Today we delve into Associations aka Dictionaries in languages like Python
Let’s do some list FU, a kind of Kung Fu with Wolfram language lists
Diving deeper into lists
Dipping into Lists
Today we see how to use Wolfram language as a Calculator using the Notebook environment
Mathematica is becoming an indispensable tool for doing all kinds of computation and it is important to know how to use it as it will leverage your problem-solving skills, allowing you focus on higher level issues of modelling solutions rather than focusing too much on calculational details.
I will be posting short lessons regularly and the good news is you don’t need to install anything locally as all examples can be run online. If you need to do any form of extensive programming you can always go to the Wolfram Cloud and click on Programming Lab and get access for free.
Instructions on running code
If you don’t have a Wolfram ID, create one as this will give you access to the Wolfram Cloud. After you have done this sign in. If you have one then simply sign into the Wolfram Cloud.
If you have downloaded the notebook file from the blog and saved it somewhere then do the following to upload it to the cloud so you can play with the code.…
Part 1 – What are Graphs?
Mathematics is full of fascinating ideas and concepts. These can, however, be very challenging to tackle and make sense of, especially when you are put under pressure to answer questions about them! In this post, and those to come, I hope to share some insight into these concepts without getting too formal. Where some definitions and more technical bits are introduced, they will be explained at end of the post: look out for the dagger symbols!
To begin, let’s ask what we do in mathematics. The first step in any area of maths is almost always to abstract things. We take some concept we want to be able to work with and pull out the essential ideas. From a bunch of maps we may take out just destinations and the routes between them; from 3D objects we may only need to know what ways we can rotate them and still see the same thing; from a collection of algorithms we may only care about how long they take to run on a computer, and so on.…
The distance problem
If I want to know how far I walked during an hour, I can ask how far I walked in the first five minutes, and how far I walked in the second five minutes, and how far I walked in the third five minutes, etc. and add them all together. ie. I could write:
Where is the distance walked in the five minutes. To calculate a distance, we need to know how fast we are going, and for how long. In fact:
where you can think of velocity as the same thing as speed (though there are subtle differences which you will find out about later). This formula works if the velocity is constant, but what if it is changing. Well, if we have a graph of velocity against time, then we can think about splitting the graph into intervals (like the five minute intervals above), and approximating that during a small interval of time, the velocity is roughly constant.…
I wanted to put up a little summary of some of the most important things to remember from the end of last semester. There was a sudden input of new concepts, so let’s put some of them down here to get a clear reminder of what we need to know. A few things in this post:
- The antiderivative
- Sigma notation
- Areas under curves
An antiderivative of a function on an open interval is a function such that:
Note that we say an antiderivative, not the antiderivative. There can be many functions whose derivatives give the same thing. While we know that:
And therefore we can say that is an antiderivative of . However, we can also say that:
So is also an antiderivative of . In fact for any constant it is true that is an antiderivative of . We write this statement as:
This is called the indefinite integral of with respect to x.…
Unsolved!: The History and Mystery of the World’s Greatest Ciphers from Ancient Egypt to Online Secret Societies by Craig P. Bauer – A review
This is a book of some impressive magnitude, both in terms of the time span that it covers (being millennia), as well as the ways in which it discusses the context and content of the ciphers, most of which, as the title suggests, are unsolved. The book starts with perhaps the most mysterious of all unbroken ciphers: The Voynich Manuscript (the entirety of which can be found here). This story in itself is perhaps the most fascinating in the history of all encrypted documents, and that we still don’t know if it truly contains anything of interest, or is just a cleverly constructed (though several hundred year old) hoax makes it all the more intriguing.
The writing rather effortlessly weaves between the potential origin stories, the history of the ownership of the manuscript and the attempts to decode it.…