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Serge Lang (French:; May 19, 1927 – September 12, 2005) was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra .
Serge Lang published a book Diophantine Geometry in the area in 1962, and by this book he coined the term "Diophantine geometry". [1] The traditional arrangement of material on Diophantine equations was by degree and number of variables , as in Mordell 's Diophantine Equations (1969).
Concerning general linear maps, linear endomorphisms, and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other parts of mathematics.
The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size. The books in this series tend to be written at a more elementary level than the similar Graduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and ...
Introduction to Linear Algebra, Fifth Edition (2016) [21] [22] Differential Equations and Linear Algebra (2014) Differential Equations and Linear Algebra - New Book Website; Essays in Linear Algebra (2012) Algorithms for Global Positioning, with Kai Borre (2012) An Analysis of the Finite Element Method, with George Fix (2008) Computational ...
When T is a compact linear map between two Banach spaces V and W, then the transpose T′ is compact. This can be proved using the Arzelà–Ascoli theorem. When V is a Hilbert space, there is an antilinear isomorphism i V from V onto its continuous dual V′. For every bounded linear map T on V, the transpose and the adjoint operators are ...
Serge Lang gave an extension of the Nullstellensatz to the case of infinitely many generators: Let κ {\textstyle \kappa } be an infinite cardinal and let K {\textstyle K} be an algebraically closed field whose transcendence degree over its prime subfield is strictly greater than κ {\displaystyle \kappa } .
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size (with variable numbers of pages).
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