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 […]
Read More "G. Probability Copy"G. Calculus
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 […]
Read More "G. Probability"G. Linear Algebra
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, […]
Read More "G. Markov Chain Monte Carlo"I Ching
by Alfred Huang During twenty-two years of confinement, even though I could not remember the sixty-four guards (hexagrams), I fully comprehended the Tao of I, the essence of the the I Ching which holds that when events proceed to their extremes they give birth to their opposites. Every day I read the official six-page newspaper […]
Read More "I Ching"The Chumash – Genesis 21-25
21. The birth of Isaac. If someone prays for mercy on behalf of another when he himself needs that very same thing, he is answered first. 21:3. In order to be truly strong, one must be able to laugh at the world and its seemingly insuperable obstacles. 21:10. any relationship with wicked people would have […]
Read More "The Chumash – Genesis 21-25"Maths – Puzzle 2
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 […]
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