William Wade Dunham (born 1947) is an American writer who was originally trained in topology but became interested in the history of mathematics and specializes in Leonhard Euler. He has received several awards for writing and teaching on this subject. [1]
Dunham received his BS from the University of Pittsburgh in 1969, his MS from Ohio State in 1970, and his PhD from the same institution in 1974. [2]
Dunham won the American Association of Publishers' award for writing the Best Mathematics Book of 1994 for his book The Mathematical Universe. [1] In his book Euler: The Master of Us All, he examines Leonhard Euler's impressive mathematical work. [3] [4] He received a Lester R. Ford Award in 2006 for his expository article Touring the Calculus, [5] and the Chauvenet Prize in 2022 for his article The Early (and Peculiar) History of the Möbius Function. [6]
In 2007, Dunham gave a lecture about Euler's product-sum formula and its relationship to analytic number theory, as well as discussed Euler's evaluation of a non-trivial integral at the celebration of "Year of Euler" by the Euler Society. [7] He published a chapter "Euler and the Fundamental Theorem of Algebra" in the book The Genius of Euler published in 2007 to commemorate the 300th birthday of Euler. [8] [9]
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The number e is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of the natural logarithm function. It is the limit of as n tends to infinity, an expression that arises in the computation of compound interest. It is the value at 1 of the (natural) exponential function, commonly denoted It is also the sum of the infinite series There are various other characterizations; see § Definitions and § Representations.
Leonhard Euler was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus. He introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.
In mathematics, Euler's identity is the equality where
Joseph-Louis Lagrange, also reported as Giuseppe Luigi Lagrange or Lagrangia, was an Italian mathematician, physicist and astronomer, later naturalized French. He made significant contributions to the fields of analysis, number theory, and both classical and celestial mechanics.
Paul Richard Halmos was a Hungarian-born American mathematician and probabilist who made fundamental advances in the areas of mathematical logic, probability theory, operator theory, ergodic theory, and functional analysis. He was also recognized as a great mathematical expositor. He has been described as one of The Martians.
In mathematics education, precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus, thus the name precalculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.
Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series. Many elements of calculus appeared in ancient Greece, then in China and the Middle East, and still later again in medieval Europe and in India. Infinitesimal calculus was developed in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz independently of each other. An argument over priority led to the Leibniz–Newton calculus controversy which continued until the death of Leibniz in 1716. The development of calculus and its uses within the sciences have continued to the present.
The Carus Mathematical Monographs is a monograph series published by the Mathematical Association of America. Books in this series are intended to appeal to a wide range of readers in mathematics and science.
In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by or equivalently where and denote the circumradius and inradius respectively. The theorem is named for Leonhard Euler, who published it in 1765. However, the same result was published earlier by William Chapple in 1746.
The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field. His seminal work had a profound impact in numerous areas of mathematics and he is widely credited for introducing and popularizing modern notation and terminology.
Judith Victor Grabiner is an American mathematician and historian of mathematics, who is Flora Sanborn Pitzer Professor Emerita of Mathematics at Pitzer College, one of the Claremont Colleges. Her main interest is in mathematics in the eighteenth and nineteenth centuries.
This is a timeline of pure and applied mathematics history. It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic" stage, in which comprehensive notational systems for formulas are the norm.
Introductio in analysin infinitorum is a two-volume work by Leonhard Euler which lays the foundations of mathematical analysis. Written in Latin and published in 1748, the Introductio contains 18 chapters in the first part and 22 chapters in the second. It has Eneström numbers E101 and E102.
Carl Gottlieb Ehler is considered a mathematician, specifically due to his post as an astronomer in Berlin. He was mayor of the Prussian capital of Danzig from March 1741 until his death.
Harold Mortimer Edwards, Jr. was an American mathematician working in number theory, algebra, and the history and philosophy of mathematics.
Zero to the power of zero, denoted by 00, is a mathematical expression that is either defined as 1 or left undefined, depending on context. In algebra and combinatorics, one typically defines 00 = 1. In mathematical analysis, the expression is sometimes left undefined. Computer programming languages and software also have differing ways of handling this expression.
Margaret Bunting Wyman Tent, also known by her pen name M. B. W. Tent, was an American mathematics educator and writer. She was the author of several bestselling books.
Daniel "Dan" Simon Kalman is an American mathematician and winner of nine awards for expository writing in mathematics.
