By D. Wang

ISBN-10: 3211832416

ISBN-13: 9783211832417

By D. Wang

ISBN-10: 3211832416

ISBN-13: 9783211832417

the improvement of polynomial-elimination ideas from classical idea to trendy algorithms has passed through a tortuous and rugged course. this is saw L. van der Waerden's removing of the "elimination conception" bankruptcy from from B. his vintage sleek Algebra in later variations, A. Weil's wish to cast off "from algebraic geometry the final lines of removal theory," and S. Abhyankar's sug gestion to "eliminate the eliminators of removing conception. " The renaissance and popularity of polynomial removing owe a lot to the arrival and strengthen of mod ern computing know-how, according to which powerful algorithms are applied and utilized to diversified difficulties in technological know-how and engineering. within the final decade, either theorists and practitioners have increasingly more learned the importance and tool of removal tools and their underlying theories. lively and broad examine has contributed loads of new advancements on algorithms and smooth ware instruments to the topic, which were largely stated. Their functions have taken position from natural and utilized arithmetic to geometric modeling and robotics, and to man made neural networks. This publication presents a scientific and uniform remedy of removing algo rithms that compute numerous 0 decompositions for structures of multivariate poly nomials. The principal thoughts are triangular units and structures of alternative types, by way of which the decompositions are represented. the must haves for the innovations and algorithms are effects from simple algebra and a few wisdom of algorithmic mathematics.

By Alexey Stakhov,Samuil Aranson,Scott Olsen

ISBN-10: 9814678295

ISBN-13: 9789814678292

This designated booklet overturns our principles approximately non-Euclidean geometry and the fine-structure consistent, and makes an attempt to resolve long-standing mathematical difficulties. It describes a normal thought of "recursive" hyperbolic features in keeping with the "Mathematics of Harmony," and the "golden," "silver," and different "metallic" proportions. Then, those theories are used to derive an unique option to Hilbert's Fourth challenge for hyperbolic and round geometries. in this trip, the publication describes the "golden" qualitative thought of dynamical platforms in line with "metallic" proportions. eventually, it provides an answer to a Millennium challenge through constructing the Fibonacci specific thought of relativity as an unique physical-mathematical resolution for the fine-structure consistent. it really is meant for a large viewers who're attracted to the heritage of arithmetic, non-Euclidean geometry, Hilbert's mathematical difficulties, dynamical structures, and Millennium Problems.

**Contents:**

- The Golden Ratio, Fibonacci Numbers, and the "Golden" Hyperbolic Fibonacci and Lucas Functions
- The arithmetic of concord and common thought of Recursive Hyperbolic Functions
- Hyperbolic and round strategies of Hilbert's Fourth challenge: find out how to the Recursive Non-Euclidean Geometries
- Introduction to the "Golden" Qualitative thought of Dynamical structures according to the math of Harmony
- The uncomplicated phases of the Mathematical method to the Fine-Structure consistent challenge as a actual Millennium Problem
- Appendix: From the "Golden" Geometry to the Multiverse

**Readership:** complicated undergraduate and graduate scholars in arithmetic and theoretical physics, mathematicians and scientists of other specializations drawn to historical past of arithmetic and new mathematical ideas.

By Leonid Ryvkin

ISBN-10: 3658123893

ISBN-13: 9783658123895

Leonid Ryvkin provides a prompted and self-sustained

introduction to n-plectic geometry with a different specialize in symmetries. The

relevant algebraic buildings from scratch are built. the writer generalizes

known symplectic notions, particularly observables and symmetries, to the n-plectic

case, culminating in fixing the life query for co-moment maps for

general pre-n-plectic manifolds. ultimately partial effects scattered alongside the

literature are derived from our basic result.

By Matthias Kreck,Wolfgang Lück

ISBN-10: 3764371412

ISBN-13: 9783764371418

These lecture notes include a guided travel to the Novikov Conjecture and similar conjectures because of Baum-Connes, Borel and Farrell-Jones. they start with fundamentals approximately better signatures, Whitehead torsion and the s-Cobordism Theorem. Then an advent to surgical procedure thought and a model of the meeting map is gifted. utilizing the answer of the Novikov conjecture for exact teams a few functions to the category of low dimensional manifolds are given.

By Mohammed Hichem Mortad

ISBN-10: 9814583812

ISBN-13: 9789814583817

The booklet bargains an exceptional creation to topology via solved routines. it really is more often than not meant for undergraduate scholars. such a lot workouts are given with certain solutions.

**Contents:**

*Exercises and Solutions:*- General Notions: units, features et al.
- Metric Spaces
- Topological Spaces
- Continuity and Convergence
- Compact Spaces
- Connected Spaces
- Complete Metric Spaces
- Function Spaces

**Readership:** Undergraduate scholars and academics in topology.

By Harald Scheid,Wolfgang Schwarz

ISBN-10: 3662503220

ISBN-13: 9783662503225

Das Buch richtet sich an Studierende in Lehramtsstudiengängen aller Schulstufen sowie an Lehrende des Faches Mathematik. Es enthält den fachwissenschaftlichen Hintergrund der Geometrie des aktuellen Mathematikunterrichts einschließlich rechnerischer Methoden, streift aber auch zahlreiche darüber hinausführende Themen wie die Geometrie der komplexen Zahlen, die sphärische Trigonometrie, die Graphentheorie, endliche Geometrien und Modelle nichteuklidischer Geometrien. Zahlreiche Anwendungsbeispiele und ca. three hundred Aufgaben mit Lösungen machen das Buch zu einer effektiven Arbeitsgrundlage.

Die vorliegende five. Auflage ist vollständig überarbeitet. Inhaltlich wurde der Themenkreis Bandornamente ausgebaut, und das Thema projektive Geometrie wurde neu aufgenommen.

Stimme zum Buch:

„Ein vielseitiges Buch, das alle Facetten der Elementargeometrie aufgreift und Bezüge aufzeigt. Geeignet, den Horizont zu erweitern und zum Studieren und Entdecken anzuregen.“ *Prof. Dr. Andreas Filler, Humboldt-Universität Berlin *

By Lev Bukovský

ISBN-10: 3034800053

ISBN-13: 9783034800051

ISBN-10: 3034803214

ISBN-13: 9783034803212

The swift improvement of set thought within the final fifty years, customarily by way of acquiring lots of independence effects, strongly stimulated an knowing of the constitution of the genuine line. This e-book is dedicated to the research of the genuine line and its subsets taking into consideration the hot result of set thought. each time attainable the presentation is finished with out the entire axiom of selection. because the ebook is meant to be self-contained, all important result of set thought, topology, degree thought, and descriptive set concept are revisited with the aim of doing away with superfluous use of an axiom of selection. The duality of degree and classification is studied in a close demeanour. numerous statements referring to homes of the genuine line are proven to be undecidable in set conception. The metamathematics in the back of set idea is presently defined within the appendix. each one part features a sequence of routines with extra results.

By Yu.G. Reshetnyak,E. Primrose,V.N. Berestovskij,I.G. Nikolaev

ISBN-10: 3642081258

ISBN-13: 9783642081255

This ebook comprises surveys on smooth study into non-regular Riemannian geometry, performed often by way of Russian mathematicians. insurance examines two-dimensional Riemannian manifolds of bounded curvature and metric areas whose curvature lies among given constants. This ebook might be immensely worthy to graduate scholars and researchers in geometry, specifically Riemannian geometry.

By Magnus J. Wenninger

ISBN-10: 048640921X

ISBN-13: 9780486409214

ISBN-10: 0521222796

ISBN-13: 9780521222792

Well-illustrated, functional method of growing star-faced round kinds that could function simple constructions for geodesic domes. entire directions for making versions from round bands of paper with only a ruler and compass. Discusses tessellation, or tiling, and the way to make round types of the semiregular solids and concludes with a dialogue of the connection of polyhedra to geodesic domes and instructions for development types of domes. ". . . very friendly reading." — *Science.* 1979 edition.

By Izrail M. Gelfand,Mikhail Kapranov,Andrei Zelevinsky

ISBN-10: 0817636609

ISBN-13: 9780817636609

ISBN-10: 0817647708

ISBN-13: 9780817647704

"This e-book revives and greatly expands the classical idea of resultants and discriminants. many of the major new result of the e-book were released previous in additional than a dozen joint papers of the authors. The booklet well enhances those unique papers with many examples illustrating either previous and new result of the theory."—**Mathematical Reviews**