Combinatorics

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Basic Combinatorics- Part 1

Duration: 13:15
Updated: 03 Sep 2014

Introduction to combinations and permutations.

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Getting Exactly Two Heads (Combinatorics)

Duration: 10:00
Updated: 11 Aug 2013

Learn more: http://www.khanacademy.org/video?v=8TIben0bJpU A different way to think about the probability of getting 2 heads in 4 flips.

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Introduction to Combinatorics : Principles of Math

Duration: 1:38
Updated: 15 Aug 2014

Subscribe Now: http://www.youtube.com/subscription_center?add_user=Ehow Watch More: http://www.youtube.com/Ehow Combinatorics is a very important course in t...

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Lecture 1 . Enumerative Combinatorics (Federico Ardila)

Duration: 68:24
Updated: 18 Aug 2014

Much of enumerative combinatorics concerns the question: "Count the number a_n of elements of a set S_n for n=1,2,..." We discuss four types of answers: an e...

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Lecture 2 . Enumerative Combinatorics (Federico Ardila)

Duration: 72:08
Updated: 08 Aug 2014

We discuss two basic principles of enumeration: the multiplication and addition principle. We use them to count permutations, subsets, and compositions. Lect...

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How To Do Combinatorics In Poker

Duration: 20:31
Updated: 23 Aug 2014

http://nitreg.com How do you figure out combinatorics in poker? Watch this video and find out. The math is fairly easy and I show you a couple of examples to...

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Combinatorics with Day[9]: Bijections

Duration: 15:01
Updated: 04 Sep 2014

Combinatorics with Day[9]: Bijections.

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GMAT Content: Combinations and Permutations | Kaplan Test Prep

Duration: 6:23
Updated: 06 Aug 2013

Combinations and Permutations can be among the hardest of GMAT math concepts. Generally, these rarely-tested concepts aren't worth focusing on until you've m...

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Probability using Combinatorics

Duration: 15:08
Updated: 26 May 2013

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Algebra II: binomial Expansion and Combinatorics

Duration: 12:49
Updated: 24 Jun 2014

65 (done another way) - 66, combinatorics and binomial expansions.

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Unizor - -Combinatorics - Combinations with Repetitions

Duration: 23:03
Updated: 06 Jun 2014

In this lecture we will discuss a different type of combinations - the combinations with repetitions. Assume, again, that we have to pick K objects out of a ...

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Combinatorics Problems

Duration: 8:28
Updated: 16 Jan 2013

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GMAT Online Math - Permutation & Combinatorics 1 | Manhattan Review GMAT Prep

Duration: 6:26
Updated: 07 Aug 2014

http://www.manhattanreview.com/gmat-online/. This video covers the permutation and combinatorics problems in the GMAT Math Problem Solving section. Manhattan...

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Unizor - Combinatorics - Simple Permutations Problems 1

Duration: 21:51
Updated: 23 May 2014

Don't try to recall any formula. Instead, use the logic and count available choices. Problem 1 Using the logic of permutations, determine how many 3-digit nu...

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Unizor - Combinatorics - Permutations

Duration: 18:10
Updated: 12 May 2014

Combinatorics is a much newer part of mathematics than such classical subjects as Geometry or Algebra. Very important stimulus to its development was the Theory of Probabilities, which is the next subject in this course. Later on, Game Theory and contemporary Computer Science were the other fields of application of the combinatorics. The subject of Permutations is calculating the number of possibilities of putting certain number of objects in certain order. Examples are numerous. For instance, you have to visit 3 different places A, B and C. The order in which you visit them can be ABC, ACB, BAC, BCA, CAB and CBA. Actually, these 6 different ways to visit 3 places are the only possible ones, there are no other ways of putting them in the order of visiting. In many cases it's very important to know how many possibilities to do something like this visiting exists. That's the task of calculating the permutations. The simplest form of permutations is putting N objects in some order. For example, we have numbers from 1 to N and want to write them down in some order. We can write them in ascending order, in descending order or in many other types of order. But what is the number of different ways we can write them down? Ordering of N objects assumes that we have to choose the object #1, then, among other objects we have to choose the object #2, then among whatever is left we have to choose the object #3 etc. Continuing this process to the end, we finally get to object #N. For #1 object we have N candidates. With each of them there remain N−1 candidates for #2 spot. So, we have N·(N−1) choices for the first 2 places. With each of them there remain N−2 candidates for #3 spot, which brings the total number of variants for the first 3 places to N·(N−1)·(N−2). Continuing this process to all N places, we come up with the total number of variants to position N objects in some order equal to N·(N−1)·(N−2)·...·2·1. This quantity is usually written in the form N! and pronounced "N factorial". At this point we'd like to suggest certain criticism to many textbooks that explain this more or less in the same way. The explanation above is just the explanation, not a proof. So, to stop at this point, as many textbooks do, cannot be considered a truly mathematical approach. We have to prove it, and that's exactly what we are going to do next. Proof We are going to prove by induction that the number of permutations of N different objects equals to N·(N−1)·(N−2)·...·2·1 = N! (that is, N factorial) Induction step 1. The formula is obviously correct for N=1 because it produces the result 1 and there is only one way to position a single object in some order. Induction step 2. Assume that the formula is correct for N=K, that is that the number of permutations of K objects is K!. Induction step 3. Consider we have N=K+1 objects. Each permutation (the way of ordering) of these objects involves positioning of the first K objects in some way (and there are K! of these ways, as we assumed on step 2) and placing the (K+1)th object somewhere among these first K objects. The (K+1)th object can stand before the first, between the first and the second, between the second and the third,..., between (K−1)th and Kth objects and, finally, after the Kth object. This constitutes K+1 different positions for the (K+1)th object. Therefore, for any permutation of the first K objects there are K+1 different permutations of the whole set of K+1 objects. Hence, the total number of permutations of K+1 objects equals to K! multiplied by (K+1). But K! · (K+1) = (K+1)!, as follows from the definition of the "factorial" as a product of all natural numbers from 1 to a given number. That proves that the formula retains its form when we move from N=K objects to N=K+1 objects. This completes the proof. We will use the symbol P(N) to designate the number of permutations of N objects. We, therefore, have proved that P(N) = N!

http://wn.com/Unizor_-_Combinatorics_-_Permutations

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Why Blockers Matter...Intro to Combinatorics | Poker Tips

Duration: 14:49
Updated: 09 Dec 2013

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Unizor - Combinatorics - Advanced Problems 1.1.

Duration: 21:22
Updated: 11 Aug 2014

Problem 1 What is the number of partial permutations of N given objects by K objects under a restriction that each such partial permutation must contain X pa...

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Intuitive connection between binomial expansion and combinatorics

Duration: 4:15
Updated: 27 Mar 2014

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Square One TV: "Combo Jombo" by Regina

Duration: 3:41
Updated: 28 Jun 2014

Square One TV video about combinatorics sung by Regina. Check her out in the also entertaining totally 80's McGruff "Don't Use Drugs" music video PSA.

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Creating a Part - Using Combinatorics I

Duration: 13:21
Updated: 02 Aug 2013

Watch the video about Combinatorics here... https://www.youtube.com/watch?v=TnsEi0R0xCk The progression... vi IV I V Em C G D The shapes... Em - x75453 C - x...

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Enumerative combinatorics

Duration: 13:29
Updated: 25 Aug 2014

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Combination (Combinatorics & Probability) Cards Word Problem #1

Duration: 4:31
Updated: 31 Jul 2014

For many similar practice questions and video explanations, visit us at: http://www.acemymathcourse.com.

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Math 12 Combinatorics Tutorial 2012

Duration: 43:32
Updated: 05 May 2014

Mr. Dueck's Lessons. More lessons at www.pittmath.com.

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photo: AP / Ted S. Warren

File - Physicist and best-selling author Stephen Hawking appears in Seattle, Saturday, June 16, 2012.

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Stephen Hawking warns Terminator-style artificial intelligence could wipe out humankind

South China Morning Post

03 Dec 2014

British theoretical physicist Stephen Hawking has warned that development of artificial intelligence could mean the end of humanity. In an interview with the BBC, the scientist said such technology could rapidly evolve and overtake mankind, a scenario like that envisaged in the ”Terminator” movies. “The primitive forms of artificial intelligence we already have, have proved very useful....

photo: AP / Andrew Medichini

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Iran bombs Isis in Iraq, says US

The Guardian

03 Dec 2014

Pentagon says air strikes may be first of their kind and were not co-ordinated with US-led coalition against Islamic State. F-4E Phantom fighter jets flown by Iran in a file photograph. Photograph. Behrouz Mehri/AFP/Getty ... ....

photo: AP Photo / Karel Prinsloo

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Gunmen kill 36 workers in a Kenyan quarry near Somalia border: media

Reuters

02 Dec 2014

Citizen Television said the 36 workers were killed when suspected al Shabaab militants from Somalia attacked the quarry....

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Warwick Mathematicians awarded Philip Leverhulme prizes (The University of Warwick)

noodls

11 Nov 2014

The theory of combinatorial limits is a recently emerged and rapidly evolving area of mathematics, which led to opening new links between analysis, combinatorics, computer science, group theory and probability theory. The analytic view of large discrete structures resulted in a substantial progress on many notoriously difficult extremal combinatorics questions....

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Factbox - Breakthrough Prize laureates

Yahoo Daily News

10 Nov 2014

MOUNTAIN VIEW CALIF. (Reuters) - Here are the Breakthrough Prize winners for 2014.. LIFE SCIENCES. - C ... - Jennifer A ... MATHEMATICS ... - Terence Tao, the University of California, Los Angeles, for numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory ... FUNDAMENTAL PHYSICS (one prize, shared) ... Supernova Cosmology Project Team. Greg Aldering, Brian J. Boyle, Patricia G....

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Factbox: Breakthrough Prize laureates

Yahoo Daily News

10 Nov 2014

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Pioneering scientists share £23m Breakthrough prize pot at US awards

The Guardian

10 Nov 2014

Breakthrough prizes may elevate scientists to rock-star status, showering the finest minds in science with lucrative awards ... Photograph. Bebert Bruno/Rex Features ... They deserve to be recognised as heroes.” ... The damage is sufficient to destroy the virus ... Terence Tao, University of California, Los Angeles, for numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory ... ....

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Inside the mind of teenage maths genius Alex Gunning

The Australian

17 Oct 2014

ALEX Gunning is not very good at the trumpet ... Scales and arpeggios. boring ... The competitors attacked the questions with combinatorics and graph theory; they grappled with functional equations, polynomials and geometric inequalities ... Combinatorics, he explains, is “well, counting stuff, but not really that”. Figuring out the probability of winning TattsLotto division three could be considered a combinatorics problem ... ....

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UBC gets $11.6M boost for 16 Canada Research Chairs (UBC - University of British Columbia)

noodls

17 Oct 2014

(Source. UBC - University of British Columbia). The University of British Columbia has received $11.6 million for 16 new and renewed federally funded Canada Research Chairs ... BACKGROUND. UBC's newly appointed CRCs are. ... Sabin Cautis, Canada Research Chair in Mathematics, Faculty of Science. Cautis is a leading mathematician focusing on algebraic geometry, geometric representation theory, knot invariants, categorification and combinatorics....

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Renowned mathematician to visit VCU (Virginia Commonwealth University)

noodls

13 Oct 2014

(Source. Virginia Commonwealth University). Monday, Oct. 13, 2014 ... Edmonds is credited with initiating the search for polynomial-time combinatorial algorithms, defining the class NP, producing one of the first non-trivial polynomial-time algorithms (for matching in a general graph), and starting the field of polyhedral combinatorics ... distributed by ... (noodl. 25431710) ....

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Muses Labs Brings Software Expertise to Alzheimer’s Disease Therapeutics

Business Wire

08 Oct 2014

RESEARCH TRIANGLE PARK, N.C.--(BUSINESS WIRE)--Muses Labs (http.//museslabs.com), which creates software-based systems to enable personalized therapy for the treatment of complex diseases, announces the development of its first offering for addressing Alzheimer’s disease ... “Because of the explosive combinatorics, the solution to Alzheimer’s disease is a systems-optimization problem,” says the Chief Technology Officer of Muses Labs, Dr....

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Carleton University’s Math Enrichment Centre Boosts Math Education for Elementary and Secondary Students (Carleton University)

noodls

03 Sep 2014

(Source. Carleton University). Media Invited to Attend Open Day as Students Learn Algebra of the Rubik's Cube on Sept. 10, 2014 ... That's why Carleton University's School of Mathematics and Statistics offers math enrichment programs for grade school and high school students in the Math Enrichment Centre ... 10 at 5 p.m ... 5 at 10 p.m ... Topics of study include sequences, combinatorics, probability, geometry, logic and mathematical games ... 17, 2014....

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Biomathematics: the great frontier of the 21st century?

The Irish Times

21 Aug 2014

Once upon a time, biology meant zoology and botany, the study of animals and plants ... Many problems in biology have been solved using mathematics already developed in other areas – network analysis, group theory, differential equations, probability, chaos theory and combinatorics – but completely new mathematical techniques may be required to solve some tough problems in the life sciences ...   Complex behaviour ... Body networks....

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Maryam Mirzakhani: 'The more I spent time on maths, the more excited I got'

The Guardian

13 Aug 2014

The first woman to win the prestigious Fields Medal prize discusses her life as a mathematician. Maryam Mirzakhani, professor of mathematics at Stanford University. She recently became the first woman to win the Fields Medal. Photograph. Stanford University ... When I entered Harvard, my background was mostly combinatorics and algebra ... There are also connections with theoretical physics, topology, and combinatorics ... ....

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Sharif university students shine at IMC 2014

Irna

06 Aug 2014

Professor Morteza Fotouhi Firouzabad accompanied the students ... Problems were posed from the fields of algebra, analysis (real and complex), geometry and combinatorics. The working language was English....

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Camp shows that math equals fun (Queen's University)

noodls

06 Aug 2014

(Source. Queen's University). 2014-08-05 ... By Andrew Carroll, Gazette editor. Mathematics is fun ... And they know that it's true ... "I wish there was this opportunity when I was in high school to say, 'Oh look, there's this thing called number theory which is really interesting and there's combinatorics where you count things in different ways and there's algebra which is this very abstract way of seeing groups of things," she says ... Ms ... Ms....

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Combination (Combinatorics & Probability) Cards Word Problem #1

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GMAT Content: Combinations and Permutations | Kaplan Test Prep

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Unizor - Combinatorics - Permutations

Why Blockers Matter...Intro to Combinatorics | Poker Tips

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