Learn R interactively with the swirl package. "Infinite Sets" Published in the St. John's Review, XLIV, 2 (1998) 35-59. Copyright © 1998, Peter Suber. This crash course is designed to stand alone. But it also functions as the appendix to my essay, Infinite Reflections. Don't be surprised if this is easier than you thought. Set theory requires no algebra or calculus. It is much more primitive than those branches of mathematics, and rests on very simple notions. What will be difficult? Almost a definition. Abbreviation. Definition. Notation. Definition. Notation. Definition. Definition. Notation. Putting two infinite sets into one-to-one correspondence is an infinite task, and we don't pretend that we can do it (that is, finish it) in finite time. We will soon see that there are infinite sets larger than the set of natural numbers (Theorem 3 below), and for them no such sequences can be constructed.
Definition. B iff |A| = |B|. This definition applies to infinite as well as to finite sets. Definition. Notation. Reminder. Definition. Definition. Notable Properties of Specific Numbers at MROB. These are some numbers with notable properties. (Most of the less notable properties are listed here.) Other people have compiled similar lists, but this is my list — it includes the numbers that I think are important (-: A few rules I used in this list: Everything can be understood by a typical undergraduate college student. If multiple numbers have a shared property, that property is described under one "representative" number with that property.
When a given number has more than one type of property, the properties are listed in this order: 1. 2. 3. 4. Due to blatant personal bias, I only give one entry each to complex, imaginary, negative numbers and zero, devoting all the rest (27 pages) to positive real numbers. This page is meant to counteract the forces of Munafo's Law of Mathematical Discourse.
. (1+i)/√2 = 0.707106... + 0.707106...i One of the square roots of i. But you don't need that to find the square root of i. (a+bi)2 = i a2 + 2abi - b2 = i Then just put the real parts together: i. Math ∩ Programming | A place for elegant solutions. 37 Data-ish Blogs You Should Know About. You might not know it, but there are actually a ton of data and visualization blogs out there. I'm a bit of a feed addict subscribing to just about anything with a chart or a mention of statistics on it (and naturally have to do some feed-cleaning every now and then). In a follow up to my short list last year, here are the data-ish blogs, some old and some new, that continue to post interesting stuff. Data and Statistics By the Numbers - Column from The New York Times visual Op-ed columnist, Charles Blow, who also used to be NYT's graphics director.Data Mining - Matthew Hurst, scientist at Microsoft's MSN, also the co-creator of BlogPulse.Statistical Modeling - We might disagree on certain things, but Andrew's blog is one of the few active pure statistics blogs.The Numbers Guy - Data-minded reporting from Carl Bialik of the Wall Street Journal.Basketball Geek - Like statistical analysis and basketball?
Statistical/Analytical Visualization Maps Design & Infographics Others Worth Noting. Untitled. 3D World Simulation. Alan Schoen geometry. Monte Carlo Integration. 3.2 Monte Carlo methods. Next: 3.3 Variational Monte Carlo Up: 3. Quantum Monte Carlo Previous: 3.1 Introduction Contents Subsections Monte Carlo methods were first developed as a method for estimating integrals that could not be evaluated analytically. Although many statistical techniques are now included in the category of ``Monte Carlo methods''[16,17], the method used in this thesis is principally Monte Carlo integration. 3.2.1 Monte Carlo integration A straightforward application of Monte Carlo is the evaluation of definite integrals. By application of the mean value theorem of calculus, the integral may be approximated by where the points fully cover the range of integration.
Tends to the exact value A conventional choice for the points would be a uniform grid. These methods are highly effective for low dimensional integrals. Increases as . Randomly, from a given probability distribution by Monte Carlo methods. If points are selected at random over the interval , the Monte Carlo estimate of the integral, equation. ArmcSept06.pdf (application/pdf Object) Acceptance-Rejection Sampling - Wiki Course Notes. From Wiki Course Notes Acceptance-Rejection Sampling - May 14, 2009 Today, we continue the discussion on sampling (generating random numbers) from general distributions with the Acceptance/Rejection Method. Acceptance/Rejection Method Suppose we wish to sample from a target distribution f(x) that is difficult or impossible to sample from directly.
Suppose also that we have a proposal distribution g(x) from which we have a reasonable method of sampling (e.g. the uniform distribution) . , accepting samples drawn in successions from with ratio close to 1 will yield a sample that follows the target distribution f(x); on the other hand we would reject the samples if the ratio is not close to 1. The following graph shows the pdf of f(x) (target distribution) and (proposal distribution) At x=7; sampling from will yield a sample that follows the target distribution f(x) At x=9; we will reject samples according to the ratio after sampling from Proof Note the following: (Bayes' theorem) So, Therefore, as required.
InverseTransformation.pdf (application/pdf Object) Inverse transform sampling - eNotes.com Reference.