Symmetry: A Mathematical Exploration by Kristopher Tapp

By Kristopher Tapp

This textbook is ideal for a math path for non-math majors, with the objective of encouraging powerful analytical considering and exposing scholars to dependent mathematical ideas.  It contains many themes ordinarily present in sampler classes, like Platonic solids, Euler’s formulation, irrational numbers, countable units, diversifications, and an explanation of the Pythagorean Theorem.  All of those issues serve a unmarried compelling target: realizing the mathematical styles underlying the symmetry that we notice within the actual global round us.

The exposition is attractive, specified and rigorous.  The theorems are visually inspired with intuitive proofs acceptable for the meant audience.  scholars from all majors will benefit from the many attractive themes herein, and should come to raised delight in the robust cumulative nature of arithmetic as those subject matters are woven jointly right into a unmarried attention-grabbing tale concerning the ways that gadgets might be symmetric.

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Twistors in Mathematics and Physics (London Mathematical by T. N. Bailey,R. J. Baston

By T. N. Bailey,R. J. Baston

Twistor conception has turn into a various topic because it has unfold from its origins in theoretical physics to functions in natural arithmetic. This 1990 choice of assessment articles covers the significant growth made in quite a lot of functions corresponding to relativity, integrable platforms, differential and quintessential geometry and illustration idea. The articles discover the wealth of geometric rules which offer the unifying topics in twistor conception, from Penrose's quasi-local mass development in relativity, to the learn of conformally invariant differential operators, utilizing options of illustration theory.

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Frobenius Algebras and 2-D Topological Quantum Field by Joachim Kock

By Joachim Kock

This 2003 e-book describes a amazing connection among topology and algebra, specifically that second topological quantum box theories are similar to commutative Frobenius algebras. the right formula of the concept and its facts is given by way of monoidal different types, and the most objective of the e-book is to boost those techniques from an straight forward point, and extra in general function an advent to specific viewpoints in arithmetic. instead of simply proving the theory, it truly is proven how the end result matches right into a extra basic trend relating common monoidal different types for algebraic buildings. all through, the emphasis is at the interaction among algebra and topology, with graphical interpretation of algebraic operations, and topological buildings defined algebraically when it comes to turbines and family members. The e-book will turn out necessary to scholars or researchers coming into this box who will examine a number of recent concepts that might end up helpful for destiny work.

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Non-Euclidean Geometries: 581 (Mathematics and Its by András Prékopa,Emil Molnár

By András Prékopa,Emil Molnár

'From not anything i've got created a brand new diversified world,' wrote János Bolyai to his father, Wolgang Bolyai, on November three, 1823, to enable him understand his discovery of non-Euclidean geometry, as we name it this day. the result of Bolyai and the co-discoverer, the Russian Lobachevskii, replaced the process arithmetic, opened the way in which for contemporary actual theories of the 20 th century, and had an influence at the heritage of human tradition. The papers during this quantity, which commemorates the 2 hundredth anniversary of the start of János Bolyai, have been written by way of best scientists of non-Euclidean geometry, its historical past, and its functions. a few of the papers current new discoveries in regards to the lifestyles and works of János Bolyai and the background of non-Euclidean geometry, others care for geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and functions in physics.

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Elementary Differential Geometry by Christian Bär

By Christian Bär

The hyperlink among the actual global and its visualization is geometry. This easy-to-read, generously illustrated textbook provides an uncomplicated advent to differential geometry with emphasis on geometric effects. heading off formalism up to attainable, the writer harnesses uncomplicated mathematical talents in research and linear algebra to unravel fascinating geometric difficulties, which arrange scholars for extra complicated research in arithmetic and different medical fields comparable to physics and desktop technology. the big variety of subject matters contains curve idea, an in depth examine of surfaces, curvature, edition of sector and minimum surfaces, geodesics, round and hyperbolic geometry, the divergence theorem, triangulations, and the Gauss-Bonnet theorem. The part on cartography demonstrates the concrete significance of straight forward differential geometry in purposes. truly built arguments and proofs, color illustrations, and over a hundred routines and suggestions make this publication perfect for classes and self-study. the single must haves are twelve months of undergraduate calculus and linear algebra.

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Mumford-Tate Groups and Domains: Their Geometry and by Mark Green,Phillip A. Griffiths,Matt Kerr

By Mark Green,Phillip A. Griffiths,Matt Kerr

Mumford-Tate teams are the basic symmetry teams of Hodge concept, a subject matter which rests on the heart of latest complicated algebraic geometry. This booklet is the 1st entire exploration of Mumford-Tate teams and domain names. Containing easy conception and a wealth of latest perspectives and effects, it is going to develop into a necessary source for graduate scholars and researchers.

Although Mumford-Tate teams could be outlined for common constructions, their concept and use so far has generally been within the classical case of abelian kinds. whereas the ebook does study this sector, it specializes in the nonclassical case. the final conception seems to be very wealthy, resembling within the unforeseen connections of finite dimensional and endless dimensional illustration idea of actual, semisimple Lie teams. The authors provide the total type of Hodge representations, an issue that are supposed to develop into a customary within the finite-dimensional illustration thought of noncompact, actual, semisimple Lie teams. in addition they point out that during the longer term, a connection turns out able to be made among Lie teams that admit discrete sequence representations and the examine of automorphic cohomology on quotients of Mumford-Tate domain names via mathematics teams. Bringing jointly complicated geometry, illustration thought, and mathematics, this e-book opens up a clean standpoint on a huge subject.

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Geometry II (Universitext) by Marcel Berger,Michael Cole,Silvio Levy

By Marcel Berger,Michael Cole,Silvio Levy

This is the second one of a two-volume textbook that gives a truly readable and full of life presentation of enormous elements of geometry within the classical feel. for every subject the writer offers a theorem that's esthetically enjoyable and simply acknowledged, even supposing the facts might be particularly not easy and hid. one more robust trait of the booklet is that it presents a finished and unified reference resource for the sphere of geometry within the complete breadth of its subfields and ramifications.

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Singularities of the Minimal Model Program (Cambridge Tracts by János Kollár,Sándor Kovács,Sándor Kovács

By János Kollár,Sándor Kovács,Sándor Kovács

This booklet provides a entire therapy of the singularities that seem within the minimum version software and within the moduli challenge for forms. The examine of those singularities and the improvement of Mori's application were deeply intertwined. Early paintings on minimum versions depended on specified research of terminal and canonical singularities yet many later effects on log terminal singularities have been got as effects of the minimum version application. fresh paintings at the abundance conjecture and on moduli of sorts of normal kind depends upon sophisticated houses of log canonical singularities and conversely, the sharpest theorems approximately those singularities use newly built specific situations of the abundance challenge. This ebook untangles those interwoven threads, proposing a self-contained and entire concept of those singularities, together with many formerly unpublished results.

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Das Undenkbare denken: Die Rezeption der nichteuklidischen by Klaus Volkert

By Klaus Volkert

Das Buch behandelt die Rezeptionsgeschichte der nichteuklidischen Geometrie im Zeitraum von 1860 bis 1900. Dabei werden die historischen und institutionellen Rahmenbedingungen dargestellt; breiten Raum nehmen die philosophischen, wissenschaftstheoretischen und didaktischen Diskussionen um die neue Geometrie ein. Zahlreiche Originaltexte - viele davon speedy unbekannt - werden vorgestellt. Ein Fokus liegt auf der Verbreitung der nichteuklidischen Geometrie in breiteren Kreisen wie z. B. der Mathematiklehrerschaft.

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The Geometry of Jet Bundles (London Mathematical Society by D. J. Saunders

By D. J. Saunders

the aim of this publication is to supply an creation to the speculation of jet bundles for mathematicians and physicists who desire to learn differential equations, fairly these linked to the calculus of diversifications, in a latest geometric method. one of many subject matters of the e-book is that first-order jets could be regarded as the traditional generalisation of vector fields for learning variational difficulties in box conception, and such a lot of of the structures are brought within the context of first- or second-order jets, ahead of being defined of their complete generality. The booklet features a evidence of the neighborhood exactness of the variational bicomplex. a data of differential geometry is thought via the writer, even if introductory chapters contain the mandatory historical past of fibred manifolds, and on vector and affine bundles. Coordinate-free suggestions are used all through, even though coordinate representations are usually utilized in proofs and whilst contemplating applications.

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