- published: 24 Mar 2012
- views: 2500
- author: John Kooz
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India
India (
i/ˈɪndiə/), officially the Republic of India (Bhārat Gaṇarājya), is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world. Bounded by the Indian Ocean on the south, the Arabian Sea on the south-west, and the Bay of Bengal on the south-east, it shares land borders with Pakistan to the west;China, Nepal, and Bhutan to the north-east; and Burma and Bangladesh to the east. In the Indian Ocean, India is in the vicinity of Sri Lanka and the Maldives; in addition, India's Andaman and Nicobar Islands share a maritime border with Thailand and Indonesia.
Home to the ancient Indus Valley Civilisation and a region of historic trade routes and vast empires, the Indian subcontinent was identified with its commercial and cultural wealth for much of its long history. Four of the world's major religions—Hinduism, Buddhism, Jainism, and Sikhism—originated here, whereas Zoroastrianism, Christianity, and Islam arrived in the 1st millennium CE and also helped shape the region's diverse culture. Gradually annexed by and brought under the administration of the British East India Company from the early 18th century and administered directly by the United Kingdom from the mid-19th century, India became an independent nation in 1947 after a struggle for independence that was marked by non-violent resistance led by Mahatma Gandhi.
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Abraham ibn Ezra
Rabbi Abraham Ben Meir Ibn Ezra (Hebrew: אברהם אבן עזרא or ראב"ע, Arabic ابن عزرا; also known as Abenezra) (1089 — 1164) was born at Tudela, Navarre Tudela, Navarre (now in Spain) in 1089, and died c. 1167, apparently in Calahorra. He was one of the most distinguished Jewish men of letters and writers of the Middle Ages. Ibn Ezra excelled in philosophy, astronomy/astrology, mathematics, poetry, linguistics, and exegesis; he was called The Wise, The Great and The Admirable Doctor.
He was born at Tudela[citation needed], (current day province of Navarre) when the town was under the Muslim rule of the emirs of Zaragoza. Later he lived in Córdoba. In Granada, it is said, he met his future friend (and perhaps his father-in-law) Yehuda Halevi. He left Spain before 1140 to escape persecution of the Jews by the new fanatical regime of the Almohads. He led a life of restless wandering, which took him to North Africa, Egypt (in 1109, maybe in the company of Yehuda Halevi), the Land of Israel, Italy (Rome in 1140-1143, Lucca, Mantua, Verona), Southern France (Rodez, Narbonne, Béziers), Northern France (Dreux), England (London, and Oxford in 1158), and back again to Narbonne in 1161, until his death on January 23 or 28, 1167, the exact location unknown: maybe at Calahorra at the border of Navarre and Aragon, or maybe in Rome or in the Holy Land.
wn.com/Abraham_ibn_Ezra -
Archimedes
Archimedes of Syracuse (Ancient Greek: Ἀρχιμήδης; c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.
Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulae for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.
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Blaise Pascal
Blaise Pascal (French pronunciation: [blɛz paskal]; 19 June 1623 – 19 August 1662), was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalizing the work of Evangelista Torricelli. Pascal also wrote in defense of the scientific method.
In 1642, while still a teenager, he started some pioneering work on calculating machines, and after three years of effort and 50 prototypes he invented the mechanical calculator. He built twenty of these machines (called the Pascaline) in the following ten years. Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. Following Galileo and Torricelli, in 1646 he refuted Aristotle's followers who insisted that nature abhors a vacuum. Pascal's results caused many disputes before being accepted.
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Chrysippus
Chrysippus of Soli (Ancient Greek: Χρύσιππος ὁ Σολεύς, Chrysippos ho Soleus; c. 279 BC – c. 206 BC) was a Greek Stoic philosopher. He was a native of Soli, Cilicia, but moved to Athens as a young man, where he became a pupil of Cleanthes in the Stoic school. When Cleanthes died, around 230 BC, Chrysippus became the third head of the school. A prolific writer, Chrysippus expanded the fundamental doctrines of Zeno of Citium, the founder of the school, which earned him the title of Second Founder of Stoicism.
Chrysippus excelled in logic, the theory of knowledge, ethics and physics. He created an original system of propositional logic in order to better understand the workings of the universe and role of humanity within it. He adhered to a deterministic view of fate, but nevertheless sought a role for personal freedom in thought and action. Ethics, he taught, depended on understanding the nature of the universe, and he taught a therapy of extirpating the unruly passions which depress and crush the soul. He initiated the success of Stoicism as one of the most influential philosophical movements for centuries in the Greek and Roman world.
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Hassler Whitney
Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, and characteristic classes.
Hassler Whitney was the son of First District New York Supreme Court judge Edward Baldwin Whitney and Josepha (Newcomb) Whitney, the grandson of Yale University Professor of Ancient Languages William Dwight Whitney, the great-grandson of Connecticut Governor and US Senator Roger Sherman Baldwin, and the great-great-great-grandson of American founding father Roger Sherman.
Hassler Whitney's maternal grandparents were astronomer and celestial mechanician Simon Newcomb and Mary Hassler Newcomb (the granddaughter of the first superintendent of the Coast Survey Ferdinand Hassler).
He married Margaret R. Howell, May 30, 1930; children: James Newcomb, Carol, Marian; married Mary Barnett Garfield, January 16, 1955; children: Sarah Newcomb, Emily Baldwin; and married Barbara Floyd Osterman, February 8, 1986.
wn.com/Hassler_Whitney -
Hipparchus
Hipparchus/hɪˈpɑːrkəs/, or more correctly Hipparchos (Greek: Ἵππαρχος, Hipparkhos; c. 190 BC – c. 120 BC), was a Greek astronomer, geographer, and mathematician of the Hellenistic period. He is considered the founder of trigonometry.
Hipparchus was born in Nicaea (now Iznik, Turkey), and probably died on the island of Rhodes. He is known to have been a working astronomer at least from 162 to 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Chaldeans from Babylonia. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. His other reputed achievements include the discovery of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue. It would be three centuries before Claudius Ptolemaeus' synthesis of astronomy would supersede the work of Hipparchus; it is heavily dependent on it in many areas.
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Isaac Newton
Sir Isaac Newton PRS MP (25 December 1642 – 20 March 1727 [NS: 4 January 1643 – 31 March 1727]) was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived." His monograph Philosophiæ Naturalis Principia Mathematica, published in 1687, lays the foundations for most of classical mechanics. In this work, Newton described universal gravitation and the three laws of motion, which dominated the scientific view of the physical universe for the next three centuries. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws, by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the Scientific Revolution.
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Jacob Bernoulli
Jacob Bernoulli (also known as James or Jacques) (27 December 1654 – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.
Jacob Bernoulli was born in Basel, Switzerland. Following his father's wish, he studied theology and entered the ministry. But contrary to the desires of his parents, he also studied mathematics and astronomy. He traveled throughout Europe from 1676 to 1682, learning about the latest discoveries in mathematics and the sciences. This included the work of Robert Boyle and Robert Hooke.
He became familiar with calculus through a correspondence with Gottfried Leibniz, then collaborated with his brother Johann on various applications, notably publishing papers on transcendental curves (1696) and isoperimetry (1700, 1701). In 1690, Jacob Bernoulli became the first person to develop the technique for solving separable differential equations.
Upon returning to Basel in 1682, he founded a school for mathematics and the sciences. He was appointed professor of mathematics at the University of Basel in 1687, remaining in this position for the rest of his life.
wn.com/Jacob_Bernoulli -
Paul Erdős
Paul Erdős (occasionally spelled Erdos or Erdös; Hungarian: Erdős Pál, pronounced [ˈɛrdøːʃ ˈpaːl]; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory. He is also known for his "legendarily eccentric" personality.
Paul Erdős was born in Budapest, Hungary on March 26, 1913. He was the only surviving child of Anna and Lajos Erdős (formerly Engländer); his siblings died before he was born, aged 3 and 5. His parents were both Jewish mathematicians from a vibrant intellectual community. His fascination with mathematics developed early—at the age of three, he could calculate how many seconds a person had lived.
Both of Erdős's parents were high school mathematics teachers, and Erdős received much of his early education from them. Erdős always remembered his parents with great affection. At 16, his father introduced him to two of his lifetime favorite subjects—infinite series and set theory. During high school, Erdős became an ardent solver of the problems proposed each month in KöMaL, the Mathematical and Physical Monthly for Secondary Schools. Erdős later published several articles in it about problems in elementary plane geometry.
wn.com/Paul_Erdős -
Plutarch
Plutarch (English pronunciation: /'pluːtɑːk/; Greek: Πλούταρχος, Ploútarkhos, Koine Greek: [plŭːtarkʰos]) then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus (Μέστριος Πλούταρχος),c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia. He was born to a prominent family in Chaeronea, Boeotia, a town about twenty miles east of Delphi.
Plutarch was born in 46 AD in the small town of Chaeronea, in the Greek region known as Boeotia. His family was wealthy. The name of Plutarch's father has not been preserved, but it was probably Nikarchus (Greek: Nίκαρχoς), from the common habit of Greek families to repeat a name in alternate generations. The name of Plutarch's grandfather was Lamprias, as he attested in Moralia and in his Life of Antony.
His brothers, Timon and Lamprias, are frequently mentioned in his essays and dialogues, where Timon is spoken of in the most affectionate terms. Rualdus, in his 1624 work Life of Plutarchus, recovered the name of Plutarch's wife, Timoxena, from internal evidence afforded by his writings. A letter is still extant, addressed by Plutarch to his wife, bidding her not give way to excessive grief at the death of their two year old daughter, who was named Timoxena after her mother. Interestingly, he hinted at a belief in reincarnation in that letter of consolation.
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Sushruta
Suśruta (Sanskrit: सुश्रुत (sʊʃɾʊt̪), fl. 800 BCE) was an ancient Indian surgeon and is the author of the book Suśruta Saṃhitā, in which he describes over 300 surgical procedures, 120 surgical instruments and classifies human surgery in eight categories. He lived, taught and practiced his art on the banks of the Ganges in the area that corresponds to the present day city of Varanasi in North India.
Because of his seminal and numerous contributions to the science and art of surgery he is also known by the title "Father of Surgery." Much of what is known about this inventive surgeon is contained in a series of volumes he authored, which are collectively known as the Sushruta Samhita.
Sushruta was educated in Varanasi.
wn.com/Sushruta
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Totally Understand Combinatorics - Permutations and Combinations! - Awesome Sexy Math Ep4
- Order: Reorder
- Duration: 16:51
- Updated: 08 Feb 2013
Awesome Sexy Math - Episode 4: Combinatorics Recorded 2012/01/23ish. www.twitter.com www.validateyourlife.com http www.awesomesexymath.com In this episode we cover notation of combinations and permutations the definition of combinations and permutations mnemonics for remembering which is which and more! Notes on the vid itself. This is one of my fave vids I've made. I like the content and the presentation. I am REALLY looking forward to learning and then making more of these and adding cool video effects. The problem of to where do I upload them is an annoying temporary snag that I need to resolve, however. I put a lot of time into creating, learning, planning, filming, and editing these I like making these math vids a lot and want to make more math vids, but I alas! I am snagged!!! I don't know to which channel to upload them. Maybe I will put them on vimeo hhmm nice. Or a youtube account but I don't know which youtube account. Anyways, I am proud of and really like this vid. This is a common problem I want to resolve. I do work, I put a lot of focus and time into making something. I make the thing (a vid in this case) and then get stumped on to where to upload it. So TWO huge problems to sharing work that I do: Slow as heck upload speed. Deciding to where to upload the vids. I have numerous youtube accounts but when I do something different and/or particularly polished, I am uncertain on where to put such a vid hhmm. Anyways, good times.
http://wn.com/Totally_Understand_Combinatorics_Permutations_and_Combinations!_Awesome_Sexy_Math_Ep4
Awesome Sexy Math - Episode 4: Combinatorics Recorded 2012/01/23ish. www.twitter.com www.validateyourlife.com http www.awesomesexymath.com In this episode we cover notation of combinations and permutations the definition of combinations and permutations mnemonics for remembering which is which and more! Notes on the vid itself. This is one of my fave vids I've made. I like the content and the presentation. I am REALLY looking forward to learning and then making more of these and adding cool video effects. The problem of to where do I upload them is an annoying temporary snag that I need to resolve, however. I put a lot of time into creating, learning, planning, filming, and editing these I like making these math vids a lot and want to make more math vids, but I alas! I am snagged!!! I don't know to which channel to upload them. Maybe I will put them on vimeo hhmm nice. Or a youtube account but I don't know which youtube account. Anyways, I am proud of and really like this vid. This is a common problem I want to resolve. I do work, I put a lot of focus and time into making something. I make the thing (a vid in this case) and then get stumped on to where to upload it. So TWO huge problems to sharing work that I do: Slow as heck upload speed. Deciding to where to upload the vids. I have numerous youtube accounts but when I do something different and/or particularly polished, I am uncertain on where to put such a vid hhmm. Anyways, good times.
Combinatorics: N choose K, permutations and subsets
- Order: Reorder
- Duration: 5:37
- Updated: 06 Feb 2013
Why is n-choose-k the correct way to count stuff.
http://wn.com/Combinatorics_N_choose_K,_permutations_and_subsets
Why is n-choose-k the correct way to count stuff.
- published: 22 Apr 2010
- views: 5895
- author: ProfessorElvisZap
Algebra II: binomial Expansion and Combinatorics
- Order: Reorder
- Duration: 12:49
- Updated: 03 Feb 2013
Learn more: www.khanacademy.org 65 (done another way) - 66, combinatorics and binomial expansions
http://wn.com/Algebra_II_binomial_Expansion_and_Combinatorics
Learn more: www.khanacademy.org 65 (done another way) - 66, combinatorics and binomial expansions
- published: 24 Dec 2008
- views: 32354
- author: khanacademy
Combinatorics with Day[9]: Bijections
- Order: Reorder
- Duration: 15:01
- Updated: 08 Feb 2013
Combinatorics with Day[9]: Bijections
http://wn.com/Combinatorics_with_Day_9_Bijections
Aba Math Rap: Graph Theory and Enumerative Combinatorics
- Order: Reorder
- Duration: 9:39
- Updated: 29 May 2012
On 4/20 in 2011, aBa delivers his first Bowdoin College combinatorial rap to his students. Song is divided into two cases. Rapping of Case 1 begins at the 0:41 time marker. Case 2 begins at 3:44.
http://wn.com/Aba_Math_Rap_Graph_Theory_and_Enumerative_Combinatorics
On 4/20 in 2011, aBa delivers his first Bowdoin College combinatorial rap to his students. Song is divided into two cases. Rapping of Case 1 begins at the 0:41 time marker. Case 2 begins at 3:44.
- published: 03 May 2011
- views: 1526
- author: abukuse
Introduction to Combinatorics (part 1)
- Order: Reorder
- Duration: 8:31
- Updated: 28 Mar 2012
This is the lecture covering the Fundamental Counting Principle, tree diagrams, and factorials.
http://wn.com/Introduction_to_Combinatorics_part_1
This is the lecture covering the Fundamental Counting Principle, tree diagrams, and factorials.
- published: 24 Sep 2008
- views: 15721
- author: bethjonesmath
Introduction to Combinatorics : Principles of Math
- Order: Reorder
- Duration: 1:38
- Updated: 08 Feb 2013
Subscribe Now: www.youtube.com Watch More: www.youtube.com Combinatorics is a very important course in the field of math and is often covered in upper-level classes. Get an introduction to Combinatorics with help from a longtime mathematics educator in this free video clip. Expert: Jimmy Chang Filmmaker: Jimmy Chang Series Description: When teaching mathematics to a beginner, you're always going to want to focus on a few key principles to further that education as much as possible in the most straightforward way. Learn about basic mathematics principles with help from a longtime mathematics educator in this free video series.
http://wn.com/Introduction_to_Combinatorics_Principles_of_Math
Subscribe Now: www.youtube.com Watch More: www.youtube.com Combinatorics is a very important course in the field of math and is often covered in upper-level classes. Get an introduction to Combinatorics with help from a longtime mathematics educator in this free video clip. Expert: Jimmy Chang Filmmaker: Jimmy Chang Series Description: When teaching mathematics to a beginner, you're always going to want to focus on a few key principles to further that education as much as possible in the most straightforward way. Learn about basic mathematics principles with help from a longtime mathematics educator in this free video series.
- published: 16 Nov 2012
- views: 231
- author: eHow
Math 12 Apr 18 Combinatorics Tutorial 2011
- Order: Reorder
- Duration: 59:51
- Updated: 20 May 2012
lessons, dueck, physics, math
http://wn.com/Math_12_Apr_18_Combinatorics_Tutorial_2011
Pathways and Combinatorics
- Order: Reorder
- Duration: 6:24
- Updated: 30 Jan 2013
Some examples of applying combinatorics to solve pathway problems. Pascals triangle is also used to compute the number of possible paths between 2 points.
http://wn.com/Pathways_and_Combinatorics
Some examples of applying combinatorics to solve pathway problems. Pascals triangle is also used to compute the number of possible paths between 2 points.
- published: 20 Aug 2008
- views: 4018
- author: coburgmaths
Getting Exactly Two Heads (Combinatorics)
- Order: Reorder
- Duration: 10:00
- Updated: 24 Jan 2013
Learn more: www.khanacademy.org A different way to think about the probability of getting 2 heads in 4 flips
http://wn.com/Getting_Exactly_Two_Heads_Combinatorics
Learn more: www.khanacademy.org A different way to think about the probability of getting 2 heads in 4 flips
- published: 10 Aug 2011
- views: 54328
- author: khanacademy
Square One TV: "Combo Jombo" by Regina
- Order: Reorder
- Duration: 3:41
- Updated: 07 Feb 2013
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.
http://wn.com/Square_One_TV_Combo_Jombo_by_Regina
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.
- published: 16 Apr 2007
- views: 17221
- author: tiradorfranco2
CHEESE COMBINATORICS at EDIBLE
- Order: Reorder
- Duration: 2:18
- Updated: 04 May 2012
CHEESE COMBINATORICS by Carl Disalvo Cheese Combinatorics provides a playful way to explore how cheeses are constituted by elements such as milk, rennet, flavour, texture and treatment. A set of dice with icons representing the elements that give form to a cheese are rolled, and cheese matching those factors is served. While these elements and their relations set the structure for the cheese experience, the character of the cheese sampled escapes simplistic reduction to formula. The version of Cheese Combinatorics presented in this show includes a look-up table for all 127 Irish farmhouse cheeses catalogued by Bord Bia [the Irish Food Board] and Sheridans Cheesemongers. Three different Irish farmhouse cheeses will be served each day of the exhibition.
http://wn.com/CHEESE_COMBINATORICS_at_EDIBLE
CHEESE COMBINATORICS by Carl Disalvo Cheese Combinatorics provides a playful way to explore how cheeses are constituted by elements such as milk, rennet, flavour, texture and treatment. A set of dice with icons representing the elements that give form to a cheese are rolled, and cheese matching those factors is served. While these elements and their relations set the structure for the cheese experience, the character of the cheese sampled escapes simplistic reduction to formula. The version of Cheese Combinatorics presented in this show includes a look-up table for all 127 Irish farmhouse cheeses catalogued by Bord Bia [the Irish Food Board] and Sheridans Cheesemongers. Three different Irish farmhouse cheeses will be served each day of the exhibition.
- published: 05 Mar 2012
- views: 358
- author: ScienceGallery
Math 12 Combinatorics Tutorial 2010
- Order: Reorder
- Duration: 54:23
- Updated: 08 Aug 2012
Mr. Dueck's Lessons
http://wn.com/Math_12_Combinatorics_Tutorial_2010
Probability using Combinatorics
- Order: Reorder
- Duration: 15:08
- Updated: 13 Feb 2013
http://wn.com/Probability_using_Combinatorics
Introduction to Analytic Combinatorics, Part I with Robert Sedgewick
- Order: Reorder
- Duration: 1:02
- Updated: 10 Feb 2013
The course "Introduction to Analytic Combinatorics, Part I" by Professor Robert Sedgewick from Princeton University, will be offered free of charge to everyone on the Coursera platform. Sign up at www.coursera.org
http://wn.com/Introduction_to_Analytic_Combinatorics,_Part_I_with_Robert_Sedgewick
The course "Introduction to Analytic Combinatorics, Part I" by Professor Robert Sedgewick from Princeton University, will be offered free of charge to everyone on the Coursera platform. Sign up at www.coursera.org
- published: 18 Apr 2012
- views: 2190
- author: CourseraVideos
DISCRETE MATHS - COMBINATORICS - LECTURE 3 (2/2) - Feb. 28th
- Order: Reorder
- Duration: 27:34
- Updated: 11 Dec 2011
Applications of the sum rule and the product rule. Problems 1 and 2 from the problem set. EUI UPM.
http://wn.com/DISCRETE_MATHS_COMBINATORICS_LECTURE_3_2_2_Feb_28th
Applications of the sum rule and the product rule. Problems 1 and 2 from the problem set. EUI UPM.
- published: 01 Mar 2011
- views: 2933
- author: UPM
GMAT Content: Combinations and Permutations | Kaplan Test Prep
- Order: Reorder
- Duration: 6:23
- Updated: 02 Jan 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 mastered algebra and geometry. But once your practice GMAT quantitative scores start rising, you'll want to watch this video to learn to crack even the toughest GMAT content!
http://wn.com/GMAT_Content_Combinations_and_Permutations_|_Kaplan_Test_Prep
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 mastered algebra and geometry. But once your practice GMAT quantitative scores start rising, you'll want to watch this video to learn to crack even the toughest GMAT content!
- published: 15 Apr 2010
- views: 2591
- author: KaplanGMAT
GMAT Online Math - Permutation & Combinatorics 1 | Manhattan Review GMAT Prep
- Order: Reorder
- Duration: 6:26
- Updated: 22 Sep 2012
www.manhattanreview.com This video covers the permutation and combinatorics problems in the GMAT Math Problem Solving section. Manhattan Review offers in-person and online GMAT courses ( www.manhattanreview.com ) and tutoring globally. In addition, we are expert in MBA admissions consulting ( www.manhattanreview.com ),TOEFL, GRE, LSAT and SAT. Our online courses offer real time teaching with a unique whiteboard technology. Our courses, tutoring and consultants are located around the world, in particular, in London, Continental Europe, the USA, Asia and the Middle East. Manhattan Review prepares young professionals to get into dream schools and careers! Please visit www.manhattanreview.com.
http://wn.com/GMAT_Online_Math_Permutation_Combinatorics_1_|_Manhattan_Review_GMAT_Prep
www.manhattanreview.com This video covers the permutation and combinatorics problems in the GMAT Math Problem Solving section. Manhattan Review offers in-person and online GMAT courses ( www.manhattanreview.com ) and tutoring globally. In addition, we are expert in MBA admissions consulting ( www.manhattanreview.com ),TOEFL, GRE, LSAT and SAT. Our online courses offer real time teaching with a unique whiteboard technology. Our courses, tutoring and consultants are located around the world, in particular, in London, Continental Europe, the USA, Asia and the Middle East. Manhattan Review prepares young professionals to get into dream schools and careers! Please visit www.manhattanreview.com.
- published: 28 Dec 2009
- views: 5213
- author: ManhattanReview
Algebra II: Functions, Combinatorics
- Order: Reorder
- Duration: 11:25
- Updated: 18 Jan 2013
Learn more: www.khanacademy.org 60-65, functions, combinations, probability
http://wn.com/Algebra_II_Functions,_Combinatorics
Learn more: www.khanacademy.org 60-65, functions, combinations, probability
- published: 23 Dec 2008
- views: 34298
- author: khanacademy
GMAT Tutoring Math - Permutation & Combinatorics 2 | Manhattan Review GMAT Prep
- Order: Reorder
- Duration: 7:06
- Updated: 04 Jan 2013
www.manhattanreview.com This video covers the permutation and combinatorics problems in the GMAT Math section. Manhattan Review offers in-person and online GMAT courses and tutoring globally. In addition, we are expert in MBA admissions consulting ( www.manhattanreview.com ), TOEFL, GRE, LSAT and SAT. Our online courses offer real time teaching with a unique whiteboard technology. Our courses, tutoring and consultants are located around the world, in particular, in London, Continental Europe, the USA, Asia and the Middle East. Manhattan Review prepares young professionals to get into dream schools and careers! Please visit www.manhattanreview.com.
http://wn.com/GMAT_Tutoring_Math_Permutation_Combinatorics_2_|_Manhattan_Review_GMAT_Prep
www.manhattanreview.com This video covers the permutation and combinatorics problems in the GMAT Math section. Manhattan Review offers in-person and online GMAT courses and tutoring globally. In addition, we are expert in MBA admissions consulting ( www.manhattanreview.com ), TOEFL, GRE, LSAT and SAT. Our online courses offer real time teaching with a unique whiteboard technology. Our courses, tutoring and consultants are located around the world, in particular, in London, Continental Europe, the USA, Asia and the Middle East. Manhattan Review prepares young professionals to get into dream schools and careers! Please visit www.manhattanreview.com.
- published: 28 Dec 2009
- views: 13438
- author: ManhattanReview
DISCRETE MATHS -- COMBINATORICS - March 21st
- Order: Reorder
- Duration: 41:34
- Updated: 05 Dec 2012
DISCRETE MATHS -- COMBINATORICS - March 21st - ESCUELA UNIVERSITARIA DE INFORMÁTICA - PACO GÓMEZ Descripción: The purpose of logic. Propositions. Declarative sentences. Formal languages. Formalization. Simple and compound statements. Connectives: negation, disjunction, exclusive or, conjunction, implication and biconditional connectives. Table truth of connectives. Converse, contrapositive and inverse of an implication. Translating English sentences to a formal language. Necessary and sufficient conditions.
http://wn.com/DISCRETE_MATHS_-_COMBINATORICS_March_21st
DISCRETE MATHS -- COMBINATORICS - March 21st - ESCUELA UNIVERSITARIA DE INFORMÁTICA - PACO GÓMEZ Descripción: The purpose of logic. Propositions. Declarative sentences. Formal languages. Formalization. Simple and compound statements. Connectives: negation, disjunction, exclusive or, conjunction, implication and biconditional connectives. Table truth of connectives. Converse, contrapositive and inverse of an implication. Translating English sentences to a formal language. Necessary and sufficient conditions.
- published: 08 Aug 2011
- views: 1042
- author: UPM
DISCRETE MATHS -- COMBINATORICS - March 11th
- Order: Reorder
- Duration: 90:39
- Updated: 08 Aug 2011
DISCRETE MATHS -- COMBINATORICS - March 11th - ESCUELA UNIVERSITARIA DE INFORMÁTICA - PACO GÓMEZ Descripción: Discrete probability. Random experiments. Outcomes. Sample space. Probability functions. Elementary events. Event operations in terms of set operations. Properties of events. Laplace's rule. Examples. Problem set: problems 15 - 17
http://wn.com/DISCRETE_MATHS_-_COMBINATORICS_March_11th
DISCRETE MATHS -- COMBINATORICS - March 11th - ESCUELA UNIVERSITARIA DE INFORMÁTICA - PACO GÓMEZ Descripción: Discrete probability. Random experiments. Outcomes. Sample space. Probability functions. Elementary events. Event operations in terms of set operations. Properties of events. Laplace's rule. Examples. Problem set: problems 15 - 17
- published: 08 Aug 2011
- views: 870
- author: UPM
more combinatorics probability
- Order: Reorder
- Duration: 5:16
- Updated: 17 Aug 2012
card probabilities using combinatorics
http://wn.com/more_combinatorics_probability
photo: AP
16 Feb 2013
February 16, 2013 -- Updated 0115 GMT (0915 HKT). Did you see the meteor? Share your images with CNN iReport. Moscow (CNN) -- A meteor streaked through the skies above Russia's Urals region Friday morning before exploding with a flash and boom that shattered glass in buildings and left about 1,000 people hurt, authorities said ... The injured included more than 200 children ... The meteor leaves a white streak through the sky ... HIDE CAPTION ... 1. 2....(size: 14.9Kb)
photo: AP / Nasha gazeta, www.ng.kz
15 Feb 2013
A meteor streaked across the sky above Russia's Ural Mountains today morning, causing sharp explosions and injuring more than 400 people, many of them hurt by broken glass. "There was panic. People had no idea what was happening ... Fragments of the meteor fell in a thinly populated area of the Chelyabinsk region, the Emergency Ministry said in a statement ... ....(size: 1.7Kb)
photo: UN / Mark Garten
16 Feb 2013
The United States has called on North Korea not to take any further provocative actions after report of plans for more nuclear tests. Friday's statement came after the North conducted its third nuclear test on Tuesday, drawing global condemnation ... Meanwhile, North Korea's leader has made his first public appearance since Tuesday's controversial nuclear test. ... Al Jazeera's Harry Fawcett, reporting from Seoul, said ... 479 Source.....(size: 7.5Kb)
photo: AP / Office of the Supreme Leader
17 Feb 2013
TEHRAN — Iran’s supreme leader said Saturday that his country was not seeking nuclear weapons but added that if Iran ever decided to build them, no “global power” could stop it. Related. Nuclear Watchdog Says No Deal Reached With Iran (February 15, 2013). Connect With Us on Twitter. Follow @nytimesworld for international breaking news and headlines. Twitter List. Reporters and Editors ... Mr ... During the same session, Mr....(size: 5.9Kb)
photo: AP
14 Feb 2013
In their hurry to flee last month, al Qaeda fighters left behind a crucial document. Tucked under a pile of papers and trash is a confidential letter, spelling out the terror network's strategy for conquering northern Mali and reflecting internal discord over how to rule the region ... Comparing the relationship of al Qaeda to Mali as that of an adult to an infant, he urges them to be more gentle, like a parent ... Ad Feedback ... - AP. ....(size: 12.4Kb)
noodls
30 Jan 2013
(Source. Virginia Tech - Virginia Polytechnic Institute and State University). BLACKSBURG, Va., Jan. 30, 2013 - J.P ... He is a member of the American Statistical Association, Institute of Mathematical Statistics, the Institute for Combinatorics and its Applications, and has been a three-time president of the Virginia Chapter of the American Statistical Association ... ... distributed by ... (noodl. 17370221) ....(size: 3.6Kb)
Yahoo Daily News
30 Jan 2013
Mathematical equations aren't just useful — many are quite beautiful. And many scientists admit they are often fond of particular formulas not just for their function, but for their form, and the simple, poetic truths they contain ... General relativity ... [Einstein Quiz ... Standard model ... "A very cool fact! The combinatorics of the vertices, edges and faces is capturing something very fundamental about the shape of a sphere," Adams said ... ....(size: 12.0Kb)
CBS News
30 Jan 2013
Mathematical equations aren't just useful -- many are quite beautiful. And many scientists admit they are often fond of particular formulas not just for their function, but for their form, and the simple, poetic truths they contain ... General relativity ... Wohlstadter ... [Einstein Quiz ... Calculus ... "A very cool fact! The combinatorics of the vertices, edges and faces is capturing something very fundamental about the shape of a sphere," Adams said....(size: 13.1Kb)
The Charlotte Observer
21 Jan 2013
Kavi Jain is taking his love of math to Harvard and MIT. A 16-year-old junior at the N.C. School of Science and Mathematics in Durham, he’ll compete on the eight-member N.C. team Feb. 16 in the Harvard-MIT Mathematics Tournament ... “We have a pretty strong team.” ... First, they will have to take three individual tests in algebra, geometry, and combinatorics (essentially, counting), each with a 50-minute time limit ... ....(size: 2.8Kb)
noodls
09 Jan 2013
(Source. Indiana University). Last modified. Wednesday, January 9, 2013 IU Distinguished Professor Larsen receives Moore Prize from American Mathematical Society ... FOR IMMEDIATE RELEASE. Jan. 9, 2013. BLOOMINGTON, Ind ... A full professor at IU since 2001, Larsen in 2011 was promoted to the rank of distinguished professor for his work at the interface of arithmetic algebraic geometry, combinatorial group theory, combinatorics and number theory....(size: 5.6Kb)
noodls
11 Dec 2012
(Source. The University of Warwick). The University of Warwick has been awarded £5 million in prestigious European funding for a wide range of research including work on white dwarfs and solar weather ... They are designed to support ground-breaking, high-risk projects that open up new directions in their respective research fields ... And Dr Oleg Pikhurko was awarded £900,000 for mathematical research into the field of extremal combinatorics....(size: 3.6Kb)
Detroit news
30 Nov 2012
By Janet Lorin Bloomberg News Comments. Zoom. Hanlon ). Concord, N.H. â The provost at the University of Michigan has been chosen as the 18th president of Dartmouth College in New Hampshire ... As a mathematician, Hanlon focuses on probability and combinatorics, the study of finite structures and their significance as they relate to bioinformatics, computer science and other fields, Dartmouth said ... Tweet ... A A A. Join the Conversation ... Down Up....(size: 9.2Kb)
PR Newswire
29 Nov 2012
As a mathematician, Hanlon focuses on probability and combinatorics, the study of finite structures and their significance as they relate to bioinformatics, computer science, and other fields. He is an expert on topics such as computational genetics and cryptology and built a world-class combinatorics group at that consistently ranks among the top five in the nation....(size: 13.7Kb)
noodls
29 Nov 2012
For Immediate Release. November 29, 2012. College of Arts and Sciences Commemorates 25th Anniversary with Beineke Medal Presentation. Key Info ... (left to right) Peter Dragnev, interim chair, Department of Mathematics, Lowell W ... Lowell W ... Lowell W ... The Lowell W ... Beineke joined the Department of Mathematical Sciences at IPFW in 1965 and is an internationally recognized expert in the fields of graph theory and combinatorics ... ####. distributed by....(size: 3.8Kb)
The New York Times
29 Nov 2012
Philip J. Hanlon, the provost of the University of Michigan, will be the next president of Dartmouth College, starting in July. Related. Times Topic. Dartmouth College. Dr. Hanlon, 57, a mathematician whose work focuses on probability and combinatorics, will take office on July 1, succeeding Jim Yong Kim, who resigned in April to become the president of the World Bank. The interim president, Carol L ... Hanlon arrives ... Dr ... Indeed, Dr ... Dr ... campaign....(size: 7.5Kb)
noodls
15 Nov 2012
Posted in College of Arts & Sciences, Faculty/Staffon November 15, 2012. Belmont professors selected five times since 2000 for statewide honor ... Dr. Pinter, who is currently in Washington, D.C ... Belmont will be holding its own celebration to honor Dr. Pinter on Nov. 27 from 3-5 p.m ... Pinter's nomination ... In addition to regularly teaching general education mathematics courses and the upper-level combinatorics course, he also teaches Analytics....(size: 7.8Kb)
CNBC
12 Nov 2012
U.S. Treasurys, high quality corporate bonds and to a lesser extent select high-yield bonds are the investments of choice, even if their already unattractive — and in some cases unprofitable — yields budge a little bit in either direction, analysts say ... For contrarians such as Ram Bhagavatula, managing director of the hedge fund Combinatorics Capital, the interest rate equation is about to change ... Loan demand is picking up ... Strategies ... ... ....(size: 18.3Kb)
noodls
09 Nov 2012
Last modified. Friday, November 9, 2012 American Mathematical Society's first class of fellows includes six from IU Bloomington. FOR IMMEDIATE RELEASE. Nov. 9, 2012. BLOOMINGTON, Ind ... Temam ... Bedford is a professor emeritus with a Ph.D ... from the University of Michigan and specializes in probability theory on graphs, combinatorics, statistical mechanics, ergodic theory and harmonic analysis; Temam, a College Professor, holds a Ph.D ... (noodl....(size: 4.0Kb)
Not to be confused with combinatoriality.
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics).
Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry,[1] and combinatorics also has many applications in optimization, computer science, ergodic theory and statistical physics. Many combinatorial questions have historically been considered in isolation, giving an ad hoc solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is graph theory, which also has numerous natural connections to other areas. Combinatorics is used frequently in computer science to obtain formulas and estimates in the analysis of algorithms.
A mathematician who studies combinatorics is called a combinatorialist.
History[link]
Main article: History of combinatorics
Basic combinatorial concepts and enumerative results appeared throughout the ancient world. In 6th century BCE, physician Sushruta asserts in Sushruta Samhita that 63 combinations can be made out of 6 different tastes, taken one at a time, two at a time, etc., thus computing all 26-1 possibilities. Roman historian Plutarch discusses an argument between Chrysippus (3rd century BCE) and Hipparchus (2nd century BCE) of a rather delicate enumerative problem, which was later shown to be related to Schröder numbers.[2][3] In the Ostomachion, Archimedes (3rd century BCE) considers a tiling puzzle.
In the Middle Ages, combinatorics continued to be studied, largely outside of the European civilization. Notably, an Indian mathematician Mahavira (c. 850) provided the general formulae for the number of permutations and combinations.[citation needed] The philosopher and astronomer Rabbi Abraham ibn Ezra (c. 1140) established the symmetry of binomial coefficients, while a closed formula was obtained later by the talmudist and mathematician Levi ben Gerson (better known as Gersonides), in 1321.[4] The arithmetical triangle— a graphical diagram showing relationships among the binomial coefficients— was presented by mathematicians in treatises dating as far back as the 10th century, and would eventually become known as Pascal's triangle. Later, in Medieval England, campanology provided examples of what is now known as Hamiltonian cycles in certain Cayley graphs on permutations.[5]
During the Renaissance, together with the rest of mathematics and the sciences, combinatorics enjoyed a rebirth. Works of Pascal, Newton, Jacob Bernoulli and Euler became foundational in the emerging field. In the modern times, the works by J. J. Sylvester (late 19th century) and Percy MacMahon (early 20th century) laid the foundation for enumerative and algebraic combinatorics. Graph theory also enjoyed an explosion of interest at the same time, especially in connection with the four color problem.
In the second half of 20th century, combinatorics enjoyed a rapid growth, which led to establishment of dozens of new journals and conferences in the subject.[6] In part, the growth was spurred by new connections and applications to other fields, ranging from algebra to probability, from functional analysis to number theory, etc. These connections shed the boundaries between combinatorics and parts of mathematics and theoretical computer science, but at the same time led to a partial fragmentation of the field.
Approaches and subfields of combinatorics[link]
Enumerative combinatorics[link]
Main article: Enumerative combinatorics
Enumerative combinatorics is the most classical area of combinatorics, and concentrates on counting the number of certain combinatorial objects. Although counting the number of elements in a set is a rather broad mathematical problem, many of the problems that arise in applications have a relatively simple combinatorial description. Fibonacci numbers is the basic example of a problem in enumerative combinatorics. The twelvefold way provides a unified framework for counting permutations, combinations and partitions.
Analytic combinatorics[link]
Main article: Analytic combinatorics
Analytic combinatorics concerns the enumeration of combinatorial structures using tools from complex analysis and probability theory. In contrast with enumerative combinatorics which uses explicit combinatorial formulae and generating functions to describe the results, analytic combinatorics aims at obtaining asymptotic formulae.
Partition theory[link]
Main article: Partition theory
Partition theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to q-series, special functions and orthogonal polynomials. Originally a part of number theory and analysis, it is now considered a part of combinatorics or an independent field. It incorporates the bijective approach and various tools in analysis, analytic number theory, and has connections with statistical mechanics.
Graph theory[link]
Main article: Graph theory
Graphs are basic objects in combinatorics. The questions range from counting (e.g., the number of graphs on n vertices with k edges) to structural (e.g., which graphs contain Hamiltonian cycles) to algebraic questions (e.g., given a graph G and two numbers x and y, does the Tutte polynomial TG(x,y) have a combinatorial interpretation?). It should be noted that while there are very strong connections between graph theory and combinatorics, these two are sometimes thought of as separate subjects.[7]
Design theory[link]
Main article: Combinatorial design
Design theory is a study of combinatorial designs, which are collections of subsets with certain intersection properties. Block designs are combinatorial designs of a special type. This area is one of the oldest parts of combinatorics, such as in Kirkman's schoolgirl problem proposed in 1850. The solution of the problem is a special case of a Steiner system, which systems play an important role in the classification of finite simple groups. The area has further connections to coding theory and geometric combinatorics.
Finite geometry[link]
Main article: Finite geometry
Finite geometry is the study of geometric systems having only a finite number of points. Structures analogous to those found in continuous geometries (Euclidean plane, real projective space, etc.) but defined combinatorially are the main items studied. This area provides a rich source of examples for Design theory. It should not be confused with Discrete geometry (Combinatorial geometry).
Order theory[link]
Main article: Order theory
Order theory is the study of partially ordered sets, both finite and infinite. Various examples of partial orders appear in algebra, geometry, number theory and throughout combinatorics and graph theory. Notable classes and examples of partial orders include lattices and Boolean algebras.
Matroid theory[link]
Main article: Matroid theory
Matroid theory abstracts part of geometry. It studies the properties of sets (usually, finite sets) of vectors in a vector space that do not depend on the particular coefficients in a linear dependence relation. Not only the structure but also enumerative properties belong to matroid theory. Matroid theory was introduced by Hassler Whitney and studied as a part of the order theory. It is now an independent field of study with a number of connections with other parts of combinatorics.
Extremal combinatorics[link]
Main article: Extremal combinatorics
Extremal combinatorics studies extremal questions on set systems. The types of questions addressed in this case are about the largest possible graph which satisfies certain properties. For example, the largest triangle-free graph on 2n vertices is a complete bipartite graph Kn,n. Often it is too hard even to find the extremal answer f(n) exactly and one can only give an asymptotic estimate.
Ramsey theory is another part of extremal combinatorics. It states that any sufficiently large configuration will contain some sort of order. It is an advanced generalization of the pigeonhole principle.
Probabilistic combinatorics[link]
Main article: Probabilistic method
In probabilistic combinatorics, the questions are of the following type: what is the probability of a certain property for a random discrete object, such as a random graph? For instance, what is the average number of triangles in a random graph? Probabilistic methods are also used to determine the existence of combinatorial objects with certain prescribed properties (for which explicit examples might be difficult to find), simply by observing that the probability of randomly selecting an object with those properties is greater than 0. This approach (often referred to as the probabilistic method) proved highly effective in applications to extremal combinatorics and graph theory. A closely related area is the study of finite Markov chains, especially on combinatorial objects. Here again probabilistic tools are used to estimate the mixing time.
Often associated with Paul Erdős, who did the pioneer work on the subject, probabilistic combinatorics was traditionally viewed as a set of tools to study problems in other parts of combinatorics. However, with the growth of applications to analysis of algorithms in computer science, as well as classical probability, additive and probabilistic number theory, the area recently grew to become an independent field of combinatorics.
Algebraic combinatorics[link]
Main article: Algebraic combinatorics
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra. Within the last decade or so, algebraic combinatorics came to be seen more expansively as the area of mathematics where the interaction of combinatorial and algebraic methods is particularly strong and significant. One of the fastest developing subfields within algebraic combinatorics is combinatorial commutative algebra.
Combinatorics on words[link]
Main article: Combinatorics on words
Combinatorics on words deals with formal languages. It arose independently within several branches of mathematics, including number theory, group theory and probability. It has applications to enumerative combinatorics, fractal analysis, theoretical computer science, automata theory and linguistics. While many applications are new, the classical Chomsky–Schützenberger hierarchy of classes of formal grammars is perhaps the best known result in the field.
Geometric combinatorics[link]
Main article: Geometric combinatorics
Geometric combinatorics is related to convex and discrete geometry, in particular polyhedral combinatorics. It asks, for example, how many faces of each dimension can a convex polytope have. Metric properties of polytopes play an important role as well, e.g. the Cauchy theorem on rigidity of convex polytopes. Special polytopes are also considered, such as permutohedra, associahedra and Birkhoff polytopes. We should note that combinatorial geometry is an old fashioned name for discrete geometry.
Topological combinatorics[link]
Main article: Topological combinatorics
Combinatorial analogs of concepts and methods in topology are used to study graph coloring, fair division, partitions, partially ordered sets, decision trees, necklace problems and discrete Morse theory. It should not be confused with combinatorial topology which is an older name for algebraic topology.
Arithmetic combinatorics[link]
Main article: Arithmetic combinatorics
Arithmetic combinatorics arose out of the interplay between number theory, combinatorics, ergodic theory and harmonic analysis. It is about combinatorial estimates associated with arithmetic operations (addition, subtraction, multiplication, and division). Additive combinatorics refers to the special case when only the operations of addition and subtraction are involved. One important technique in arithmetic combinatorics is the ergodic theory of dynamical systems.
Infinitary combinatorics[link]
Main article: Infinitary combinatorics
Infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets. It is a part of set theory, an area of mathematical logic, but uses tools and ideas from both set theory and extremal combinatorics.
Gian-Carlo Rota used the name continuous combinatorics[8] to describe probability and measure theory, since there are many analogies between counting and measure.
Related fields[link]
Combinatorial optimization[link]
Combinatorial optimization is the study of optimization on discrete and combinatorial objects. It started as a part of combinatorics and graph theory, but is now viewed as a branch of applied mathematics and computer science, related to operations research, algorithm theory and computational complexity theory.
Coding theory[link]
Coding theory started as a part of design theory with early combinatorial constructions of error-correcting codes. The main idea of the subject is to design efficient and reliable methods of data transmission. It is now a large field of study, part of information theory.
Discrete and computational geometry[link]
Discrete geometry (also called combinatorial geometry) also began a part of combinatorics, with early results on convex polytopes and kissing numbers. With the emergence of applications of discrete geometry to computational geometry, these two fields partially merged and became a separate field of study. There remain many connections with geometric and topological combinatorics, which themselves can be viewed as outgrowths of the early discrete geometry.
Combinatorics and dynamical systems[link]
Combinatorial aspects of dynamical systems is another emerging field. Here dynamical systems can be defined on combinatorial objects. See for example graph dynamical system.
Combinatorics and physics[link]
There are increasing interactions between combinatorics and physics, particularly statistical physics. Examples include an exact solution of the Ising model, and a connection between the Potts model on one hand, and the chromatic and Tutte polynomials on the other hand.
See also[link]
- Combinatorial biology
- Combinatorial chemistry
- Combinatorial data analysis
- Combinatorial game theory
- Combinatorial group theory
- Phylogenetics
- List of combinatorics topics
Notes[link]
- ^ Björner and Stanley, p. 2
- ^ R.P. Stanley, "Hipparchus, Plutarch, Schröder, and Hough", Amer. Math. Monthly 104 (1997), no. 4, 344-350.
- ^ L. Habsieger, M. Kazarian, S. Lando, On the second number of Plutarch, Amer. Math. Monthly 105 (1998), no. 5, 446.
- ^ History of Combinatorics, chapter in a textbook.
- ^ Arthur T. White, ”Ringing the Cosets,” Amer. Math. Monthly 94 (1987), no. 8, 721-746; Arthur T. White, ”Fabian Stedman: The First Group Theorist?,” Amer. Math. Monthly 103 (1996), no. 9, 771-778.
- ^ See Journals in Combinatorics and Related Fields and Conferences on Combinatorics
- ^ 2-Digit MSC Comparison, by Daniel P. Sanders.
- ^ Continuous and profinite combinatorics
References[link]
- Björner, A. and Stanley, R.P., A Combinatorial Miscellany
- Graham, R.L., Groetschel M., and Lovász L., eds. (1996). Handbook of Combinatorics, Volumes 1 and 2. Elsevier (North-Holland), Amsterdam, and MIT Press, Cambridge, Mass. ISBN 0-262-07169-X.
- Lindner, Charles C. and Christopher A. Rodger (eds.) Design Theory, CRC-Press; 1st. edition (October 31, 1997). ISBN 0-8493-3986-3.
- van Lint, J.H., and Wilson, R.M. (2001). A Course in Combinatorics, 2nd Edition. Cambridge University Press. ISBN 0-521-80340-3.
- Stanley, Richard P. (1997, 1999). Enumerative Combinatorics, Volumes 1 and 2. Cambridge University Press. ISBN 0-521-55309-1, ISBN 0-521-56069-1.
- Combinatorial Analysis – an article in Encyclopædia Britannica Eleventh Edition
- Riordan, John (1958). An Introduction to Combinatorial Analysis, Wiley & Sons, New York (republished).
External links[link]
 |
Wikimedia Commons has media related to: Combinatorics |
 |
Look up combinatorics in Wiktionary, the free dictionary. |
- Combinatorics, a MathWorld article with many references.
- Combinatorics, from a MathPages.com portal.
- The Hyperbook of Combinatorics, a collection of math articles links.
- The Two Cultures of Mathematics by W. T. Gowers, article on problem solving vs theory building
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This page contains text from Wikipedia, the Free Encyclopedia - http://en.wikipedia.org/wiki/Combinatorics
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This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
| 3-2-1 Contact | |
|---|---|
| File:321 Contact2.png Original Opening title of 3-2-1 Contact |
|
| Format | Children's television series/Education |
| Created by | Samuel Y. Gibbon, Jr. |
| Starring | Varied, see article |
| Theme music composer | Tom Anthony |
| Country of origin | United States |
| No. of episodes | 225 and 8 Specials |
| Production | |
| Running time | 30 minutes |
| Broadcast | |
| Original channel | PBS |
| Audio format | Mono (1980–1984) Stereo (1985–1988) |
| Original run | January 14, 1980, September 1, 1991 (3-2-1 Classroom Contact) – November 18, 1988, May 1, 1992 (3-2-1 Classroom Contact) |
3-2-1 Contact is an American science educational television show that aired on PBS from 1980 to 1988, and an adjoining children's magazine. The show, a production of the Children's Television Workshop, teaches scientific principles and their applications. Dr. Edward G. Atkins, who was responsible for much of the scientific content of the show, felt that the TV program wouldn't replace a classroom but would open the viewers to ask questions about the scientific purpose of things.[1]
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History[link]
3-2-1 Contact was the brainchild of Samuel Y. Gibbon, Jr., who had been the executive producer of The Electric Company for CTW from 1971 to 1977. (Gibbon actually left CTW before Contact's production began, though he was still credited as "Senior Consultant.")
The first season of 65 programs began airing January 14, 1980 on select PBS member stations; it featured a cast of three college students who discussed science in an on-campus room known as the Workshop. The first season came to an end on April 11, 1980, but funds for more episodes were not sufficient until 1982.
When production resumed for the second season, which premiered on October 17, 1983, the show presented a more realistic appearance, as the new cast convened in a suburban basement (these segments were shot at Reeves Teletape, which also housed Sesame Street at the time). This cast continued until October 18, 1985. Ozzie Alfonso was Contact's new director and Al Hyslop its executive producer.
When the fifth season began on September 22, 1986, a third cast was introduced. However, unlike the previous casts, they did not meet in any specific setting; instead, they appeared in various taped and filmed segments. Episodes continued to be produced through November 1988.
For a time in the mid-1980s, the program was co-produced with the French television network FR3 and featured several new French cast members in addition to the American cast. From 1982 to 1983 the program was aired in Spain with dubbed-over versions of the American original broadcasts, and some local add-ons with four Spanish cast members: Sonia Martínez, Luis Bollain, Fernando Rueda and Marifé Rodríguez.[2] Another Spanish version of the broadcast was aired from 1990 to 1992.
From September 1, 1991 until May 1, 1992, an edited version of the series titled 3-2-1 Classroom Contact was produced, specifically for in-school viewing.
It was reported in 1984 that 3-2-1 Contact had an audience of over 7 million viewers and was broadcast in 26 countries including West Germany, France, Italy and Spain making their own dubbed-over versions.[1]
Broadcasters wanted the children to record the episodes without being afraid of infringement of copyright violations.[1]
Hosts[link]
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And as themselves:
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The Bloodhound Gang[link]
Main article: The Bloodhound Gang (TV series)
A frequent segment of the show was The Bloodhound Gang, a series about a group of young detectives who used science to solve crimes. Episodes of the series needed to be run in regular sequence for understandable viewing, as many Bloodhound Gang mysteries were cut among two or three Contact episodes.
The magazine[link]
Three months before the show premiered, a print magazine of the same name that also focused on science was released. In 1985, the magazine absorbed some of the content of sibling publication Enter (which went out of print that same year), including reader submissions of computer programs written in the BASIC computer language as well as reviews of popular computer programs. A new feature called "The Slipped Disk Show" appeared in mid-1985, starring a fictional disc jockey who answered computer-related questions submitted by readers.
Beginning in 1987, the magazine also featured content from another CTW production, Square One Television. Such content frequently took the form of a two-page comic strip, often parodying a popular show or movie of the time, with a math-related question at the end.
The Bloodhound Gang mysteries also made the leap to the magazine, but they were subsequently replaced with a series entitled The Time Team in September 1990. These stories found teenage characters Sean Nolan and Jenny Lopez traveling to different time periods in the past and future. Their surroundings and personal encounters were described with great detail, educating readers as to the customs of various cultures throughout history, and – on trips to the future – often pushing present day hot-button issues. For example, a 1993 story saw the duo traveling to what appeared to be a prehistoric forest, but near the end, they found a Brazil flag, a newspaper clipping from 1995, and a bulldozer at work: this was in fact a Brazilian rainforest being levelled.
In 1996, The Time Team was replaced by a comic serial, Cosmic Crew, which focused on the adventures of a group of teenagers and their robot butler in space. Their first story arc (which ran for more than a year) had them trying to figure out a series of riddles relating to places in the solar system in order to claim a treasure (which turned out to be a scholarship fund). Another story arc had a delinquent (who had been a villain in the first arc) join them in order to chase down a gang of other delinquents. Despite being effectively replaced, a few Time Team stories were run whenever there were gaps between installments of Cosmic Crew.
Many of the magazine's cover stories involved current events, such as 1990s oil fires in the Middle East. In addition, the magazine offered a games section in which most of the games were related to the stories in the issue.
In 1996, CTW presumably concluded that faithful readers from the late 1980s and early 1990s had long since moved on, and the magazine began to reprint non-time-sensitive stories from years past. For example, a 1991 article on the geography of the Galápagos Islands – a relatively unchanging subject – could very well re-appear in an identical format a half a decade later.
Under Sesame Workshop the magazine later became Contact Kids, removing the original reference to the television show. Production of the magazine was suspended indefinitely in 2001.
After production[link]
Though the show went off the air in 1988, it appeared in reruns from 1999 to 2003 on the cable television network Noggin, then a joint venture of CTW and Nickelodeon. Occasionally, shows were also rerun on Nickelodeon's Cable in the Classroom time period. For all these Nickelodeon and Noggin airings, the series was rated TV-Y7 (possibly due to the target audience). It also still aired on some PBS stations as reruns from 1989 to 1998 before it was switched to Noggin in 1999. As of 2003, Noggin no longer airs any shows produced by Sesame Workshop. The shows were modified for the shorter running time on these networks to allow for their interstitials.
Sources of funding[link]
Funding for 3-2-1 Contact was provided by the following:[3]
- National Science Foundation (January 14, 1980–November 18, 1988)
- United States Department of Education (January 14, 1980–November 18, 1988)
- Corporation for Public Broadcasting (January 14, 1980–November 18, 1988)
- Andrew W. Mellon Foundation (January 14, 1980–November 18, 1988)
- IBM Corporation (January 14, 1980–November 18, 1988)
- Carnegie Corporation of New York (October 31, 1983-November 18, 1988)
Five sponsors funded the show for its entire run. They were originally supposed to fund for 20 new episodes until 1989.[1]
References[link]
- ^ a b c d Hechinger, Fred M. (10/02/1984), About Education; Forgotten TV Audience: Children "The New York Times", page C.9. Accessed on August 14, 2007
- ^ La Vanguardia, February 12, 1982, April 4, 1983.
- ^ http://www.lib.umd.edu/NPBA/papers/ctw321c.pdf
External links[link]
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http://wn.com/3-2-1_Contact
Related pages:
http://es.wn.com/3, 2, 1... contacto
This page contains text from Wikipedia, the Free Encyclopedia - http://en.wikipedia.org/wiki/3-2-1_Contact
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This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
