Combinatorics

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Basic Combinatorics- Part 1

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Duration: 13:15
Updated: 26 Apr 2013

Introduction to combinations and permutations

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Getting Exactly Two Heads (Combinatorics)

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Duration: 10:00
Updated: 11 Aug 2013
author: khanacademy

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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MathHistory29: Combinatorics

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Duration: 41:01
Updated: 03 Jun 2015

We give a brief historical introduction to the vibrant modern theory of combinatorics, concentrating on examples coming from counting problems, graph theory and generating functions. In particular we look at partitions and Euler's pentagonal theorem, Fibonacci numbers, the Catalan sequence, the Erdos Szekeres theorem, Ramsey theory and the Kirkman Schoolgirls problem.

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Introduction to Combinatorics : Principles of Math

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Duration: 1:38
Updated: 15 Aug 2014
author: eHow

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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Combination formula

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Duration: 11:17
Updated: 21 Nov 2014

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Lecture 1 . Enumerative Combinatorics (Federico Ardila)

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Duration: 68:24
Updated: 18 Aug 2014
author: Federico Ardila

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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Die rolling probability | Probability and combinatorics | Precalculus | Khan Academy

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Duration: 5:15
Updated: 13 Jul 2015

We're thinking about the probability of rolling doubles on a pair of dice. Let's create a grid of all possible outcomes. Watch the next lesson: https://www.khanacademy.org/math/precalculus/prob_comb/independent_events_precalc/v/lebron-asks-about-the-chances-of-making-10-free-throws?utm_source=YT&utm;_medium=Desc&utm;_campaign=Precalculus Missed the previous lesson? https://www.khanacademy.org/math/precalculus/prob_comb/independent_events_precalc/v/getting-at-least-one-heads?utm_source=YT&utm;_medium=Desc&utm;_campaign=Precalculus Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus! About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Precalculus channel: https://www.youtube.com/channel/UCBeHztHRWuVvnlwm20u2hNA?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Extremal and Probabilistic Combinatorics Aula 1 Parte 1

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Duration: 47:42
Updated: 03 Feb 2015

Extremal and Probabilistic Combinatorics In this course we will introduce the student to the basic theorems and proof techniques in extremal graph theory and probabilistic combinatorics. We shall emphasize the close links between these two areas, and provide the background material for modern research fields such as additive combinatorics, monotone and hereditary properties, and graph limits. We also discuss some simple but powerful applications of techniques from functional analysis and linear algebra. The course has no prerequisites. Programa: 1. Ramsey Theory: Finite and infinite versions. Erdös' random proof of the lower bound. Van der Waarden's Theorem. Statement of Szemerédi's Theorem. 2. Extremal Graph Theory: The theorems of Turán, Erdös-Stone and Kovari-Sós-Turán. 3. The Erdös-Renyi Random Graph: Graphs with high girth and chromatic number. Extremal number of C2k. 1st and 2nd moment methods. Janson's inequality. The giant component. 4. Analytic and Algebraic Methods: The Kneser graph and the Borsuk-Ulam Theorem. The Frankl-Wilson inequality and Borsuk's Conjecture. 5. The Szemerédi Regularity Lemma: Statement and applications, e.g., proof of Erdös-Stone, Erdös-Frankl-Rödl. Proof of Roth's Theorem via the triangle-removal lemma. 6. Dependent Random Choice: Applications, including the proof of the Balog-Szemerédi-Gowers Theorem. Robert Morris

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Counting and Combinatorics in Discrete Math Part 1

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Duration: 10:23
Updated: 01 Dec 2014

This is part 1 of learning basic counting and combinations in discrete mathematics. I will give some examples to get you introduced to the idea of finding combinations.

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Combinatorics with Day[9]: Bijections

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Duration: 15:01
Updated: 04 Sep 2014
author: day9fan

Combinatorics with Day[9]: Bijections.

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Unizor - Combinatorics - Permutations

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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!

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

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Duration: 6:26
Updated: 07 Aug 2014
author: ManhattanReview

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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Algebra II: binomial Expansion and Combinatorics

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Duration: 12:49
Updated: 24 Dec 2008

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

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Probability using Combinatorics

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Duration: 15:08
Updated: 26 May 2013
author: Pam Ela

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Alexander Postnikov (MIT) The Combinatorics of the Grassmanian I

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Duration: 89:36
Updated: 22 Jan 2015

Alexander Postnikov (MIT) The Combinatorics of the Grassmanian I

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How To Do Combinatorics In Poker

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Duration: 20:31
Updated: 23 Aug 2014
author: nitregpoker

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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Basic Combinatorics

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Duration: 26:47
Updated: 11 Jun 2014
author: MrCHSMath

I created this video with the YouTube Video Editor (http://www.youtube.com/editor)

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Combinatorics: N choose K, permutations and subsets

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Duration: 5:37
Updated: 15 Jul 2013
author: Professor Elvis Zap

Why is n-choose-k the correct way to count stuff.

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Simple Combinatorics

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Duration: 3:56
Updated: 10 Jun 2013
author: DeucesCracked

Entity walks through how to quickly and accurately count combinations of hands. This skill will help you understand what hands your opponent is likely to hol...

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Unizor - Combinatorics - Advanced Problems 1.1.

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Duration: 21:22
Updated: 11 Aug 2014
author: Zor Shekhtman

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

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Duration: 14:49
Updated: 09 Dec 2013

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Handshaking combinations

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Duration: 7:29
Updated: 21 Nov 2014

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Unizor - Combinatorics - Simple Permutations Problems 1

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Duration: 21:51
Updated: 23 May 2014
author: Zor Shekhtman

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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Kenya has a billion barrels of oil that might not be going anywhere

Quartz

17 Oct 2015

Fidgety oil companies and investors heaved a sigh of relief in August when Kenya and Uganda announced they had picked a route for the world’s longest heated pipeline. Finally, there was a plan for getting the estimated 1 billion barrels in Kenya’s remote northwest out of the country ... With low oil prices as low as they are, it seems more likely that the project will be put on ice ... ....

photo: AP / Eduardo Verdugo

File - Joaquin "El Chapo" Guzman is escorted to a helicopter in handcuffs by Mexican navy marines at a navy hanger in Mexico City, Saturday, Feb. 22, 2014.

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Joaquin 'El Chapo' Guzman, world's most-wanted druglord, evades capture, but is hurt

The Times of India

17 Oct 2015

MEXICO CITY. Fugitive drug kingpin Joaquin "El Chapo" Guzman fled during a failed operation to recapture him in northwestern Mexico in recent days, injuring his leg and face, the government said Friday ... "Due to these actions and to avoid his arrest, the fugitive escaped in a hurry (in recent days), which according to the information that was collected, caused him injuries to his leg and face," the government said in a statement ... AFP ) ... ....

photo: AP / Darko Bandic

People walks towards Hungary after disembarking from a train in Botovo, on the Croatia-Hungary border, Friday, Oct. 16, 2015. Hungary clamped down on its border with Serbia with a barrier on Sept. 15 and says it will close down its border with Croatia to migrants starting at midnight.

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Migrant crisis: Slovenia braces after Hungary border closure

BBC News

17 Oct 2015

Migrants have begun arriving in Slovenia by bus from Croatia, after Hungary shut its border with Croatia to try to stem the numbers arriving en route to western Europe. Hungary closed its frontier, reinforced with a razor-wire fence, at midnight local on Friday. Many of the migrants aim to continue north to Austria and Germany ... But the country will keep accepting refugees as long as Austria and Germany's borders remain open, she said ... ....

photo: AP / Emrah Gurel

File - Turkish Air Force fighter planes land at Incirlik Air Base, on the outskirts of the city of Adana, southern Turkey, Thursday, July 30, 2015.

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Turkey shoots down 'unidentified aircraft' near border with Syria

The Independent

16 Oct 2015

Turkish fighter jets have shot down an "unidentified aircraft", reported to be a drone, that intruded into its airspace near the border with Syria ... MORE. Aircraft shot down could possibly be drone shot down near Kilis, #Turkey....

photo: Creative Commons / Attar-Aram Syria

File - Efqa spring in Palmyra, Syria. The Islamic State destroyed a number of the site's buildings in 2015, despite its classification as a World Heritage Site by UNESCO.

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UN's Blue Helmets to protect world's heritage from IS: Italy

Yahoo Daily News

17 Oct 2015

Italy said Saturday that UNESCO has approved its suggestion to have the United Nation's famous Blue Helmets protect heritage sites around the world from attacks by Islamist militants ... Franceschini called for the UN to "immediately define the operational aspects of this international task force" ... ide/cw ....

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Understanding complexity theory, part 1

The Examiner

10 Oct 2015

This series will be an exposition of complexity theory with the help of John Holland's Complexity. A Very Short Introduction. The word "complexity" is no longer a colloquial noun ... … forms can proliferate because the more complex arise out of a combinatoric play upon the simpler.… [E] volution is not to be understood as a series of tournaments for the occupation of a fixed set of environmental niches ... (p ... (p. 209)" ... ....

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Campus Connection, Oct. 5, 2015 (University of Wisconsin - LaCrosse)

Public Technologies

04 Oct 2015

(Source. University of Wisconsin - LaCrosse) UWL math students' skills add up for Winona company ... Read more » UWL visiting scholar to discuss effectiveness of diversity, inclusion ... 14 ... 15 ... 5 ... Monday, Oct ... 6 ... 7 ... 7 ... Kim, Mathematics, co-authored the article 'Combinatorics and geometry of transportation polytopes. An update' in Contemporary Mathematics (volume on Discrete Geometry and Algebraic Combinatorics), volume 625, pages 37-76, August 2014....

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College of Arts and Sciences allocates $1 million to new diversity initiatives (University of Delaware) ...

Public Technologies

01 Oct 2015

Assistant professors in the Department of Mathematical Sciences - Douglas Rizzolo, who focuses on probability and stochastic processes with connections to combinatorics and statistical mechanics; Mahya Ghandehari, who conducts research on non-commutative harmonic analysis as well as combinatorics and who studies large networks such as Facebook; and ......

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Missoula Students Flock to UM for Math Day Oct. 2 (The University of Montana)

Public Technologies

30 Sep 2015

(Source. The University of Montana). MISSOULA - The University of Montana's 2015 Math Day will begin at 8.30 a.m. Friday, Oct ... Running the approximate length of a school day, Math Day offers a variety of hands-on workshops about topics that go beyond the classroom, including knots, geometric solids, combinatorics, cryptography and more ... ###. Contact....

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Perfect Timing: For Fabrizio Zanello, the Watchword is Patek (Michigan Technological University)

Public Technologies

29 Sep 2015

(Source. Michigan Technological University). September 29, 2015-. Six is a perfect number, as any mathematician knows ... For in the world of watches, Patek is as perfect as it gets ... Years later, as a doctoral student at Queen's University in Canada, Zanello researched algebra; now he focuses on algebra and combinatorics and has held appointments at MIT, Notre Dame, the University of Genoa and the Royal Institute of Technology in Sweden....

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Professor Szpankowski honored with Purdue's inaugural 2015 Arden L. Bement Jr. Award (Purdue University)

Public Technologies

24 Sep 2015

(Source. Purdue University) September 24, 2015. WEST LAFAYETTE, Ind ... Bement Jr. Award ... This award, announced Thursday (Sept ... "Professor Szpankowski is a visionary ... Bement Jr ... His research interests include the analysis and design of algorithms, information theory including multimedia compression, random structures, analytic combinatorics, bioinformatics, performance evaluation, networking, and stability problems in distributed systems....

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Get ready for a game of numbers

The Hindu

14 Sep 2015

Love to rack your brains for decimals or fractions? Here is a chance to test your proficiency in numbers. The Regional Mathematical Olympiad, which aims to spot talented students in Mathematics, will offer the young talents an opportunity to match their skills with the best in the State ... The syllabus will roughly be of the Plus Two level. Thrust areas will be Geometry, Number Theory, Algebra and Combinatorics ... 0484-257 7518) or P.M ... ....

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College of Liberal Arts & Sciences to welcome new faculty (KU - The University of ...

Public Technologies

11 Sep 2015

(Source. KU - The University of Kansas). LAWRENCE - The College of Liberal Arts & Sciences will welcome its new faculty members with a reception at 3.30 p.m. Thursday, Sept. 17, at The Commons at the University of Kansas. All faculty and staff are invited to attend ... The College also recruited faculty to two named professorships. the Roy A ... Emily Witt, Department of Mathematics, assistant professor, specializing in algebra-combinatorics;....

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Accelerating molecular simulations of proteins using Bayesian inference on weak information

PNAS

02 Sep 2015

Abstract ... For example, we instruct the computer “to form a hydrophobic core,” “to form good secondary structures,” or “to seek a compact state.” This kind of information has been too combinatoric, nonspecific, and vague to help guide MD simulations before ... ....

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Junior Wins National Math Championship (Boise State University)

Public Technologies

28 Aug 2015

(Source. Boise State University). As Boise State's mathematics department has discovered, plug junior Ian Cavey into nearly any equation and you'll like the resulting product ... While at the MAA conference, Cavey also entered - and won - the 2015 annual US National Collegiate Mathematics Championship, a national problem-solving competition that tests 20 participants on linear algebra, combinatorics, calculus and number theory ... (noodl....

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Free lessons in animation from Pixar

The Examiner

27 Aug 2015

Are you a Pixar fan? Do you aspire to be a Pixar animator when your grow up or retire? Then I have the study program for you and it is free. Pixar in a Box - a new online resource that explores the academic concepts behind Pixar Animation Studios’ creative process - goes live on KhanAcademy.org ... ● How combinatorics are used to create crowds, like the swarm of robots in WALLŸE ... I guess that means math is important, even for artists ... ....

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Sequencing of Barley Genome Achieves New Milestone (University of California, Riverside)

Public Technologies

25 Aug 2015

(Source ... RIVERSIDE, Calif ... "Tim and I were able to work very closely in all the steps of the project from the experimental design in the wet lab to the final analysis of the results; the major challenge was how to handle the very large number of barley samples and for this we designed a novel approach to sequencing that exploited deep results in combinatorics," Lonardi said ... Key innovations on the computational side are ... Tel....

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Professor Jon Keating appointed new Chair of Heilbronn Institute (University of Bristol)

Public Technologies

24 Aug 2015

(Source. University of Bristol). Professor Jon Keating has been appointed Chair of the Heilbronn Institute for Mathematical Research, which celebrates its ten-year anniversary in October this year ... Members' fields of expertise include topics in number theory, algebraic geometry, algebra, combinatorics, probability, quantum information, computational statistics and statistical learning ... Professor Keating said ... distributed by ... (noodl....

Branches of Mathematics

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Applied mathematics

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