Which kind of section should you choose?
- If you contemplate being a physics concentrator, you would benefit by being in the
- In any event, if you are planning to take either the Physics 15-16 sequence or Physics
11 and other physics or Applied Science courses, you should enroll in either a Regular
or a Physics section.
- If you are planning to concentrate in BioChemical Sciences, then you are strongly urged
by that department to enroll in a BioChem section.
- If you plan to major in economics or other social sciences, the BioChem section might
be your best choice.
- If you plan to major in Computer Science, then you should find the Computer Science
section to be the most relevant.
- No matter what, you can't go wrong in a Regular section so if you aren't sure of your
major, take a Regular section.
Use any Harvard computer to telnet to 'hilbert.math.harvard.edu'.
When prompted to 'login', type 'section'. At the password prompt, press 'enter'.
Follow the online instructions from here. Alternately, from any web browser, go to the Math Department's
home page, http://www.math.harvard.edu, and click on the "sectioning"
link on the upper right corner of the page. This done, follow the instructions.
If there is a problem with your section assignment, contact Susan Milano in office 308 of the science
center of via email at email@example.com).
Course Head: Clifford Taubes, Science Center 504,
email firstname.lastname@example.org .
Drop in office hours on Mondays 9:30-11 and Fridays 2-3:30.
Prerequisites: Math 1b with a satisfactory grade, or AB-BC score of at least 4, or scores
of at least 20, 8, 4 on the respective three Harvard University Math Placement Tests.
Textbooks: All of the sections require Multivariable Calculus by Ostebee and Zorn with
the Student Solutions Manual, published by Saunders College Publishing. The BioChem
sections also require Fundamentals of Biostatistics by Rosner, published by Duxbury
Press. The Computer Science section requires a special course pack that reproduces
Chapters 13 and 14 from Calculus, Vol II by Apostol. These books are available at the
Harvard Coop exept for the Computer Science section's course pack, which can be obtained
in the basement of the Science Center. In this regard, just ask for the Math 21a Computer
Science section course pack.
Class meetings and problem sessions: The first class meeting, which everyone should
attend, is on Thursday, September 13 at 8am in Science Center lecture hall C. Except for
this one meeting and for the course wide exams, you meet in your assigned section. The
section meets for a total of three hours per week, either one hour each on Mondays,
Wednesdays and Fridays, or for one and one half hours each on Tuesdays and Thursdays.
Each student is also assigned to a 1-hour math problem session, conducted weekly by a
course assistant. The meeting time for the problem session will be arranged in your section
during the first week of classes. You may attend more than one problem session per week;
and the schedule of all problem sessions will be posted on the Math 21a website and on the
Calculus Office bulletin board outside of Science Center 308.
The first meeting of MWF sections is on Monday, September 17 at the posted time.
The first meeting for the TTh sections is on Tuesday, September 18.
Homework: A substantial problem set will be assigned once each week to be turned in as
instructed in the subsequent week. You are strongly encouraged to discuss the homework
with your fellow students and to form study groups to work these assignments. However,
you must write up the solutions by yourself, and you must note the names of your
coworkers somewhere on the homework. (This last point is simply a matter of professional
ethics.) The lowest homework score will be disregarded when your average homework
grade is computed.
The weekly homework assignments will be posted on the Math 21a web site. The
answers to the homework assignments will appear after the due date on the web site as well.
Moreover, selected problems from the homework will be discussed in the problem sessions.
Homework assignments that are submitted after their assigned due date will be
accepted at my discretion. In any event, no more than two late homework assignments will
be accepted per student over the course of the semester.
In addition to the weekly homework assignment, various problems of a more routine
sort will be suggested for the subsequent class meeting. These are not to be turned as their
answers are either in the Student Solutions Manual or will be provided otherwise. However,
you are strongly urged to work them on your own or with others in the class because their
purpose is to supply practice with the techniques and ideas that are presented in the lectures.
By the way, you are also strongly encouraged to try on your own other problems from the
text to hone your ability with the concepts and techniques. Don't feel that you should limit
yourself to the suggested problems. In this regard, note that the Student Solution Manual
answers most of the odd numbered problems in the Ostebee and Zorn book.
Computer assignments: There will be three specially designated assignments during the
semester whose purpose is to introduce you to graphing and mathematical manipulation
computer programs. The use of computer technology to solve mathematical problems is
one of the great advances of our age, and so I want all of you to have at least a fleeting
introduction to this side of the subject. No prior knowledge of the relevant software
technology is required to work these assignments. More details will come later in the
Exams: There are two course-wide "midterms" and a final. The first midterm will take
place on Wednesday, October 10 from 7-9pm in Science Center lecture halls C and D, and
the second on Wednesday, November 14, from 7:30-9:30pm in Science Center C & E.
Please note that the times and rooms differ for the two midterms. In any event, be sure to
mark these dates on your calendar now, as no make-ups will be given. The final exam is
scheduled by the University for a date in January. According to the Course Catalogue, the
preliminary schedule has the final on Tuesday, January 22. The University will confirm this
date later in the semester.
Grading: Your final grade will be based on your performance on the homework (30%), the
computer assignments (3%), the two midterms (10% for the first and 15% for the second),
and the final (42%). A small upward adjustment in the grade is possible when the final is
dramatically better than the average of the midterms and the homework.
Computers and calculators: The visualization of surfaces and other geometric
phenomena is an important aspect of this course. In as much as computerized graphing
programs aid you to develop this ability, you are encouraged to employ them as part of the
learning process. In this regard, the scheduled computer assignments are designed to
introduce you to the tool of computer graphing and mathematical manipulation.
However, be forewarned that for the purposes of this course, computers should be
considered solely as an aid to the development of geometric intuition. This course is
teaching various concepts whose applications may or may not be facilitated by a computer.
However, without a strong understanding of the underlying concepts, the computer won't be
much use. The point here is that computers can do many things, but they can't yet think for
you. As powerful as today's computers are (and tomorrow's will be), none of us will live
to see the day when they can turn pig feed into gold.
In any event, the use of computers and other electronic aids will not be permitted
during exams. (Bring only your brain and some pencils.) With this in mind, note that
various homework problems ask you to sketch or otherwise describe various geometric
objects. With the exception of the specially designated computer assignments, you are
strongly advised to struggle with these first without electronic aids, as they may be quite
trivial with a graphing program.
Words of Caution and Advice: This course will be more demanding then your previous
mathematics courses at Harvard and elsewhere. In particular, the assignments will be time
consuming and you should plan now to set aside regular hours to wrestle with them. It is
virtually impossible to do well in this course without working the homework assignments in
a timely fashion. Note also that this course is fast paced, and new material builds on old.
Thus, do not fall behind. If you find yourself falling behind, please contact your section's
teacher immediately to discuss options for personal help. Indeed, Harvard provides many
services along these lines for its students, and your section teacher can help you find them.
When you are working your assignments, keep in mind that your success in this
course will require more than just memorizing formulas and "plugging in values".
Numerical calculations are still important, but play a smaller role than in 1-variable calculus.
Here is the key to success:
(In this regard, you will consistently battle with homework and exam problems that differ significantly from
material discussed in class.)
Understand the underlying concepts and then work enough
problems so that you can employ them in any example thrown at you.