Applied mathematics Books

Book SynopsisBasic Statistics for Social Research offers an introduction to core general statistical concepts and methods. It covers procedural aspects of the application of statistical methods for data-description; and hypothesis-testing; distributions, tabulations, central tendency, variability, independence, correlation and regression.Table of ContentsTables and Figures ix Preface xv About the Authors xix Part I Univariate Description 1 Chapter 1 Using Statistics 3 Why Study Statistics? 4 Tasks for Statistics: Describing, Inferring, Testing, Predicting 4 Statistics in the Research Process 9 Basic Elements of Research: Units of Analysis and Variables 14 Chapter 2 Displaying One Distribution 25 Summarizing Variation in One Variable 26 Frequency Distributions for Nominal Variables 26 Frequency Distributions for Ordinal Variables 32 Frequency Distributions for Interval/Ratio Variables 38 Summarizing Data Using Excel 43 Chapter 3 Central Tendency 81 The Basic Idea of Central Tendency 82 The Mode 83 The Median 88 The Mean 95 Chapter 4 Dispersion 113 The Basic Idea of Dispersion 114 Dispersion of Categorical Data 115 Dispersion of Interval/Ratio Data 121 Chapter 5 Describing the Shape of a Distribution 149 The Basic Ideas of Distributional Shape 150 The Shape of Nominal and Ordinal Distributions 152 Unimodality 158 Skewness 163 Kurtosis 169 Some Common Distributional Shapes 175 Chapter 6 The Normal Distribution 187 Introduction to the Normal Distribution 188 Properties of Normal Distributions 189 The Standard Normal, or Z, Distribution 192 Working with Standard Normal (Z) Scores 194 Finding Areas “Under the Curve” 197 Part II Inference and Hypothesis Testing 209 Chapter 7 Basic Ideas of Statistical Inference 211 Introduction to Statistical Inference 212 Sampling Concepts 214 Central Tendency Estimates 219 Assessing Confidence in Point Estimates 229 Chapter 8 Hypothesis Testing for One Sample 247 Hypothesis Testing 248 The Testing Process 250 Tests about One Mean 258 Tests about One Proportion 267 Chapter 9 Hypothesis Testing for Two Samples 279 Comparing Two Groups 280 Comparing Two Groups’ Means 280 Comparing Two Groups’ Proportions 289 Non independent Samples 296 Using Excel for Two-Sample Tests 301 Interpreting Group Differences 302 Chapter 10 Multiple Sample Tests of Proportions: Chi-Squared 313 Comparing Proportions across Several Groups 314 Testing for Multiple Group Differences 315 Describing Group Differences 327 Chapter 11 Multiple Sample Tests for Means: One-Way ANOVA 337 Comparing Several Group Means with Analysis of Variance 338 Analyzing Variance and the F-Test 339 Analyzing Variance 342 The F-Test 350 Comparing Means 356 Part III Association and Prediction 369 Chapter 12 Association with Categorical Variables 371 The Concept of Statistical Association 372 Association with Nominal Variables 375 Association with Ordinal Variables 391 Chapter 13 Association of Interval/Ratio Variables 425 Visualizing Interval/Ratio Association 426 Significance Testing for Interval/Ratio Association 434 Chapter 14 Regression Analysis 453 Predicting Outcomes with Regression 454 Simple Linear Regression 454 Applying Simple Regression Analysis 465 Multiple Regression 469 Applying Multiple Regression 474 Chapter 15 Logistic Regression Analysis 489 Predicting with Nonlinear Relationships 490 Logistic Regression 492 The Logistic Regression Model 492 Interpreting Effects in Logistic Regression 493 Estimating Logistic Regression Models with Maximum Likelihood 495 Applying Logistic Regression 496 Assessing Partial Effects 498 Extending Logistic Regression 499 Appendix Chi-Squared Distribution: Critical Values for Commonly Used Alpha=0.05 and Alpha=0.01 505 F-Distribution: Critical Values for Commonly Used Alpha=0.05 and Alpha=0.01 507 Standard Normal Scores (Z-Scores), and Cumulative Probabilities (Proportion of Cases Having Scores below Z) 511 Student’s t-Distribution: Critical Values for Commonly Used Alpha Levels 517 Index 519

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Book SynopsisFirst published in 1967, Professor Batchelor's classic text on fluid dynamics is still one of the foremost texts in the subject. The careful presentation of the underlying theories of fluids is still timely and applicable. This re-issue should ensure that a new generation of graduate students see the elegance of Professor Batchelor's presentation.Trade Review'This book gives an excellent introduction to fluid dynamics … many interesting and important photographs of fluid flows are included in order to help the students who do not have an opportunity of observing flow phenomena in a laboratory. The book also contains exercises at the end of each chapter. In comparison with many currently available books, I find this book by Batchelor especially stimulating and useful for students of applied mathematics and engineering.' L. Debnath, Zentralblatt MATH' … a must-read for a proper understanding of the subject …' ResonanceTable of ContentsPreface; Conventions and notation; 1. The physical properties of fluids; 2. Kinematics of the flow field; 3. Equations governing the motion of a fluid; 4. Flow of a uniform incompressible viscous fluid; 5. Flow at large Reynolds number: effects of viscosity; 6. Irrotational flow theory and its applications; 7. Flow of effectively inviscid liquid with vorticity; Appendices.

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Book SynopsisAn introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. The heart of the book is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact.Table of ContentsIntroduction; 1. Foundations; 2. Cohomology, bundles and morphisms; 3. Orbifold K-theory; 4. Chen-Ruan cohomology; 5. Calculating Chen-Ruan cohomology; Bibliography; Index.

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Book SynopsisDo there exist Lorentzian manifolds all of whose light-like geodesics are periodic? A surprising fact is that such manifolds exist in abundance in (2 + 1)-dimensions (though in higher dimensions they are quite rare). This book deals with the deformation theory of M2,1 (which furnishes almost all the known examples of these objects).Table of Contents*Frontmatter, pg. i*Contents, pg. v*Foreword, pg. 1*Part I. A relativistic approach to Zoll phenomena, pg. 16*Part II. The general theory of Zollfrei deformations, pg. 27*Part III. Zollfrei deformations of M2,1, pg. 53*Part IV. The generalized x-ray transform, pg. 98*Part V. The Floquet theory, pg. 189*Bibliography, pg. 223

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Book SynopsisThis book explains the Lorentz mathematical group in alanguage familiar to physicists. This new edition extends applications tooptical sciences and includes five new chapters on applications in statisticalphysics, condensed matter physics. quantum optics and quantum information and artificialintelligence.

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Book SynopsisPreface to the Third Edition.- Preface to the Second Edition.- Preface to the First Edition.- The Dirac Delta Function and Delta Sequences.- The Schwartz-Sobolev Theory of Distributions.- Additional Properties of Distributions.- Distributions Defined by Divergent Integrals.- Distributional Derivatives of Functions with Jump Discontinuities.- Tempered Distributions and the Fourier Transforms.- Direct Products and Convolutions of Distributions.- The Laplace Transform.- Applications to Ordinary Differential Equations.- Applications to Partial Differential Equations.- Applications to Boundary Value Problems.- Applications to Wave Propagation.- Interplay between Generalized Functions and the Theory of Moments.- Linear Systems.- Miscellaneous Topics.- References.- Index.Trade Review"This book on generalized functions is suitable for physicists, engineers and applied mathematicians. The author presents the notion of generalized functions, their properties and their applications for solving ordinary differential equations and partial differential equations. ... The author demonstrates through various examples that familiarity with generalized functions is very helpful for students in mathematics, physical sciences and technology. The proposed exercises are very good for better understanding of notions and properties presented in the chapters. The book contains new topics and important features." —Mathematica "The advantage of this text is in carefully gathered examples explaining how to use corresponding properties.... Even the standard material connecting with partial and ordinary differential equations is rewritten in modern terminology." —Zentralblatt (Review of a previous edition) "The author has done an excellent job in presenting examples and in displaying the calculational techniques associated with distributions and the applications. Throughout the book there are a wealth of examples concerning the distributional topics and caluclations introduced and concering the applications, and the examples are presented in detail." ---Zentralblatt (Review of the 1st edition) "The collaboration of physicists or engineers and mathematics, which is more and more popular and necessary in modern investigations, requires…a common language. The book under review provides this language…. [It] is a well written book, most of the material is accessible to senior undergraduate and graduate students in mathematical, physical and engineering sciences…. [The] book will [also] be useful…for specialists in ODEs, PDEs, functional analysis, [and] physicists, engineers, and lecturers." —Acta. Sci. Math. (Review of a previous edition) "An exceptionally clear exposition... The exercises at the end of each chapter are well-chosen." —The American Mathematical Monthly (Review of a previous edition) "This fully revised edition of well-received book expands the treatment of fundamental concepts and theoretical background material delineates connections to a variety of applications in mathematical physics, elasticity, wave propagation, magnetohydrodynamics, linear systems, probability and statistics, optical control problems in economics, and more. It has many new topics and [features] driven by additional examples and exercises. . . It presents a wealth of applications that connot be found in any other single source. the book will be important reading for graduate students in physics and engineering." --- Educational Book ReviewTable of ContentsPreface to the Third Edition * Preface to the Second Edition * Preface to the First Edition * Chapter 1. The Dirac Delta Function and Delta Sequences * 1.1 The Heaviside Function * 1.2 The Dirac Delta Function * 1.3 The Delta Sequences * 1.4 A Unit Dipole * 1.5 The Heaviside Sequences * Exercises * Chapter 2. The Schwartz-Sobolev Theory of Distributions * 2.1 Some Introductory Definitions * 2.2 Test Functions * 2.3 Linear Functionals and the Schwartz–Sobolev Theory of Distributions * 2.4 Examples * 2.5 Algebraic Operations on Distributions * 2.6 Analytic Operations on Distributions * 2.7 Examples * 2.8 The Support and Singular Support of a Distribution Exercises * Chapter 3. Additional Properties of Distributions * 3.1 Transformation Properties of the Delta Distributions * 3.2 Convergence of Distributions * 3.3 Delta Sequences with Parametric Dependence * 3.4 Fourier Series * 3.5 Examples * 3.6 The Delta Function as a Stieltjes Integral Exercises * Chapter 4. Distributions Defined by Divergent Integrals * 4.1 Introduction * 4.2 The Pseudofunction H(x)/x n , n = 1, 2,3, * 4.3 Functions with Algebraic Singularity of Order m * 4.4 Examples * Exercises * Chapter 5. Distributional Derivatives of Functions with Jump Discontinuities * 5.1 Distributional Derivatives in R 1 * 5.2 Moving Surfaces of Discontinuity in R n , n 2 * 5.3 Surface Distributions * 5.4 Various Other Representations * 5.5 First-Order Distributional Derivatives * 5.6 Second Order Distributional Derivatives * 5.7 Higher-Order Distributional Derivatives * 5.8 The Two-Dimensional Case * 5.9 Examples * 5.10 The Function Pf ( l/r ) and its Derivatives * Chapter 6. Tempered Distributions and the Fourier Transforms * 6.1 Preliminary Concepts * 6.2 Distributions of Slow Growth (Tempered Distributions) * 6.3 The Fourier Transform * 6.4 Examples * Exercises * Chapter 7. Direct Products and Convolutions of Distributions * 7.1 Definition of the Direct Product * 7.2 The Direct Product of Tempered Distributions * 7.3 The Fourier Transform of the Direct Product of Tempered Distributions * 7.4 The Convolution * 7.5 The Role of Convolution in the Regularization of the Distributions * 7.6 The Dual Spaces E and E' * 7.7 Examples * 7.8 The Fourier Transform of the Convolution * 7.9 Distributional Solutions of Integral Equations * Exercises * Chapter 8. The Laplace Transform * 8.1 A Brief Discussion of the Classical Results * 8.2 The Laplace Transform of the Distributions * 8.3 The Laplace Transform of the Distributional Derivatives and Vice Versa * 8.4 Examples * Exercises * Chapter 9. Applications to Ordinary Differential Equations * 9.1 Ordinary Differential Operators * 9.2 Homogeneous Differential Equations * 9.3 Inhomogeneous Differentational Equations: The Integral of a Distribution * 9.4 Examples * 9.5 Fundamental Solutions and Green's Functions * 9.6 Second Order Differential Equations with Constant Coefficients * 9.7 Eigenvalue Problems * 9.8 Second Order Differential Equations with Variable Coefficients * 9.9 Fourth Order Differential Equations * 9.10 Differential Equations of n th Order * 9.11 Ordinary Differential Equations with Singular Coefficients * Exercises * Chapter 10. Applications to Partial Differential Equations * 10.1 Introduction * 10.2 Classical and Generalized Solutions * 10.3 Fundamental Solutions * 10.4 The Cauchy–Riemann Operator * 10.5 The Transport Operator * 10.6 The Laplace Operator * 10.7 The Heat Operator * 10.8 The Schroedinger Operator * 10.9 The Helmholtz Operator * 10.10 The Wave Operator * 10.11 The Inhomogeneous Wave Equation * 10.12 The Klein–Gordon Operator * Exercises * Chapter 11. Applications to Boundary Value Problems * 11.1 Poisson's Equation * 11.2 Dumbbell-Shaped Bodies * 11.3 Uniform Axial Distributions * 11.4 Linear Axial Distributions * 11.5 Parabolic Axial Distributions * 11.6 The Four-Order Polynomial Distribution, n = 7; Spheroidal Cavities * 11.7 The Polarization Tensor for a Spheroid * 11.8 The Virtual Mass Tensor for a Spheroid * 11.9 The Electric and Magnetic Polarizability Tensors * 11.10 The Distributional Approach to Scattering Theory * 11.11 Stokes Flow * 11.12 Displacement-Type Boundary Value Problems in Elastostatics * 11.13 The Extension to Elastodynamics * 11.14 Distributions on Arbitrary Lines * 11.15 Distributions on Plane Curves * 11.16 Distributions on a Circular Disk * Chapter 12. Applications to Wave Propagation * 12.1 Introduction * 12.2 The Wave Equation * 12.3 First-Order Hyperbolic Systems * 12.4 Aerodynamic Sound Generation * 12.5 The Rankine–Hugoniot Conditions * 12.6 Wave Fronts That Carry Infinite Singularities * 12.7 Kinematics of Wave Fronts * 12.8 Derivation of the Transport Theorems for Wave Fronts * 12.9 Propagation of Wave Fronts Carrying Multilayer Densities * 12.10 Generalized Functions with Support on the Light Cone * 12.11 Examples * Chapter 13. Interplay Between Generalized Functions and the Theory of Moments * 13.1 The Theory of Moments * 13.2 Asymptotic Approximation of Integrals * 13.3 Applications to the Singular Perturbation Theory * 13.4 Applications to Number Theory * 13.5 Distributional Weight Functions for Orthogonal Polynomials * 13.6 Convolution Type Integral Equations Revisited * 13.7 Further Applications * Chapter 14. Linear Systems * 14.1 Operators * 14.2 The Step Response * 14.3 The Impulse Response * 14.4 The Response to an Arbitrary Input * 14.5 Generalized Functions as Impulse Response Functions * 14.6 The Transfer Function * 14.7 Discrete-Time Systems * 14.8 The Sampling Theorem * Chapter 15. Miscellaneous Topics * 15.1 Applications to Probability and Statistics * 15.2 Applications to Mathematical Economics * 15.3 Periodic Generalized Functions * 15.4 Microlocal Theory * References * Index

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Book SynopsisA concise treatment of the fundamentals of thermodynamics is presented in this book. In particular, emphasis is placed on discussions of the second law, a unique feature of thermodynamics, which states the limitations of converting thermal energy into mechanical energy. The entropy function that permits the loss in the potential of a real thermodynamic process to be assessed, the maximum possible work in a process, and irreversibility and equilibrium are deduced from the law through physical and intuitive considerations. They are applicable in mitigating waste heat and are useful for solving energy, power, propulsion and climate-related issues.The treatment is not restricted to properties and functions of ideal gases. The ideal gas assumption is invoked as a limiting case. Reversible paths between equilibrium states are obtained using reversible heat engines and reversible heat pumps between environment and systems to determine the entropy changes and the maximum work. The coTable of Contents1. Fundamental Concepts. 2. Equation of State. 3. First Law of Thermodynamics. 4. Second Law of Thermodynamics. 5. Entropy. 6. Reversible Work, Availability and Irreversibility. 7. Thermodynamic State Functions. 8. Thermodynamic Coefficients and Specific Heats. 9. Thermodynamic Equilibrium. 10. Equilibrium of Species in a Chemically Reacting System. 11. Statistical Thermodynamics.

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Book SynopsisBasics of Ramsey Theory serves as a gentle introduction to Ramsey theory for students interested in becoming familiar with a dynamic segment of contemporary mathematics that combines ideas from number theory and combinatorics. The core of the of the book consists of discussions and proofs of the results now universally known as Ramsey's theorem, van der Waerden's theorem, Schur's theorem, Rado's theorem, the HalesJewett theorem, and the Happy End Problem of Erdos and Szekeres. The aim is to present these in a manner that will be challenging but enjoyable, and broadly accessible to anyone with a genuine interest in mathematics.Features Suitable for any undergraduate student who has successfully completed the standard calculus sequence of courses and a standard first (or second) year linear algebra course Filled with visual proofs of fundamental theorems Contains numerous exercises (with their solutions) acceTable of Contents1. Introduction: Pioneers and Trailblazers. 1.1. Complete Disorder is Impossible. 1.2 Paul Erdős. 1.3. Frank Plumpton Ramsey. 1.4 Ramsey Theory. 2. Ramsey’s Theorem. 2.1. The Pigeonhole Principle. 2.2. Acquaintances and Strangers. 2.3. Ramsey’s Theorem for Graphs. 2.4. Ramsey’s Theorem: Infinite Case. 2.5. Ramsey’s Theorem: General Case. 2.6. Exercises. 3. van der Waerden’s Theorem. 3.1. Bartel van der Waerden. 3.2. van der Waerden’s Theorem: 3–Term Arithmetic Progressions. 3.3. Proof of van der Waerden’s Theorem. 3.4. van der Waerden’s Theorem: How Far and Where? 3.5. van der Waerden’s Theorem: Some Related Questions. 3.6. Exercises. 4. Schur’s Theorem and Rado’s Theorem. 4.1 Issai Schur. 4.2. Schur’s Theorem. 4.3. Richard Rado. 4.4 Rado’s Theorem. 4.5. Exercises. 5. The Hales–Jewett Theorem. 5.1. Combinatorial Lines. 5.2. Generalized Tic–Tac–Toe Game. 5.3. The Hales–Jewett Theorem. 5.4. Exercises. 6. Happy End Problem. 6.1. The Happy End Problem: Triangles, Quadrilaterals, and Pentagons. 6.2. The Happy End Problem – General Case. 6.3. Erdős–Szekeres’ Upper and Lower Bounds. 6.4. Progress on the Conjecture OF Erdős and Szekeres. 6.5. Exercises. 7. Solutions.

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Book SynopsisThis fully updated and expanded new edition continues to provide the most readable, concise, and easy-to-follow introduction to thermal physics.While maintaining the style of the original work, the book now covers statistical mechanics and incorporates worked examples systematically throughout the text. It also covers more problems, and incorporates some essential updates, such as discussions on superconductivity, magnetism, Bose-Einstein condensation, and climate change.Anyone who needs to acquire an intuitive understanding of thermodynamics from the first principles will find this third edition indispensable.Selling Pointsâ Provides the most concise and accessible introduction to thermodynamics starting from first principles, with many more worked examples and problems.â Incorporates statistical mechanics in two brand-new chapters.â Systematically incorporates more worked examples after introducing a new concept to show what the results mean numerically.â Continues to address the subtleties in a way unmatched by any other text, for topics such as the meaning of thermodynamic functions.â Offers a significant update on areas such as superconductivity, magnetism, Bose-Einstein condensation, climate change, and physics of information.Andrew Rex is a professor of physics at the University of Puget Sound in Tacoma, Washington. He earned a BA in physics at Illinois Wesleyan University in 1977 and a PhD in physics at the University of Virginia in 1982. At Virginia he worked under the direction of Bascom S. Deaver Jr on the development of new superconducting materials. After completing requirements for his PhD, he joined the faculty at Puget Sound. Dr Rexâs primary research interest is in the foundations of the second law of thermodynamics. He has published research articles and, jointly with Harvey Leff, two comprehensive monographs on the subject of Maxwellâs demon (1990, 2003). Dr Rex has coauthored several widely used textbooksâModern Physics for Scientists and Engineers (1993, 2000, 2006, 2013, 2021), Integrated Physics and Calculus (2000), and Essential College Physics (2010, 2021)âand the popular science book Commonly Asked Questions in Physics, also published by Taylor & Francis/CRC Press.

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Book SynopsisThis book is one of its own kind. It is not an encyclopedia or a hands-on tutorial that traps readers in the tutorial hell. It is a distillation of just one common Python user's learning experience. The experience is packaged with exceptional teaching techniques, careful dependence unraveling and, most importantly, passion.Learning Advanced Python by Studying Open Source Projects helps readers overcome the difficulty in their day-to-day tasks and seek insights from solutions in famous open source projects. Different from a technical manual, this book mixes the technical knowledge, real-world applications and more theoretical content, providing readers with a practical and engaging approach to learning Python.Throughout this book, readers will learn how to write Python code that is efficient, readable and maintainable, covering key topics such as data structures, algorithms, object-oriented programming and more. The author's passion for Python shines through in tTable of ContentsIntroductionChapter 1 ◾ The Data Model of PythonChapter 2 ◾ Selected Topics of Python ClassesChapter 3 ◾ Concurrency in PythonChapter 4 ◾ Asynchronous Programming in PythonChapter 5 ◾ Power Up Your Python FunctionsChapter 6 ◾ Selected OOP Design Best PracticesChapter 7 ◾ Testing in a Pistachio Shell

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Book SynopsisMachine learning is an exciting topic with a myriad of applications. However, most textbooks are targeted towards computer science students. This, however, creates a complication for scientists across the physical sciences that also want to understand the main concepts of machine learning and look ahead to applica- tions and advancements in their fields.This textbook bridges this gap, providing an introduction to the mathematical foundations for the main algorithms used in machine learning for those from the physical sciences, without a formal background in computer science. It demon- strates how machine learning can be used to solve problems in physics and engineering, targeting senior undergraduate and graduate students in physics and electrical engineering, alongside advanced researchers.All codes are available on the author''s website: CLab (nau.edu)They areTable of ContentsChapter 1: Multivariate Calculus. Chapter 2: Probability Theory. Chapter 3: Dimensionality Reduction. Chapter 4: Cluster Analysis. Chapter 5: Vector Quantization Techniques. Chapter 6: Regression Models. Chapter 7: Classification. Chapter 8: Feedforward Networks. Chapter 9: Advanced Network Architectures. Chapter 10: Value Methods. Chapter 11: Gradient Methods. Chapter 12: Population-Based Metaheuristic Methods. Chapter 13: Local Search methods. Appendix A: Sufficient Statistic. Appendix B: Graphs. Appendix C: Sequential Minimization Optimization. Appendix D: Algorithmic Differentiation. Appendix E: Batch Normalizing Transform. Appendix F: Divergence of Two Gaussian Distributions. Appendix G: Continuous-time Bellman's Equation. Appendix H: Conjugate Gradient. Appendix I: Importance Sampling. References. Index.

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Book SynopsisThis is a how to guide for making beginning calculations in modern physics. The academic level is second year college physical science and engineering students. The calculations are performed in Mathematica, and stress graphical visualization, units, and numerical answers. The techniques show the student how to learn the physics without being hung up on the math. There is a continuing movement to introduce more advanced computational methods into lower-level physics courses. Mathematica is a unique tool in that code is written as human readable much like one writes a traditional equation on the board.Key Features:Concise summary of the physics concepts.Over 300 worked examples in Mathematica.Tutorial to allow a beginner to produce fast results.The companion code for this book can be found here:Table of Contents1. Basis of Modern Physics 2. Thermal Radiation 3. Key Processes 4. Special Relativity 5. Bohr Model 6. Particle in a Box 7. Quantum Harmonic Oscillator 8. Hydrogen Atom 9. Statistical Physics 10. Astrophysics Appendix A: Mathematica Starter Appendix B: Physical Constants

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Book SynopsisThe number e, the function ex, the logarithmic function in (x) and different hyperbolic functions like cosh (x), sinh (x) make frequent appearances in science and engineering textbooks. Students often fail to appreciate the significance of these mathematical symbols. This book clearly illustrates why such abstract mathematical entities are needed to represent some aspects of physical reality. It provides an overview of different types of numbers and functions along with their historical background and applications. It contains four chapters covering number system, exponential function, logarithmic functions and hyperbolic functions along with the concept of complex angle.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan)Table of Contents1. On Different Types of Numbers 1.1 The beginning of the journey 1.2 Extension of Number Field 1.2.1 Negative Number 1.2.2 Fraction and Rational Number 1.2.3 Irrational Number 1.2.4 Imaginary (or Quadrature Number) 1.2.5 Quaternion 1.2.6 Infinitesimal and Hyper-real Numbers; Bibliography2. On e & ex 2.1 Introduction 2.2 Backdrop in which e emerged as the outcome of continuous compounding 2.3 Outcome of decrease through continuous compounding 2.4 e as an infinite series 2.5 Proof of convergence of two sequences of e 2.6 Proof of Irrationality of e 2.7 Function ex 2.8 Interesting features of exponential functions ex and emx 2.9 Story of snails or an informal explanation of e1 vis-à-vis ei 2.9.1 e as a distance travelled along a road 2.9.2 ei as a distance travelled in a field 2.10 General function eiθ = limn→∞(1 + iθ/n )n 2.11 Infinite series representation of cos θ and sin θ 2.12 Raising the power of e by complex angle (α + iθ) 2.13 Rotating vector and concept of complex frequency 2.14 cos θ and sin θ in terms of exponential functions 2.15 Ellipse from two rotating planar vectors 2.16 Problems related to division of a number 2.16.1 Maximisation of the function x x 2.16.2 Dividing a number into several equal parts such that their product is maximum 2.17 Minimisation of the function xx 2.18 Computation of ii 2.19 Examples of 1st order differential equation 2.20 Example of 2nd order differential equation 2.21 Miscellaneous examples 2.21.1 Radioactive Disintegration 2.21.2 Advance of Chemical Reaction 2.21.3 Logistic growth 2.22 Matrix Exponential eA 2.23 Chronology of development of concepts related to e ; Bibliography 3. Logarithm 3.1 Introduction 3.2 Logarithm as artificial numbers facilitating computation 3.3 Logarithmic Function as an integral 3.4 A story of the historical development of logarithm as an area 3.5 Reverse Problem 3.6 Some useful properties of logarithmic functions 3.7 Expressing logarithm as a series 3.7.1 Alternate Method of Derivation of Logarithmic Series 3.7.2 Searching for a method with a higher rate of convergence 3.7.3 Further improvement of the method described in section 3.7.2 3.8 Logarithmic curves 3.8.1 Observations on the curve for the function y = ln x 3.8.2 Curve for the function y = ln(–x ) and y = ln |x | 3.9 Leibnitz-Gregory Series for π 3.10 Schellbach’s modified series for π 3.11 Logarithm as a limit of a product 3.12 Torricelli’s Trumpet 3.13 Logarithm of a complex number 3.14 Resolving an apparent contradiction 3.15 Applications 3.15.1 Inductance of a two wire line3.15.2 Capacitance of a two wire line 3.15.3 Loudness of sound 3.15.4 Magnitude of earthquake 3.15.5 Acidity of a substance 3.16 Chronology of development of the concepts related to logarithm; Bibliography 4. Concept of Complex Angle and Hyperbolic Functions 4.1 Introduction 4.2 Angle in terms of the area swept over during rotation 4.3 Vector viewpoint and the concept of imaginary angle 4.4 Angle due to stretching or shrinking and the concept of real angle 4.5 Complex Angle 4.6 Hyperbolic angle and Hyperbolic Functions for a hyperbola 4.7 Area swept by a straight line moving over a hyperbola 4.8 From the hyperbola x 2 – y 2 = 1 to the hyperbola u.v = 1126 4.9 Calculation of hyperbolic angle from the curve v = 1/u 4.10 The tip of a straight line moving over the curve v = 1/u 129 4.11 Trigonometric functions of imaginary variable and Hyperbolic functions 4.12 Trigonometric and Hyperbolic functions of complex angle α + iβ 4.13 Applications 4.13.1 A DC Voltage Source (V) is switched on to an LC circuit 4.13.2 A DC Voltage Source is switched on to a RLC circuit 4.13.3 Catenary 4.13.4 A Leaky Direct Current Line 4.13.5 Dynamics of moving bodies 4.14 Graphs of different hyperbolic functions 4.15 Are the hyperbolic functions periodic? 4.16 Expressions for inverse hyperbolic functions 4.17 Infinite series representation of cosh x and sinh x 4.18 Historical Development of the concept of hyperbolic functions ; Bibliography

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Book SynopsisGraphs & Digraphs, Seventh Edition masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory. This classic text, widely popular among students and instructors alike for decades, is thoroughly streamlined in this new, seventh edition, to present a text consistent with contemporary expectations.Changes and updates to this edition include: A rewrite of four chapters from the ground up Streamlining by over a third for efficient, comprehensive coverage of graph theory Flexible structure with foundational Chapters 16 and customizable topics in Chapters 711 Incorporation of the latest developments in fundamental graph theory Statements of recent groundbreaking discoveries, even if proofs are beyond scope Completely reorganized chapters on traversability, connectiviTable of Contents1 Graphs 1.1 Fundamentals 1.2 Isomorphism 1.3 Families of graphs 1.4 Operations on graphs 1.5 Degree sequences 1.6 Path and cycles 1.7 Connected graphs and distance 1.8 Trees and forests 1.9 Multigraphs and pseudographs 2 Digraphs 2.1 Fundamentals 2.2 Strongly connected digraphs 2.3 Tournaments 2.4 Score sequences 3 Traversability 3.1 Eulerian graphs and digraphs 3.2 Hamiltonian graphs 3.3 Hamiltonian digraphs 3.4 Highly hamiltonian graphs 3.5 Graph powers 4 Connectivity 4.1 Cut-vertices, bridges, and blocks 4.2 Vertex connectivity 4.3 Edge-connectivity 4.4 Menger's theorem 5 Planarity 5.1 Euler's formula 5.2 Characterizations of planarity 5.3 Hamiltonian planar graphs 5.4 The crossing number of a graph 6 Coloring 6.1 Vertex coloring 6.2 Edge coloring 6.3 Critical and perfect graphs 6.4 Maps and planar graphs 7 Flows 7.1 Networks 7.2 Max-flow min-cut theorem 7.3 Menger's theorems for digraphs 7.4 A connection to coloring 8 Factors and covers 8.1 Matchings and 1-factors 8.2 Independence and covers 8.3 Domination 8.4 Factorizations and decompositions 8.5 Labelings of graphs 9 Extremal graph theory 9.1 Avoiding a complete graph 9.2 Containing cycles and trees 9.3 Ramsey theory 9.4 Cages and Moore graphs 10 Embeddings 10.1 The genus of a graph 10.2 2-Cell embeddings of graphs 10.3 The maximum genus of a graph 10.4 The graph minor theorem 11 Graphs and algebra 11.1 Graphs and matrices 11.2 The automorphism group 11.3 Cayley color graphs 11.4 The reconstruction problem

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Book SynopsisPuzzle and Proof: A Decade of Problems from the Utah Math Olympiad is a compilation of the problems and solutions for the first 10 years of the Utah Math Olympiad. The problems are challenging but should be understandable at a high school level. Besides putting all problems in one place (70 in total), which have not previously appeared in print, the book provides additional inspiration for many of the problems and will contain the first published solutions for 10 problems that were originally published on the contest flyer. The book will be a fantastic resource for anyone who enjoys mathematical and/or logic puzzles or is interested in studying for mathematics competitions.Features 70 carefully designed, high-quality high-school level math proof problems, with full solutions Detailed pictures and diagrams throughout to aid understanding Suitable for anyone with high school-level mathematics skills with an interest in furth

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Book SynopsisNow considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content.Published nearly forty years after the first edition, this long-awaited Second Edition also: Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 < p < 2 Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of HÃlder continuous functions and the space of functions of bounded mean oscillation

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Book SynopsisThis book presents a focused, readable account of the principal physical and mathematical ideas at the heart of fluid dynamics. Graduate students in engineering, applied math and physics taking their first graduate course in fluids will find this book invaluable in providing the background in physics and mathematics necessary to pursue advanced study. The exposition follows an arc through the subject building towards a detailed derivation of the NavierâStokes and energy equations followed by many examples of their use in studying the dynamics of fluid flows. Modern tensor analysis is used to simplify the mathematical derivations thus allowing a clearer view of the physics. The motivation behind many fundamental concepts such as Bernoulli's equation and the stream function are included. Many exercises are designed with a view toward using MATLAB or equivalent to simplify and extend the analysis of fluid motion including developing flow simulations based on techniques described in the bTable of Contents1. Introduction; 2. Eulerian and Lagrangian viewpoints, paths and streamlines; 3. Stream function; 4. Helmholtz decomposition; 5. Sources, sinks and vortices; 6. Doublets and their applications; 7. Complex potential; 8. Accelerating reference frames; 9. Fluids at rest; 10. Incompressibility and mass conservation; 11. Stress tensor - existence and symmetry; 12. Stress tensor in Newtonian fluids; 13. Navier–Stokes equation; 14. Thermodynamic considerations; 15. Energy equation; 16. Complete equations of motion; 17. Applications of Bernoulli's equation and control volumes; 18. Vorticity; 19. Applications to viscous flow; 20. Laminar boundary layers; 21. Some applications to convective heat and mass transfer.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisMaple is a powerful symbolic computation system that is widely used in universities around the world. This short introduction gives readers an insight into the rules that control how the system works, and how to understand, fix, and avoid common problems. Topics covered include algebra, calculus, linear algebra, graphics, programming, and procedures. Each chapter contains numerous illustrative examples, using mathematics that does not extend beyond first-year undergraduate material. Maple worksheets containing these examples are available for download from the author''s personal website. The book is suitable for new users, but where advanced topics are central to understanding Maple they are tackled head-on. Many concepts which are absent from introductory books and manuals are described in detail. With this book, students, teachers and researchers will gain a solid understanding of Maple and how to use it to solve complex mathematical problems in a simple and efficient way.Trade Review'Thompson (Univ. of Liverpool, UK) clearly knows the 'gotchas' that most often plague beginners (and others!) and provides pointed guidance; extracting the same vital information buried in longer and more systematic treatises and manuals can certainly prove a challenge. Summing Up: Recommended. Lower-division undergraduates and above; faculty and professionals.' D. V. Feldman, CHOICETable of Contents1. Introduction; 2. Getting started; 3. Algebra and calculus; 4. Solving equations; 5. Linear algebra; 6. Graphics; 7. Programming; 8. Procedures; 9. Example programs; Appendix A. Other ways to run Maple; Appendix B. Terminating characters; Index of Maple notation.

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Book SynopsisYou've Never Seen What You've Always Needed to Know Until Now Invisible forces are at work. They push and shove on everything you buy or sell. They affect every concept you want to take to market, all the suppliers you'll deal with, and every customer you'll ever see. To be successful, you need to understand them. See them in detail in ways not possible with other methods. Hypernomics: Using Hidden Dimensions to Solve Unseen Problems discovers that markets behave according to previously unknown laws set by the buyers and sellers within them. It reveals those rules and how to detect, describe, and deploy them to your advantage. It doesn't change economics so much as reveal it. It's like a microscope looking at pond water, a telescope tilted to the sky, sonar scanning the bottom of the ocean. Hypernomics lets you see into markets in ways you can't with the unaided eye. Sailors never navigate without a map. You shouldn't either, since your ship coulTable of ContentsIntroduction 1 CHAPTER 1 A Brief History of Position and Direction 9 Ancient Maps 9 Geography Begins 13 Math and Position Problems 13 Summary 26 Vignette: Restaurant Math 27 CHAPTER 2 Four-Dimensional Systems 29 Dot Plots Begin 29 "X" Marks the Spot 30 Most Markets Don't Address Commodities 31 Cartesian Systems and Negativity 33 Geography Is Never Negative 38 Plotting in Four Dimensions 52 Summary 56 CHAPTER 3 Five-Dimensional Systems 57 Physical Changes over Time 57 Economic Changes over Time 62 Summary 69 CHAPTER 4 Value 71 Human Traits 71 What Does Value Mean in Hypernomics? 75 Determining Value 77 The Market as Laboratory 79 Summary 91 Vignette: The Value of Expanding One's Limits 92 CHAPTER 5 Demand 95 Demand Frontiers 95 Aggregate Demand 102 Average Demand 104 Minimum Demand 105 Proxy Demand 106 Submarket, Sub-Submarket, and Mission Market Demand Curves 107 Product Demand Curves 109 Summary 110 A Hypernomics Vignette: The Value of and Demand for Money 111 CHAPTER 6 Price and Quantity Determination 121 The General Problem Calls for Specifics 121 The Neoclassical View: The Law of Supply and Demand 122 Ferrous Blunder: Universal Claim of Upward-Sloping Supply Curves 125 The Hypernomics View: The Law of Value and Demand 128 Summary 133 A Hypernomics Vignette: The Law of Value and Demand 134 CHAPTER 7 Market Mapping and Financial Cat Scans 137 Got Eggs? 137 Market Map Boundaries 141 Feature and Price Gap Maps 143 Financial Cat Scans 146 Summary 155 CHAPTER 8 Aiming and Missing 157 Neoclassical Aiming 157 Immediate Aiming 158 Immediate Aiming in Hypernomics 163 Ultimate Aiming 165 Ultimate Aiming in Hypernomics 167 Summary 170 CHAPTER 9 N-Dimensional Systems 173 Common Object 1—Pie 174 Common Object 2—Logarithmic Scaling 176 Common Object 3—Rolodex 178 Common Object 4—Concentric Circle 180 Common Object 5—Parallelograms (as in Extendable Mirrors) 181 Starting from (0,0,0,0. . .0) 182 Summary 200 CHAPTER 10 An Amazon Mining Expedition 201 Summary 210 CHAPTER 11 More 211 Vignette: What Do Markets Look Like to Viruses? 213 CHAPTER 12 Appendix: Using Hypernomics on Your Own 217 Stating the Problem 220 Data Collection 221 Data Entry 223 Data Manipulation 225 Data Interpretation 229 Summary 235 Vignette: The Importance of Going Deep into the Data 237 CHAPTER 13 Neoclassical Economics and Hypernomics Differences 241 Glossary 243 References 247 Index 279

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Book SynopsisWith a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus.  Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse''s lemma and the Poincaré lemma.  The ideas behind most topics can be understood with just two or three variables.  The book incorporates modern computational tools to give visualization real power.  Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps.  The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books.  This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics.  Prerequisites are an introduction to linear algebra and multivariable calculus.  There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry.  The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.Trade ReviewFrom the reviews:“Many concepts in calculus and linear algebra have obvious geometric interpretations. … This book differs from other advanced calculus works … it can serve as a useful reference for professors. … it is the adopted course resource, its inclusion in a college library’s collection should be determined by the size and interests of the mathematics faculty. Summing Up … . Upper-division undergraduate through professional collections.” (C. Bauer, Choice, Vol. 48 (8), April, 2011)“The author of this book sees an opportunity to bring back a more geometric, visual and physically-motivated approach to the subject. … The author makes exceptionally good use of two and three-dimensional graphics. Drawings and figures are abundant and strongly support his exposition. Exercises are plentiful and they cover a range from routine computational work to proofs and extensions of results from the text. … Strong students … are likely to be attracted by the approach and the serious meaty content.” (William J. Satzer, The Mathematical Association of America, January, 2011)“A new geometric and visual approach to advanced calculus is presented. … The book can be useful a textbook for beginners as well as a source of supplementary material for university teachers in calculus and analysis. … the book meets a wide auditorium among undergraduate and graduate students in mathematics, physics, economics and in other fields which essentially use mathematical models. It is also very interesting for teachers and instructors in Calculus and Mathematical Analysis.” (Sergei V. Rogosin, Zentralblatt MATH, Vol. 1205, 2011)Table of Contents1 Starting Points.-1.1 Substitution.- Exercises.- 1.2 Work and path integrals.- Exercises.- 1.3 Polar coordinates.- Exercises.- 2 Geometry of Linear Maps.- 2.1 Maps from R2 to R2.- Exercises.- 2.2 Maps from Rn to Rn.- Exercises.- 2.3 Maps from Rn to Rp, n 6= p.- Exercises.- 3 Approximations.- 3.1 Mean-value theorems.- Exercises.- 3.2 Taylor polynomials in one variable.- Exercises.- 3.3 Taylor polynomials in several variables.- Exercises.- 4 The Derivative.- 4.1 Differentiability.- Exercises.- 4.2 Maps of the plane.- Exercises.- 4.3 Parametrized surfaces.- Exercises.- 4.4 The chain rule.- Exercises.- 5 Inverses.- 5.1 Solving equations.- Exercises.- 5.2 Coordinate Changes.- Exercises.- 5.3 The Inverse Function Theorem.- Exercises.- 6 Implicit Functions.- 6.1 A single equation.- Exercises.- 6.2 A pair of equations.- Exercises.- 6.3 The general case.- Exercises.- 7 Critical Points.- 7.1 Functions of one variable.- Exercises.- 7.2 Functions of two variables.- Exercises.- 7.3 Morse’s lemma.- Exercises.- 8 Double Integrals.- 8.1 Example: gravitational attraction.- Exercises.- 8.2 Area and Jordan content.- Exercises.- 8.3 Riemann and Darboux integrals.- Exercises.- 9 Evaluating Double Integrals.- 9.1 Iterated integrals.- Exercises.- 9.2 Improper integrals.- Exercises.- 9.3 The change of variables formula.- 9.4 Orientation.- Exercises.- 9.5 Green’s Theorem.- Exercises.- 10 Surface Integrals.- 10.1 Measuring flux.- Exercises.- 10.2 Surface area and scalar integrals.- Exercises.- 10.3 Differential forms.- Exercises.- 11 Stokes’ Theorem.- 11.1 Divergence.- Exercises.- 11.2 Circulation and Vorticity.- Exercises.- 11.3 Stokes’ Theorem.- 11.4 Closed and Exact Forms.- Exercises

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Book SynopsisThis book is among the first to present the mathematical models most commonly used to solve optimal execution problems and market making problems in finance. The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making presents a general modeling framework for optimal execution problemsinspired from the Almgren-Chriss approachand then demonstrates the use of that framework across a wide range of areas.The book introduces the classical tools of optimal execution and market making, along with their practical use. It also demonstrates how the tools used in the optimal execution literature can be used to solve classical and new issues where accounting for liquidity is important. In particular, it presents cutting-edge research on the pricing of block trades, the pricing and hedging of options when liquidity matters, and the management of complex share buy-back contracts.What sets this book apart from others is that it focuses onTrade Review"This excellent monograph covers the mathematical theory of market microstructure with particular emphasis in models of optimal execution and market making. Gueant’s book is a superb introduction to these topics for graduate students in mathematical finance or quants who want to work in execution algorithms or market-making strategies."—Jose A. Scheinkman, Charles and Lynn Zhang Professor of Economics, Columbia University, and Theodore Wells '29 Professor of Economics Emeritus, Princeton University"This is a very timely book that cuts across various fields (applied mathematics, operations research, and quantitative finance). Execution costs due to market illiquidity can significantly reduce returns on investment strategies and, for this reason, affect asset prices. It is therefore important to design trading strategies minimizing these costs and to account for their effect on prices. In the last decade, ‘quants’ and researchers in quantitative finance have made considerable progress on these issues, integrating in their models changes in the way financial markets work (e.g., the development of continuous limit order books, market fragmentation, dark pools, the automation of trading, etc.). "Olivier Guéant’s book takes stock of this effort by providing a rigorous and expert presentation of mathematical tools, models, and numerical methods developed in this area. I strongly recommend it for researchers and graduate students interested in how illiquidity costs affect trading strategies and should be accounted for in asset valuation problems."—Thierry Foucault, HEC Foundation Chair Professor of Finance, HEC, Paris"This book is a must-have for quantitative analysts working at algorithmic trading desks. Olivier Guéant could have written a sophisticated book dedicated to cutting-edge research. He rather decided to put his talent at the service of a far more difficult task: deliver a clear view of modern algorithmic trading to strats or quants having decent scientific training. Scientists will find here all the needed keys to control the intraday risk of their trading models, improving their overall efficiency. Covering brokerage algorithms, market making, hedging, and share buyback techniques, this book is the definitive reference for algorithm builders.Moreover, Olivier links algorithmic trading with market microstructure during the first chapter of the book, including interesting thoughts on corporate bonds trading. On the other hand, he provides a nice introduction to mathematical economics in the Appendix. This book is resolutely more than a bunch of equations thrown on blank pages. I consider it an important step forward in the building of the mathematics of market microstructure."—Charles-Albert Lehalle, Senior Research Advisor, Capital Fund ManagementTable of ContentsIntroduction. Optimal Liquidation. Liquidity in Pricing Models. Market Making.

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Book SynopsisIn knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns (generators). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems.The book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators using Hirasawa's algorithm and extends this description to push the compilation of knot generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of the genus 4 classification, including the braid index, polynomial invariants, hyperbolic volume, and Vassiliev invariants. The final chapter presents further research related to generators, which helps rTrade Review"Diagram Genus, Generators and Applications contains a systematical study of combinatorial properties of knot diagrams. It focuses on diagrams that represent the canonical genus of a knot, i.e., the minimal genus of all Seifert surfaces for a given knot that are obtained by applying Seifert’s algorithm to diagrams of the knot. The book contains the complete classification of knots up to canonical genus 4. This classification has lots of applications … The book … will certainly become a reference in this area. It is very clearly written and contains enough background material so that it can be used by graduate-level students to learn the subject and do work in this area on their own."—Thomas Fiedler, Institut de Mathématiques, Université Paul Sabatier, Toulouse"This book provides an essential resource for anyone currently doing research or interested in doing research on surfaces in knot complements and their applications. Enough background is included so non-experts can follow the exposition and appreciate the myriad results that ensue."—Professor Colin Adams, Williams College"This monograph is a systematic account of combinatorial knot theory, with a particular focus on spanning surfaces arising from Seifert’s construction. It includes a brief and nicely written introduction to knot theory, concentrating on the background needed for a diagrammatic treatment of knots, including the range of classical and modern knot polynomials.A strong feature of this book, and indeed much of the author’s work elsewhere, is the identification of diagrammatic examples with awkward or unexpected properties, and an analysis of the techniques that can be used effectively on them. This can provide examples that can’t possibly be tackled by certain procedures, and thus directs attention to places where the current repertoire of techniques is lacking.The main topic developed is the notion of diagram genus, or canonical genus, based on Seifert’s algorithm. The related graph theory leads to the selection of a class of alternating knot diagrams, termed generators, and a substantial account of these up to genus 4 is given.This is followed by the discussion of a number of combinatorial results and conjectures. In particular, some nice results for alternating or positive knots are given and their possible extension to the case when k of the knot crossings are switched is explored for small values of k. The earlier calculations are used to extend the knowledge of these results to cover knots with fewer restrictions on their genus or crossing number.There is a good account of the combinatorics for recognizing when a knot diagram actually represents the trivial knot. It is surprisingly easy to draw diagrams of the trivial knot with relatively few crossings that do not have an immediately obvious simplification, and some examples are included in the illustrations.A further section covers the question of finding the braid index for an alternating knot, and the conditions under which the Morton-Franks-Williams bound turn out to be sharp. The concluding section is intended as an appetizer for others and includes a variety of annotated questions and conjectures.The carefully written text is aimed at a graduate-level readership. It gives a comprehensive view of combinatorial questions, both in the monograph itself and in the well-annotated bibliography, and would serve both well as a reference and a source of new ideas.Features A comprehensive account of diagram-centered results in knot theory Focus on Seifert’s construction of oriented-spanning surfaces Analysis of diagrams representing the unknot and their reduction by Reidemeister moves Careful and persuasive writing An excellent reference text and source of ideas" —H.R. Morton, Department of Mathematical Sciences, University of LiverpoolTable of ContentsIntroduction. Preliminaries. The Maximal Number of Generator Crossings and ~-Equivalance Classes. Generators of Genus 4. Unknot Diagrams, Non-Trivial Polynomials, and Achiral Knots. The Signature. Braid Index of Alternating Knots. Minimal String Bennequin Surfaces. The Alexander Polynomial of Alternating Knots. Outlook.

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Book SynopsisThe Handbook of Mathematics for Engineers and Scientists covers the main fields of mathematics and focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. To accommodate different mathematical backgrounds, the preeminent authors outline the material in a simplified, schematic manner, avoiding special terminology wherever possible.Organized in ascending order of complexity, the material is divided into two parts. The first part is a coherent survey of the most important definitions, formulas, equations, methods, and theorems. It covers arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, special functions, calculus of variations, and probability theory. Numerous specific examples clarify the methods for solving problems and equations. The second part provides many in-depth mathematical tables, including those of exact solutions of various types of equations. This concise, comprehensive compendium of mathematical definitions, formulas, and theorems provides the foundation for exploring scientific and technological phenomena.Trade Review“The book is split into two parts: methods (about 1100 pages), and tables (about 400 pages). Both parts are well structured and well written. … the coverage of the topics included is excellent … this is a fine reference text, offered at a very reasonable price …” —SIAM Review, Vol. 49, No. 3, September 2007Table of ContentsArithmetic and Elementary Algebra. Elementary Functions. Elementary Geometry. Analytic Geometry. Algebra. Limits and Derivatives. Integrals. Series. Differential Geometry. Functions of Complex Variable. Integral Transforms. Ordinary Differential Equations. First-Order Partial Differential Equations. Linear Partial Differential Equations. Nonlinear Partial Differential Equations. Integral Equations. Difference Equations and Other Functional Equations. Special Functions and Their Properties. Calculus of Variations and Optimization. Probability Theory. Mathematical Statistics. Finite Sums and Infinite Series. Integrals. Integral Transforms. Ordinary Differential Equations. Systems of Ordinary Differential Equations. First-Order Partial Differential Equations. Linear Equations and Problems of Mathematical Physics. Nonlinear Mathematical Physics Equations. Systems of Partial Differential Equations. Integral Equations. Functional Equations.

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Book SynopsisThis book is a self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra. The second half of the book gives a thorough account of probability, optimisation and dynamics.The emphasis throughout is on intuitive argument and problem-solving. All methods are illustrated by examples, exercises and problems selected from central areas of modern economic analysis. The book’s careful arrangement in short chapters enables it to be used in a variety of course formats for students with or without prior knowledge of calculus, for reference and for self-study. This new fourth edition includes two chapters on probability theory, providing the essential mathematical background for upper-level courses on economic theory, econometrics and finance.Trade Review'In spite of the wide scope of this textbook, its presentation is clear and crisp. The materials are very carefully organised. The transition from mathematical principles to economic propositions is remarkably lucid throughout the book. If a first-year undergraduate student in economics comes to ask me which one, among many books on mathematics for economists, to buy for years to come, then I would definitely tell them that this is the one.'Chiaki Hara, Institute of Economic Research, Kyoto University‘This is a great text to learn from – the authors do an excellent job providing intuitive explanations, making connections between results and illustrating the use of mathematics in solving economics problems, and there is a host of solved exercises which perform two roles: providing essential practice material and introducing further applications in economics.’Andrew Chesher, Director of The Centre for Microdata Methods and Practice, IFS and UCL -- .Table of Contents1. Linear equations2. Linear inequalities3. Sets and functions4. Quadratics, indices and logarithms5. Sequences, series and limits6. Introduction to differentiation7. Methods of differentiation8. Maxima and minima9. Exponential and logarithmic functions10. Approximations11. Matrix algebra12. Systems of linear equations13. Determinants and quadratic forms14. Functions of several variables15. Implicit relations16. Optimisation with several variables17. Principles of constrained optimisation18. Further topics in constrained optimisation19. Integration20. Aspects of integral calculus21. Probability22. Expectation23. Introduction to dynamics24. The circular functions25. Complex numbers26. Further dynamics27. Eigenvalues and eigenvectors28. Dynamic systems29. Dynamic optimisation in discrete time30. Dynamic optimisation in continuous time31. Introduction to analysis32. Metric spaces and existence theoremsNotes on further readingIndex

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Book SynopsisThis self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.Trade ReviewFrom the reviews: It explains its chosen topics clearly and simply, not including extraneous material, and is written at a level that can be understood and appreciated by undergraduate students. Indeed, the level of writing is superb in its clarity and elegance... Just as useful as the writing style are the appendices and hints. Not only does Britton give elementary presentations of some basic mathematical techniques (difference equations, ODEs and PDEs) he also gives extensive hints for the exercises, bordering on complete solutions in some cases. This is a resource that will surely prove extremely useful for all teachers of such a course...there is no denying that Essential Mathematical Biology is superbly designed for the purpose it serves, and will, I am sure, become a popular text book across the world. UK Nonlinear News Britton explains how difference and differential equations have been used to formulate theory and description in biology, but at a level accessible to undergraduate mathematics, physics or engineering majors. His very readable style achieves clear and largely jargon-free explanations with no sacrifice of mathematical rigour.....Clearly intended to be read and used as a course textbook, another attractive feature of this volume is the inclusion of interesting and relevant exercises after each subchapter section, together with an appendix of hints to help students work and understand them. Other appendixes efficiently review the mathematical techniques and concepts that are basic to the applications presented in the chapters....I believe that Essential Mathematical Biology will enrich the personal library of any scholar interested in applied differential equations. The Quarterly Review of Biology, Volume 79, No. 2 "This excellent monograph provides a very readable introduction to the most important aspects of mathematical biology. … The book contains numerous exercises, with hints for the solutions, a guide for further studies, and interesting historical comments. An index helps in finding the many concepts and equations introduced in the monograph. This is a most welcome addition to the literature." (Jean Mawhin, Bulletin of the Belgian Mathematical Society, Vol. 12 (1), 2005) "This book as a textbook covers a diversity of topics from mathematical biology. Its content is best summarized by the title of its eight substantial Chapters. … It poses questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. … includes many exercises as well as detailed solutions for them. … a good introduction for those beginners that are interested in the fast growing field of mathematical biology." (Lan-Sun Chen, Mathematical Reviews, 2003m) "Each chapter of this textbook provides a brief introduction into an important area of mathematical biology. … In addition, there are four appendices, comprising about one fourth of the whole text, which summarize important techniques … . The book is aimed at the undergraduate level … . Many exercises, together with hints for their solution, complement this text which will be useful as a first introduction." (R. Bürger, Monatshefte für Mathematik, Vol. 143 (4), 2004) "In brevity and simplicity lies the great strength of this book. It explains its chosen topics clearly and simply … that can be understood and appreciated by undergraduate students. Indeed, the level of writing is superb … . Just as useful as the writing style are the appendices and the hints. … will surely prove extremely useful for all teachers of such a course. … will, I am sure, become a popular text book across the world." (James Sneyd, UK Nonlinear News, June, 2004) "Britton writes a book that provides for an introductory account of mathematical biology. … Many examples are given … . The figures are clear and precise. All mathematical formulae, equations and models are complete, clear and readable. … The material in the book is clear and concise. The book provides the reader with a wealth of information and is well suited as a textbook for a course in mathematical biology. I highly recommend this book … . It makes a worthwhile addition." (Paul Johnson, New Zealand Mathematical Society Newsletter, Issue 90, April, 2004) "It was a great pleasure reading Essential Mathematical Biology. … the book is very well written without large jumps in the mathematical reasoning, it is also quite concise and covers a large amount of material. … The writing and style are very clear. The mathematical steps are laid out neatly with clear definitions and notation … . The book is a great contribution to students interested in mathematical biology … and a source of important insights for biological scientists." (D. Kault, The Australian Mathematical Society, Vol. 31 (1), 2004) "This book is a self-contained introduction to the fast-growing field of mathematical biology. … it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. A broad range of topics is covered … ." (L’Enseignement Mathematique, Vol. 49 (3-4), 2003) "Those of us in mathematical biology like to imagine our field on the verge of achieving critical opalescence … . it is a pleasure and challenge to share the wide spectrum of problems and approaches with eager undergraduates from various backgrounds … . Several textbooks are available, now including Essential Mathematical Biology by Nicholas Britton. The author … exemplifies interdisciplinary approaches … . Essential Mathematical Biology would serve well as a template for an advanced undergraduate or beginning graduate course … ." (Fred Adler, Physics Today, March, 2004) "Each of the eight chapters starts with a brief list of clearly expressed goals, questions or explanations, well motivating the reader to enter the chapter by introducing him into the essential biological problems and their importance. … I can fully recommend to use this ‘undergraduate mathematics textbook’ in any theoretical or practical computer course introducing into Mathematical Biology, but also for other teaching or education purposes within this interdisciplinary filed of growing importance between Mathematics, Scientific Computing, Bioinformatics, Systems Biology, Ecology, Physiology and Biomedicine." (Wolfgang Alt, Mathematical Biosciences, Vol. 208, 2007)Table of Contents1. Single Species Population Dynamics.- 2. Population Dynamics of Interacting Species.- 3. Infectious Diseases.- 4. Population Genetics and Evolution.- 5. Biological Motion.- 6. Molecular and Cellular Biology.- 7. Pattern Formation.- 8. Tumour Modelling.- Further Reading.- A. Some Techniques for Difference Equations.- A.1 First-order Equations.- A.1.1 Graphical Analysis.- A.1.2 Linearisation.- A.2 Bifurcations and Chaos for First-order Equations.- A.2.1 Saddle-node Bifurcations.- A.2.2 Transcritical Bifurcations.- A.2.3 Pitchfork Bifurcations.- A.2.4 Period-doubling or Flip Bifurcations.- A.3 Systems of Linear Equations: Jury Conditions.- A.4 Systems of Nonlinear Difference Equations.- A.4.1 Linearisation of Systems.- A.4.2 Bifurcation for Systems.- B. Some Techniques for Ordinary Differential Equations.- B.1 First-order Ordinary Differential Equations.- B.1.1 Geometric Analysis.- B.1.2 Integration.- B.1.3 Linearisation.- B.2 Second-order Ordinary Differential Equations.- B.2.1 Geometric Analysis (Phase Plane).- B.2.2 Linearisation.- B.2.3 Poincaré-Bendixson Theory.- B.3 Some Results and Techniques for rath Order Systems.- B.3.1 Linearisation.- B.3.2 Lyapunov Functions.- B.3.3 Some Miscellaneous Facts.- B.4 Bifurcation Theory for Ordinary Differential Equations.- B.4.1 Bifurcations with Eigenvalue Zero.- B.4.2 Hopf Bifurcations.- C. Some Techniques for Partial Differential Equations.- C.1 First-order Partial Differential Equations and Characteristics.- C.2 Some Results and Techniques for the Diffusion Equation.- C.2.1 The Fundamental Solution.- C.2.2 Connection with Probabilities.- C.2.3 Other Coordinate Systems.- C.3 Some Spectral Theory for Laplace’s Equation.- C.4 Separation of Variables in Partial Differential Equations.- C.5 Systems of Diffusion Equations with Linear Kinetics.- C.6 Separating the Spatial Variables from Each Other.- D. Non-negative Matrices.- D.1 Perron-Frobenius Theory.- E. Hints for Exercises.

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Book SynopsisThis compact textbook provides a foundation in mathematics for STEM students entering university. The book helps students from different disciplines and backgrounds make the transition to university. Based on the author’s teaching for many years, the book can be used as a textbook and a resource for lecturers and professors. Its accessibility is such that it is can also be used by students in their final year in school before university and help them continue their mathematical studies at college. The book is designed so that students will return to the book repeatedly as their undergraduate careers progress. Although compact and concise, it loses no rigour. All the topics are carefully explained meaningfully, not just presented as a set of rules or rote-learned procedures. Table of ContentsTrigonometry.- Real and Complex Numbers.- Vector Algebra.- Matrices.- Differentiation.

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Book SynopsisThis compact textbook provides a foundation in mathematics for STEM students entering university. The book helps students from different disciplines and backgrounds make the transition to university. Based on the author’s teaching for many years, the book can be used as a textbook and a resource for lecturers and professors. Its accessibility is such that it is can also be used by students in their final year in school before university and help them continue their mathematical studies at college. The book is designed so that students will return to the book repeatedly as their undergraduate careers progress. Although compact and concise, it loses no rigour. All the topics are carefully explained meaningfully, not just presented as a set of rules or rote-learned procedures. Table of ContentsTrigonometry.- Real and Complex Numbers.- Vector Algebra.- Matrices.- Differentiation.

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Book SynopsisThis monograph provides a concise overview of nonlinear internal wave theory. It serves as a self-contained reference for both students of mathematics as well as scientific professionals by presenting the material in two parts, isolating the narrative analysis from the mathematical detail. This unique format allows the text to remain accessible to oceanographers and researchers outside of mathematics by presenting a range of relevant theories on their own terms. Conversely, it enables applied mathematicians to understand how the conversation between mathematics and sciences proceeds in a field that has developed through a combination of the two. In addition, the text is supplemented by hands-on Matlab software, as the book incorporates a collection of working codes that enable readers to reproduce all theoretical figures in the text, with modification potential to fit a range of applications including a number of mini-projects outlined throughout the text.Table of ContentsPreface.- Background and Equation Summaries.- Derivations: Linear, Weakly Nonlinear and Conjugate Flow Theory.- Using Linear and Weakly Nonlinear Theory.- Exact Internal Solitary Waves.- Exact Internal Hydraulics.- Mode-2 Waves.- Concluding Thoughts.

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Book SynopsisThis book explores recent topics in quantitative finance with an emphasis on applications and calibration to time-series. This last aspect is often neglected in the existing mathematical finance literature while it is crucial for risk management. The first part of this book focuses on switching regime processes that allow to model economic cycles in financial markets. After a presentation of their mathematical features and applications to stocks and interest rates, the estimation with the Hamilton filter and Markov Chain Monte-Carlo algorithm (MCMC) is detailed. A second part focuses on self-excited processes for modeling the clustering of shocks in financial markets. These processes recently receive a lot of attention from researchers and we focus here on its econometric estimation and its simulation. A chapter is dedicated to estimation of stochastic volatility models. Two chapters are dedicated to the fractional Brownian motion and Gaussian fields. After a summary of their features, we present applications for stock and interest rate modeling. Two chapters focuses on sub-diffusions that allows to replicate illiquidity in financial markets. This book targets undergraduate students who have followed a first course of stochastic finance and practitioners as quantitative analyst or actuaries working in risk management.Trade Review“Hainaut has written a book which in such panorama has a position of its own and which should be considered with great interest. … the book should definitely be considered an excellent and warmly recommended read. It is likely that it will be soon become a reference for those interested in modern topics and for young researchers in particular.” (Gianluca Cassese, zbMATH 1512.91001, 2023)Table of ContentsPreface.- Acknowledgements.- Notations.- 1. Switching Models: Properties and Estimation.- 2. Estimation of Continuous Time Processes by Markov Chain Monte Carlo.- 3. Particle Filtering and Estimation.- 4. Modeling of Spillover Effects in Stock Markets.- 5. Non-Markov Models for Contagion and Spillover.- 6. Fractional Brownian Motion.- 7. Gaussian Fields for Asset Prices.- 8. Lévy Interest Rate Models With a Long Memory.- 9. Affine Volterra Processes and Rough Models.- 10. Sub-Diffusion for Illiquid Markets.- 11. A Fractional Dupire Equation for Jump-Diffusions.- References.

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Book SynopsisThis book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information.In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with some kind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately.Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use. Table of ContentsIntroduction.- Topological foundations, hypercomplexes and homology.- Weighted complexes, cohomology and Laplace operators.- The Laplace operator and the geometry of graphs.- Metric spaces and manifolds.- Linear methods: Kernels, variations, and averaging.- Nonlinear schemes: Clustering, feature extraction and dimension reduction.- Manifold learning, the scheme of Laplacian eigenmaps.- Metrics and curvature.

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Book SynopsisThe aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods.Modelling and simulating the mechanisms that cells use to move, self-organise and develop in tissues is not only fundamental to an understanding of embryonic development, but is also relevant in tissue engineering and in other environmental and industrial processes involving the growth and homeostasis of biological systems. Growth and organization processes are also important in many tissue degeneration and regeneration processes, such as tumour growth, tissue vascularization, heart and muscle functionality, and cardio-vascular diseases.Table of ContentsPreface.- Cell-based, continuum and hybrid models of tissue dynamics.- The Diffusion Limit of Transport Equations in Biology.- Mathematical Models of the Interaction of Cells and Cell Aggregates with the Extracellular Matrix.- Mathematical modeling of morphogenesis in living materials.- Multiscale computational modelling and analysis of cancer invasion.

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Book SynopsisThis introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.Trade Review"(The book is) a lean and largely self-contained introduction to the modern theory of probability, aimed at advanced undergraduate or beginning graduate students. The 28 short chapters belie the book's genesis as polished lecture notes; the exposition is sleek and rigorous and each chapter ends with a supporting collection of mainly routine exercises. ... The authors make it clear what luggage is required for this exhilarating trek,... a good knowledge of advanced calculus, some linear algebra, and some "mathematical sophistication". With this understood, the itinerary is immaculately paced and planned with just the right balances of technical ascents and pauses to admire the scenery. Within the constraints of a slim volume, it is hard to imagine how the authors could have done a more effective or more attractive job." The Mathematical Gazette, Vol. 84, No 500, 2000 "The authors provide the shortest path through the twenty-eight chapter headings. The topics are treated in a mathematically and pedagogically digestible way. The writing is concise and crisp: the average chapter length is about eight pages. ... Numerous exercises add to the value of the text as a teaching tool. In conclusion, this is an excellent text for the intended audience."Short Book Reviews, Vol. 21, No. 2, 2001Table of Contents1. Introduction 2. Axioms of Probability 3. Conditional Probability and Independence 4. Probabilities on a Countable Space 5. Random Variables on a Countable Space 6. Construction of a Probability Measure 7. Construction of a Probability Measure on R 8. Random Variables 9. Integration with Respect to a Probability Measure 10. Independent Random Variables 11. Probability Distributions on R 12. Probability Distributions on Rn 13. Characteristic Functions 14. Properties of Characteristic Functions 15. Sums of Independent Random Variables 16. Gaussian Random Variables (The Normal and the Multivariate Normal Distributions) 17. Convergence of Random Variables 18. Weak Convergence 19. Weak Convergence and Characteristic Functions 20. The Laws of Large Numbers 21. The Central Limit Theorem 22. L2 and Hilbert Spaces 23. Conditional Expectation 24. Martingales 25. Supermartingales and Submartingales 26. Martingale Inequalities 27. Martingales Convergence Theorems 28. The Radon-Nikodym Theorem

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisWhat is a game? Classically, a game is perceived as something played by human beings. Its mathematical analysis is human-centered, explores the structures of particular games, economic or social environments and tries to model supposedly 'rational' human behavior in search of appropriate 'winning strategies'. This point of view places game theory into a very special scientific corner where mathematics, economics and psychology overlap and mingle.This book takes a novel approach to the subject. Its focus is on mathematical models that apply to game theory in particular but exhibit a universal character and thus extend the scope of game theory considerably.This textbook addresses anyone interested in a general game-theoretic view of the world. The reader should have mathematical knowledge at the level of a first course in real analysis and linear algebra. However, possibly more specialized aspects are further elaborated and pointers to relevant supplementary literature are given. Moreover, many examples invite the reader to participate 'actively' when going through the material. The scope of the book can be covered in one course on Mathematical Game Theory at advanced undergraduate or graduate level.

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Book SynopsisThis book explores recent developments in theoretical research and mathematical modelling of real-world complex systems, organized in four parts. The first part of the book is devoted to the mathematical tools for the design and analysis in engineering and social science study cases. We discuss the periodic evolutions in nonlinear chemical processes, vibro-compact systems and their behaviour, different types of metal–semiconductor self-assembled samples, made of silver nanowires and zinc oxide nanorods. The second part of the book is devoted to mathematical description and modelling of the critical events, climate change and robust emergency scales. In three chapters, we consider a climate-economy model with endogenous carbon intensity and the behaviour of Tehran Stock Exchange market under international sanctions. The third part of the book is devoted to fractional dynamic and fractional control problems. We discuss the novel operational matrix technique for variable-order fractional optimal control problems, the nonlinear variable-order time fractional convection–diffusion equation with generalized polynomials The fourth part of the book concerns solvability and inverse problems in differential and integro-differential equations. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists and urban planners.Table of ContentsAlbert C.J. Luo, The Chinese Calligraphy in Memory of Professor Valentin Afraimovich (1945-2018) Chapter 01: Mayra Angélica Bárcenas-Castro, Ramón Díaz de León-Zapata, Saúl Almazán-Cuéllar, Efrén Flores-García, Gustavo Vera-Reveles, José Vulfrano González-Fernández, Applications of the fundamentals of Bézier curves Chapter 02: Siyu Guo, Albert C. J. Luo On complex periodic evolutions of a periodically diffused Brussellator Chapter 03: Victor Bazhenov, Olga Pogorelova, Tatiana Postnikova Analysis of Intermittent and Quasi-periodic Transitions to Chaos in Vibro-impact System with Continuous Wavelet Transform Chapter 04: Lev A. Ostrovsky, Yury A. Stepanyants Complex Dynamics of Solitons in Rotating Fluids Chapter 05: Dmitry V. Kovalevsky A Climate-Economy Model with Endogenous Carbon Intensity Chapter 06: Abootaleb Shirvani, Dimitri Volchenkov A Regulated Market Under Sanctions. On Tail Dependence Between Oil, Gold, and Tehran Stock Exchange Index Chapter 07: Dmitry V. Kovalevsky and Mara Manez Costa Dynamics of Water-Constrained Economies Affected by Climate Change: Nonlinear and Stochastic Effects Chapter 08: H. Hassani, J. A. Tenreiro Machado An efficient operational matrix technique for variable-order fractional optimal control problems Chapter 09: H. Hassani, J. A. Tenreiro Machado, Z. Avazzadeh, E. Naraghirad Solving nonlinear variable-order time fractional convection-diffusion equation with generalized polynomials Chapter 10: C. Connell McCluskey ,Vitali Vougalter Inverse problems for some systems of parabolic equations Chapter 11: Vitali Vougalter, Vitaly Volpert Solvability In The Sense Of Sequences For Some Non Fredholm Operators With The Bi-Laplacian

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Book SynopsisThis book introduces machine learning methods in finance. It presents a unified treatment of machine learning and various statistical and computational disciplines in quantitative finance, such as financial econometrics and discrete time stochastic control, with an emphasis on how theory and hypothesis tests inform the choice of algorithm for financial data modeling and decision making. With the trend towards increasing computational resources and larger datasets, machine learning has grown into an important skillset for the finance industry. This book is written for advanced graduate students and academics in financial econometrics, mathematical finance and applied statistics, in addition to quants and data scientists in the field of quantitative finance. Machine Learning in Finance: From Theory to Practice is divided into three parts, each part covering theory and applications. The first presents supervised learning for cross-sectional data from both a Bayesian and frequentist perspective. The more advanced material places a firm emphasis on neural networks, including deep learning, as well as Gaussian processes, with examples in investment management and derivative modeling. The second part presents supervised learning for time series data, arguably the most common data type used in finance with examples in trading, stochastic volatility and fixed income modeling. Finally, the third part presents reinforcement learning and its applications in trading, investment and wealth management. Python code examples are provided to support the readers' understanding of the methodologies and applications. The book also includes more than 80 mathematical and programming exercises, with worked solutions available to instructors. As a bridge to research in this emergent field, the final chapter presents the frontiers of machine learning in finance from a researcher's perspective, highlighting how many well-known concepts in statistical physics are likely to emerge as important methodologies for machine learning in finance.Trade Review“This book is, however, a well-structured and self-contained graduate textbook on ML applications in finance. Exercises and some applications are included at the end of each chapter and the Python code used in this book makes use of the Python Tensor Flow library. This book could also serve as a useful reference book for researchers and practitioners in quantitative finance.” (Gilles Teyssière, Mathematical Reviews, February, 2023)“Each part is introduced with background information, examples of relevant practical applications, and references to the most recent scientific literature. … The book covers all essential areas of machine learning with relevance to quantitative finance. … An additional strong advantage of this book is the clear and consistent structure of its chapters. … Overall, the book covers multiple machine learning approaches with advanced technical exposition and is therefore especially suitable as an academic reference point, especially on Reinforcement Learning.” (Antoniya Shivarova, Financial Markets and Portfolio Management, Issue 35, 2021)“This volume aims to present a broad yet technical treatment of (ML) algorithms used by financial practitioners and scholars alike. … the book fills a large void. … This encourages reproducibility as well as learning by doing, which is highly appreciated.” (Guillaume Coqueret, Quantitative Finance, October 15, 2020)Table of ContentsChapter 1. Introduction.- Chapter 2. Probabilistic Modeling.- Chapter 3. Bayesian Regression & Gaussian Processes.- Chapter 4. Feed Forward Neural Networks.- Chapter 5. Interpretability.- Chapter 6. Sequence Modeling.- Chapter 7. Probabilistic Sequence Modeling.- Chapter 8. Advanced Neural Networks.- Chapter 9. Introduction to Reinforcement learning.- Chapter 10. Applications of Reinforcement Learning.- Chapter 11. Inverse Reinforcement Learning and Imitation Learning.- Chapter 12. Frontiers of Machine Learning and Finance.

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