Pretty much every pdf file that is linked to from this website I downloaded from Library Genesis.

Please go here for your “free education”. And don’t take out any ridiculous student loans. or vote for the Democrats.

If I was more organized then I would link to a page telling you how to download the pdf file yourself. Rather than linking to the actual file. But I’m not that organized.

If you would like to sue me for copyright violation, then you probably can. But it would be a huge waste of time for everybody. Especially you.

If you send me a politely worded email then I will remove the offending pdf. Simples.

If you can’t do basic arithmetic, then it doesn’t matter how “good looking” you are – you are going to be at a major disadvantage for the rest of your life.

There are 10 types of people in the world. Those who understand binary and those who don’t.

Which one are you?

Here is a very basic tutorial on how to turn decimals into binary and vice-versa. Make sure you understand it. This is primary school stuff.

The other skill that you were supposed to learn in primary school – but apparently nobody did – is how to add fractions. Can you tell me what a half plus a third is?

Is it more than one? Or less than one? If you are not sure then watch the video below.

Whenever you are solving any kind of basic arithmetical problem, you should always estimate the answer before trying to find the exact answer.

Knowing how to calculate percentages in your head also won’t kill you. And might even save you some money.

If you can’t do this, then you have to pay the stupid tax. For the rest of your life.

You would surprised how many people try to enrol in University level math classes without knowing how to perform basic arithmetic. But it is actually not that hard.

If you need tutoring on any of these subjects, then my rates are $100 per hour. Melbourne CBD.

My style of teaching is harsh but fair. I will just make you do examples over and over and over again. Until you get it right.

I am not currently “practicing” as a mathematician. But this is a subject that interests me greatly:

Also this paper: Trust is Risk. This technology, when it is properly implemented, will change everything.

Finally, I’m willing to put money on Yaakov Hoch being the “Real” Satochi Nakamoto. How many people actually know what a “Merkle Tree” is? About three people.

Once upon a time, before there was Javascript and YouTube. People just used to make their home pages using plain HTML. There weren’t even really any images.

Suppose there are a thousand users of the internet – all of them high energy particle physicists. Each user has their own homepage. Each homepage contains some text, and some links to the homepages of their friends.

You can imagine this as a directed graph. Each node is a user with a homepage. And each arrow is a hyperlink between homepages.

This information can also be represented by an “adjacency matrix“. The entry in row 2 and column 4 of the matrix is the number of links going from the home page of user 2 to the homepage of user 4.

The “astute reader” will observe that if if we multiply the above matrix with itself five times, then the entry in row 2 and column 4 of the result will be the number of ways you can get from vertex 2 to vertex 4 in five steps. Magic.

Isn’t that clever? Now you are an expert on matrix multiplication. Go and make yourself a cup of tea before reading the rest of this article.

What we need to imagine now is that a user starts at their own homepage. Then randomly clicks on a link to go to another page. Then randomly clicks on a link to go to another page. Then clicks on a link to go to another page. Etc….

The number in the row 2 and column 4 of the “transition matrix” tells us the probability that our random “web surfer” will click on the link from node 2 to node 4. Check it on the example.

We let this “random walk” go on for a long time, and are interested in what proportion of time our random “web surfer” spends on each page.

To be more precise, we are interested in the “probability” that our random “web surfer” will be on any given page – after being giver a sufficient amount of time to wander around. This is known as the Stationary Distribution.

The first woman to win the fields medal in mathematics is Maryam Mirzakhani, from Tehran. Her area of research is “Riemann surfaces and their Moduli spaces”. A brief summary is available on Arxiv.org.

She unfortunately passed away from breast cancer in July 2017 at the age of 40, leaving behind a husband and daughter.

Felix Klein is probably the most famous mathematicians that you have never heard of. With the “Erlangen program” he redefined what we even mean by Geometry.

Image shamelessly stolen from the website of Jos Leys. There are many other beautiful images here, so please take a look.