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Book
When least is best : how mathematicians discovered many clever ways to make things as small (or as large) as possible
Author:
ISBN: 0691220387 9780691218762 Year: 2021 Publisher: Princeton, New Jersey : Princeton University Press,

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Abstract

A mathematical journey through the most fascinating problems of extremes and how to solve them. What is the best way to photograph a speeding bullet? How can lost hikers find their way out of a forest? Why does light move through glass in the least amount of time possible? When Least Is Best combines the mathematical history of extrema with contemporary examples to answer these intriguing questions and more. Paul Nahin shows how life often works at the extremes--with values becoming as small (or as large) as possible--and he considers how mathematicians over the centuries, including Descartes, Fermat, and Kepler, have grappled with these problems of minima and maxima. Throughout, Nahin examines entertaining conundrums, such as how to build the shortest bridge possible between two towns, how to vary speed during a race, and how to make the perfect basketball shot. Moving from medieval writings and modern calculus to the field of optimization, the engaging and witty explorations of When Least Is Best will delight math enthusiasts everywhere.

Keywords

Mathematics --- Maxima and minima. --- MATHEMATICS / History & Philosophy. --- History. --- Minima --- Math --- Science --- AP Calculus. --- Addition. --- Almost surely. --- American Mathematical Monthly. --- Arc (geometry). --- Calculation. --- Cambridge University Press. --- Cartesian coordinate system. --- Catenary. --- Central angle. --- Chain rule. --- Change of variables. --- Circumference. --- Clockwise. --- Convex function. --- Coordinate system. --- Curve. --- Cycloid. --- Cylinder (geometry). --- Derivative. --- Diameter. --- Differential calculus. --- Differential equation. --- Dimension. --- Dynamic programming. --- Elementary function. --- Equation. --- Equilateral triangle. --- Euler–Lagrange equation. --- Fermat's principle. --- Fluxion. --- Geometry. --- Honeycomb conjecture. --- Hyperbolic function. --- Hypotenuse. --- Illustration. --- Inequality of arithmetic and geometric means. --- Instant. --- Integer. --- Isoperimetric problem. --- Iteration. --- Jensen's inequality. --- Johann Bernoulli. --- Kinetic energy. --- Length. --- Line (geometry). --- Line segment. --- Linear programming. --- Logarithm. --- Mathematical maturity. --- Mathematical problem. --- Mathematician. --- Mathematics. --- Newton's method. --- Notation. --- Parabola. --- Parametric equation. --- Partial derivative. --- Perimeter. --- Philosopher. --- Physicist. --- Pierre de Fermat. --- Polygon. --- Polynomial. --- Potential energy. --- Princeton University Press. --- Projectile. --- Pumping station. --- Pythagorean theorem. --- Quadratic equation. --- Quadratic formula. --- Quantity. --- Ray (optics). --- Real number. --- Rectangle. --- Refraction. --- Refractive index. --- Regiomontanus. --- Requirement. --- Result. --- Right angle. --- Right triangle. --- Science. --- Scientific notation. --- Second derivative. --- Semicircle. --- Sign (mathematics). --- Simple algebra. --- Simplex algorithm. --- Snell's law. --- Special case. --- Square root. --- Summation. --- Surface area. --- Tangent. --- Trigonometric functions. --- Variable (mathematics). --- Vertex angle. --- Writing.


Book
The new era in American mathematics, 1920-1950
Author:
ISBN: 0691233810 Year: 2022 Publisher: Princeton : Princeton University Press,

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Abstract

As the Roaring Twenties lurched into the Great Depression, to be followed by the scourge of Nazi Germany and World War II, American mathematicians pursued their research, positioned themselves collectively within American science, and rose to global mathematical hegemony. How did they do it? This book explores the institutional, financial, social, and political forces that shaped and supported this community in the first half of the 20th century. In doing so, Karen Hunger Parshall debunks the widely held view that American mathematics only thrived after European émigrés fled to the shores of the United States.

Keywords

Mathematics --- HISTORY / United States / 20th Century. --- MATHEMATICS / History & Philosophy. --- Research. --- Research --- History --- United States. --- Math --- Science --- Mathematical research --- ABŞ --- ABSh --- Ameerika Ühendriigid --- America (Republic) --- Amerika Birlăshmish Shtatlary --- Amerika Birlăşmi Ştatları --- Amerika Birlăşmiş Ştatları --- Amerika ka Kelenyalen Jamanaw --- Amerika Qūrama Shtattary --- Amerika Qŭshma Shtatlari --- Amerika Qushma Shtattary --- Amerika (Republic) --- Amerikai Egyesült Államok --- Amerikanʹ Veĭtʹsėndi︠a︡vks Shtattnė --- Amerikări Pĕrleshu̇llĕ Shtatsem --- Amerikas Forenede Stater --- Amerikayi Miatsʻyal Nahangner --- Ameriketako Estatu Batuak --- Amirika Carékat --- AQSh --- Ar. ha-B. --- Arhab --- Artsot ha-Berit --- Artzois Ha'bris --- Bí-kok --- Ē.P.A. --- EE.UU. --- Egyesült Államok --- ĒPA --- Estados Unidos --- Estados Unidos da América do Norte --- Estados Unidos de América --- Estaos Xuníos --- Estaos Xuníos d'América --- Estatos Unitos --- Estatos Unitos d'America --- Estats Units d'Amèrica --- Ètats-Unis d'Amèrica --- États-Unis d'Amérique --- Fareyniḳṭe Shṭaṭn --- Feriene Steaten --- Feriene Steaten fan Amearika --- Forente stater --- FS --- Hēnomenai Politeiai Amerikēs --- Hēnōmenes Politeies tēs Amerikēs --- Hiwsisayin Amerikayi Miatsʻeal Tērutʻiwnkʻ --- Istadus Unidus --- Jungtinės Amerikos valstybės --- Mei guo --- Mei-kuo --- Meiguo --- Mî-koet --- Miatsʻyal Nahangner --- Miguk --- Na Stàitean Aonaichte --- NSA --- S.U.A. --- SAD --- Saharat ʻAmērikā --- SASht --- Severo-Amerikanskie Shtaty --- Severo-Amerikanskie Soedinennye Shtaty --- Si︠e︡vero-Amerikanskīe Soedinennye Shtaty --- Sjedinjene Američke Države --- Soedinennye Shtaty Ameriki --- Soedinennye Shtaty Severnoĭ Ameriki --- Soedinennye Shtaty Si︠e︡vernoĭ Ameriki --- Spojené obce severoamerické --- Spojené staty americké --- SShA --- Stadoù-Unanet Amerika --- Stáit Aontaithe Mheiriceá --- Stany Zjednoczone --- Stati Uniti --- Stati Uniti d'America --- Stâts Unîts --- Stâts Unîts di Americhe --- Steatyn Unnaneysit --- Steatyn Unnaneysit America --- SUA (Stati Uniti d'America) --- Sŭedineni amerikanski shtati --- Sŭedinenite shtati --- Tetã peteĩ reko Amérikagua --- U.S. --- U.S.A. --- United States of America --- Unol Daleithiau --- Unol Daleithiau America --- Unuiĝintaj Ŝtatoj de Ameriko --- US --- USA --- Usono --- Vaeinigte Staatn --- Vaeinigte Staatn vo Amerika --- Vereinigte Staaten --- Vereinigte Staaten von Amerika --- Verenigde State van Amerika --- Verenigde Staten --- VS --- VSA --- Wááshindoon Bikéyah Ałhidadiidzooígíí --- Wilāyāt al-Muttaḥidah --- Wilāyāt al-Muttaḥidah al-Amirīkīyah --- Wilāyāt al-Muttaḥidah al-Amrīkīyah --- Yhdysvallat --- Yunaeted Stet --- Yunaeted Stet blong Amerika --- ZDA --- Združene države Amerike --- Zʹi︠e︡dnani Derz︠h︡avy Ameryky --- Zjadnośone staty Ameriki --- Zluchanyi︠a︡ Shtaty Ameryki --- Zlucheni Derz︠h︡avy --- ZSA --- Η.Π.Α. --- Ηνωμένες Πολιτείες της Αμερικής --- Америка (Republic) --- Американь Вейтьсэндявкс Штаттнэ --- Америкӑри Пӗрлешӳллӗ Штатсем --- САЩ --- Съединените щати --- Злучаныя Штаты Амерыкі --- ولايات المتحدة --- ولايات المتّحدة الأمريكيّة --- ولايات المتحدة الامريكية --- 미국 --- États-Unis --- É.-U. --- ÉU --- Academia Sinica. --- Acta Arithmetica. --- Aftermath of World War II. --- American Association of Physics Teachers. --- American Council on Education. --- American Institute of Physics. --- American Journal of Mathematics. --- American Mathematical Monthly. --- American Mathematical Society. --- American Statistical Association. --- Analytic continuation. --- Annals of Mathematical Statistics. --- Annals of Mathematics. --- Annals of Science. --- Applied mathematics. --- Bulletin of the American Mathematical Society. --- Chancellor (education). --- Characterization (mathematics). --- Complex number. --- Connecticut College. --- Division algebra. --- Duke Mathematical Journal. --- Edward R. Murrow. --- Estimation theory. --- Euclidean space. --- European Mathematical Society. --- Fourier series. --- Fundamenta Mathematicae. --- Georg Cantor. --- Hilbert's fifth problem. --- Hyperbolic partial differential equation. --- Ideal (ring theory). --- International Congress of Mathematicians. --- Intersection theory. --- Introduction to general relativity. --- John von Neumann. --- Joint Policy Board for Mathematics. --- London Mathematical Society. --- Mathematical Association of America. --- Mathematical physics. --- Mathematical table. --- Mathematician. --- Mathematics. --- Methoden der mathematischen Physik. --- Minkowski space. --- National Council of Teachers of Mathematics. --- National Defense Research Committee. --- National Science Board. --- New Century. --- New Direction (think tank). --- New Math. --- New York Public Library. --- New York University Press. --- New York University. --- Nucleic acid sequence. --- Number theory. --- Patrician (ancient Rome). --- Physicist. --- Polish Academy of Sciences. --- Prime number theorem. --- Probability and statistics. --- Projection (mathematics). --- Purdue University. --- Pure mathematics. --- Quaternion algebra. --- Richard Dedekind. --- Riemann hypothesis. --- Riemannian geometry. --- Selective Training and Service Act of 1940. --- Semisimple algebra. --- Spectral theorem. --- Statistician. --- The Herald-Sun (Durham, North Carolina). --- Theoretical physics. --- Theory. --- Undergraduate degree. --- University of Notre Dame. --- Washington University in St. Louis. --- Whitney embedding theorem. --- Word problem (mathematics education). --- World war.

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