Notions of Convexity by Lars Hörmander

By Lars Hörmander

The first chapters of this booklet are dedicated to convexity within the classical experience, for services of 1 and several other genuine variables respectively. this offers a history for the research within the following chapters of similar notions which take place within the idea of linear partial differential equations and intricate research similar to (pluri-)subharmonic services, pseudoconvex units, and units that are convex for helps or singular helps with appreciate to a differential operator. furthermore, the convexity stipulations that are suitable for neighborhood or international lifestyles of holomorphic differential equations are mentioned, best as much as Trépreau’s theorem on sufficiency of (capital Greek letter Psi) for microlocal solvability within the analytic category.

At the start of the publication, no necessities are assumed past calculus and linear algebra. afterward, easy proof from distribution thought and sensible research are wanted. In a number of areas, a extra wide heritage in differential geometry or pseudodifferential calculus is needed, yet those sections might be bypassed without lack of continuity. the most important a part of the booklet may still hence be available to graduate scholars in order that it will probably function an creation to advanced research in a single and a number of other variables. The final sections, despite the fact that, are written typically for readers conversant in microlocal analysis.

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Dirac Operators in Riemannian Geometry by Thomas Friedrich

By Thomas Friedrich

For a Riemannian manifold $M$, the geometry, topology and research are interrelated in ways in which are largely explored in smooth arithmetic. Bounds at the curvature may have major implications for the topology of the manifold. The eigenvalues of the Laplacian are certainly associated with the geometry of the manifold. For manifolds that admit spin (or $\textrm{spin}^\mathbb{C}$) constructions, one obtains extra details from equations concerning Dirac operators and spinor fields. in terms of four-manifolds, for instance, one has the amazing Seiberg-Witten invariants. during this textual content, Friedrich examines the Dirac operator on Riemannian manifolds, specifically its reference to the underlying geometry and topology of the manifold. The presentation contains a evaluate of Clifford algebras, spin teams and the spin illustration, in addition to a overview of spin constructions and $\textrm{spin}^\mathbb{C}$ buildings. With this starting place validated, the Dirac operator is outlined and studied, with unique recognition to the instances of Hermitian manifolds and symmetric areas. Then, convinced analytic homes are confirmed, together with self-adjointness and the Fredholm estate. a massive hyperlink among the geometry and the research is equipped by means of estimates for the eigenvalues of the Dirac operator when it comes to the scalar curvature and the sectional curvature. issues of Killing spinors and suggestions of the twistor equation on $M$ bring about effects approximately no matter if $M$ is an Einstein manifold or conformally resembling one. eventually, in an appendix, Friedrich offers a concise advent to the Seiberg-Witten invariants, that are a robust device for the examine of four-manifolds. there's additionally an appendix reviewing important bundles and connections. This designated booklet with dependent proofs is acceptable as a textual content for classes in complex differential geometry and international research, and will function an creation for extra research in those parts. This variation is translated from the German variation released by way of Vieweg Verlag.

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The Story of Euclid by W.b. Frankland

By W.b. Frankland

The publication has no illustrations or index. it can have various typos or lacking textual content. even though, buyers can obtain a unfastened scanned reproduction of the unique infrequent ebook from the publisher's web site (GeneralBooksClub.com). you may as well preview excerpts of the e-book there. dealers also are entitled to a loose trial club within the normal Books membership the place they could make a choice from greater than one million books for free of charge. unique writer: London, G. Newnes, restricted; book date: 1902; matters: Geometry; Euclid's parts; Euclid's parts; arithmetic / Geometry / common; arithmetic / background

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Poncelet's Theorem by Leopold Flatto

By Leopold Flatto

Poncelet's theorem is a recognized bring about algebraic geometry, courting to the early a part of the 19th century. It matters closed polygons inscribed in a single conic and circumscribed approximately one other. the concept is of significant intensity in that it pertains to a wide and numerous physique of arithmetic. There are numerous proofs of the theory, none of that's straightforward. a very appealing function of the concept, that is simply understood yet tricky to turn out, is that it serves as a prism during which it is easy to study and savour loads of attractive arithmetic. The author's unique examine in queuing conception and dynamical structures figures prominently within the publication. This ebook stresses the trendy method of the topic and includes a lot fabric no longer formerly to be had in booklet shape. It additionally discusses the relation among Poncelet's theorem and a few points of queueing conception and mathematical billiards. The facts of Poncelet's theorem provided during this e-book relates it to the speculation of elliptic curves and exploits the truth that such curves are endowed with a gaggle constitution. The publication additionally treats the true and degenerate instances of Poncelet's theorem. those circumstances are fascinating in themselves, and their proofs require another issues. the true case is dealt with via applying notions from dynamical structures. the fabric during this booklet may be comprehensible to a person who has taken the traditional classes in undergraduate arithmetic. to accomplish this, the writer has incorporated within the ebook initial chapters facing projective geometry, Riemann surfaces, elliptic capabilities, and elliptic curves. The publication additionally includes a variety of figures illustrating quite a few geometric thoughts.

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Geometry in Ancient and Medieval India by T. A. Saraswati Amma

By T. A. Saraswati Amma

This booklet is a geometric survey of the Sanskrit and Prakrt clinical and quasi-scientific literature and finishing with the early a part of the seventeenth century. The paintings seeks to blow up the speculation that the Indian mathematical genius used to be predominantly genius was once predominantly algebraic and computational and that's eschewed proofs and rationales.

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The Pythagorean Theorem. Crown Jewel of Mathematics by John C. Sparks

By John C. Sparks

The Pythagorean Theorem, Crown Jewel of arithmetic is a common creation to the Pythagorean Theorem and its many functions all through arithmetic. The e-book encompasses a historic improvement of the Pythagorean Theorem through a chain of proofs that bring up in sophistication as centuries development. additionally in the publication are chapters addressing mathematical spinoffs together with trigonometry, puzzles, and interests.

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Viewpoints : mathematical perspective and fractal geometry by Marc Frantz

By Marc Frantz

An undergraduate textbook dedicated completely to relationships among arithmetic and artwork, Viewpoints is splendid for math-for-liberal-arts classes and arithmetic classes for positive arts majors. The textbook incorporates a wide selection of classroom-tested actions and difficulties, a chain of essays by way of modern artists written particularly for the ebook, and a plethora of pedagogical and studying possibilities for teachers and students.

Viewpoints makes a speciality of mathematical parts: point of view concerning drawing man-made types and fractal geometry relating to drawing average varieties. Investigating points of the 3-dimensional international for you to comprehend mathematical thoughts at the back of the paintings, the textbook explores paintings issues together with comedian, anamorphic, and classical artwork, in addition to images, whereas proposing such mathematical rules as percentage, ratio, self-similarity, exponents, and logarithms. trouble-free difficulties and profitable suggestions empower scholars to make actual, subtle drawings. own essays and brief biographies by means of modern artists are interspersed among chapters and are observed by way of photographs in their paintings. those wonderful artists--who comprise mathematicians and scientists--examine how arithmetic impacts their artwork. obtainable to scholars of all degrees, Viewpoints encourages experimentation and collaboration, and captures the essence of creative and mathematical production and discovery.

  • Classroom-tested actions and challenge fixing
  • Accessible difficulties that flow past ordinary artwork university curriculum
  • Multiple suggestions of various trouble and applicability
  • Appropriate for college students of all arithmetic and paintings degrees
  • Original and particular essays through modern artists
  • Forthcoming: Instructor's guide (available in basic terms to teachers)

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