This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation. Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily-understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics. Topics are addressed in the context of familiar objects; easily-understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity. ELEMENTARY CONCEPTS. Numbers, Sets and Functions. Language and Proofs. Properties of Functions. Induction. PROPERTIES OF NUMBERS. Counting and Cardinality. Divisibility. Modular Arithmetic. The Rational Numbers. DISCRETE MATHEMATICS. Combinatorial Reasoning. Two Principles of Counting. Graph Theory. Recurrence Relations. CONTINUOUS MATHEMATICS. The Real Numbers. Sequences and Series. Continuity. Differentiation. Integration. The Complex Numbers. For anyone interested in learning how to understand and write mathematical proofs, or a reference for college professors and high school teachers of mathematics.

Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)

Science & Math

West, Douglas B.

D’Angelo, John P.

Mathematics

Pearson

Developing logical thinking and fundamental mathematical ideas, and using problems that pique students' mathematical curiosity, this work aims to prepare readers for all upper-division mathematics courses and improve their skills in presenting coherent arguments.

Mathematical Thinking: Problem-Solving and Proofs

West, Douglas Brent

PRENTICE/HALL

Several Complex Variables and the Geometry of Real Hypersurfaces (Studies in Advanced Mathematics)

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved). Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.

Routledge

CRC-Press

Linear and Complex Analysis for Applications (Advances in Applied Mathematics)

Linear and Complex Analysis for Applications aims to unify various parts of mathematical analysis in an engaging manner and to provide a diverse and unusual collection of applications, both to other fields of mathematics and to physics and engineering. The book evolved from several of the author's teaching experiences, his research in complex analysis in several variables, and many conversations with friends and colleagues. It has three primary goals: <ul> <li>to develop enough linear analysis and complex variable theory to prepare students in engineering or applied mathematics for advanced work,</li> <li style="list-style: none"> </li> </ul> <ul> <li>to unify many distinct and seemingly isolated topics,</li> <li style="list-style: none"> </li> </ul> <ul> <li>to show mathematics as both interesting and useful, especially via the juxtaposition of examples and theorems.</li> <li style="list-style: none"> </li> </ul> The book realizes these goals by beginning with reviews of Linear Algebra, Complex Numbers, and topics from Calculus III. As the topics are being reviewed, new material is inserted to help the student develop skill in both computation and theory. The material on linear algebra includes infinite-dimensional examples arising from elementary calculus and differential equations. Line and surface integrals are computed both in the language of classical vector analysis and by using differential forms. Connections among the topics and applications appear throughout the book. The text weaves abstract mathematics, routine computational problems, and applications into a coherent whole, whose unifying theme is linear systems. It includes many unusual examples and contains more than 450 exercises.

This integrated book begins by discussing Fourier series, Hilbert spaces and the Fourier transform on the real line, and then turns to the heart of the text, geometric considerations. The concept of orthogonality weaves the material into a coherent whole.

Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry (Cornerstones)

Birkhauser

Linear and Complex Analysis for Applications aims to unify various parts of mathematical analysis in an engaging manner and to provide a diverse and unusual collection of applications, both to other fields of mathematics and to physics and engineering. The book evolved from several of the author’s teaching experiences, his research in complex analysis in several variables, and many conversations with friends and colleagues. It has three primary goals: <ol>
<li>to develop enough linear analysis and complex variable theory to prepare students in engineering or applied mathematics for advanced work,</li> <li>to unify many distinct and seemingly isolated topics,</li> <li>to show mathematics as both interesting and useful, especially via the juxtaposition of examples and theorems.</li> </ol> The book realizes these goals by beginning with reviews of Linear Algebra, Complex Numbers, and topics from Calculus III. As the topics are being reviewed, new material is inserted to help the student develop skill in both computation and theory. The material on linear algebra includes infinite-dimensional examples arising from elementary calculus and differential equations. Line and surface integrals are computed both in the language of classical vector analysis and by using differential forms. Connections among the topics and applications appear throughout the book. The text weaves abstract mathematics, routine computational problems, and applications into a coherent whole, whose unifying theme is linear systems. It includes many unusual examples and contains more than 450 exercises.

This textbook provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric considerations. This chapter includes complex differential forms, geometric inequalities from one and several complex variables, and includes some of the author's original results. The concept of orthogonality weaves the material into a coherent whole. This textbook will be a useful resource for upper-undergraduate students who intend to continue with mathematics, graduate students interested in analysis, and researchers interested in some basic aspects of Cauchy-Riemann (CR) geometry. The inclusion of several hundred exercises makes this book suitable for a capstone undergraduate Honors class. This second edition contains a significant amount of new material, including a new chapter dedicated to the CR geometry of the unit sphere. This chapter builds upon the first edition by presenting recent results about groups associated with CR sphere maps. From reviews of the first edition: The present book developed from the teaching experiences of the author in several honors courses. …. All the topics are motivated very nicely, and there are many exercises, which make the book ideal for a first-year graduate course on the subject. …. The style is concise, always very neat, and proofs are given with full details. Hence, I certainly suggest this nice textbook to anyone interested in the subject, even for self-study. Fabio Nicola, Politecnico di Torino, Mathematical Reviews D’Angelo has written an eminently readable book, including excellent explanations of pretty nasty stuff for even the more gifted upper division players .... It certainly succeeds in hooking the present browser: I like this book a great deal. Michael Berg, Loyola Marymount University, Mathematical Association of America

<div>This monograph systematically explores the theory of rational maps between spheres in complex Euclidean spaces and its connections to other areas of mathematics.&nbsp; Synthesizing research from the last forty years, the author aims for accessibility by balancing abstract concepts with concrete examples.&nbsp; Numerous computations are worked out in detail, and more than 100 optional exercises are provided throughout for readers wishing to better understand challenging material.</div> <div> </div> The text begins by presenting core concepts in complex analysis and a wide variety of results about rational sphere maps.&nbsp; The subsequent chapters discuss combinatorial and optimization results about monomial sphere maps, groups associated with rational sphere maps, relevant complex and CR geometry, and some geometric properties of rational sphere maps.&nbsp; Fifteen open problems appear in the final chapter, with references provided to appropriate parts of the text. These problems will encourage readers to apply the material to future research. <div> </div> <div>Rational Sphere Maps will be of interest to researchers and graduate students studying several complex variables and CR geometry.&nbsp; Mathematicians from other areas, such as number theory, optimization, and combinatorics, will also find the material appealing.</div> <div> </div> <div>See the author's research web page for a list of typos, clarifications, etc.: https://faculty.math.illinois.edu/~jpda/research.html </div>

Rational Sphere Maps (Progress in Mathematics, 341)

See the best price to sell, buy, or rent books by D’Angelo, John P.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by D’Angelo, John P.

See the best price to sell, buy, or rent books by D’Angelo, John P.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)

Mathematical Thinking: Problem-Solving and Proofs

Several Complex Variables and the Geometry of Real Hypersurfaces (Studies in Advanced Mathematics)

Several Complex Variables and the Geometry of Real Hypersurfaces (Studies in Advanced Mathematics)

Linear and Complex Analysis for Applications (Advances in Applied Mathematics)

Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry (Cornerstones)

Linear and Complex Analysis for Applications (Advances in Applied Mathematics)

Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry (Cornerstones)

Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry (Cornerstones)

Rational Sphere Maps (Progress in Mathematics, 341)