Category: Algebra

By Robert G. Underwood

This article goals to supply graduate scholars with a self-contained advent to subject matters which are on the vanguard of recent algebra, specifically, coalgebras, bialgebras and Hopf algebras. The final bankruptcy (Chapter four) discusses a number of purposes of Hopf algebras, a few of that are additional built within the author’s 2011 book, An advent to Hopf Algebras. The ebook can be utilized because the major textual content or as a supplementary textual content for a graduate algebra direction. necessities for this article contain typical fabric on teams, jewelry, modules, algebraic extension fields, finite fields and linearly recursive sequences.

The ebook involves 4 chapters. bankruptcy 1 introduces algebras and coalgebras over a box ok; bankruptcy 2 treats bialgebras; bankruptcy three discusses Hopf algebras and bankruptcy four comprises 3 functions of Hopf algebras. each one bankruptcy starts off with a quick evaluation and ends with a suite of workouts that are designed to check and toughen the cloth. workouts variety from easy purposes of the idea to difficulties which are devised to problem the reader. Questions for additional research are supplied after chosen routines. such a lot proofs are given intimately, although a number of proofs are passed over in view that they're past the scope of this booklet.

By Catherine Berry

The common language of numbers has allowed contributors to go beyond cultural variations and make collaborative efforts to appreciate the realm mathematically. even though a lot of those mathematicians may perhaps by no means have met the predecessors who made their very own paintings attainable, their collective works shape the rules of arithmetic because it is understood this day. The books during this sequence introduce scholars not just to the theories and formulation that shape the root of every box of arithmetic, yet to the people who devoted their lives to pushing numerical obstacles. exact diagrams offer visible sum.

By G. Shilov

By George Gabriel Stokes

Sir George Stokes (1819-1903) validated the technological know-how of hydrodynamics together with his legislations of viscosity describing the speed of a small sphere via a viscous fluid. He released no books, yet used to be a prolific lecturer and author of papers for the Royal Society, the British organization for the development of technology, the Victoria Institute and different mathematical and clinical associations. those gathered papers (issued among 1880 and 1905) are for this reason the one on hand checklist of the paintings of an exceptional and influential mathematician, who was once Lucasian Professor of arithmetic in Cambridge for over fifty years, grasp of Pembroke university, President of the Royal Society (1885-1890), affiliate Secretary of the Royal fee at the collage of Cambridge and a Member of Parliament for the college.

By Lawvere F.W.

By Kurt-Ulrich Witt

Internet, Soziale Netzwerke, Spiele, Smartphones, DVDs, digitaler Rundfunk und digitales Fernsehen funktionieren nur deshalb, weil zu ihrer Entwicklung und Anwendung mathematisch abgesicherte Verfahren zur Verfügung stehen. Dieses Buch vermittelt Einsichten in grundlegende Konzepte und Methoden der Linearen Algebra, auf denen diese Verfahren beruhen. Am Beispiel fehlertoleranter Codierung wird einführend gezeigt, wie diese Konzepte und Methoden in der Praxis eingesetzt werden, und am Beispiel von Quantenalgorithmen, die möglicherweise in Zukunft eine Rolle spielen, wird deutlich, dass die Lineare Algebra zeitinvariante Konzepte, Methoden und Verfahren bereitstellt, mit denen IT-Technologien konzipiert, implementiert, angewendet und weiterentwickelt werden können. Wegen seiner didaktischen Elemente wie Vorgabe von Lernzielen, Zusammenfassungen, Marginalien und einer Vielzahl von Übungen mit Musterlösungen eignet sich das Buch nicht nur als Begleitlektüre zu entsprechenden Informatik- und Mathematik-Lehrveranstaltungen, sondern insbesondere auch zum Selbststudium.

By Karpfinger C., Kiechle H.

By Garrett P.

By Manfred Stockhausen (auth.)