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Mathematics

Cheat Sheet: Classification of States In Markov Chains

I created a brief summary of definitions and theorems related to basic classification of Markov chain states. There is even a couple of diagrams that helped me learn some of the rules. Download, enjoy, and let me know what I can improve!

September 5, MMXI — Mathematics.

How To Solve First Order Linear ODEs Using Integrating Factor

Multiplication by integrating factor is my favorite method of solving first order linear ordinary differential equations.

June 24, MMXI — Mathematics.

On The Finiteness Of Life Experience

There’s a great new comic at Spiked Math: It’s a small world (after all). Be sure to check it out even if you are not a mathematician. Using mathematical reasoning, the comic asserts that the number of ways you could lead your life is finite, in other words, there is a limit to what you could do in your life. I strongly disagree, and I can disprove this assertion using the very same tool: mathematics :-)

May 26, MMXI — Mathematics, Infinity, Philosophy.

Mother’s Day 2e3 + 11

Did you remember to give your mother a flower?

May 9, MMXI — Humor, Mathematics.

Simulating Markov Chains In Mathematica

A Markov chain is a sequence of random variables (states) satisfying the Markov property: the probability of the current state depends only on the state that immediately preceded it. In other words, the past state and the future state are stochastically independent. How can we simulate such chains in Wolfram Mathematica?

April 26, MMXI — Mathematics.

Deriving Common Trigonometric Identities

There are quite a few identities concerning trigonometric functions. The most commonly used are the cosine and sine of double angles and the cosine and sine of the sum or difference of two angles. It might be perhaps surprising that these formulae can be easily derived with the help of basic complex analysis and algebra. Personally, I find it much easier to derive most of the formulae whenever I need them instead of remembering them all.

April 14, MMXI — Mathematics.

Poincaré on Mathematical Elegance

“Mathematicians attach a great importance to the elegance of their results, and this is not mere dilettantism. What is it that gives us the feeling of elegance in a solution or a demonstration?…”

April 11, MMXI — Mathematics, Philosophy.

Solving Separable Ordinary Differential Equations

Simple guide to solving separable differential equations, plus explanation how it works.

March 24, MMXI — Mathematics.

Infinity Plus Three (Maths For Normal People III)

Are there more even numbers than odd numbers? How much can we take away from infinity to keep it infinite? And how much is “ten times infinity”? Is it more than “twenty times infinity”? Do these questions have a meaning at all? Let us delve into the depths of the infinite oceans once again!

Of Macbeth And 100,000 Monkeys (Maths For Normal People II)

Do you know what the largest natural number is? Where do the borders of the infinite realm lie? And how many monkeys does it take to write the complete works of Shakespeare? Come hither, ye finite mortal, and behold the glory of eternity that men have created in their minds!