Kategoria BISAC: Mathematics >> Geometry - General

Designed for mathematics majors and other students who intend to teach mathematics at the secondary school level, College Geometry: A Unified Development unifies the three classical geometries within an axiomatic framework. The author develops the axioms to include Euclidean, elliptic, and hyperbolic geometry, showing how geometry has real and far-reaching implications. He approaches every topic as a fresh, new concept and carefully defines and explains geometric principles.

The book begins with elementary ideas about points, lines, and distance, gradually...

In questo libro matematica e arte si incontrano, confrontando ed esplorando tre oggetti-concetti: nodi, buchi e spazi. Oggetti fisici e concetti astratti allo stesso tempo, i nodi e i buchi sono strumenti di creazione e generatori di forme: si intrecciano e si compenetrano su piu piani, ridefinendo le configurazioni e le dinamiche dello spazio.

Anche se generalmente non ne siamo consapevoli, nodi e buchi sono onnipresenti, pervadono la nostra vita quotidiana e noi stessi. Queste forme danno luogo a una rigenerazione continua della realta e partecipano al senso del vero e del bello...

Der vorliegende Band wurde fur die Neuauflage von Aloys Krieg, einem Schuler von Herrn Koecher, erganzt und aktualisiert. Wichtigste Erganzungen sind der Spektralsatz fur selbstadjungierte Endomorphismen in euklidischen und unitaren Vektorraumen sowie die Anwendung der Jordanschen Normalform auf Differentialgleichungen. Auch sind neue Ubungsaufgaben hinzugekommen.

Aus den Rezensionen: ..". ein erfreulicher Lichtblick. Ohne die klare theoretische Linie zu verwirren, versteht der Autor Querverbindungen zur Geometrie, Algebra, Zahlentheorie und (Funktional-) Analysis immer wieder...

Das vorliegende Buch gibt eine Einfuhrung in die klassische Integralgeometrie und ihre praktischen Anwendungen in der Stereologie und der Bildrekonstruktion. Daher wird vor allem die elementare zweidimensionale Integralgeometrie und ihre praktisch bedeutsame Verallgemeinerung auf den dreidimensionalen Fall vorgestellt. Inhaltliche Schwerpunkte sind: Grundlagen der Konvexgeometrie, Integralgeometrie und Radon-Transformation. Zahlreiche anschauliche Beispiele und Anwendungen zeigen die grundlegende Bedeutung des Gebietes fur Bildauswertungen in der Biologie, Medizin, Petrographie und...

An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students.

Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related...

From reviews of the first edition:

"In the world of mathematics, the 1980's might well be described as the "decade of the fractal." Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact,...

Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays.

This book covers categories, homological algebra and sheaves in a systematic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond.

The authors present the general theory of categories and functors, emphasising inductive and projective limits, tensor categories, representable functors,...

From the editors of the popular Making Mathematics with Needlework, this book presents projects that highlight the relationship between types of needlework and mathematics. Chapters start with accessible overviews presenting the interplay between mathematical concepts and craft expressions. Following sections explain the mathematics in more detail, and provide suggestions for classroom activities. Each chapter ends with specific crafting instructions. Types of needlework included are knitting, crochet, needlepoint, cross-stitch, quilting, temari balls, beading, tatting, and string...

Der heutige Hochschulunterricht fur Mathematiker grundet meist auf Abstraktion und fuhrt vom Allgemeinen zum Speziellen. Die Methode hat Vorteile, sie starkt das Denkvermogen und meidet lastige Wiederholungen. Doch sie "stellt den Pflug vor die Ochsen," weil Abstraktion auf Spezialfalle baut, die dem Lernenden oft fremd sind. So bleibt der Erfolg den Glucklichen vorbehalten, die den Weg von der Abstraktion zu den Beispielen finden. Dieses Lehrbuch fuhrt von zwei Spezialfallen zur Allgemeinheit und grundet nicht auf Abstraktion. Die Beweise der abstrakten Algebra werden zuerst am konkreten...