Princeton Lectures
Author: Princeton University
Publisher:
Published: 1920
Total Pages: 50
ISBN-13:
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Complex Analysis
Author: Elias M. Stein
Publisher: Princeton University Press
Published: 2010-04-22
Total Pages: 398
ISBN-13: 1400831156
DOWNLOAD EBOOKWith this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Neoclassical Finance
Author: Stephen A. Ross
Publisher: Princeton University Press
Published: 2009-04-11
Total Pages: 120
ISBN-13: 1400830206
DOWNLOAD EBOOKNeoclassical Finance provides a concise and powerful account of the underlying principles of modern finance, drawing on a generation of theoretical and empirical advances in the field. Stephen Ross developed the no arbitrage principle, tying asset pricing to the simple proposition that there are no free lunches in financial markets, and jointly with John Cox he developed the related concept of risk-neutral pricing. In this book Ross makes a strong case that these concepts are the fundamental pillars of modern finance and, in particular, of market efficiency. In an efficient market prices reflect the information possessed by the market and, as a consequence, trading schemes using commonly available information to beat the market are doomed to fail. By stark contrast, the currently popular stance offered by behavioral finance, fueled by a number of apparent anomalies in the financial markets, regards market prices as subject to the psychological whims of investors. But without any appeal to psychology, Ross shows that neoclassical theory provides a simple and rich explanation that resolves many of the anomalies on which behavioral finance has been fixated. Based on the inaugural Princeton Lectures in Finance, sponsored by the Bendheim Center for Finance of Princeton University, this elegant book represents a major contribution to the ongoing debate on market efficiency, and serves as a useful primer on the fundamentals of finance for both scholars and practitioners.
Machine Learning in Asset Pricing
Author: Stefan Nagel
Publisher: Princeton University Press
Published: 2021-05-11
Total Pages: 156
ISBN-13: 0691218706
DOWNLOAD EBOOKA groundbreaking, authoritative introduction to how machine learning can be applied to asset pricing Investors in financial markets are faced with an abundance of potentially value-relevant information from a wide variety of different sources. In such data-rich, high-dimensional environments, techniques from the rapidly advancing field of machine learning (ML) are well-suited for solving prediction problems. Accordingly, ML methods are quickly becoming part of the toolkit in asset pricing research and quantitative investing. In this book, Stefan Nagel examines the promises and challenges of ML applications in asset pricing. Asset pricing problems are substantially different from the settings for which ML tools were developed originally. To realize the potential of ML methods, they must be adapted for the specific conditions in asset pricing applications. Economic considerations, such as portfolio optimization, absence of near arbitrage, and investor learning can guide the selection and modification of ML tools. Beginning with a brief survey of basic supervised ML methods, Nagel then discusses the application of these techniques in empirical research in asset pricing and shows how they promise to advance the theoretical modeling of financial markets. Machine Learning in Asset Pricing presents the exciting possibilities of using cutting-edge methods in research on financial asset valuation.
Kurt Gödel
Author: Maria Hämeen-Anttila
Publisher: Springer Nature
Published: 2021-12-15
Total Pages: 133
ISBN-13: 3030872963
DOWNLOAD EBOOKParis of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Gödel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel's incompleteness theorem. Gödel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of the credit of this seeming faux pas going to Gödel. The second is a problem still wide open. Gödel worked on it for years, with no definitive results; The best he could offer was a start with the arithmetic of the entire numbers. This book, Gödel's lectures at the famous Princeton Institute for Advanced Study in 1941, shows how far he had come with Hilbert's second problem, namely to a theory of computable functionals of finite type and a proof of the consistency of ordinary arithmetic. It offers indispensable reading for logicians, mathematicians, and computer scientists interested in foundational questions. It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers. The book also gives insights into the conceptual and formal work that is needed for the solution of profound scientific questions, by one of the central figures of 20th century science and philosophy.
Real Analysis
Author: Elias M. Stein
Publisher: Princeton University Press
Published: 2009-11-28
Total Pages: 423
ISBN-13: 1400835569
DOWNLOAD EBOOKReal Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis:
Fourier Analysis
Author: Elias M. Stein
Publisher: Princeton University Press
Published: 2011-02-11
Total Pages: 326
ISBN-13: 1400831237
DOWNLOAD EBOOKThis first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Princeton Lectures On Biophysics (Volume 1) - Proceedings Of The First Princeton Lectures
Author: William Bialek
Publisher: World Scientific
Published: 1993-03-10
Total Pages: 426
ISBN-13: 9814553301
DOWNLOAD EBOOKMany biological phenomena are especially interesting from a physical point of view, and recent developments have made it possible to perform quantitative, 'physics-style' experiments on many different biological systems. In this volume, composed largely of lectures at a summer workshop for students in 1991, many of those emerging problems in biophysics are surveyed, with emphasis on the confrontation between theory and experiment. The topics range from the structure and dynamics of individual biological molecules to the computational strategies of the nervous system.
Paris-Princeton Lectures on Mathematical Finance 2010
Author: Areski Cousin
Publisher: Springer Science & Business Media
Published: 2011-06-29
Total Pages: 374
ISBN-13: 3642146597
DOWNLOAD EBOOKThe Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.
Investors and Markets
Author: William F. Sharpe
Publisher: Princeton University Press
Published: 2008-07
Total Pages: 231
ISBN-13: 0691138508
DOWNLOAD EBOOK"Nobel Prize-winning financial economist William Sharpe shows that investment professionals cannot make good portfolio choices unless they understand the determinants of asset prices." -- Provided by publisher.
