Note-taking

I found a way to enter LaTeX in Personal Brain thoughts. Exporting a plex to a website is simple. I hope to demo it soon. I publish my work via Opera Unite which means that I don't have to upload files to a server because the web server runs as an Opera process / thread on my computer. I don't leave it on 24/7 though. The exciting part is that you can use Personal Brain to:
- manage your mathematical notes in LaTeX ( plexes of 300,000 thoughts exist );
- query thoughts;
- reorganize database structure instantly;
- publish thoughts to a website;
- export thoughts to other programs;
- import thoughts ( Mathematica, for example can export notebooks to LaTex ).

Personal Brain is a sort of Mind Manager without the constraint that everything has to fit in a tree structure. They have a Microsoft sort of version scheme: home, business, enterprise. The home version is free, it's not an expiring trial.

Personal Brain website

Doing Graph Theory

What is Graph Theory like? ( After a few weeks of study anyway. ) Let's take the The Konigsberg Bridges problem as an example. This problem marks the start of Graph Theory and was solved by Leonhard Euler. The question was to find a route through the city crossing each bridge only once. Then the Graph Theorist enters the scene.

He translates the relevant parts of the city to a graph such that the seven bridges become seven edges and the various city areas shrink to mere vertices. He translates the original question to a question about the graph: is this graph Eulerian? If so, then the answer to the original question is yes.

But what exactly is an Eulerian graph? An Eulerian graph is a connected graph which contains an Eulerian trail. A graph theorists knows a theorem which helps him to decide if the graph contains an Eulerian trail. We however, have to explain first the words connected graph and Eulerian trail. An Eulerian trail is a closed trail that includes every edge. Again. Two new words! Closed trail and edge ( = connection between two vertices. ) A closed trail is a trail with start and finish at the same vertex ( = a dot in a graph. ) A trail is a walk in which all edges, but not necessarily all vertices, are different. A walk of length k is a succession of k edges of the form uv, vw, wx, ..., yz. This walk is denoted by uvwx...yz, and is referred to as a walk between u and z. Remains the word connected graph. A graph is connected if there is a path between each pair of vertices.


Why not show all these definitions, relations and corresponding theorems in a graph?! Exactly. ( There is an aspect of self-reference here but I lack the knowledge of terms to exactly describe it. Maybe after M381. )

I created this graph using Personal Brain. It is possible to share and publish brains on the internet in order to collaborate on some project. MT365 is the first course I am using Personal Brain for. It is too soon to evaluate though.

Personal Brain 5.5 released

TheBrain.com released version 5.5 of Personal Brain. The update is free for version 5 users. Among 150 or so ( minor, but ) new features they have added ESP(!) to your brain. That is the brain monitors what you are doing in another application via clip- and/or keyboard and moves within the Plex accordingly. Cool feature. It, indeed, 'senses' what is required of the Brain. - Btw. I am now using PB consistently for Abstract Algebra.

Improving the study process

Studying is a process which can be improved continuously. There are tons of books written with advice on how to do this. I intend to try to improve my own way of studying. I have found several books on the subject, will browse them and select one or two which I will read through. But before I do that I want to define some key statistics which I can monitor so that I can measure the effects of changes I might implement. - In order to facilitate the monitoring I started to use Personal Brain as a study tool. - ( More later. )

P.S.

I had my life to live over again, I would have made a rule to read some poetry and listen to some music at least once a week; for perhaps the parts of my brain now atrophied would have thus been kept active through use. The loss of these tastes is a loss of happiness, and may possibly be injurious to the intellect, and more probably to the moral character, by enfeebling the emotional part of our nature.
—Charles Darwin