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Ask HN: What math principles are much easier to grok as code?]]]

4 points by jawns 11y ago

ianamartin 11y ago
I don't know if this qualifies as "Math" per se, but I just read a book on Bayesian statistical analysis that demonstrated in Python code how to accomplish certain things while also explaining the rationale. It was very good and helped me "grok" Bayesian stuff in a way that I hadn't been able to purely by reading academic material. I also learned a few things about Python from that book. It is called Think Bayes. Disclosure: I am in no way affiliated with this book, its author, or its publisher. I'm just a guy who wanted what it had to offer and found it very useful as an addition to my formal training. As a sidenote, I would say that, while a lot of statistics is easier to understand with code than it is with the math; the math is very important. Understanding the math is key to understanding the limitations of any given statistical procedure and to understanding the needed assumptions about a data set before any approach can be decided on. We have a lot of issues in modern scientific thought that are based in people understanding code and not understanding math where people figure out how to run a statistical procedure on a dataset, but don't bother to understand if that procedure should be run on that particular data. These kinds of errors happen from Climatology to Neuroscience. It's widespread. I think they are fundamentally math principles, but I think it's fair if people disagree with me. My tl;dr respsone is this: always take the hard way. You will benefit in the long run. Find a teacher or a website that will take you down the hard path. It will be good for you. Once you understand the concept, the code will be obvious.
dennybritz 11y ago
I think many Machine Learning algorithms (and optimization techniques) become clearer when you actually implement them. Writing out the for loops instead of looking at 6 nested summations helped me to understand the runtime complexity of algorithms, and why some things are and aren't feasible to compute. Often it's useful to go start from the "stupidest" implementation and then optimize it. At the end you'll arrive at the formulas that were given to you ;)
bjourne 11y ago
Abstract algebra and group theory. For example strings under concatenation (append) forms a semigroup. Another example is addition of durations (say you are writing scheduling software and want to calculate: 2 days and 3 hours + 4 hours) which I believe forms an abelian group. Finding examples of rings and more complex algebraic structures in programming is left as an exercise for the reader. :)

4 points by jawns 11y ago

I don't know if this qualifies as "Math" per se, but I just read a book on Bayesian statistical analysis that demonstrated in Python code how to accomplish certain things while also explaining the rationale. It was very good and helped me "grok" Bayesian stuff in a way that I hadn't been able to purely by reading academic material. I also learned a few things about Python from that book. It is called Think Bayes. Disclosure: I am in no way affiliated with this book, its author, or its publisher. I'm just a guy who wanted what it had to offer and found it very useful as an addition to my formal training. As a sidenote, I would say that, while a lot of statistics is easier to understand with code than it is with the math; the math is very important. Understanding the math is key to understanding the limitations of any given statistical procedure and to understanding the needed assumptions about a data set before any approach can be decided on. We have a lot of issues in modern scientific thought that are based in people understanding code and not understanding math where people figure out how to run a statistical procedure on a dataset, but don't bother to understand if that procedure should be run on that particular data. These kinds of errors happen from Climatology to Neuroscience. It's widespread. I think they are fundamentally math principles, but I think it's fair if people disagree with me. My tl;dr respsone is this: always take the hard way. You will benefit in the long run. Find a teacher or a website that will take you down the hard path. It will be good for you. Once you understand the concept, the code will be obvious.

dennybritz 11y ago

I think many Machine Learning algorithms (and optimization techniques) become clearer when you actually implement them. Writing out the for loops instead of looking at 6 nested summations helped me to understand the runtime complexity of algorithms, and why some things are and aren't feasible to compute. Often it's useful to go start from the "stupidest" implementation and then optimize it. At the end you'll arrive at the formulas that were given to you ;)

bjourne 11y ago

Abstract algebra and group theory. For example strings under concatenation (append) forms a semigroup. Another example is addition of durations (say you are writing scheduling software and want to calculate: 2 days and 3 hours + 4 hours) which I believe forms an abelian group. Finding examples of rings and more complex algebraic structures in programming is left as an exercise for the reader. :)