41. Nut03s the distribution of primes in arithmetic progressions, and of the Prime Number Theorem,but the course is much more than just the proof of two famous theorems. http://www.renyi.hu/~dezso/budsem/04spring/nut2_04s.html

Topics in Number Theory NUT2 Instructor: Dr. Antal BALOG Text: Selected chapters of Harold Davenport, Multiplicative Number Theory. In case of departing from the book, and also for gaining some preliminary routine, supplements will be handed out. Prerequisite: General mathematical experience of the undergraduate level is expected. This includes elementary algebra (Abelian groups, vector spaces, systems of linear equations) and calculus (limits, derivatives, integration, infinite series). A first course of number theory (divisibility, congruences, Chinese Remainder Theorem, primitive roots and power residues) and a course of complex function theory (analytic functions, continuation, power series, complex line integrals, calculation of residues) are essential , although the basic concepts of the applied theories and theorems will always be explained. Taking CLX parallel to this course is enough. Course description: Our aim is to provide a classical introduction to analytic number theory, focused on the connection between the zeros of the Riemann z (s) -function and prime numbers. We will follow the history and development of a beautiful discipline, rich in problems, methods and ideas. The highlights are a proof of Dirichlet's Theorem about the distribution of primes in arithmetic progressions, and of the Prime Number Theorem, but the course is much more than just the proof of two famous theorems.

42. DIMACS Seminar famous theorems, previously thought to close the book, state that these are thefull set of division (or normed) algebras with $1$ over the real numbers. http://dimacs.rutgers.edu/Events/2002/abstracts/smith.html

DIMACS Seminar Title: Quaternions, octonions, and now, 16-ons and $2^n$-ons; New kinds of numbers. Speaker: Warren D. Smith , DIMACS, Rutgers University, and Temple University Mathematics Department Date: Friday September 13, 2002, 1:10 pm Location: DIMACS Seminar Room, CoRE Building, Room 431A, Rutgers University. Abstract: The ``Cayley-Dickson process,'' starting from the real numbers, successively yields the complex numbers (dimension 2), quaternions (4), and octonions (8). Each contains all the previous ones as subalgebras. Famous Theorems, previously thought to close the book, state that these are the full set of division (or normed) algebras with $1$ over the real numbers. Their properties keep degrading: the reals are ordered and self-conjugate, but the complex numbers lose these properties; at the quaternions we lose commutativity; and at the octonions we lose associativity. If one keeps Cayley-Dickson doubling to get the 16D ``sedenions,'' zero-divisors appear. We introduce a different doubling process which also produces the complexes, quaternions, and octonions, but keeps going to yield $2^n$-dimensional normed algebraic structures

43. Mathematics - Wikipedia, The Free Encyclopedia Applied mathematics. Mechanics Numerical analysis Optimization Probability Statistics Financial mathematics. famous theorems and conjectures. http://en.wikipedia.org/wiki/Mathematics

Mathematics From Wikipedia, the free encyclopedia. Mathematics is commonly defined as the study of patterns of structure, change , and space ; more informally, one might say it is the study of 'figures and numbers'. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation ; other views are described in Philosophy of mathematics . Mathematics might be seen as a simple extension of spoken and written languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships. The specific structures that are investigated by mathematicians often have their origin in the natural sciences , most commonly in physics , but mathematicians also define and investigate structures for reasons purely internal to mathematics, because the structures may provide, for instance, a unifying generalization for several subfields, or a helpful tool for common calculations. Finally, many mathematicians study the areas they do for purely aesthetic reasons, viewing mathematics as an art form rather than as a practical or applied science . Some mathematicians like to refer to their subject as "the Queen of Sciences". Mathematics is often abbreviated to math (in American English ) or maths (in British English Table of contents 1 Overview and history of mathematics 2 Topics in mathematics 2.1 Quantity

44. Math Words Page 11 Here is a link to Euclid s proof. The Pythagorean Theorem is one ofthe most famous theorems in all of math. Because so much has http://www.pballew.net/arithm11.html

Pg 11 Back to Math Words Alphabetical Index Antiparallels Almost every geometry student learns that a line through two sides of a triangle parallel to the third side (DE in figure) will cut off a triangle, ADE, that is similar to the original triangle ABC. Almost none of them are shown that the reflection of such a parallel line segment in the angle bisector will produce another segment cutting off a triangle AE'D' that is also similar to ABC. Such a segment is called an antiparallel . The antiparallel also creates a quadrilateral of the remaining piece of the triangle which is always cyclic, and therefore can be circumscribed. The opposite sides of any cyclic quadrilateral are thus referred to as antiparallels also, since extending any two opposite sides will create a pair of similar triangles also. In the famous books on the conic sections by Apollonius of Pergia he refers to this as a triangle lying "subcontrary wise". The only two planes cut through a cone that will produce a circle are the cuts parallel to the base, and the cut subcontrary or anti-parallel to the base. (book I, Proposition 9) Arbelos was the Greek word for a knife used by a shoemaker to cut and trim leather. The name was applied by Archimedes (about 250 BC) to the region below bounded by three semi-circles.

45. EPGY University Mathematics M152 Study of Z; famous theorems about Primes; Pythagorean Triples, DiophantineEquations, Fermat s Last Theorem; The Euclidean Algorithm http://www-epgy.stanford.edu/courses/math/M152/?lessons

46. Course.asp Using this background, three famous theorems are proved the PaleyWienertheorem, the Foures-Segal theorem and the sampling theorem. http://washer.ee.ic.ac.uk/www/course.asp?c=C1.6&s=C1

47. Mathematics And Statistics - MATH419 The Prime Number Theory . The prime number theorem is one of the most fundamentaland famous theorems of Mathematics. It answers an obvious question...... http://www.maths.lancs.ac.uk/department/study/years/fourth/modules/math419

48. Combinatorics Of Finite Sets me to an area of combinatorics which I knew very little about, namely extremalset problems and their solutions which fall under famous theorems by famous http://all-computer-books.co.uk/Combinatorics_of_Finite_Sets.html

Home Search High Volume Orders Links ... On Line Algorithms Additional Subjects Island Methods General Food Harry Weinger Richard Noss ... Guide to Enterprise IT Architecture Featured Books Combinatorics of Finite Sets When one thinks of combinatorics of finite sets, he or she might first think of codes and designs. But this book introduced me to an area of combinatorics which I knew very little about, namely extremal set problems and their solutions which fall under famous Theorems by famous mathematicians: Erdos-Ko-Rado, Sperner, and Kruskal-Katona to name a few. I found these topics fascinating and fun to think about, which is in large part due to the author's coherent style, organization, explanation, a... Written by Ian Anderson Published by Dover Pubns (May 2002) ISBN 0486422577 Price $12.95 This is the book from which I learnt Combinatorics the Erdosian way. One of the most pleasing qualities of the book is the bite-sized chapters. Perhaps this is one of the first books to start this trend. An earlier reviewer mentions the Ramsey theory chapter which I too would recommend. The chapters on Intersecting hypergraphs, Kruskal-Katona theorem, LittlewoodOfford problem, Fourfunctions theorem are other gems which come to mind readily. The proofs are crisp and the way the theorems ar... Written by Bila Bollob¡s Published by Cambridge University Press (July 1986) ISBN 0521337038 Price $25.00

49. No Title One of Poincaré s famous theorems showed that if f is a local equivalent mapbetween two small pieces of the sphere , then f must be extended as an http://www.math.uh.edu/~dean/REU/sji.html

Proposal for the summer program Shanyu Ji I propose some topics on CR geometry. More precisely, we study the geometry and analysis on the unit balls in C n CR geometry studies properties of the boundary of a domain in C n . As we know, in mathematics, it is very important to study the relationship between a domain and its boundry. For example, the well-known Stokes's theorem, the Gauss-Bonnet formula, etc. f is a local equivalent map between two small pieces of the sphere , then f must be extended as an automorphism of the unit ball B . His theorem has been extended into many different levels. If one considers maps from B n to B N with N greater than n , i.e., the positive codimension case, Webster proved in 1978 that any such map from B n to B n n greater than or equal to 3) must be a trivial map, up to automorphisms of balls. In 1982, Faran proved that there are exactly four such maps from B to B , up to automorphisms of balls. Let us denote these four maps by F F F and F It remains a natural question: given any map F is isomorphic to which map F j (up to automorphsims of balls)?

50. Pythagorean Theorem One of the most famous of theorems from geometry (and/or trigonometry) is Pythagoras’brain child “The sum of the squares of the sides of a right triangle http://www.halexandria.org/dward096.htm

Pythagorean Theorem One of the most famous of theorems from geometry (and/or trigonometry) is Pythagoras’ brain child: “The sum of the squares of the sides of a right triangle equals the square of the hypotenuse.” One of the best examples of the theorem is the classic 3 - 4 - 5 triangle. Clearly, But the theorem works for any right triangle (a right triangle being a triangle where one of the interior angles equals 90 degrees, and with the “hypotenuse” as the longest side, and opposite the 90 degree angle.) In general, a b d Another special case is: F F Ha! The Golden Mean strikes again! The Pythogorean Brotherhood The theorem may not have been entirely the personal work of Phythagoras, but may have evolved from the Pythagoreans (the sum total of the members who followed the teaching of Pythagoras). As such, the Pythagoreans were a minor tradition during Classical Greece an apparent combination of Greek philosophy and eastern ideas. The philosophical school was founded by Pythagoras himself circa 530 B.C.E. Many stories have been told about Pythagoras and his achievements, including his having competed and won prizes in the Olympic wrestling games at the age of eighteen, his having travelled to Egypt and Babylonia in order to learn the ancient wisdom of the priests there (thus the infusion of “eastern ideas”), and his alleged ability to tame a bear or stop an eagle in midair with a few magical words. He was also a masterful musician and physician, and had a Public Relations effort that way ahead of its time!

51. Pythagoras' Theorem - By Seth Y-Maxwell He also created theorems. One of his most famous theorem was a 2 +b 2 =c2. Attention. If You have any information on different proofs email me. http://www.geocities.com/CapeCanaveral/Launchpad/3740/

By: Seth Yoshioka-Maxwell You can view one of the images by clicking once on the picture you want. Pythagoras was a great Mathematician who was the first to create the music scale of today. He also created theorems. One of his most famous theorem was: a +b =c Attention If You have any information on different proofs e-mail me. I would love to add more proofs to my site. Thank you. +b =c NEW ! Pythagorean Theorem Proof Calculator Pythagorean Theorem Joke President Garfield's Proof of the Pythagorian Theorem Main page ... Notify-mail Page and graphics designed by Seth Yoshioka-Maxwell

52. Theorem Of The Month Any odd prime is either 1 or 3 more than a multiple of 4. A famous theorem of Fermatasserts that if p is 1 more than a multiple of 4 then two squares suffice. http://www.shef.ac.uk/puremath/theorems/

Other Theorems of the Month Font problems? Lagrange's four-square theorem Theorem 1 If n is a natural number then there exist integers x, y, z, w such that n = x +y +z +w This theorem was proved by Lagrange in 1770, though it had been stated without proof in 1621, by Bachet. Ask somebody to give you random three-digit numbers, and for each one see if you can find four squares that do it. They are always out there somewhere. For example, 260 = 15 To get an idea of how to approach the theorem, consider the problem of representing a number n as a sum of just two squares; in other words, we want to find integers x and y such that n = x +y . Equivalently, we want to find a point (x,y) with integer coordinates on the circle centred at the origin with radius n. The following picture shows the circles with radii The circles that contain an integer point (represented by a black dot) are drawn in green; those that do not are shown in red. For example, the third circle has radius 3 and does not contain an integer point, so there are no integers x,y with x +y The question of which numbers can be represented as a sum of two squares is studied in For example, take n = 4693000. This can be factored as 2

53. Science Jokes:10. ANECDOTES ABOUT FAMOUS SCIENTISTS about the apocryphal story about the MIT student who cornered the famous John von Todayhe proved two theorems before lunch. Your dog must be a genius, said http://www.xs4all.nl/~jcdverha/scijokes/10.html

10. ANECDOTES ABOUT FAMOUS SCIENTISTS Index Comments and Contributions previous page mathematics Top of page Bottom of page Index Send comment ... Special Category: Ernest Rutherford physics Top of page Bottom of page Index Send comment ... Special Category: Ernest Rutherford From: chollanamdo#NoSpam.mindspring.com (The Sanity Inspector) Too bad Kelvin largely remembered as a fount of regrettable quotations these dayshe *did* do a lot of heavy lifting to get us from then to now. I came into the room, which was half dark, and presently spotted Lord Kelvin in the audience and realized that I was in for trouble at the last part of my speech dealing with the age of the earth, where my views conflicted with his. To my relief, Kelvin fell fast asleep, but as I came to the important point, I saw the old bird sit up, open an eye and cock a balefule glance at me! Then a sudden inspiration came, and I said Lord Kelvin had limited the age of the earth, *provided no new source (of energy) was discovered.* That prophetic utterance refers to what we are now considering tonight, radium! Behold! the old boy beamed upon me. Ernest Rutherford mathematics Top of page Bottom of page Index Send comment From: entropy#NoSpam.pawl.rpi.edu (Mark-Jason Dominus)

54. History Of Mathematics - The Most Famous Teacher The Most famous Teacher. 300 BC in Alexandria, first stated his five postulatesin his book The Elements that forms the base for all of his later theorems. http://members.aol.com/bbyars1/euclid.html

The Most Famous Teacher Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later theorems. His first postulates were 1. To draw a straight line from any point to any other. 2. To produce a finite straight line continuously in a straight line. 3. To describe a circle with any center and any distance. 4. That all right angles are equal to each other. 5. That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, if produced indefinitely, meets on that side on which are the angles less than the two right angles. To each triangle, there exists a similar triangle of arbitrary magnitude. Several other attempts to prove or disprove the fifth postulate have followed, notably that of Girolamo Saccheri. He assumed the fifth postulate to be false and attempted to derive a contradiction. Another mathematician, Gauss, started working on the postulate as early as 1792 while 15 years old. In 1813, after making little progress, he wrote In 1817, Gauss stated that the fifth postulate was independent from the other postulates, and therefore needed no proof from the others, and begun to work on a different geometry in which multiple lines can be parallel to another line through a given point. In fact, the fifth postulate has been called "the one sentence in the history of science that has given rise to more publication than any other."

55. Atlas: Uniqueness Theorems In The Calculus Of Variations By The Method Of Transf In a similar way E. Noether showed in 1918 her famous theorem that tranformationsgroups, which leave L invariant, imply a conservation law. http://atlas-conferences.com/c/a/l/o/39.htm

Atlas Document # calo-39 Equadiff 2003 - International Conference on Differential Equations July 2226, 2003 LUC Diepenbeek Hasselt, Belgium Organizers Freddy Dumortier (Chair, LUC Diepenbeek), Henk Broer (Univ. Groningen), Jean-Pierre Gossez (Univ. Libre Bruxelles), Jean Mawhin (Univ. Cath. Louvain-la-Neuve), Andre Vanderbauwhede (Univ. Gent), Sjoerd Verduyn Lunel (Univ. Leiden) View Abstracts Conference Homepage Uniqueness theorems in the calculus of variations by the method of transformation groups by Wolfgang Reichel Departement Mathematik, Universitaet Basel, Rheinsprung 21, CH-4051 Basel A classical question in the calculus of variations is the following: when does a functional L e e in IR , which map A into itself, and there interaction with L . If the group strictly decreases the values of L , i.e., if L [g e L , then u is the only critical point, provided structural assumptions on L hold. In a similar way E. Noether showed in 1918 her famous theorem that tranformations groups, which leave L invariant, imply a conservation law. Numerous examples of the uniquenes principle are found for elliptic boundary value problems, the theory of elasticity, and in geometric analysis.

56. Re: Pappus-Guldinus Theorem By Julio Gonzalez Cabillon The author deals with the following problem when P. Guldin (15771643)announced his famous theorem, did he plagiarize Pappus? http://mathforum.org/epigone/math-history-list/gehswoibon/1.5.4.32.1997120402572

Re: Pappus-Guldinus theorem by Julio Gonzalez Cabillon reply to this message post a message on a new topic Back to messages on this topic Back to math-history-list Subject: Re: Pappus-Guldinus theorem Author: jgc@adinet.com.uy Date: The Math Forum

57. Famous Theories From a theory of incompleteness to how to pack spheres in a box this week we feature ten of the most famous theories in modern history. But although they may be famous, they are not necessarily http://www.freewebsurveys.com/topics/famoustheories.cfm

Ads_kid=0;Ads_bid=0;Ads_xl=0;Ads_yl=0;Ads_xp='';Ads_yp='';Ads_opt=0;Ads_wrd='';Ads_prf='';Ads_par='';Ads_cnturl='';Ads_sec=0;Ads_channels='Pop'; Ads_kid=0;Ads_bid=0;Ads_xl=468;Ads_yl=60;Ads_xp='';Ads_yp='';Ads_opt=0;Ads_wrd='';Ads_prf='';Ads_par='';Ads_cnturl='';Ads_sec=0;Ads_channels='Full'; Home News Science Forums Hypographies ... Science Shop Sunday, 6 June 2004 Hypography Science sites Amazon.com Hypographies Famous Theories From a theory of incompleteness to how to pack spheres in a box: this week we feature ten of the most famous theories in modern history. Created by Tormod Guldvog Last updated September 14 2001 Most of us have heard about these theories, or at least some of them. But although they may be famous, they are not necessarily easy to understand. Take Kepler's Conjecture, for example. It simply states that there is an ultimate way to pack spheres into a box. It has taken centuries of experiments and calculations to show that there are in fact an endless number of ways to do it - and scientists have yet to prove that there is one way which is better than the others. Another great idea is Drake's Equation, which is meant to show that there is a good possibility that there are aliens out there. It is perhaps the least scientific of all the ideas we feature below, but it is also much easier to understand than the rest.

58. Fermat Biography In fact, his most famous work Fermat s Last Theorem remained withouta proof until 1993 when Andrew J. Wiles provided the first proof. http://math.about.com/library/blfermatbio.htm

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Homework Help Mathematics Home ... Math Tutors zau(256,152,145,'gob','http://z.about.com/5/ad/go.htm?gs='+gs,''); Math Help and Tutorials Math Formulas Math Lesson Plans Math Tutors ... Help zau(256,138,125,'el','http://z.about.com/0/ip/417/0.htm','');w(xb+xb); Stay Current Subscribe to the About Mathematics newsletter. Search Mathematics Pierre de Fermat French Number Theorist More Fermat Photos Mathematicians Number Theory Join the Discussion Questions About Fermat? Post Here Forum Membership is Free! Join Today Related Resources Fermat's Last Theorem Proof: Fermat's Theorem Fermat's Proof History of Math Background: P ierre de Fermat (pronounced Fair-mah) was born in Beaumont-de-Lomagne, France in August of 1601 and died in 1665. He is considered to be one of the greatest mathematicians of the seventeenth century. Fermat's father was a leather merchant and his mother's family was in the legal profession. Fermat attended a Franciscan monastery before moving on to obtain a Bachelor's Degree in civil law from the University of Orleans in 1631. He married, had five children and practiced law. For the most part, Math was a hobby for Fermat. Fermat was a busy lawyer and did not let his love of math completely take over his time. It's been said that Fermat never wanted anything to be published as he considered math to be his hobby. The only one thing he did publish - he did so anonymously. He sent many of his papers by mail to some of the best mathematicians in France. It was his link with Marin Mersenne that gave Fermat his international reputation. Fermat loved to dabble in math and rarely provide his proofs (evidence or procedures for reaching conclusions), he would state theorems but neglected the proofs! In fact, his most Famous work 'Fermat's Last Theorem' remained without a proof until 1993 when

59. Three Theorems On Parabolas three theorems on parabolas In the Cartesian plane, pick a point with coordinates (subtle hint!) and construct (1) the set S of segments s joining with the points , and (2) the set B http://rdre1.inktomi.com/click?u=http://planetmath.org/encyclopedia/ThreeTheorem

60. The Role Of Pivoting In Proving Some Fundamental Theorems Of Linear The Role of Pivoting in Proving Some Fundamental theorems of Linear Algebra This paper contains a new approach to some classical theorems of linear algebra (Steinitz, matrix rank, RoucheKronecker http://rdre1.inktomi.com/click?u=http://citeseer.ist.psu.edu/333106.html&y=0

Page 3     41-60 of 93    Back | 1  | 2  | 3  | 4  | 5  | Next 20