This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book." --MATHSCINET
This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable, the level being gauged for graduate students. It treats several topics in geometric function theory as well as potential theory in the plane, covering in particular: conformal equivalence for simply connected regions, conformal equivalence for finitely connected regions, analytic covering maps, de Branges' proof of the Bieberbach conjecture, harmonic functions, Hardy spaces on the disk, potential theory in the plane. A knowledge of integration theory and functional analysis is assumed.
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
This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book." --MATHSCINET
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 chapters cover more advanced topics, such as representations of $C^*$-algebras, compact perturbations, and von Neumann algebras. Major results, such as the Sz.-Nagy Dilation Theorem, the Weyl-von Neumann-Berg Theorem, and the classification of von Neumann algebras, are covered, as is a treatment of Fredholm theory. The last chapter gives an introduction to reflexive subspaces, which along with hyperreflexive spaces, are one of the more successful episodes in the modern study of asymmetric algebras. Professor Conway's authoritative treatment makes this a compelling and rigorous course text, suitable for graduate students who have had a standard course in functional analysis.
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.
`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.
This book illustrates connections between various courses taken by undergraduate mathematics majors. As such it can be used as a text for a capstone course. The chapters are essentially independent, and the instructor can choose the topics that will form the course and thus tailor the syllabus to suit the backgrounds and abilities of the students. At the end of such a course the graduating seniors should glimpse mathematics not as a series of independent courses but as something more like an integrated body of knowledge. The book has numerous exercises and examples so that the student has many opportunities to see the material illustrated and fleshed out.
In a certain sense, subnormal operators were introduced too soon because the theory of function algebras and rational approximation was also in its infancy and could not be properly used to examine the class of operators. The progress in the last several years grew out of applying the results of rational approximation." from the Preface. This book is the successor to the author's 1981 book on the same subject. In addition to reflecting the great strides in the development of subnormal operator theory since the first book, the present work is oriented towards rational functions rather than polynomials. Although the book is a research monograph, it has many of the traits of a textbook including exercises. The book requires background in function theory and functional analysis, but is otherwise fairly self-contained. The first few chapters cover the basics about subnormal operator theory and present a study of analytic functions on the unit disk. Other topics included are: some results on hypernormal operators, an exposition of rational approximation interspersed with applications to operator theory, a study of weak-star rational approximation, a set of results that can be termed structure theorems for subnormal operators, and a proof that analytic bounded point evaluations exist.
Let [script lowercase]f be any analytic function defined in a neighborhood of the non-empty set [italic]E and let [script]S([italic]E) denote the set of all operator having spectrum included in [italic]E. In this paper the closure and interior of the set [script lowercase]f([script]S([italic]E)) [identical equality] {[script lowercase]f([italic]A): [italic]A [set membership] [script]S([italic]E)} are characterized. Some applications serve to illustrate the interplay between the analyticity of the functions and the spectral behavior of the operators.
Let S be a subnormal operator on a Hilbert space [script]H with minimal normal extension [italic]N operating on [italic]K, and let [lowercase Greek]Mu be a scalar valued spectral measure for [italic]N. If [italic]P[infinity symbol]([lowercase Greek]Mu) denotes the weak star closure of the polynomials in [italic]L[infinity symbol]([lowercase Greek]Mu) = [italic]L1[infinity symbol]([lowercase Greek]Mu) then for [script]f in [italic]P[infinity symbol]([lowercase Greek]Mu) it follows that [script]f([italic]N) leaves [script]H invariant; if [script]f([italic]S) is defined as the restriction of [script]f([italic]N) to [script]H then a functional calculus for [italic]S is obtained. This functional calculus is investigated in this paper.
In this wide-ranging study of the politics of memory in Northern Ireland, Brian Conway examines the 'career' of the commemoration of Bloody Sunday, and looks at how and why the way this historic event is remembered has undergone change over time. Drawing on original empirical data, he provides new insights into the debate on collective memory.
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 fascinating multidisciplinary cultural analysis of the figure of Bolívar that will be uniquely useful to those attempting to grapple with the influence of this figure on the Latin American imagination. Conway's persuasive and subtle analyses of historical, literary, and visual sources demonstrate how the authoritative image of Bolívar was constructed, appropriated, and contested from the independence period through the present."--Mary Beth Tierney-Tello, Wheaton College The Cult of Bolívar explores the Latin American cult of Simón Bolívar in modern literature through a broad array of texts that include fiction, children's literature, poetry, journalism, and presidential speeches. The image of Simón Bolívar (1783-1830) has been central to debates about Latin American identity since the 19th century and has been continually readapted to address current problems. This study examines the interplay of myth and disillusionment in modern representations of Bolívar. After outlining the emergence of the Cult of Bolívar during the Wars of Independence and the early national period, Christopher Conway uses novels to frame in-depth discussions of issues central to Bolivarian nationalism: the deification of the hero, monuments and iconoclasm, fatherhood and sexuality, and the promise and failure of modernity. This interdisciplinary study argues that representations of Bolívar trace the difficult and often contradictory processes by which nationalism imagines its past, present, and future. In addition to original archival research about the rise of Bolivarian nationalism in the 19th century and literary analyses of key novels such as Gabriel García Márquez's The General in His Labyrinth, Conway includes discussions of contemporary Latin American art and presidential politics. He utilizes gender studies and a broad spectrum of Bolivariana to frame our understanding of different aspects of hero worship. Also covered are controversial representations of Bolívar that resulted in public outcries in Latin America, such as Juan Dávila's hermaphroditic painting of Simón Bolívar and Denzil Romero's pornographic novel about Bolívar's mistress, Manuela Sáenz. Christopher B. Conway is assistant professor of Hispanic studies at Brown University. He is the editor of Peruvian Traditions by Ricardo Palma (2003) and has published articles on Latin American literature in Hispanic Review, Revista de Crítica Literaria, Latinoamericana, and other international journals.
In fact, Saskatchewan students now pay significantly higher tuition and fees than do most students in the U. S. The average tuition and other fees at public four-year universities in the United States this year are shown in Table 2. The average tuition and additional compulsory fees at Saskatchewan's three universities, $5,526, are higher than tuition and fees in three of the six regions in the U. [...] Tuition and fees in each of the various colleges/faculties at U of S and U of R are shown in Table 3. Tuition fees in Dentistry at the U of S are the highest in Canada. [...] Revenue for capital projects at the U of S has increased at an average rate of 60% in each of the years from 1999-00 to 2003-04, amounting to a total of $45.8 million in 2003-04, according to the annual U of S financial statements. [...] The majority of this funding comes from the province, though the construction of the CLS synchrotron at the U of S has resulted in large increases in federal contributions. [...] Thus, while total provincial funding for universities has increased over the past decade more in Saskatchewan than in other provinces, a significant portion of the increase in the past five years has been for research and capital expenses, and not for the operation of educational programs at the universities.
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