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Showing posts from November, 2016

Sorting as a Means of Shuffling in Racket

Racket is a derivative of Lisp, and it was also the language used in my first computer science class in college.  It is a functional language which encourages thinking in terms of composing simple functions to accomplish possibly complex goals.  When I was a lab assistant for the class, I recall having a conversation with the professor about how to shuffle a list of numbers in the language, and I came up with an interesting solution which I will talk about in this post.

In Racket, you can sort a list of anything by calling the sort function along with a list, and a function to compare any two items in the list.  An example use is (sort (list 4 1 3 2) <) which produces (list 1 2 3 4).  Since shuffling isn't natively supported in Racket and the simplest shuffling algorithms are not suitable for functional languages with lists instead of arrays, we have to be creative to achieve shuffling behavior.  My idea to shuffle a list was simple: replace the function to compare two items wi…

Fun Math Puzzles

A decent portion of my blog posts are about mathematical puzzles -- and in particular probability problems.  Unfortunately, since most of the traffic to this blog comes from google searches, those posts don't get nearly as many viewers as some of my other posts.   In order to increase viewership to my other content, I am creating this post to act as a central location where I list off and link to every challenge problem I have talked about on this blog.  If you are like me and like solving fun math problems, then you should check out the posts and try to solve the questions for yourself.  If you come up with a neat solution, feel free to share your solutions in the comments.  Here are the problems in the order that I blogged about them:
A Fun Puzzle from ProbabilityAnalyzing an Unfair GameCounting Special Non-Descending SequencesAnalyzing Randomly Descending SequencesRandom Walk on a Complete GraphPattern in Pascals TriangleMathematics and Darts!Triangles Containing the OriginInves…

Neural Networks Simplified

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Artificial Neural Networks, and specifically deep neural networks have been gaining a lot of attention recently, and they are being used successfully across many disciplines. I first encountered neural networks a few years ago, but after hearing the term "backpropagation" and having no idea what it meant I feared that neural networks may be too complicated for me to understand. I made no attempts to truly understand them until recently, and have found that they are actually very easy to understand. I'm writing this blog post share my perspective on how to think about neural networks without jumping directly into the math.  This post is intended for beginners interested in machine learning using neural networks.  By the end of this blog post, you should be able to understand basics of neural networks enough to talk about them intelligently. And if you are so inclined, you can do a deeper dive into the mathematics that underlies the idea.

In this blog post I will talk a…