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A Course in Operator Theory
Operator theory is a significant part of many important areas of modern mathematics: functional analysis, differential equations, index theory, representation theory, mathematical physics, and more. This text covers the central themes of operator theory, presented with the excellent clarity and style that readers have come to associate with Conway's writing. Early chapters introduce and review material on $C^*$-algebras, normal operators, compact operators, and non-normal operators. Some of the major topics covered are the spectral theorem, the functional calculus, and the Fredholm index. In addition, some deep connections between operator theory and analytic functions are presented. Later c...
A Course in Functional Analysis
This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first graduate course in functional analysis....Many interesting and important applications are included....It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author." --MATHEMATICAL REVIEWS
Complex Analysis
The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) ...
A First Course in Analysis
This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.
A Course in Abstract Analysis
This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. This material can easily be covered in a semester. The second half of the book treats basic functional analysis and can also be covered in a semester. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and C*-algebras. It concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single variable and the elements of metric spaces. Following the author's belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.
A Course in Point Set Topology
This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.
Functions of One Complex Variable
This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - I) arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.
The Verbal Communication of Emotions
This book pulls together new research and theory on the verbal communication of emotions by an international, cross-disciplinary group of recognized experts in affective communication. The book's goal is to provide readers with a comprehensive view of current research and encourage cross-disciplinary interaction. Topics include analyses of literal and figurative expressions for emotions, studies of the use of metaphor and other figurative expressions for emotion, analysis of the role of conversational partners in creating emotional meaning, and the effects of culture on emotional communication. The chapters are organized into three broad areas: background theory, figurative language use, and...
On Being a Department Head, a Personal View
`For years, higher education prospered. It loudly proclaimed that college graduates command far greater lifetime incomes. Ample funding followed. We produced. But that argument has begun to sour. A college degree has long since stopped being a guarantee of prosperity or even job security. Society has begun to question its support for universities. In this environment, mathematicians and all academics must begin to change, compete, and seek resources that will be used with greater care. It is the only solution if we hope to maintain the integrity of the enterprise.... I want to offer advice to department heads out there. I want to try to educate the rank and file about a variety of aspects of the job of being a department head. I also want to tell you my opinion about this job and perhaps also a little about love, death, and the vagaries of the human condition.' --- from the Preface This unique book presents a witty, well-written personal view about the experience of being a department head. Those in academia will profit from the author's inside view, and other department heads and chairs -- new and old -- will benefit from the experiences of this keenly observant colleague.
Broken but Beautiful
American church participation has plummeted in recent decades. Abuse scandals and hypocrisy hang in the air. Weekly, I talk to friends and neighbors who have left church, even as many still identify as Christians. I get what they're saying. When I consider the pain that so many have experienced in church life, the body of Christ sure seems broken. It's no wonder many don't find church to be worth it. But maybe there's more to the story. As a child, my family experienced deep crisis. I felt alone and vulnerable. Into that void, the church stepped in. I discovered a family, a people that have my back and forever changed my life. Even now, I see tangible ways the church works for the common good. The church possesses a resilient beauty that continually pushes through the brokenness. If we love Jesus, we have to eventually ask what Jesus loves. Surprising to me at times, Jesus loves the church, despite her brokenness. If we learn to see what Jesus sees, we'll discover a powerful, often untapped means towards human flourishing. No other social group offers what the church offers. Yes, the church is broken, but there's more. She's beautiful.
