Explaining Markov Chains
March 6, 2015
Do you know what a Markov chain is? If not read about “Markov Chains” on the Circuits of Imagination blog:
“A Markov chain is a set of transitions from one state to the next; Such that the transition from the current state to the next depends only on the current state, the previous and future states do not effect the probability of the transition. A transitions independence from future and past sates is called the Markov property.”
This boils down to Markov chains are a way to explain patterns that happen over time and were once used to document human behavior. The chains are not the best way to model human behavior, because they only exist in the present. They do not take into account past or future experiences, otherwise called “memoryless.” The chains can only rely on the action that previously occurred
Markov chains are useful to identify abnormal behavior in systems that don’t exhibit the Markov Property. How? If the system keeps making the wrong decisions based of its program, then it can be diagnosed and repaired. The post explains how the Markov chains are used in coding and provides an example to illustrate how developers can recognize them.
Whitney Grace, March 06, 2015
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Books about Math
January 21, 2015
We’ve run across a list of books that should interest to anyone who would like to understand more about mathematics. These are not textbooks with which to expand our math skills, but rather volumes that take a look at the mathematics field itself. Blogger Kelly J. Rose shares “5 Insanely Great Books About Mathematics You Should Read.” Rose writes:
“I’ve been asked over and over for good books about mathematics for a layperson, someone who hasn’t taken advanced courses in university and is more simply interested in learning about what math is, and some of the more interesting historical figures and results from mathematics. Ironically, when you are a mathematics major at Waterloo, you get the opportunity in 4th year to take a course on the history of mathematics and you get introduced to a few really good books that start to explain the mindset and philosophy behind mathematics and not simply just the theorems and proofs. Here are the 5 books about I most recommend to those who want to understand the mathematical mind and philosophy.”
A few highlights: for a comprehensive history of the field, there’s A History of Mathematics by Carl B. Boyer. For an understanding of what it is like to live the life of a mathematician, it seems Rose cannot recommend The Mathematical Experience by Philip J. David and Reuben Hersh highly enough. Then there’s Proofs and Refutations by Imre Lakatos; Rose says this is likely the most advanced book on his list, yet calls it a quick read. He prescribes it to anyone considering a career in mathematics. Check out the post for more recommendations.
Cynthia Murrell, January 21, 2015
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