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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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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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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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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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

http://wn.com/Extremal_and_Probabilistic_Combinatorics_Aula_1_Parte_1

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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.

http://wn.com/Counting_and_Combinatorics_in_Discrete_Math_Part_1

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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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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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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!

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

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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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Combination formula

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Duration: 11:17
Updated: 21 Nov 2014

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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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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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Combinatorics: Venn Diagrams and the Inclusion-Exclusion Principle

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Duration: 13:12
Updated: 30 May 2014
author: Paul Griffin

A look at Venn Diagrams and the Inclusion-Exclusion Principle. Includes the solution to a question from Richard G. Brown's "Advanced Mathematics: Precalculus...

http://wn.com/Combinatorics_Venn_Diagrams_and_the_Inclusion-Exclusion_Principle

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0.4 Analytic Combinatorics 2915)

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Duration: 29:16
Updated: 27 Apr 2014
author: Wenlong ZHAO

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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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Probability using Combinatorics

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

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Combinatorics Problems

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Duration: 8:28
Updated: 16 Jan 2013
author: Catherine Boersma

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Introduction to Analytic Combinatorics, Part I with Robert Sedgewick

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Duration: 1:02
Updated: 01 May 2014
author: CourseraVideos

The course "Introduction to Analytic Combinatorics, Part I" by Professor Robert Sedgewick from Princeton University, will be offered free of charge to everyo...

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Permutations and Combinations 1

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Duration: 3:45
Updated: 05 Sep 2014
author: Khan Academy

U12_L2_T3_we1 Permutations and Combinations 1 More free lessons at: http://www.khanacademy.org/video?v=oQpKtm5TtxU Content provided by TheNROCproject.org - (...

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photo: US Navy / PM3 Joseph M. Buliavac

File - A child playing with a toy in a daycare. The Morale Welfare and Recreation Child Development Center on board Naval Support Activity Mid-South in Millington, Tenn. provides daycare services for dependent children ages six weeks to five years old of military personnel.

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For working mothers, flextime, childcare key issues

The Himalayan

23 Sep 2015

New York, September 22. Flextime, childcare options and paid maternity leave are the key issues for working mothers in the United States and what set companies apart as best places to work, employment experts said today. Top corporations are already providing those benefits and more to some of the 24 million mothers with children under the age of 18 in the US workforce, but many other firms still do not have policies in place ... ....

photo: Via YouTube

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Anger at Sumatra tame elephant death: Probably poisoned, 3-foot tusks hacked off

The Examiner

22 Sep 2015

The death of a tame Sumatra elephant has caused anger and outrage that has now spread across the globe. Yongki lived in a wild life refuge and he was a very friendly elephant that often worked with rangers who would patrol the forest looking for poachers ... ....

photo: NSA

File - Floor of the National Security Operations Center in Fort Meade, Maryland, headquarters of the National Security Agency.

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US intelligence services accused of 'mass, indiscriminate surveillance'

The Guardian

23 Sep 2015

European companies may have to review practice of storing digital data with US internet companies, in fresh victory for Austrian privacy campaigner Max Schrems. @owenbowcott. European companies may have to review their widespread practice of storing digital data with US internet companies after a court accused America’s intelligence services of conducting “mass, indiscriminate surveillance” ... Related ... Related. NSA files decoded ... ....

photo: AP / Susan Walsh

Pope Francis talks with President Barack Obama, accompanied by first lady Michelle Obama, after arriving at Andrews Air Force Base in Md., Tuesday, Sept. 22, 2015.

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Obama to Bask in Pope's Aura, But Francis Wants Economic Justice

Bloomberg

23 Sep 2015

When Pope Francis meets Barack Obama at the White House on Wednesday, the president will bask in his guest’s moral authority and iconic popularity. But the first pontiff from Latin America is likely to exploit those assets to pressure his host on U.S. global economic leadership. On Francis’s first full day in the country, Obama and as many as 15,000 guests will welcome him on the South Lawn of the White House ... “The U.S ... affords ... ....

photo: US Army / Public Domain

File - Alaskan National Guard Sgt. Brain Reid talks with a local Afghan child during a dismounted patrol to a Department of Public Works facility Aug. 8, 2012, in Kandahar, Afghanistan.

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US soldiers say they’re ordered to ignore Afghan soldiers who sexually abuse young boys

The Independent

22 Sep 2015

The last time Lance Corporal Gregory Buckley Jr spoke to his father, the Marine told him in 2012 that he could hear Afghan police sexually abusing children. “At night we can hear them screaming, but we’re not allowed to do anything about it,” George Buckley Sr told the New York Times. “My son said that his officers told him to look the other way because it’s their culture.” ... They don’t know our Marines are sick to their stomachs.”. --> ... ....

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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....

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Penn State Beaver faculty publications are announced (Penn State Beaver)

Public Technologies

18 Aug 2015

(Source. Penn State Beaver) Penn State Beaver faculty publications are announced. 8/17/2015 - ... Dr. Zhongyuan Che, associate professor of mathematics, coauthored "Sharp bounds on the size of pairable graphs and pairable bipartite graphs," which can be found online in the Australasian Journal of Combinatorics., Volume 62(2) (2015 ... LXXII, No ... Her research interests include graph theory and combinatorics as well as bioinformatics....

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Commutative Algebraist Joins Mathematical Sciences Department (University of Arkansas)

Public Technologies

17 Aug 2015

(Source. University of Arkansas) Aug. 17, 2015. FAYETTEVILLE, Ark. - Paolo Mantero will join the Department of Mathematical Sciences this fall as an assistant professor in the J. William Fulbright College of Arts and Sciences ... Mantero's primary research focus is commutative algebra and its interactions with algebraic geometry, combinatorics and homological algebra ... "The department is thrilled to welcome Dr ... Contacts ... J ... J ... distributed by....

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Gifted and talented students converge on campus for 'BRAINways Academicus' (Central Queensland University)

Public Technologies

04 Aug 2015

(Source. Central Queensland University). Published.04 August 2015. CQUniversity Associate VC (Rockhampton Region) Kim Harrington welcomes the BRAINways Academicus event participants ... BRAINways EDUCATION is an independent, non-funded organisation, whose programs provide learning opportunities for highly able and gifted students which are tailored for their special educational needs ... Years P-2. The Wonderful World of Combinatorics ... Years 3-5....

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From Marzipan to Mathematics

Huffington Post

03 Aug 2015

Thoughts of mathematics are never far from my mind - a hazard of the profession as mathematician, perhaps ... What can I say? I can't help myself ... Or the hints of "combinatorics" in the resolution of the question of "how many croissants did we get?" ... Number theory, combinatorics, geometry, topology, dynamics, all going on in front of me ... Combinatorics underlies much of real-time scheduling and operations research and database management ... ....

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Undergraduate researchers present work at seventh annual symposium (West Virginia University)

Public Technologies

22 Jul 2015

(Source. West Virginia University) ... The symposium takes place Thursday, July 23 at the Erickson Alumni Center from 11.30 a.m ... NanoSAFE Research Experiences for Undergraduates (REU); STEM Summer Undergraduate Research Experiences (SURE); WVU Honors-administered SURE ; the Center for Neuroscience Summer Undergraduate Research Internships (SURI); the Brazil Scientific Mobility Program and the Graph Theory and Combinatorics Math REU ... -WVU-....

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J.P. Morgan named American Statistical Association Fellow (Virginia Tech - Virginia Polytechnic Institute and State University)

Public Technologies

24 Jun 2015

(Source. Virginia Tech - Virginia Polytechnic Institute and State University). BLACKSBURG, Va., June 24, 2015 - Virginia Tech's J.P. Morgan was named a Fellow of the American Statistical Association (ASA), the nation's preeminent professional statistical society ... His research interests focus primarily on experimental design, combinatorics, and discrete optimization ... Morganstein, ASA president, said ... Morgan will be honored at an Aug ... (noodl....

Branches of Mathematics

Pure mathematics

Applied mathematics

Related Topics

Basic Combinatorics- Part 1

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