About Math 22b
- Math 22b is a continuation of Math 22a at Harvard. We learn here linear algebra, differential equations and harmonic analysis (Fourier theory).
- This course is structured similarly as
Math 22a of Fall 2018.
- It features also a gentle introduction into proofs. (*)
(*) Maybe it is good to quote from "Bressoud's book: Proofs and Confirmations"
What is the role of proof in mathematics? In recent years we have seen a
rebellion against teaching mathematics as a procession of irrefutable
logical arguments that build from fundamental principles to universal
truths. In this age of computer exploration of the patterns of mathematics,
the pendulum has swung so far that some have proclaimed ""The Death of Proof"
(Horgan 1993). Traditional proofs are disappearing from the high school
and even early college curricula. This loss should not be mourned if
what we are giving up is the misconception of mathematics as a formal
system without need for scientific exploration, experimentation and
discovery. But there is a very real danger that in our enthusiasm to
jettison what is false, we will lose the very essence of mathematics
which is inextricably tied to proofs.
