Send questions of potential general interest to
math21a@fas.harvard.edu.
Question:Is this course curved?

Answer:
"Curving" is the process of assigning letter grades to numerical grades. This is
given by a function from [0,100] to the finite set {A,A,B+,B,B,C+,C,C,D+,D,DF}, the "curve".
By definition, since letter grades have to be submitted to the registrar, this has to be done
for any course. There is no point to assign letter grades to midterms because it is stupid enough
that one has to do it once, at the end. At midterms, students can gauge their standing by comparing
their score with the mean and standard deviation, bearing in mind that they compete with "la creme de la creme"
of brain power. What students often mean with "curving"
is whether there are a certain percentage of students getting A's, a certain percentage B's
etc. This is not done. What would one do for example if everybody had a perfect
score? Yes, it is as likely as being hit by a ball lightning on
October 2nd in Emerson 105 while taking the exam, but if everybody would ace the course, then everybody would also
get the fullest score.

Question:
Is math21a suitable for math concentrators?

Answer:
Aspiring mathematicians should also consider math23, math25 or math55, where proofs
are important. Math21a has had a many math and applied concentrators in the past.
Math21a covers all the standard multivariable calculus you ever need and has more
applications than any other multivariable calculus course at Harvard.
Look at previous
exhibits. While some of our homework is applied, we refrain from proofs or
knowledge from other sciences in exams. You find some old exam problems on Olivers
personal website.

Question:
Why is multivariable calculus important?

Answer:
It is the culturally richest mathematical theory we know. It was used to conquer
the microscale and understand quantum mechanics in order to answer questions
what we are made of
and the macroscale, when trying to understand the motions of stars and galaxies and
answer questions where we come from. It might surprise that the mesoscale is even harder
to understand mathematically. We live in the golden age of this exploration. We have
learned how to look into our bodies using tomography, scan geometric objects using cameras
and manufacture objects using 3D printers. We learn to build robots of the size of bees
or replicate the world on the computer using 3D maps in which we can fly around or play computer games.
It is ironic that at a time when multivariable calculus is used
to build billion dollar profit endeavors (movies like Avatar, games like GTA, page rank algorithms
are three examples where geometry has made more than a billion in a short time),
some have started to question whether we should teach calculus.
Yes, there are other fields which are important, like discrete mathematics and
I'm its biggest fan.
But it is also true that without a solid calculus knowledge, it would be much
more difficult to make progress there. Additionally, many discrete math courses
go for the lowest denominator and remain stuck with trivialities. A pedagogical problem with discrete math
is that there is no obvious mountain to climb, while in calculus there is a clear peak to reach: the fundamental
theorem of calculus. Calculus is a prototype theory which teaches you
not only a subject, but teaches you some harder teaching patterns and intuition. This can be useful
for a surgeon to navigate the body, for a statistician building a model, for an economist to
understand the massive multiplayer game called economy or for a sociologist to understand social
networks. One of the main ideas of calculus is that one can solve difficult problems like summation problems
by understanding simpler problems by looking at the rate of change. Yes, it is still hard, but difficult
things most often are also rewarding. Maybe also look also at this.
or this.
