MATH 130A Functions of a Real Variable Spring 2005
Instructor: Dr. Bin Lu
Office: Brighton Hall 132
Phone: 278-6698
E-mail: binlu@csus.edu
Webpage: http://www.csus.edu/indiv/b/binlu/
Office Hours: Mon, Wed, Friday from 9-10 or by appointment
Text: Fundamental Ideas of Analysis by Michael Reed, published by Wiley
Prerequisites: Math 32, Math 45, and Math 108
Course Description: The first semester will consist of a rigorous development of the theory of real-valued
sequences and continuity and integration for functions of one real variable
Objective. Our objective is to cover the foundations of calculus. The emphasis of this course is to develop
a thorough understanding of the calculus, so thorough that within this subject you know definitions
precisely, you can read proofs and other mathematical material critically and you can take hold of a
mathematical statement and either devise a proof or give a counterexample.
Midterm and Final. There will be three midterms (will be announced later) and final exam (cumulative).
Once you have taken the final, or any other midterms, a re-take is not allowed.
Homework and Quizzes: There will be weekly homework, due on Mondays. Homework is an essential
component of the course and will help to prepare you for exams. No late homework will be accepted.
There will also be quizzes each week based on or similar to the homework problems and the problems
discussed during class.
Make-up Policy: In general, missed quizzes or exams may not be made up, unless the instructor is notified
BEFORE the time of the exam or quiz AND the absence occurs for a legitimate reason. If you must miss an
exam for a verifiable emergency, notify me and the main math office (916-278-6534) IMMEDIATELY.
Homework and Quiz Drops: To account for quizzes or homework assignments missed for circumstances
beyond your control, your lowest quiz (or homework assignment) for the semester will be dropped. This
means that if you miss a quiz or homework assignment for ANY reason, legitimate or otherwise, it will
count as your drop. Please turn in every assignment! If you have no idea how to start a problem, you can
make a good start by writing: 1. an accurate statement of the question; 2. an accurate definition of each
technical term in the question ; 3. an accurate statement of at least one theorem related to the question, or at
least one good example to illustrate what is to be proved. In many cases, you will then see better how to
proceed with the proof.
Attendance: Students are expected to attend every scheduled class and to be familiar with the University
Class Attendance policy as it appears in the General Catalog. It is the student's responsibility to keep
informed of any announcements, syllabus adjustments, or policy changes made during scheduled classes.
Students who miss two or more class sessions during the first week of classes may be administratively
dropped from this class unless they discuss their absences with the instructor during the first week.
Grading: Your grade will be determined by your performance on homework assignments, quizzes, and
exams, and will be figured according to the point system described below.
Three In-Class Tests:
Homework:
Quizzes
Final Exam:
Important Dates:
Test 1. Feb.25;
Test 2. April 1;
300 points
100 points
100 points
200 points
Test 3, May 6;
A: 90% of total points
B: 80% of total points
C: 70% of total points
D: 60% of total points
Final Exam: Wed. May 18, 8-10:00am
Tips:
It is a good idea to take notes and study your notes on a constant basis, sometimes rewrite them with more
details, perhaps organize them in a binder together with exercises and questions and applications. You can
make all of this an easier process by staying up-to-date, right on top of things, so that you can get more
questions answered and achieve more insight during class. When there is a gap in your understanding, try
to get it closed as soon as possible. You can help yourself by asking me questions either in class or outside
of class.
In this course, almost every question and every exercise is a matter of writing a proof--that is, an argument
that is convincing, clear, and sound (by the standards which it is my job to set forth). Most of you will be
writing mathematical proofs for the first time. Some will be proofs that you've seen before, some will be
proofs that you're devising on your own. The way to learn how is to practice, to write proofs, get them
criticized, understand what's missing, write them again. Hence the importance in this course of the written
exercises.
You don't understand a theorem (or lemma, or proposition) unless you know and understand its proof. One
studies a theorem by asking questions about it: Why is each part of the hypothesis needed, and how is it
used in the proof? Why couldn't the theorem still be true with a weaker hypothesis, or with a stronger
conclusion? What variants on the theorem might be proved in a similar way? The easiest question I will ask
you about a theorem on a test will be to prove it. You may ask, Should I memorize proofs? A facetious but
just answer is, You should study the proof until you can't forget it. Actually, memorization may be a
sensible first step in the study of a theorem; but then when you test your memorization by trying to write
down the proof, you will find that it's a grasp of the concepts that is really needed.
Read the book:
Do not expect to read a math book fast. Read the book actively. Try to be convinced that you understand
each line before going on to the next. An assignment to "read Section x" includes not just a thorough
reading but also doing a few of the exercises at the end.
Personal advice:
Have due respect for what you're up against in your academic program. Take care of your health and of
your general well-being. You need to be in good physical condition to succeed (and to stay awake in class).
Get the physical exercise that you need, and eat properly. Do what you need to do to assure that you have
helpful conditions in the places where you live, work, and sleep. If you have emotional problems, get help,
or at least find a friend to talk to; don't go it alone, and don't despair.