[youtube https://www.youtube.com/watch?v=bXK-cEAOvac?rel=0]

There aren’t many Python books that talk about Data Structures. One of the reasons could be that Python provides a rich set of collections like list, dict, queue, set etc. that writing a new Data Structure might be unnecessary. That being the case, it is always helpful to know the time complexity of various operations in list, dict,etc. For some of the algorithms based on trees and graphs, there is no option but to build an abstract data structure to suit the problem one is trying to solve.

Mathematicians find it easier to understand and enjoy ideas which are clever rather than subtle. Measure theory is subtle rather than clever and so requires hard work to master. -- T. W. Körner

Laplace Transform is a very useful technique as it can be used in a ton of problems in various contexts. Here’s a random sample of the places where it’s use makes computations elegant : Solving Difference equations in various Queueing configurations. Renewal theory – Solving Key Renewal equation. Solving specific type of ODEs. Solving specific type of PDEs. Computing convolution of two functions.

Complex Algebra crops up in a ton of places in applied math. I came across an application of complex algebra in the context of Inverse Laplace transforms and could not understand some aspects of it. Looked around a bit and stumbled on this book that seemed to explain the principles of complex analysis in an elegant way. Let me summarize some of the main points in the book. Chapter 1: What do I need to know?