الصفحة 65
الصفحة 65
A Natural Introduction to Probability Theory
According to Leo Breiman (1968), probability theory has a right and a left hand. The right hand refers to rigorous mathematics, and the left hand refers to ‘pro- bilistic thinking’. The combination of these two aspects makes probability theory one of the most exciting ?elds in mathematics. One can study probability as a purely mathematical enterprise, but even when you do that, all the concepts that arisedo haveameaningontheintuitivelevel.Forinstance,wehaveto de?newhat we mean exactly by independent events as a mathematical concept, but clearly, we all know that when we ?ip a coin twice, the event that the ?rst gives heads is independent of the event that the second gives tails.
A Modern Theory of Factorial Design
Factorial design plays a fundamental role in efficient and economic experimentation with multiple input variables and is extremely popular in various fields of application, including engineering, agriculture, medicine and life sciences. Factorial experiments are often used in case studies in quality management and Design for Six Sigma (DFSS).Factorial design plays a fundamental role in efficient and economic experimentation with multiple input variables and is extremely popular in various fields of application, including engineering, agriculture, medicine and life sciences. Factorial experiments are often used in case studies in quality management and Design for Six Sigma (DFSS).
A Modern Introduction to Probability and Statistics : Understanding Why and How
A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to the students. In addition the book contains over 350 exercises, half of which have answers, of which half have full solutions. A website at www.springeronline.com/1-85233-896-2 gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite for the book is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to useful modern methods such as the bootstrap.
A Mathematical Introduction to Conformal Field Theory
The first part of this book gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. In particular, the conformal groups are determined and the appearance of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. The second part surveys some more advanced topics of conformal field theory, such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.
A History of Physical Theories of Comets, From Aristotle to Whipple
The book describes the major physical theories of comets in the past two millennia. It demonstrates the evolution of ideas about the nature, position, motion and physical constitution of comets from Aristotle to Whipple. Unlike the available works on the history of comets, which either illustrate relatively short periods in the history of physical cometology or portray a landscape view without adequate details, the present study focuses on details of each theory. It also investigates the interaction between observational and mathematical astronomy, and the physical sciences in defining the properties of comets.
A High-Performance Logical Framework -- All About Maude : How to Specify, Program, and Verify Systems in Rewriting Logic
This book gives a comprehensive account of Maude, a language and system based on rewriting logic. Many examples are used throughout the book to illustrate the main ideas and features of Maude, and its many possible uses. Maude modules are rewrite theories. Computation with such modules is - cient deduction by rewriting. Because of its logical basis and its initial model semantics,aMaude module defines a precise mathematical model.This means that Maude and its formal tool environment can be used in three, mutually reinforcing ways: • as a declarative programming language; • as an executable formal specification language; and • as a formal verification system. Maude’s rewriting logic is simple, yet very expressive. This gives Maude good representational capabilities as a semantic framework to formally represent a wide range of systems, including models of concurrency, distributed al- rithms, network protocols, semantics of programming languages, and models of cell biology. Rewriting logic is also an expressive universal logic,making Maude a fiexible logical framework in which many difierent logics and - ference systems can be represented and mechanized. This makes Maude a useful metatool to build many other tools, including those in its own formal tool environment. Thanks to the logic’s simplicity and the use of advanced semi-compilation techniques, Maude has a high-performance implementation, making it competitive with other declarative programming languages.
A Geometry of Approximation : Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns
A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost.
A General introduction to data analytics
A guide to the principles and methods of data analysis that does not require knowledge of statistics or programming. A guide to the reasoning behind data mining techniques. A unique illustrative example that extends throughout all the chapters. Exercises at the end of each chapter and larger projects at the end of each of the text’s two main parts
A Field Guide to Algebra
Focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will hear about equations, both polynomial and differential, and about the algebraic structure of their solutions. In explaining these concepts, the author also provides comments on their historical development and leads the reader along many interesting paths. In addition, there are theorems from analysis: as stated before, the transcendence of the numbers pi and e, the fact that the complex numbers form an algebraically closed field, and also Puiseux's theorem that shows how one can parametrize the roots of polynomial equations, the coefficients of which are allowed to vary. There are exercises at the end of each chapter, varying in degree from easy to difficult. To make the book more lively, the author has incorporated pictures from the history of mathematics, including scans of mathematical stamps and pictures of mathematicians.
A Dressing Method in Mathematical Physics
The monograph is devoted to the systematic presentation of the so called "dressing method" for solving differential equations (both linear and nonlinear) of mathematical physics. The essence of the dressing method consists in a generation of new non-trivial solutions of a given equation from (maybe trivial) solution of the same or related equation.
A Course on Mathematical Logic
This is a short, distinctive, modern, and motivated introduction to mathematical logic for senior undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in knowing what logic is concerned with and who would like to learn Gödel’s incompleteness theorems should find this book particularly convenient. The treatment is thoroughly mathematical, and the entire subject has been approached like a branch of mathematics. Serious efforts have been made to make the book suitable for the classroom as well as for self-reading. The book does not strive to be a comprehensive encyclopedia of logic. Still, it gives essentially all the basic concepts and results in mathematical logic. The book prepares students to branch out in several areas of mathematics related to foundations and computability such as logic, axiomatic set theory, model theory, recursion theory, and computability.
A Course in Derivative Securities : Introduction to Theory and Computation
Aims at a middle ground between the introductory books on derivative securities and those that provide advanced mathematical treatments. It is written for mathematically capable students who have not necessarily had prior exposure to probability theory, stochastic calculus, or computer programming. It provides derivations of pricing and hedging formulas (using the probabilistic change of numeraire technique) for standard options, exchange options, options on forwards and futures, quanto options, exotic options, caps, floors and swaptions, as well as VBA code implementing the formulas. It also contains an introduction to Monte Carlo, binomial models, and finite-difference methods.
A Concise Introduction to Mathematical Logic
This book is unique in that it is more concise than most others; the material is treated in a streamlined fashion. This allows the lecturer to select the material for a one-semester course on a topic more easily. These initial chapters cover just the material for an introductory course on mathematical logic combined with the necessary material from set theory. Chapter 3 is partly of a descriptive nature, providing a view towards decision problems, automated theorem proving, non-standard models and related subjects. The other chapters contain material on logic programming for computer scientists, model theory, recursion theory, Gödel's Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed where appropriate.
A Benchmark Approach to Quantitative Finance
The general framework is used to provide an understanding of the nature of stochastic volatility. The book is intended for a wide audience that includes quantitative analysts, postgraduate students and practitioners in finance, economics and insurance. It aims to be a self-contained, accessible but mathematically rigorous introduction to quantitative finance for readers that have a reasonable mathematical or quantitative background. Finally, the book should stimulate interest in the benchmark approach by describing some of its power and wide applicability.
40 Puzzles and Problems in Probability and Mathematical Statistics
"40 Puzzles and Problems in Probability and Mathematical Statistics" is intended to teach the reader to think probabilistically by solving challenging, non-standard probability problems. The motivation for this clearly written collection lies in the belief that challenging problems help to develop, and to sharpen, our probabilistic intuition much better than plain-style deductions from abstract concepts. The selected problems fall into two broad categories. Problems related to probability theory come first, followed by problems related to the application of probability to the field of mathematical statistics. All problems seek to convey a non-standard aspect or an approach which is not immediately obvious.
25 Years of Model Checking : History, Achievements, Perspectives
Model checking technology is among the foremost applications of logic to computer science and computer engineering. The model checking community has achieved many breakthroughs, bridging the gap between theoretical computer science and hardware and software engineering, and it is reaching out to new challenging areas such as system biology and hybrid systems. Model checking is extensively used in the hardware industry and has also been applied to the verification of many types of software. Model checking has been introduced into computer science and electrical engineering curricula at universities worldwide and has become a universal tool for the analysis of systems.
104 Number Theory Problems : From the Training of the USA IMO Team
This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas, conjectures, and conclusions in writing. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.
103 Trigonometry Problems : From the Training of the USA IMO Team
103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solved using only elementary high school mathematics techniques.
