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Kilmer S: An Introduction to Point-Set
Topology

An Introduction to Point-Set Topology

This book, the 15th of 15 related monographs on Cubic Dynamic Systems, discusses crossing and product cubic systems with a crossing-linear and self-quadratic product vector field. The author discusses series of singular equilibriums and hyperbolic-to-hyperbolic-scant flows that are switched through the hyperbolic upper-to-lower saddles and parabola-saddles and circular and hyperbolic upper-to-lower saddles infinite-equilibriums. Series of simple equilibrium and paralleled hyperbolic flows are also discussed, which are switched through inflection-source (sink) and parabola-saddle infinite-equilibriums. Nonlinear dynamics and singularity for such crossing and product cubic systems are presented. In such cubic systems, the appearing bifurcations are: parabola-saddles, hyperbolic-to-hyperbolic-secant flows, third-order saddles (centers) and parabola-saddles (saddle-center).&nbsp;&nbsp;<ul><li>Develops a theory of crossing and product cubic systems with a crossing-linear and self-quadratic product vector field;</li><li>Presents equilibrium series with hyperbolic-to-hyperbolic-scant flows and with paralleled hyperbolic flows;</li><li>Shows equilibrium series switching bifurcations by up-down hyperbolic upper-to-lower saddles, parabola-saddles, et al.</li></ul>

Crossing-linear and Self-quadratic Product Vector Field

Two-dimensional Crossing and Product Cubic Systems, Vol. II

Dedicated to Valentin Poénaru

Essays on Topology

Differential algebra explores properties of solutions of systems of (ordinary or partial, linear or non-linear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration and symmetry analysis of differential equations. These proceedings consist of tutorial and survey papers presented at the Second International Workshop on Differential Algebra and Related Topics at Rutgers University, Newark in April 2007. As a sequel to the proceedings of the First International Workshop, this volume covers more related subjects, and provides a modern and introductory treatment to many facets of differential algebra, including surveys of known results, open problems, and new, emerging, directions of research. It is therefore an excellent companion and reference text for graduate students and researchers.

Differential Algebra and Related Topics II

Calculus for the Curious

Get the whole story on fractions Fractions are one of the toughest concepts to master for young mathematicians. Fractions For Dummies makes it easier, with clear explanations, step-by-step solutions, and plenty of example problems-including word problems and tips on how to solve them. You'll also explore the world of decimals and percentages, and you'll learn how all these concepts are related. Students who understand fractions can cook, budget, tip at restaurants, and succeed in their future math learning. Make fractions a piece of pie with this Dummies guide! Inside... <ul><li>Basic math operations with fractions</li> <li>Clear, easy explanations</li> <li>Tips for solving word problems</li> <li>Convert between fractions, decimals, and percents</li> <li>Working with mixed numbers</li> <li>New fraction strategies being taught in schools</li></ul>

Fractions For Dummies

Weight representations are representations that include many important examples studied by both mathematicians and physicists. Using a combination of algebraic, geometric, and combinatorial methods, description of various classes (simple and indecomposable) of representations is provided in the book. The book serves advanced graduate students and junior researchers who work in the field of representation theory of Lie algebras.

Weight Representations

The Mending of Broken Bones reveals that far from a set of mundane exercises, algebra is the delicate craft of untangling numerical puzzles to uncover the hidden patterns and surprising behaviors of the numbers themselves. As Paul Lockhart shows, you don't have to be a mathematician to experience the joy and creativity of mathematical discovery.

A Modern Guide to Classical Algebra

The Mending of Broken Bones

Problem Solving in Mathematics and Beyond

"Geometry is often seen as one of the most beautiful aspects of mathematics. This beauty is probably a result of the fact that one can "see" this aspect of mathematics. Most people are exposed to the very basic elements of geometry throughout their schooling, concentrated in the secondary school curriculum. High schools in the United States offer one year of concentrated geometry teaching, allowing students to observe how a mathematician functions, since everything that is accepted beyond the basic axioms must be proved. However, as the course is only one year long, a great amount of geometry remains to be exposed to the general audience. That is the challenge of this book, wherein we will present a plethora of amazing geometric relationships. We begin with the special relationship of the Golden Ratio, before considering unexpected concurrencies and collinearities. Next, we present some surprising results that arise when squares and similar triangles are placed on triangle sides, followed by a discussion of concyclic points and the relationship between circles and various linear figures. Moving on to more advanced aspects of linear geometry, we consider the geometric wonders of polygons. Finally, we address geometric surprises and fallacies, before concluding with a chapter on the useful concept of homothety, which is not included in the American year-long course in geometry"--

Journey Through The Wonders Of Plane Geometry, A

These lecture notes offer a general overview of a two-dimensional topological field theory called the Poisson Sigma Model. It is based on a series of talks given by the author at the University of California, Berkeley and the University of Massachusetts, Amherst in the fall of 2018 and the spring of 2019. This book contains an introduction to symplectic, Poisson and graded geometry, the path space construction for Lie algebroids via the reduced phase space of the Poisson Sigma Model, and the Cattaneo-Felder interpretation of Kontsevich's star product via Feynman diagrams. It also describes in detail particular cases of the Poisson Sigma Model, including constant, linear (2-dimensional BF-theory) and quadratic Poisson structures. The target audience of this book is graduate students and researchers with an interest in the mathematical aspects of classical and quantum field theory. No prior exposure to physics or Poisson geometry is required.

Introduction To The Poisson Sigma Model, An

Signal processing is ubiquitous in many fields of science and engineering. This textbook is tailored specifically for graduate students and presents linear algebra, which is requisite knowledge in these fields, in a form explicitly targeted to signal processing and related disciplines. Written by an experienced author with over 35 years of expertise in signal processing research and teaching, this book provides the necessary foundation in a focused and accessible manner, offering a practical approach to linear algebra without sacrificing rigor. Emphasis is placed on a deeper conceptualization of material specific to signal processing so students may more readily adapt this knowledge to actual problems in the field. Since other emerging areas, such as machine learning, are closely related to signal processing, the book also provides the necessary background in this discipline. The book includes many examples and problems relevant to signal processing, offering explanations and insights that are difficult to find elsewhere.Fundamentals of Linear Algebra for Signal Processing&nbsp;will allow students to master the essential knowledge of linear algebra for signal processing. It is also an essential guide for researchers and practitioners in biomedical, electrical, chemical engineering, and related disciplines.<ul><li>All necessary algebraic concepts commonly used in the signal processing context are covered;</li><li>A rich set of carefully-constructed signal processing examples is provided throughout the text;</li><li>Designed as a primary text in linear algebra for engineering and science graduate students.</li></ul>

Signal processing is ubiquitous in many fields of science and engineering. This textbook is tailored specifically for graduate students and presents linear algebra, which is requisite knowledge in these fields, in a form explicitly targeted to signal processing and related disciplines. Written by an experienced author with over 35 years of expertise in signal processing research and teaching, this book provides the necessary foundation in a focused and accessible manner, offering a practical approach to linear algebra without sacrificing rigor. Emphasis is placed on a deeper conceptualization of material specific to signal processing so students may more readily adapt this knowledge to actual problems in the field. Since other emerging areas, such as machine learning, are closely related to signal processing, the book also provides the necessary background in this discipline. The book includes many examples and problems relevant to signal processing, offering explanations and insights that are difficult to find elsewhere.Fundamentals of Linear Algebra for Signal Processing&nbsp;will allow students to master the essential knowledge of linear algebra for signal processing. It is also an essential guide for researchers and practitioners in biomedical, electrical, chemical engineering, and related disciplines.

Fundamentals of Linear Algebra for Signal Processing

This book covers computational group theory (CGT), an active, rapidly expanding field at the interface of mathematics and computer science. It is the first systematic effort to establish computing with infinite matrix groups on the same footing as the rest of CGT. The book emphasizes practical methods based on results of linear group theory, solutions of fundamental algorithmic problems, and provision of software. Additionally, the book sets out a research program to make further progress in the area.

This book covers computational group theory (CGT), an active, rapidly expanding field at the interface of mathematics and computer science. It is the first systematic effort to establish computing with infinite matrix groups on the same footing as the rest of CGT. The book emphasizes practical methods based on results of linear group theory, solutions of fundamental algorithmic problems, and provision of software. Additionally, the book sets out a research program to make further progress in the area.

Linear Groups and Computation

Dieses Lese‐, Lern‐ und Nachschlagebuch stellt die Mathematik von den Basics bis zur Analysis anhand zentraler Fragen übersichtlich auf Einzelseiten dar.
Es ist für alle geschrieben,

die Mathe verstehen wollen oder müssen,
die das Wesentliche auf einen Blick finden wollen,
die visuell denken,
die nur das lesen wollen, was sie gerade brauchen.

Besonders an dem Buch ist,

dass jede Seite eine zentrale Frage behandelt und in sich abgeschlossen ist,
dass ich so schreibe, wie ich es dir mündlich erklären würde,
dass ich alles mithilfe möglichst einfacher Beispiele erkläre,
dass du links eine Erklärung findest und direkt rechts dazu Beispiele,
dass ich ganz am Anfang anfange, sodass du vorab nichts wissen musst.

Behandelt werden ganz grundlegende, aber auch fortgeschrittene Fragen – etwa:

Wie erweiterst und kürzt du Brüche?
Was bedeutet „genau dann, wenn“?
…
Wie bestimmst du die Ableitung der Umkehrfunktion?
Wann ist eine Funktion uneigentlich integrierbar?

Für die 3. Auflage wurde das Buch weiter optimiert und um zusätzliche Themen ergänzt. Nun kannst du es gut parallel zu einem Vorkurs oder Brückenkurs lesen. Es wird dir gefallen,

wenn du Schulstoff wiederholen willst,
wenn du dich auf die Mathematik im Studium vorbereiten willst, oder
wenn du dich einfach für Mathe interessierst.

Mit 130 ergänzenden Fragen und Antworten in der Springer-Nature-Flashcards-App kannst du dich spielerisch mit dem Stoff beschäftigen und deinen Lernerfolg überprüfen.
Die Autorin
Adriane Gründers (Pseudonym) hat in mathematischer Physik promoviert und ist in einem wissenschaftsnahen Unternehmen tätig. Die Vermittlung von Mathematik ist ihr ein Herzensanliegen. Sie ist fest davon überzeugt, dass viel mehr Menschen die Mathematik verstehen und dabei Freude haben können, als dies derzeit der Fall ist. Hierzu möchte das Buch einen Beitrag leisten.

Dieses Lese‐, Lern‐ und Nachschlagebuch stellt die Mathematik von den Basics bis zur Analysis anhand zentraler Fragen übersichtlich auf Einzelseiten dar.Es ist für alle geschrieben,<ul><li>die Mathe verstehen wollen oder müssen,</li><li>die das Wesentliche auf einen Blick finden wollen,</li><li>die visuell denken,</li><li>die nur das lesen wollen, was sie gerade brauchen.</li></ul>Besonders an dem Buch ist,<ul><li>dass jede Seite eine zentrale Frage behandelt und in sich abgeschlossen ist,</li><li>dass ich so schreibe, wie ich es dir mündlich erklären würde,</li><li>dass ich alles mithilfe möglichst einfacher Beispiele erkläre,</li><li>dass du links eine Erklärung findest und direkt rechts dazu Beispiele,</li><li>dass ich ganz am Anfang anfange, sodass du vorab nichts wissen musst.</li></ul>Behandelt werden ganz grundlegende, aber auch fortgeschrittene Fragen – etwa:<ul><li>Wie erweiterst und kürzt du Brüche?</li><li>Was bedeutet „genau dann, wenn“?</li><li>…</li><li>Wie bestimmst du die Ableitung der Umkehrfunktion?</li><li>Wann ist eine Funktion uneigentlich integrierbar?</li></ul>Für die 3. Auflage wurde das Buch weiter optimiert und um zusätzliche Themen ergänzt. Nun kannst du es gut parallel zu einem Vorkurs oder Brückenkurs lesen. Es wird dir gefallen,<ul><li>wenn du Schulstoff wiederholen willst,</li><li>wenn du dich auf die Mathematik im Studium vorbereiten willst, oder</li><li>wenn du dich einfach für Mathe interessierst.</li></ul>Mit 130 ergänzenden Fragen und Antworten in der Springer-Nature-Flashcards-App kannst du dich spielerisch mit dem Stoff beschäftigen und deinen Lernerfolg überprüfen.

240 Themen zum Nachlesen und Verstehen auf jeweils einer Seite

Mathe übersichtlich: Von den Basics bis zur Analysis

An Introduction to Point-Set Topology

Bibliografische Angaben

Schlagworte

Bibliografische Angaben

Schlagworte

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