathematician who made some of the most important contributions to
theoretical and applied computer science in the last forty years. He
died in 2002. Here
he states an argument for the primary importance of abstraction. The
title is *Why Johnny can't understand*.

Almost surely the most important concept in Math
311 is the limit of a
sequence. Students may not realize how complicated sequences can be.
One "real" sequence is the decimal digits of
*pi*. Consider the problem of computing perhaps the initial
trillion (that's 10^{12}) of these decimal digits. A
discussion of the methods needed for such investigation may help
you appreciate the difficulties involved and the need for
understanding the theory underlying sequences. This is the content of
Math 311.

**Syllabus**

I'll try in the first week or so to gauge how quickly we will cover
material. Here is a list of recommended
textbook problems. Most of chapter 1 should be known to students. The
real work is in chapters 2 and 3. Then we'll go on and cover as much
of chapters 4, 5, 6, and 7 as we can. Certainly some "triage" will
need to be made: a severe selection of material to be covered from the
later chapters.
**[MORE TO COME!]**

**Grading**

There will be two exams in class and a three-hour cumulative
final. There will be graded homework, both workshop writeups from
material to be handed out and problems from the text. There will be
quizzes in class of various types, some of which may not be
announced. Students may be asked to present material. All of this will
be blended to create a number to be translated into a term grade. The
likely weight of these components is now (before the semester begins
-- things might change!) 15% for each in-class exam, 30% points for
the final, 20% for class participation, and 20% for homework.

**Office hour(s)**

My office is in Hill Center: Hill 542, telephone number: (732)
445-3074. I usually check e-mail several times a day so it is probably
the best way to communicate with me: greenfie@math.rutgers.edu
**[MORE TO COME!]**
It is my job *and my
pleasure* to teach and interact with students. **Please feel free
to visit me!**
I also encourage you to
ask questions via e-mail or after almost any class or to make an
appointment at a mutually convenient time.

**
Maintained by
greenfie@math.rutgers.edu and last modified 1/15/2003.
**