# Math 22b Spring 2019

## 22b Linear Algebra and Vector Analysis

# 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. (*)

*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.*