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Author: Theo Bühler Publisher: American Mathematical Soc. ISBN: 147044190X Category : Functional analysis Languages : en Pages : 466
Book Description
It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzelà–Ascoli theorem, elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops the three fundamental principles of functional analysis (uniform boundedness, open mapping theorem, Hahn–Banach theorem) and discusses reflexive spaces and the James space. Chapter 3 introduces the weak and weak topologies and includes the theorems of Banach–Alaoglu, Banach–Dieudonné, Eberlein–Šmulyan, Kre&ibreve;n–Milman, as well as an introduction to topological vector spaces and applications to ergodic theory. Chapter 4 is devoted to Fredholm theory. It includes an introduction to the dual operator and to compact operators, and it establishes the closed image theorem. Chapter 5 deals with the spectral theory of bounded linear operators. It introduces complex Banach and Hilbert spaces, the continuous functional calculus for self-adjoint and normal operators, the Gelfand spectrum, spectral measures, cyclic vectors, and the spectral theorem. Chapter 6 introduces unbounded operators and their duals. It establishes the closed image theorem in this setting and extends the functional calculus and spectral measure to unbounded self-adjoint operators on Hilbert spaces. Chapter 7 gives an introduction to strongly continuous semigroups and their infinitesimal generators. It includes foundational results about the dual semigroup and analytic semigroups, an exposition of measurable functions with values in a Banach space, and a discussion of solutions to the inhomogeneous equation and their regularity properties. The appendix establishes the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a one-or-two-semester course on functional analysis for beginning graduate students. Prerequisites are first-year analysis and linear algebra, as well as some foundational material from the second-year courses on point set topology, complex analysis in one variable, and measure and integration.
Author: Theo Bühler Publisher: American Mathematical Soc. ISBN: 147044190X Category : Functional analysis Languages : en Pages : 466
Book Description
It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzelà–Ascoli theorem, elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops the three fundamental principles of functional analysis (uniform boundedness, open mapping theorem, Hahn–Banach theorem) and discusses reflexive spaces and the James space. Chapter 3 introduces the weak and weak topologies and includes the theorems of Banach–Alaoglu, Banach–Dieudonné, Eberlein–Šmulyan, Kre&ibreve;n–Milman, as well as an introduction to topological vector spaces and applications to ergodic theory. Chapter 4 is devoted to Fredholm theory. It includes an introduction to the dual operator and to compact operators, and it establishes the closed image theorem. Chapter 5 deals with the spectral theory of bounded linear operators. It introduces complex Banach and Hilbert spaces, the continuous functional calculus for self-adjoint and normal operators, the Gelfand spectrum, spectral measures, cyclic vectors, and the spectral theorem. Chapter 6 introduces unbounded operators and their duals. It establishes the closed image theorem in this setting and extends the functional calculus and spectral measure to unbounded self-adjoint operators on Hilbert spaces. Chapter 7 gives an introduction to strongly continuous semigroups and their infinitesimal generators. It includes foundational results about the dual semigroup and analytic semigroups, an exposition of measurable functions with values in a Banach space, and a discussion of solutions to the inhomogeneous equation and their regularity properties. The appendix establishes the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a one-or-two-semester course on functional analysis for beginning graduate students. Prerequisites are first-year analysis and linear algebra, as well as some foundational material from the second-year courses on point set topology, complex analysis in one variable, and measure and integration.
Author: Bruce E. Sagan Publisher: American Mathematical Soc. ISBN: 1470460327 Category : Education Languages : en Pages : 304
Book Description
This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.
Author: Srinivasa Ramanujan Aiyangar Publisher: American Mathematical Soc. ISBN: 9780821891254 Category : Mathematics Languages : en Pages : 366
Book Description
The letters that Ramanujan wrote to G. H. Hardy on January 16 and February 27, 1913, are two of the most famous letters in the history of mathematics. These and other letters introduced Ramanujan and his remarkable theorems to the world and stimulated much research, especially in the 1920s and 1930s. This book brings together many letters to, from, and about Ramanujan. The letters came from the National Archives in Delhi, the Archives in the State of Tamil Nadu, and a variety of other sources. Helping to orient the reader is the extensive commentary, both mathematical and cultural, by Berndt and Rankin; in particular, they discuss in detail the history, up to the present day, of each mathematical result in the letters. Containing many letters that have never been published before, this book will appeal to those interested in Ramanujan's mathematics as well as those wanting to learn more about the personal side of his life. Ramanujan: Letters and Commentary was selected for the CHOICE list of Outstanding Academic Books for 1996.
Author: J. M. Landsberg Publisher: American Mathematical Soc. ISBN: 0821869078 Category : Mathematics Languages : en Pages : 464
Book Description
Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.
Author: Sebastián Montiel Publisher: American Mathematical Soc. ISBN: 0821847635 Category : Mathematics Languages : en Pages : 395
Book Description
Offers a focused point of view on the differential geometry of curves and surfaces. This monograph treats the Gauss - Bonnet theorem and discusses the Euler characteristic. It also covers Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature.
Author: Elliott H. Lieb Publisher: American Mathematical Soc. ISBN: 0821827839 Category : Analysis Languages : en Pages : 378
Book Description
This course in real analysis begins with the usual measure theory, then brings the reader quickly to a level where a wider than usual range of topics can be appreciated. Topics covered include Lp- spaces, rearrangement inequalities, sharp integral inequalities, distribution theory, Fourier analysis, potential theory, and Sobolev spaces. To illustrate these topics, there is a chapter on the calculus of variations, with examples from mathematical physics, as well as a chapter on eigenvalue problems (new to this edition). For graduate students of mathematics, and for students of the natural sciences and engineering who want to learn tools of real analysis. Assumes a previous course in calculus. Lieb is affiliated with Princeton University. Loss is affiliated with Georgia Institute of Technology. c. Book News Inc.
Author: David Schultz Publisher: Springer Science & Business Media ISBN: 1935704036 Category : Science Languages : en Pages : 422
Book Description
Mary Grace Soccio. My writing could not please this kindhearted woman, no matter how hard I tried. Although Gifed and Talented seventh-grade math posed no problem for me, the same was not true for Mrs. Soccio’s English class. I was frustrated that my frst assignment only netted me a C. I worked harder, making re- sion afer revision, a concept I had never really put much faith in before. At last, I produced an essay that seemed the apex of what I was capable of wr- ing. Although the topic of that essay is now lost to my memory, the grade I received was not: a B?. “Te best I could do was a B??” Te realization sank in that maybe I was not such a good writer. In those days, my youthful hubris did not understand abouc t apacity bui- ing. In other words, being challenged would result in my intellectual growth— an academic restatement of Nietzsche’s “What does not destroy me, makes me stronger.” Consequently, I asked to be withdrawn from Gifed and Talented English in the eighth grade.
Author: Ken Kundert Publisher: Springer Science & Business Media ISBN: 140208045X Category : Technology & Engineering Languages : en Pages : 281
Book Description
The Verilog Hardware Description Language (Verilog-HDL) has long been the most popular language for describing complex digital hardware. It started life as a prop- etary language but was donated by Cadence Design Systems to the design community to serve as the basis of an open standard. That standard was formalized in 1995 by the IEEE in standard 1364-1995. About that same time a group named Analog Verilog International formed with the intent of proposing extensions to Verilog to support analog and mixed-signal simulation. The first fruits of the labor of that group became available in 1996 when the language definition of Verilog-A was released. Verilog-A was not intended to work directly with Verilog-HDL. Rather it was a language with Similar syntax and related semantics that was intended to model analog systems and be compatible with SPICE-class circuit simulation engines. The first implementation of Verilog-A soon followed: a version from Cadence that ran on their Spectre circuit simulator. As more implementations of Verilog-A became available, the group defining the a- log and mixed-signal extensions to Verilog continued their work, releasing the defi- tion of Verilog-AMS in 2000. Verilog-AMS combines both Verilog-HDL and Verilog-A, and adds additional mixed-signal constructs, providing a hardware description language suitable for analog, digital, and mixed-signal systems. Again, Cadence was first to release an implementation of this new language, in a product named AMS Designer that combines their Verilog and Spectre simulation engines.
Author: Martin Olsson Publisher: American Mathematical Soc. ISBN: 1470427982 Category : Mathematics Languages : en Pages : 313
Book Description
This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.
Author: Theo Bühler
Author: Theo Bühler
Author: Bruce E. Sagan
Author: Srinivasa Ramanujan Aiyangar
Author: J. M. Landsberg
Author: Sebastián Montiel
Author: Elliott H. Lieb
Author: David Schultz
Author: Joseph M. Moran
Author: Ken Kundert
Author: Martin Olsson