Testing the Techniques

     Overall, Interesting Integrals is a book I want to recommend, yet it falls short of being that useful in terms of teaching the few tricks it possesses. In chapters 1-4 of the book, the book performs pretty well, delivering, albeit easy, problems which really drive home the essence of the tricks and demonstrate their uses well. The introduction on Feynman’s trick, in particular, really drives home how well the author can deliver on making a trick both easy and usable. However, afterwards the book strives to get ahead of itself without a decent understanding of the level at which it is asking some readers to go for it. While the occasional step missing is not too big of a draw, the book fails at presenting the solutions in such a way to aid the reader’s learning. There were a few times where the book managed to simply, through some weird notation, become hard to decode without the assistance of Wolfram Alpha to pick up the slack. However, such p...

Well, I did the same analysis for chutes and ladders already. The data ( In terms of the transition matrix, move data, and some of the graphs ) is here: It was generated in a similar fashion to the data from Monopoly: 1. I created a transition matrix that determined the probability of reaching some space ( column ) from some other space ( row ). As there are many versions of Chutes and Ladders available, I modified one and used it for this analysis 2. I then created a move one scenario ( where you start on space 1 ) , and multiplied that matrix with the transitional matrix 200 or so times. 3. I finally analyzed what I got, and it was pretty cool! To summarize, here are some of the interesting conclusions that can be drawn: 1. It takes precisely 12 moves for the 100 square to be the most probable square on the board ( with a 6% chance of winning this early ) 2. It takes 28 moves for square 100 to have a 50% chance of being landed upon 3. The most probable square to land on,...

So... here's what I did: - Finished the P4E specialization I would go on to do the Python Data Science Specialization, but it turns out the auto-grader is really weird ( and thus I am getting errors that I honestly cannot test ), so I want to figure out what the errors are and find the patience necessary to bug test (Which honestly sucks in comparison to actually working on the course materials) On another note, I have decided the next endeavor will be to work on a book entitled "Vector Calculus, Linear Algebra, and Differential Manifolds", which I am very excited to read and do as it combines my LA knowledge to teach me some multivariable calculus. After working through some of the definitions and the like, I became inspired to figure out some probabilities for Monopoly distribution of places after 10,20,30,40,50, and 100 moves. So, without any context whatsoever, here is are some of the graphs of the most and least likely locations (removing the jail space to prese...