"The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory... reading is fluid and very pleasant... style is informal but far from being imprecise." -review of the first edition. New to this edition: additional applications of the theory and techniques, as well as several new proofs. This book is ideal for self-study for mathematicians and students interested in geometric and algebraic topology, functional analysis, differential equations, and applied mathematics.

800x600 Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} Smarandache Geometries as generalizations of Finsler, Riemannian, Weyl, and Kahler Geometries. A Smarandache geometry (SG) is a geometry which has at least one smarandachely denied axiom (1969). An axiom is said smarandachely denied (S-denied) if in the same space the axiom behaves differently (i.e., validated and invalided; or only invalidated but in at least two distinct ways). Thus, as a particular case, Euclidean, Lobachevsky-Bolyai-Gauss, and Riemannian geometries may be united altogether, in the same space, by some SGs. These last geometries can be partially Euclidean and partially non-Euclidean. The novelty of the SG is the fact that they introduce for the first time the degree of negation in geometry, similarly to the degree of falsehood in fuzzy or neutrosophic logic. For example an axiom can be denied in percentage of 30 Also SG are defined on multispaces, i.e. unions of Euclidean and non-Euclidean subspaces, or unions of distinct non-Euclidean spaces. As an example of S-denying, a proposition , which is the conjunction of a set i of propositions, can be invalidated in many ways if it is minimally unsatisfiable, that is, such that the conjunction of any proper subset of the i is satisfied in a structure, but itself is not. Here it is an example of what it means for an axiom to be invalidated in multiple ways [2] : As a particular axiom let's take Euclid's Fifth Postulate. In Euclidean or parabolic geometry a line has one parallel only through a given point. In Lobacevskian or hyperbolic geometry a line has at least two parallels through a given point. In Riemannian or elliptic geometry a line has no parallel through a given point. Whereas in Smarandache geometries there are lines which have no parallels through a given point and other lines which have one or more parallels through a given point (the fifth postulate is invalidated in many ways). Therefore, the Euclid's Fifth Postulate (which asserts that there is only one parallel passing through an exterior point to a given line) can be invalidated in many ways, i.e. Smarandachely denied, as follows: - first invalidation: there is no parallel passing through an exterior point to a given line; - second invalidation: there is a finite number of parallels passing through an exterior point to a given line; - third invalidation: there are infinitely many parallels passing through an exterior point to a given line.

Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side. This text acts as an introduction to the subject.

Diese Einfuhrung in das Gebiet der metrischen Raume richtet sich in erster Linie nicht an Spezialisten, sondern an Anwender der Methode aus den verschiedensten Bereichen der Naturwissenschaften. Besonders ausfuhrlich und anschaulich werden die Grundlagen von metrischen Raumen und Banach-Raumen erklart, Anhange enthalten Informationen zu verschiedenen Schlusselkonzepten der Mengentheorie (Zornsches Lemma, Tychonov-Theorem, transfinite Induktion usw.). Die hinteren Kapitel des Buches beschaftigen sich mit fortgeschritteneren Themen.

Introduction to Problem-based Learning teaches students how to work with the problem-based learning method, which requires mainly self-directed learning. Particular attention is given to the necessary skills to apply this method effectively. Why Introduction to Problem-based Llearning? • comprehensible introduction in the problem-based learning method • enables students to experience the full potential of this concept • discusses the use of digital devices Introduction to Problem-based learning provides students with the necessary skills to operate within as well as outside problem-based groups. It discusses issues like: How do you take on a problem? How do you collaborate with others? How do you deal with cultural diversity? How do you lead a tutorial group? How can you organize your studies best? Special attention is given to the use of computers, tablets and internet in a problem-based environment.

The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.

An accessible introduction to real analysis and its connection to elementary calculus Bridging the gap between the development and history of real analysis, Introduction to Real Analysis: An Educational Approach presents a comprehensive introduction to real analysis while also offering a survey of the field. With its balance of historical background, key calculus methods, and hands-on applications, this book provides readers with a solid foundation and fundamental understanding of real analysis. The book begins with an outline of basic calculus, including a close examination of problems illustrating links and potential difficulties. Next, a fluid introduction to real analysis is presented, guiding readers through the basic topology of real numbers, limits, integration, and a series of functions in natural progression. The book moves on to analysis with more rigorous investigations, and the topology of the line is presented along with a discussion of limits and continuity that includes unusual examples in order to direct readers' thinking beyond intuitive reasoning and on to more complex understanding. The dichotomy of pointwise and uniform convergence is then addressed and is followed by differentiation and integration. Riemann-Stieltjes integrals and the Lebesgue measure are also introduced to broaden the presented perspective. The book concludes with a collection of advanced topics that are connected to elementary calculus, such as modeling with logistic functions, numerical quadrature, Fourier series, and special functions. Detailed appendices outline key definitions and theorems in elementary calculus and also present additional proofs, projects, and sets in real analysis. Each chapter references historical sources on real analysis while also providing proof-oriented exercises and examples that facilitate the development of computational skills. In addition, an extensive bibliography provides additional resources on the topic. Introduction to Real Analysis: An Educational Approach is an ideal book for upper- undergraduate and graduate-level real analysis courses in the areas of mathematics and education. It is also a valuable reference for educators in the field of applied mathematics.

The land between the Mediterranean Sea and the Jordan Valley has been one of the most disputed territories in history. Since the establishment of the state of Israel in 1948, Palestinians and Israelis have each sought claim to the national identity of the land through various martial, social and scientific tactics, but no method has offered as much legitimacy and national controversy as that of the map. The Politics of Maps delves beneath the battlefield to unearth the cartographic strife behind the Israel/Palestine conflict. Blending science and technology studies, sociology, and geography with a host of archival material, in-depth interviews and ethnographies, this book explores how the geographical sciences came to be entangled with the politics, territorial claim-making, and nation-state building of Israel/Palestine. Chapters chart the cartographic history of the region, from the introduction of Western scientific and legal paradigms that seemingly legitimized and depoliticized new land regimes to the rise of new mapping technologies and software that expanded access to cartography into the public sphere. Maps produced by various sectors like the "peace camps" or the Jewish community enhanced national belonging, while others, like that of the Green Line, served largely to divide. The stories of Israel's many boundaries reveal that there is no absolute, technocratic solution to boundary-making. As boundaries continue to be controversial and the Israeli-Palestinian conflict remains intractable and unresolved, The Politics of Maps uses nationally-based cartographic discourses to provide insight into the complexity, fissures and frictions within internal political debates, illuminating the persistent power of the nation-state as a framework for forging identities, citizens, and alliances.

Our space age technology enables global communication, navigation, and power distribution that has given rise to our 'smart', interconnected and spacefaring world. Much of the infrastructure modern society depends on, to live on Earth and to explore space, is susceptible to space weather storms originating from the Sun. The Second Edition of this introductory textbook is expanded to reflect our increased understanding from more than a dozen scientific missions over the past decade. Updates include discussions of the rapidly expanding commercial space sector, orbital debris and collision hazards, our understanding of solar-terrestrial connections to climate, and the renewed emphasis of human exploration of the Moon and Mars. It provides new learning features to help students understand the science and solve meaningful problems, including some based on real-world data. Each chapter includes learning objectives and supplements that provide descriptions of the science and learning strategies to help students and instructors alike.

Digital knowledge maps are ‘at a glance’ visual representations that enable enriching, imaginative and transformative ways for teaching and learning, with the potential to enhance positive educational outcomes. The use of such maps has generated much attention and interest among tertiary education practitioners and researchers over the last few years as higher education institutions around the world begin to invest heavily into new technologies designed to provide online spaces within which to build resources and conduct activities. The key elements of this edited volume will comprise original and innovative contributions to existing scholarship in this field, with examples of pedagogical possibilities as they are currently practiced across a range of contexts. It will contain chapters that address, theory, research and practical issues related to the use of digital knowledge maps in all aspects of tertiary education and draws predominantly on international perspectives with a diverse group of invited contributors. Reports on empirical studies as well as theoretical/conceptual chapters that engage deeply with pertinent questions and issues raised from a pedagogical, social, cultural, philosophical, and/or ethical standpoint are included. Systematic literature reviews dealing with digital knowledge mapping in education are also an integral part of the volume.