Life is short, so one should read only the books that give you a new perspective on the world life and all that. This is a central tenet of my reading these days. Considering that I have probably lost more than half of my active life already, books with repetition of trivialities bother me. I stumbled on Paul Lockhart while going through the black hole of learning maths. His essay mathematician’s lament is very famous.
The topic of geometric algebra is a new fascination for me. I first read about David Hestenes while reading Bret Victor’s kill maths project. Then got a copy of David Hestenes’ new foundations of classical mechanics book. One thing led to another and then I ended up reading an old out of print book by Clifford called common sense in exact sciences. The basic premise of geometric algebra seems fascinating to me: a universal and simple mathematical theory for a wide variety of applications in Physics.
I sometimes long for those days of internet when you’d land on someone’s personal page where they’d document hard to find links about some (technical) subject matter and some commentary on them. Discovery of such links often meant that that your understanding or interest in certain subject would completely change. I also loved the painstaking effort someone would make to find and then document information for an unknown (web) traveller. There is a kind of romantic hope in doing this, similar to human beings putting out Voyagers spacecrafts with those golden record.
Click here for introduction to this series and motivation. Differential Equations An equation is about balancing two sides of a (weight) balance scale. The equations that we study in school (x + 4 = 9) are about finding the number which will balance the scale. But there could be equations for which solution which balances things is a function and not a number! Specifically, you could have equations which relate a change in certain quantity with respect to that quantity.
Click here for introduction to this series and motivation. Linear Algebra Basics There are two ways to look at matrices. One view is about a matrix representing some data (to be covered in later part of this series) Another view is: matrix encodes the operation of a linear system on its inputs. In this (3) view, a matrix represents a linear map. Matrix-vector multiplication is taking a vector represented in one coordinate system and transforming it to vector in another co-ordinate systems.
I had to study a lot of maths in higher secondary and engineering. There were 2 maths subjects for 2 years after secondary school and 3 maths subjects in the first two years of engineering. Despite studying so much maths, graduate school was a rude shock for me. I just couldn’t wrap my head around of a lot of lectures. The problem was the way maths was taught. Most of the teachers taught maths as an end in itself, mostly devoid of the most important question: “why”?