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Category: Geometry

Download Differential Geometry of Curves and Surfaces: A Concise by Victor A. Toponogov (auth.), Vladimir Y. Rovenski (eds.) PDF

By Victor A. Toponogov (auth.), Vladimir Y. Rovenski (eds.)

The examine of curves and surfaces kinds a major a part of classical differential geometry. Differential Geometry of Curves and Surfaces: A Concise Guide provides conventional fabric during this box in addition to very important principles of Riemannian geometry. The reader is brought to curves, then to surfaces, and eventually to extra complicated issues. commonplace theoretical fabric is mixed with more challenging theorems and intricate difficulties, whereas preserving a transparent contrast among the 2 levels.

Key subject matters and features:

* Covers relevant suggestions together with curves, surfaces, geodesics, and intrinsic geometry

* significant fabric at the Aleksandrov worldwide attitude comparability theorem, which the writer generalized for Riemannian manifolds (a outcome referred to now because the celebrated Toponogov comparability Theorem, one of many cornerstones of recent Riemannian geometry)

* comprises many nontrivial and unique difficulties, a few with tricks and solutions

This rigorous exposition, with well-motivated subject matters, is perfect for complicated undergraduate and first-year graduate scholars trying to input the interesting international of geometry.

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Download The Kinematic Formula in Riemannian Homogeneous Spaces by Ralph Howard PDF

By Ralph Howard

This ebook exhibits that a lot of classical imperative geometry may be derived from the coarea formulation by means of a few hassle-free suggestions. Howard generalizes a lot of classical essential geometry from areas of continuous sectional curvature to arbitrary Riemannian homogeneous areas. to take action, he offers a basic definition of an 'integral invariant' of a submanifold of the gap that's sufficiently common adequate to hide so much circumstances that come up in necessary geometry.Working during this generality makes it transparent that the kind of vital geometric formulation that carry in an area doesn't rely on the total crew of isometries, yet merely at the isotropy subgroup. As a unique case, critical geometric formulation that carry in Euclidean house additionally carry in the entire easily attached areas of continuing curvature. certain proofs of the implications and lots of examples are integrated. Requiring heritage of a one-term direction in Riemannian geometry, this e-book can be utilized as a textbook in graduate classes on differential and indispensable geometry.

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Download The Foundations of Geometry and the Non-Euclidean Plane by George E. Martin (auth.) PDF

By George E. Martin (auth.)

This e-book is a textual content for junior, senior, or first-year graduate classes characteristically titled Foundations of Geometry and/or Non­ Euclidean Geometry. the 1st 29 chapters are for a semester or 12 months path at the foundations of geometry. the rest chap­ ters might then be used for both a typical path or autonomous examine classes. one other probability, that is additionally in particular suited to in-service academics of highschool geometry, is to survey the the basics of absolute geometry (Chapters 1 -20) in a short time and start earnest research with the idea of parallels and isometries (Chapters 21 -30). The textual content is self-contained, other than that the effortless calculus is thought for a few elements of the cloth on complex hyperbolic geometry (Chapters 31 -34). There are over 650 routines, 30 of that are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic improvement of the Euclidean and hyperbolic planes, together with the class of the isometries of those planes, is balanced via the dialogue approximately this improvement. types, corresponding to Taxicab Geometry, are used exten­ sively to demonstrate concept. historic features and possible choices to the chosen axioms are sought after. The classical axiom structures of Euclid and Hilbert are mentioned, as are axiom platforms for 3­ and 4-dimensional absolute geometry and Pieri's method in keeping with inflexible motions. The textual content is split into 3 elements. The advent (Chapters 1 -4) is to be learn as fast as attainable after which used for ref­ erence if necessary.

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Download 103 Trigonometry Problems: From the Training of the USA IMO by Titu Andreescu PDF

By Titu Andreescu

103 Trigonometry Problems comprises highly-selected difficulties and recommendations utilized in the learning and trying out of the us foreign Mathematical Olympiad (IMO) crew. although many difficulties may perhaps at first look impenetrable to the amateur, so much may be solved utilizing merely undemanding highschool arithmetic techniques.

Key features:

* sluggish development in challenge hassle builds and strengthens mathematical abilities and techniques

* easy subject matters comprise trigonometric formulation and identities, their functions within the geometry of the triangle, trigonometric equations and inequalities, and substitutions concerning trigonometric functions

* Problem-solving strategies and techniques, besides useful test-taking options, offer in-depth enrichment and training for attainable participation in quite a few mathematical competitions

* accomplished creation (first bankruptcy) to trigonometric services, their family and useful homes, and their purposes within the Euclidean airplane and reliable geometry disclose complex scholars to varsity point material

103 Trigonometry Problems is a cogent problem-solving source for complicated highschool scholars, undergraduates, and arithmetic lecturers engaged in festival training.

Other books through the authors contain 102 Combinatorial difficulties: From the learning of the united states IMO Team (0-8176-4317-6, 2003) and A route to Combinatorics for Undergraduates: Counting Strategies (0-8176-4288-9, 2004).

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Download Turning Points in the History of Mathematics by Hardy Grant, Israel Kleiner PDF

By Hardy Grant, Israel Kleiner

Offers a complete evaluation of the key turning issues within the heritage of arithmetic, from historical Greece to the present
Substantial reference lists supply feedback for assets to benefit extra concerning the issues discussed
Problems and tasks are incorporated in each one bankruptcy to increase and raise figuring out of the cloth for students
Ideal source for college kids and lecturers of the background of mathematics

This booklet explores the various significant turning issues within the background of arithmetic, starting from historical Greece to the current, demonstrating the drama that has frequently been part of its evolution. learning those breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, might help remove darkness from the significance of the historical past of arithmetic for its instructing, studying, and appreciation.

Some of the turning issues thought of are the increase of the axiomatic strategy (most famously in Euclid), and the following significant adjustments in it (for instance, through David Hilbert); the “wedding,” through analytic geometry, of algebra and geometry; the “taming” of the infinitely small and the infinitely huge; the passages from algebra to algebras, from geometry to geometries, and from mathematics to arithmetics; and the revolutions within the overdue 19th and early 20th centuries that resulted from Georg Cantor’s production of transfinite set idea. The beginning of every turning aspect is mentioned, besides the mathematicians concerned and a few of the maths that resulted. difficulties and tasks are integrated in each one bankruptcy to increase and bring up figuring out of the cloth. large reference lists also are provided.

Turning issues within the heritage of arithmetic could be a worthwhile source for academics of, and scholars in, classes in arithmetic or its background. The ebook must also be of curiosity to an individual with a historical past in arithmetic who needs to
learn extra concerning the very important moments in its development.

History of Mathematics
Mathematics Education
Mathematics within the Humanities and Social Sciences

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Download Edmond Halley’s Reconstruction of the Lost Book of by Michael N. Fried PDF

By Michael N. Fried

Apollonius’s Conics used to be one of many maximum works of complex arithmetic in antiquity. The paintings comprised 8 books, of which 4 have come right down to us of their unique Greek and 3 in Arabic. by the point the Arabic translations have been produced, the 8th e-book had already been misplaced. In 1710, Edmond Halley, then Savilian Professor of Geometry at Oxford, produced an version of the Greek textual content of the Conics of Books I-IV, a translation into Latin from the Arabic types of Books V-VII, and a reconstruction of e-book VIII.

The current paintings presents the 1st entire English translation of Halley’s reconstruction of booklet VIII with supplementary notes at the textual content. It additionally comprises 1) an advent discussing facets of Apollonius’s Conics 2) an research of Edmond Halley's figuring out of the character of his enterprise into historic arithmetic, and three) an appendices giving a quick account of Apollonius’s method of conic sections and his mathematical techniques.

This e-book could be of curiosity to scholars and researchers attracted to the background of old Greek arithmetic and arithmetic within the early sleek period.

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Download Geometry and Symmetry (Dover Books on Advanced Mathematics) by Paul B. Yale PDF

By Paul B. Yale

Designed for advanced undergraduate arithmetic or physics classes, this volume focuses on "practical geometry," emphasizing themes and strategies of maximal use in all components of arithmetic. matters contain algebraic and combinatoric preliminaries, isometries and similarities, an advent to crystallography, fields and vector areas, affine areas, and projective areas. 1968 variation.

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Download The Cauchy Problem for Higher Order Abstract Differential by Ti-Jun Xiao PDF

By Ti-Jun Xiao

The major objective of this booklet is to offer the elemental idea and a few fresh de­ velopments in regards to the Cauchy challenge for larger order summary differential equations u(n)(t) + ~ AiU(i)(t) = zero, t ~ zero, { U(k)(O) = united kingdom, zero ~ okay ~ n-l. the place AQ, Ab . . . , A - are linear operators in a topological vector house E. n 1 Many difficulties in nature might be modeled as (ACP ). for instance, many n preliminary worth or initial-boundary price difficulties for partial differential equations, stemmed from mechanics, physics, engineering, regulate concept, and so forth. , could be trans­ lated into this way through in regards to the partial differential operators within the area variables as operators Ai (0 ~ i ~ n - 1) in a few functionality area E and letting the boundary stipulations (if any) be absorbed into the definition of the distance E or of the area of Ai (this suggestion of treating preliminary price or initial-boundary price difficulties was once stumbled on independently by means of E. Hille and ok. Yosida within the forties). the speculation of (ACP ) is heavily hooked up with many different branches of n arithmetic. consequently, the examine of (ACPn) is critical for either theoretical investigations and useful purposes. during the last part a century, (ACP ) has been studied extensively.

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