41. Bernoulli physics; his son, Johann bernoulli, 1746–1807, who was astronomer royal at Berlinand also studied mathematics and geography; and jacob bernoulli, 1759–89 http://www.infoplease.com/ce5/CE005708.html

HOTWORDS CITE PRINT EMAIL in All Infoplease Almanacs Biographies Dictionary Encyclopedia Home Almanacs Atlas Dictionary ... D-Day Infoplease Tools Periodic Table Conversion Tool Perpetual Calendar Year by Year ... Site Map Also from Infoplease Search Infoplease Info search tips Search Biographies Bio search tips Encyclopedia Bernoulli [both: bern OO y E Pronunciation Key Bernoulli or Bernouilli , name of a family distinguished in scientific and mathematical history. The family, after leaving Antwerp, finally settled in Basel, Switzerland, where it grew in fame. Jacob, Jacques, or James Bernoulli, calculus and of the calculus of variations , he was the first to use the word integral in solving Leibniz's problem of the isochronous curve. He wrote an important treatise on the theory of probability (1713) and discovered the series of numbers that now bear his name, i.e., the coefficients of the exponential series expansion of x e -x ). He was succeeded at Basel by his brother, Johann, Jean, or John Bernoulli, Johannis Bernoulli opera omnia. His son, Daniel Bernoulli

42. Online Encyclopedia - Jacob Bernoulli , Encyclopedia Entry for jacob bernoulli.Jakob bernoulli (December 27, 1654 August 16, 1705), also known......Encyclopedia http://www.yourencyclopedia.net/Jacob_Bernoulli

Encyclopedia Entry for Jacob Bernoulli Dictionary Definition of Jacob Bernoulli Jakob Bernoulli December 27 August 16 ), also known as Jacob Jacques or James Bernoulli was a Swiss mathematician and scientist and the older brother of Johann Bernoulli Born in Basel Switzerland in , Jakob Bernoulli met Robert Boyle and Robert Hooke on a trip to England in , after which he devoted his life to science and mathematics. He lectured at the University of Basel from , becoming Professor of Mathematics in He corresponded with Gottfried Leibniz , and thus learnt calculus , and collaborated with his brother Johann. His early papers on transcendental curves ) and isoperimetry ) are early examples of its application. His masterwork was Ars Conjectandi of , a groundbreaking work on probability theory . The terms Bernoulli trial Bernoulli Theorem , and Bernoulli Numbers result from this work, and are named after him. Home Alphabetical Index See our sister sites: Find a Resume Diplomat City Your Quotations Your Lookup ... Your Dogs Content on this site is provided for informational purposes only. We do not accept responsibility for any loss, injury or inconvenience sustained by any person resulting from information published on this site. This article is licensed under the GNU Free Documentation License . It uses material from Wikipedia see source

43. Biografi: Jacob Bernoulli Faren til jacob bernoulli, Nicolaus bernoulli var en betydningsfullborger av Basel, som var medlem av byrådet og en forhørsdommer. http://www.matematikk.org/artikkel/vis.php?id=838

44. Gradebook Example In R Assume the file looks like this Einstein, Albert 0034567 Laird, Nan 0056745 bernoulli,jacob 0098453 Camus, Albert 0089452 and that it s called roll_F99 in http://www.math.montana.edu/stat/tutorials/gradebook.example.html

Using R for Gradebook Computations Caveat: This is not the only way, and certainly not the best way to make a gradebook. You might want to check out xspread , a spreadsheet for unix, or StarOffice which includes an Excel clone. 1. Setup Setup a directory for your roll files and any other material related to your course. In unix: mkdir m170 Protect the directory so that nosey students will not have access with the unix command: chmod 700 m170 Now move to that directory and start up emacs. 2. Reading in data Your course supervisor can get you a file of the students in your section. Assume the file looks like this: Einstein, Albert 0034567 Laird, Nan 0056745 Bernoulli, Jacob 0098453 Camus, Albert 0089452 and that it's called roll_F99 in the m170 directory. It's easiest to add a row of column labels to the top of the file, so edit it in emacs to make it look like this: Lname Fname idno Einstein, Albert 0034567 Laird, Nan 0056745 Bernoulli, Jacob 0098453 Camus, Albert 0089452 Save the file with C-X C-S.

45. Biography Of Johann Bernoulli 1,1748). The bernoulli family was probably the most notable mathematical familyin world history. The three most significant were jacob, Daniel, and Johann. http://www.andrews.edu/~calkins/math/biograph/bioberno.htm

Back to the Table of Contents Johann Bernoulli (Aug. 6, 1667 - Jan. 1,1748) The Bernoulli family was probably the most notable mathematical family in world history. There were ten notable intellectuals over three generations. The three most significant were Jacob, Daniel, and Johann. Also of importance were Johann's brother Nicolaus I, Nicolaus I's son Nicolaus II, Johann's sons Nicolaus III and Johann II, and his grandsons Johann III, Jacob II, and Daniel II. However, Johann made the biggest name for himself, so we will focus on his life, and methods that resulted in his contributions to modern mathematics. Below is a list of his personal information. PERSONAL FACTS He was born in Basel, Switzerland on August 6, 1667. He died in Basel, Switzerland on January 1, 1748. He enrolled in Basel in 1683; began to study medicine in 1685. He was schooled at Basel University and earned a M.A. and M.D. He received the medicine license in 1690. In 1694, he received a doctoral dissertation in Iatromathematics. He was called the "Grandseigneur of the science of mathematics" On a darker note he had a rocky relationship with Jacob and Daniel; he frequently took part in belittling chatter with the former, and once deliberately plagiarized one of the latter's papers.

46. Bioberno The bernoulli family was probably the most notable mathematical family in worldhistory. The three most significant were jacob, Daniel, and Johann. http://www.andrews.edu/~calkins/math/biograph/199899/bioberno.htm

Back to the Table of Contents Johann Bernoulli (Aug 6,1667-Jan 1,1748) The Bernoulli family was probably the most notable mathematical family in world history. There were ten notable intellectuals over three generations. The three most significant were Jacob, Daniel, and Johann. Also of importance were Johann's brother Nicolaus I, Nicolaus I's son Nicolaus II, Johann's sons Nicolaus III and Johann II, and his grandsons Johann III, Jacob II, and Daniel II. Here is a family tree to help straighten things out. However, Johann made the biggest name for himself, so we will focus on his life, and methods that resulted in his contributions to modern mathematics. Below is a list of his personal information. PERSONAL FACTS He was born in Basel, Switzerland on August 6, 1667. He died in Basel, Switzerland on January 1, 1748. He enrolled in Basel in 1683; began to study medicine in 1685. He was schooled at Basel University and earned a M.A. and M.D. He received the medicine license in 1690. In 1694, he received a doctoral dissertation in iatromathematics. He was called the "Grandseigneur of the science of mathematics" On a darker note he had a rocky relationship with Jacob and Daniel; he frequently took part in belittling chatter with the former, and once deliberantly plagarized one of the latter's papers.

47. The Bernoullis jacob or James bernoulli was born at Bâle on December 27, 1654; in 1687 he wasappointed to a chair in mathematics in the university there; and occupied it http://www.maths.tcd.ie/pub/HistMath/People/Bernoullis/RouseBall/RB_Bernoullis.h

The Bernoullis From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball. James Bernoulli John Bernoulli Daniel Bernoulli James Bernoulli Jacob or James Bernoulli He was one of the earliest to realize how powerful as an instrument of analysis was the infinitesimal calculus, and he applied it to several problems, but did not himself invent any new processes. His great influence was uniformly and successfully exerted in favour of the use of the differential calculus, and his lessons on it, which were written in the form of two essays in 1691 and are published in the second volume of his works, shew how completely he had even then grasped the principles of the new analysis. These lectures, which contain the earliest use of the term integral, were the first published attempt to construct an integral calculus; for Leibnitz had treated each problem by itself, and had not laid down any general rules on the subject. The most important discoveries of James Bernoulli were his solution of the problem to find an isochronous curve; his proof that the construction for the catenary which had been given by Leibnitz was correct, and his extension of this to strings of variable density and under a central force; his determination of the form taken by an elastic rod fixed at one end and acted on by a given force at the other, the elastica ; also of a flexible rectangular sheet with two sides fixed horizontally and filled with a heavy liquid, the

48. Bernoulli_Nicolaus(I) Born 21 Oct 1687 in Basel, Switzerland Died 29 Nov 1759 in Basel, Switzerland.Nicolaus(I) bernoulli was a nephew of jacob bernoulli and Johann bernoulli. http://homepages.compuserve.de/thweidenfeller/mathematiker/Bernoulli_Nicolaus(I)

Nicolaus(I) Bernoulli Born: 21 Oct 1687 in Basel, Switzerland Died: 29 Nov 1759 in Basel, Switzerland Nicolaus(I) Bernoulli was a nephew of Jacob Bernoulli and Johann Bernoulli . His early education involved studying mathematics with his uncles. In fact it was Jacob Bernoulli who supervised Nicolaus's Master's degree at the University of Basel which he was awarded in 1704. Five years later he was received a doctorate for a dissertation which studied the application of probability theory to certain legal questions. In 1712 Nicolaus(I) Bernoulli toured Europe visiting Holland, England and France. It was in France that he met Montmort and the two mathematicians became close friends and collaborated on mathematical questions in a long correspondence. Nicolaus(I) Bernoulli was appointed to Galileo 's chair at Padua in 1716 which Hermann had filled immediately prior to Nicolaus's appointment. There he worked on geometry and differential equations . In 1722 he left Italy and returned to his home town to take up the chair of logic at the University of Basel. After nine years, remaining at the University of Basel, he was appointed to he chair of law. In addition to these academic appointments, he did four periods as rector of the university. J O Fleckenstein, writing in [1], describes Nicolaus(I) Bernoulli's contribution to mathematics:-

49. De L'Hopital l Hôpital wrote the first textbook on calculus in 1696 which was much influencedby the lectures of his teacher Johann bernoulli, jacob bernoulli and Leibniz. http://homepages.compuserve.de/thweidenfeller/mathematiker/hopital.html

Guillaume De l'Hôpital (1661, Paris - 1704, Paris) Guillaume De l'Hôpital wrote the first textbook on calculus in 1696 which was much influenced by the lectures of his teacher Johann Bernoulli, Jacob Bernoulli and Leibniz. L'Hôpital served as a cavalry officer but resigned because of nearsightedness. From that time on he directed his attention to mathematics. L'Hôpital was taught calculus by Johann Bernoulli in 1691. L'Hôpital was a very competent mathematician and solved the brachystochrone problem. The fact that this problem was solved independently by Newton , Leibniz and Jacob Bernoulli puts l'Hôpital in very good company. L'Hôpital's fame is based on his book Analyse des infiniment petits pour l'intelligence des lignes courbes (1692) which was the first text-book to be written on the differential calculus. In the introduction L'Hôpital acknowledges his indebtedness to Leibniz, Jacob Bernoulli and Johann Bernoulli but L'Hôpital regarded the foundations provided by him as his own ideas. In this book is found the rule, now known as L'Hôpital's rule, for finding the limit of a rational function whose numerator and denominator tend to zero at a point.

50. Malffati Problem And Jacob Bernoulli By Antreas P. Hatzipolakis Malffati Problem and jacob bernoulli by Antreas P. Hatzipolakis. reply tothis message post a message on a new topic Back to mathhistory-list http://mathforum.org/epigone/math-history-list/spouvervex

Malffati Problem and Jacob Bernoulli by Antreas P. Hatzipolakis reply to this message post a message on a new topic Back to math-history-list Subject: Malffati Problem and Jacob Bernoulli Author: xpolakis@hol.gr Date: http://www-history.mcs.st-andrews.ac.uk/history//Mathematicians/Malfatti.html The Math Forum

51. életrajzok: B február 8.—1782. március 17.) svájci matematikus és fizikus. bernoulli,jacob (1654. december 27.—1705. augusztus 16.) svájci matematikus. http://www.iif.hu/~visontay/ponticulus/eletrajzok/b.html

rovatok j¡t©k arch­vum jegyzetek mutat³k kitekintő v©lem©nyek inform¡ci³k ©letrajzok magyar¡zatok forr¡sok BABBAGE, Charles (1792. december 26.—1871. okt³ber 18.): angol matematikus, k¶zgazd¡sz, feltal¡l³, sz¡m­t³g©ptervező. Cambridge-i professzor, Munk¡ss¡ga kiterjedt a f¼ggv©nyelm©let, a sz¡m­t¡stechnika ©s a k¶zgazdas¡gtan ter¼let©re. Neki jutott elősz¶r esz©be, hogy a Jacquard (1752—1834) ¡ltal feltal¡lt lyukk¡rty¡k nemcsak a sz¶vőg©pek, hanem a mechanikus sz¡mol³g©pek vez©rl©s©re is alkalmasak lehetnek. 1822-ben ©p­tette meg a csillag¡szati ©s haj³z¡si t¡bl¡zatok sz¡m­t¡s¡ra szolg¡l³ lyukk¡rtyavez©rl©sű mechanikus sz¡mol³g©p©t (Difference Engine=differenciag©p) . K¶vetkező, műveletsorok kisz¡m­t¡s¡ra is alkalmas programozhat³ g©pe (Analitical Engine=analiz¡l³g©p) a mai modern elektronikus sz¡m­t³g©pek elődj©nek tekinthető. BABITS Mih¡ly (1883—1941): k¶ltő, ­r³, műford­t³, essz©ista, az MTA tagja (1940). A Nyugat első nemzed©k©nek kiemelkedő k©pviselője, a k©t vil¡gh¡borº k¶z¶tti magyar polg¡ri irodalom egyik ir¡ny­t³ja. A Nyugat szerkesztője (1919—29-ben Osv¡t Ernővel, 1929—33-ban M³ricz Zsigmonddal, 1933-t³l hal¡l¡ig egyed¼l). 1927-től a Baumgarten-alap­tv¡ny irodalmi kur¡tora. M¡r fiatal l­rikusk©nt a klasszikus form¡k mestere. Rokonszenvezett az 1918—19-es forradalmi mozgalmakkal; a Tan¡csk¶zt¡rsas¡g megd¶nt©se ut¡n ez©rt t¡mad¡sok ©rt©k, melyekre mentegetőző tanulm¡nnyal felelt (

52. Acquiring Statistics | Jacob Bernoulli Tales of Statisticians jacob bernoulli 6 Jan 1655 16 Aug 1705 jacob(or James, or Jacques), the son of a prosperous Protestant http://www.umass.edu/wsp/statistics/tales/bernoulli.html

Tales of Statisticians Jacob Bernoulli 6 Jan 1655 - 16 Aug 1705 Jacob's most important work was the Ars Conjectandi, which like the paper of Thomas Bayes was published only after his death (in 1713). With de Moivre's work of 1718, it is the first major treatise in the field of probability and statistics. Bernoulli's legacy, like his life, has an oppositional character. The Ars Conjectandi defines a "frequentist" or objective position as against the "expectation" or subjective position which has developed from the work of Bayes. Opposition between these two viewpoints still to some extent divides statistics into two hostile camps. One subgroup of the International Association for Statistics is called the Bernoulli Society. Bernoulli developed the binomial approach of Pascal , in which the binomial coefficients of the Arithmetical Triangle have a central place. A coin toss or other trial which can have only one of two outcomes is sometimes called a Bernoulli trial. We have avoided this and similar terms of respect, in the interest of maximum accessibility for beginning readers (for whom these Lessons are intended), but we gladly acknowledge Bernoulli's contribution on this page. Acquiring Statistics Comments to The Author Annals of Statistics / Exit to Project Home Page

53. Mathem_abbrev Isaac Battani, Abu al Bayes, Thomas Bell, Eric Temple ben Ezra, Abraham ben Gerson,Levi ben Tibbon, jacob, bernoulli, Daniel bernoulli, jacob bernoulli, jacob http://www.pbcc.cc.fl.us/faculty/domnitcj/mgf1107/mathrep1.htm

Mathematician Report Index Below is a list of mathematicians. You may choose from this list or report on a mathematician not listed here. In either case, you must discuss with me the mathematician you have chosen prior to starting your report. No two students may write a report on the same mathematician. I would advise you to go to the library before choosing your topic as there might not be much information on the mathematician you have chosen. Also, you should determine the topic early in the term so that you can "lock-in" your report topic!! The report must include: 1. The name of the mathematician. 2. The years the mathematician was alive. 3. A biography. 4. The mathematician's major contribution(s) to mathematics and an explanation of the importance. 5. A historical perspective during the time the mathematician was alive. Some suggestions on the historical perspective might be: (a) Any wars etc. (b) Scientific breakthroughs of the time (c) Major discoveries of the time (d) How did this mathematician change history etc.

54. Jacob In Directory.co.uk 8. bernoulli_jacob jacob (Jacques) bernoulli. Born jacob bernoulli s motheralso came from an important Basel family of bankers and local councillors. http://www.directory.co.uk/Jacob.htm

directory.co.uk Add to Favourites Search the directory for document.cookie="metasearch=1782609930.20480.0000"; directory.co.uk listings for "Jacob" (1 - 20 of 54) Next > Are you looking for? Jacob Riis Boehme Jacob Broom Jacob Jacob S Pillow ... History Of The 12 Tribes View By Relevance View By Search Engine MyCokeMusic downloads - Jacob Over 250,000 tracks from 10,000 artists ready for download, including exclusives and pre-releases. Where your music comes first. Sponsored by: http://www.mycokemusic.com Jacob Compare Prices at 40,000 Stores. Cheap Prices on Watches! Sponsored by: http://BizRate.com/ The Jacob Sheep Society, official website for jacob ... sheep in the UK, full details of the society, the breed, membership, ... Use the navigation bar on the left to move between different sections of the site and the links on the page header bars to move within each section. ... beautiful objects using the natural colours of the Jacob fleece, you will find all the information you need ... will find details of the Jacob Sheep Society - its history and the ...

55. Jacob Bernoulli ‚Ì•æ–Á”è BASEL jacob bernoulli. jacob bernoulli ?(147kb?). AUG. http://www.officenet.co.jp/~urakawa/be/bernoulli.html

JACOB BERNULLI‚Ì•æ–Á”è BASEL‚̑吹“°“à‚É‚ ‚é ‚i‚`‚b‚n‚a ‚a‚d‚q‚m‚n‚t‚k‚k‚h ƒXƒCƒX‚̃o[ƒ[ƒ‹‚̑吹“°‚É‚ ‚éAƒ„ƒRƒuEƒxƒ‹ƒk[ƒC‚Ì•æ–Á”è‚̎ʐ^‚Å‚·B ‰º‚Ì•û‚ɁAuÄ‚Ñ‚æ‚Ý‚ª‚¦‚év‚ÌŒ¾—t‚Æ‚Æ‚à‚ɁA—†ùiƒAƒ‹ƒLƒƒfƒX‚Ì—†ù‚É‚Ý‚¦‚éj‚ª•`‚©‚ê‚Ä‚¢‚Ü‚·B AUG. 11, ‚P‚X‚X‚W ŽB‰e C.S. IACOBUS BERNOULLI MATHIMATICUS INCOMPARABILIS ACAD. BASEL VLTRA XVIII ANNOS PROF. ACADEM. ITEM REGI AE PARIS. ET BERO‚k‚hN SO CIUS EDITES LUCUBRAT.INLUSTRI. MORBO CHRONICO MENTE AD EXTREMUN INTEGRA ANNO SAL. CIOIOCCV.D.XVI .AUGUSTI AE TATIS L.M.VII EXTINCTUS RESURPECT.PIOR.HICPR ASTOLATUR IUDITHASTUPANA XX ANNOR.VXOR CUM DUOBUS LIBERIS MARITO ET PARENTI EHEU DESIDERATISS H.M.P. RESURGO EADEM MUTAIA i’j 11s–Ú‰ºü•”‚Ì‚b‚Ì— •Ô‚µ•¶Žš‚́A‚n‚Å‘ã—p ‚Í‚¶‚߂̃y[ƒW‚É–ß‚é

56. The Mathematics Genealogy Project - Jacob Bernoulli jacob bernoulli Biography. Johann bernoulli, 1694, 27071. According to our currentonline database, jacob bernoulli has 1 students and 27072 descendants. http://www.genealogy.math.ndsu.nodak.edu/html/id.phtml?id=54440

57. Jakob Bernoulli :: Online Encyclopedia :: Information Genius Online Encyclopedia Jakob bernoulli (December 27, 1654 August 16, 1705), alsoknown as jacob, Jacques or James bernoulli was a Swiss mathematician and http://www.informationgenius.com/encyclopedia/j/ja/jakob_bernoulli.html

Quantum Physics Pampered Chef Paintball Guns Cell Phone Reviews ... Science Articles Jakob Bernoulli Online Encyclopedia Jakob Bernoulli December 27 August 16 ), also known as Jacob Jacques or James Bernoulli was a Swiss mathematician and scientist and the older brother of Johann Bernoulli Born in Basel Switzerland in , Jakob Bernoulli met Robert Boyle and Robert Hooke on a trip to England in , after which he devoted his life to science and mathematics. He lectured at the University of Basel from , becoming Professor of Mathematics in He corresponded with Gottfried Leibniz , and thus learnt calculus , and collaborated with his brother Johann. His early papers on transcendental curves ( ) and isoperimetry ) are early examples of its application. His masterwork was Ars Conjectandi of , a groundbreaking work on probability theory . The terms Bernoulli trial Bernoulli Theorem , and Bernoulli Numbers This content from wikipedia is licensed under the GNU Free Documentation License Power Supplies Hardware Information Law Advice

58. Bernoulli_Jacob(II) jacob(II) (Jacques(II)) bernoulli. Born 17 Oct jacob(II) bernoulli wasone of the sons of Johann(II) bernoulli. Following the family http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/BrnllJcb.htm

Date: TUE, 10 NOV 1998 08:50:52 GMT Connection: close Jacob(II) (Jacques(II)) Bernoulli Born: 17 Oct 1759 in Basel, Switzerland Died: 15 Aug 1789 in St Petersburg, Russia Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Jacob(II) Bernoulli was one of the sons of Johann(II) Bernoulli . Following the family tradition he took a degree in law but his interests were in mathematics and mathematical physics. In 1782 Jacob(II) Bernoulli's uncle Daniel Bernoulli died and his chair of physics in Basel became vacant. Jacob(II) applied for the chair and presented a work on mathematical physics to support his application. The decison as to who should fill the vacant chair was not made on academic grounds but was made by drawing lots. Jacob(II) Bernoulli was unlucky and he was not offered this position he would really have liked. He was then appointed as secretary to the Imperial Envoy to Turin and Venice. However, he was soon given the chance of another academic post when he received an offer from St Petersburg. He went to St Petersburg and began to write important works on mathematical physics which he presented to the St Petersburg Academy. These treatises were on elasticity, hydrostatics and ballistics. Despite the rather harsh climate, the city of St Petersburg had great attractions for Jacob(II) Bernoulli since his uncle

59. Boys jacob bernoulli was born December 27th, 1654. The tenth child of Nicolaus bernoulli,Johann was born on July 27th, 1667, twelve years after his brother jacob. http://jwilson.coe.uga.edu/EMT668/EMAT6680.Folders/Dickerson/Bernoulli/boys.html

Two Bernoulli Brothers Nicolaus Bernoulli was a merchant in Basel, Switzerland. His family were refugees fleeing from the massacre done by the Catholics in the Netherlands. The family settled in Basel only after fleeing to Frankfurt from persecution by the Spanish rulers. Nicolaus wanted his children to study religion and medicine. Fortunately, three of his sons chose a different path in life and studied mathematics. This is the story of two of the brother's lives, Jacob and Johann, and their rivalry. Jacob Bernoulli was born December 27th, 1654 In 1671 Jacob graduated from the University of Basel with a master's degree in philosophy and in 1676 with a licentiate in theology. Jacob studied philosophy and theology to oblige with his parents' wishes. While working on these degrees, Jacob also studied mathematics and astronomy against his parents wishes. Jacob was the first of the numerous Bernoullis to study mathematics. After graduation, Jacob began work as a tutor in Geneva. He traveled to France, studying with the followers of Descartes for two years. Beginning in 1681, Jacob continued his travels to the Netherlands and then to England where he continued his studies with leading mathematicians and scientists. Jacob returned to the University of Basel to teach mechanics in 1683 He turned down an appointment in the Church at this time. One year later Jacob married Judith Stupanus. Together they had a son and a daughter; neither became mathematicians.

60. Web Links For Chapter 4 Andrews, Scotland. http//wwwhistory.mcs.st-and.ac.uk/history/Mathematicians/bernoulli_jacob.html(bernoulli – jacob). Page 275. http://www.mhhe.com/math/advmath/rosen/student/webres/ch4links.mhtml

Web Links for Chapter 4 Section 4.1. The Basics of Counting Page 236 Details of the North American Numbering Plan (NANP) , the numbering plan for the Public Switched Telephone Network in North America and the Caribbean, can be found at http://www.nanpa.com (North American Numbering Plan Administration) http://www-comm.itsi.disa.mil/itu/e164.html Section 4.2. The Pigeonhole Principle Page 244 A variety of applications of the pigeonhole principle can be found on the Interactive Mathematics and Miscellany site. http://www.cut-the-knot.com/do_you_know/pigeon.html (Pigeonhole Principle) A biography and a portrait of Dirichlet can be found at the History of Mathematics Archive at the University of St Andrews, Scotland. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dirichlet.html (Dirichlet) Page 248 A biography and a photo of Frank Plumpton Ramsey can be found at the History of Mathematics Archive at the University of St Andrews, Scotland. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Ramsey.html (Ramsay) Section 4.3. Permutations and Combinations

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