(MIT Introduction to Computational Thinking and Data Science Series) Note: how to judge whether a sample is random walk or not. Note: Law of large numbers – Bernoulli Law Gambler’s fallacy: misunderstanding of LOLN. Deviations from mean will even out in the future. Story: Roulette gave 25 times of black consecutively. People came to bet […]
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G. Euler Circle – Markov Chain
linear algebra vector spaces n-tuples: linear dependence, linear combination of the spanning set; subspace of V linear independent and spanning: basis, dimension of V Theorem 1.6. Let V be a vector space over F. Then any two base of V have the same size. Linear transformation and matrices ??: T(v1) is determined by the first […]
Read More "G. Euler Circle – Markov Chain"G. Probability Copy
recognizing patterns, structure. tell two different things are the same. Applications History: Mosteller – Wallace on Federalist Papers: trying to pin down who is the author of certain papers. Govt: IQSS Finance: Gambling: games of chance – dice, cards, coins, Fermat and Pascal correspondence in 1650s. Newton helped gamblers. Life. Statistics is the logic of […]
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The art of doing mathematics is finding that special case that contains all the germs of generality. David hilbert Why we care about something (dependent variable) change due to a small change in independent change? I think it because a lot of cases in reality, the new state includes previous states. We only care what […]
Read More "G. Calculus"G. Probability
recognizing patterns, structure. tell two different things are the same. Applications History: Mosteller – Wallace on Federalist Papers: trying to pin down who is the author of certain papers. Govt: IQSS Finance: Gambling: games of chance – dice, cards, coins, Fermat and Pascal correspondence in 1650s. Newton helped gamblers. Life. Statistics is the logic of […]
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Watch this series, you will understand the first lecture totally. Simon’s general terminology can be hard to understand. For example, he uses F as a field. But in the beginning, if you simply understand it as a real number (scalar), the rest is easy to catch. The whole idea is to expand your numbers into […]
Read More "G. Linear Algebra"G. Markov Chain Monte Carlo
Requirements Markov chain Monte Carlo. This is an extremely important technique for sampling from a complicated distribution by running a Markov chain. The main algorithm is the Metropolis or Metropolis-Hasting algorithm, but there are many others. Introduction: describe the problem you are solving. Background you are assuming. Assumptions for distributions – populations, etc. Results, proof, […]
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Weighty Problem If a baseball weighs 12 ounces plus half its own weight, how much does it weigh? Entertainment Mathematical Puzzles by Martin Gardner
Read More "Maths – Puzzle 2"Maths – Distributive Property
Notes: Distributive property is one of key links in elementary school maths. Indeed, in my opinion, if you really understand three concepts: fractions, negative numbers and the distributive property before you graduate from elementary school, you are good to go to middle school maths. How to group things in different ways, array or matrix. Or […]
Read More "Maths – Distributive Property"Maths – Percent
Translate words into maths expressions. In the above case, step 2: tell the relationship between 15, ?%, and 16. Then you surely can figure out ?%. Caution: ?% = ?/100 In the above case, step 2: tell the relationship between ?%, 83, and 36. Then you surely can figure out ?%. Question: A stadium can […]
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