This post is shameless promotion of what I think is a great site – Khan Academy. If you don’t like shameless promotions, you should stop reading now. The site features a whole set of instructional videos along with a good amount of exercises. All topics are what I consider to be some basic skills of mathematics. Not basic because they are simple skills, but because they are fundamental for you to build upon. Continue reading →

# Calculus

## Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

I have just finished reading Prime Obsession by John Derbyshire. A casual math book which I will pass my thoughts and recommendations about this book in this post.

Prime Obsession is a book about the history surrounding Bernhard Riemann and the Riemann Hypothesis. A hypothesis, which is more than 150 years, and still haven’t been neither proved nor falsified. The Riemann Hypothesis tells us a lot about the Riemann zeta function and how it is linked to the distribution of primes. This link is the turning point for the whole book.

When I first encountered the book I did not like the writing style of John Derbyshire to be honest. It was in a very conversational tone. But as I progressed through the book I partly forgot about the writing style. More importantly; the content was so great that the writing style for unimportant to me.

The book covers two aspects of the Riemann hypothesis. The even chapters (oh, the author is a mathematician after all – so why not) gives the reader a historical account about European mathematics. They cover many things from a few generations before Riemann all the way to today. I loved these chapters which introduced me to a lot of the persons naming the famous theorems that we are using today such as Gauss, Euler and of course Riemann himself.

The remaining chapters (the odd ones) covers a wide range of mathematical topics. The culmination is the explanation of the Riemann hypothesis and how the non trivial zeros of the zeta function links to the distribution of the primes. Most of the chapters were written in what I would consider being an accessible way which gives a fine introduction to the mathematical topics. It is by no means a textbook that will give you the deeper understanding of the subjects it touches, but it gives you an introduction and tells you what the idea of the subject is.

The only part I didn’t grasp was a chapter on field theory, I thought it lacked something. However, it wasn’t that essential for the main result I think. The main result was a bit complicated to understand as well, but reading the last two odd chapters again helped a lot. I wont say I understand the Riemann hypothesis in the mathematical sense, but I have a conceptual idea of what it does. So this book delivered exactly what it promised to do. Besides that it also inspired me to continue the wonderful journey through mathematics.

If you haven’t read it yet, this is an obvious choice for an item on the wish list.

## Video on Difference Quotient

A few weeks ago I stumbled on a few videos on YouTube showing me something valuable. It is three videos telling about derivatives, one of the fundamentals of calculus.

The videos come from Mathtv.com which is a website with a ton of good explanatory videos on different math topics. I have only watched a few of them, but I am really impressed at the way they explain it. They have a channel on YouTube where there are a lot of videos, some which I haven’t found on the website, so check out both places. I think you will share my enthusiasm about the site once you see these videos. They also have a YouTube channel which seems to have a slightly different set of videos in them. Continue reading →