The Big Bang of Numbers
Our universe has multiple origin stories, from religious creation myths to the Big Bang of scientists. But if we leave those behind and start from nothing--no matter, no cosmos, not even empty space--could we create a universe using only math? Irreverent, richly illustrated, and boundlessly creative, The Big Bang of Numbers invites us to try.In this new mathematical origin story, mathematician and novelist Manil Suri creates a natural progression of ideas needed to design our world, starting with numbers and continuing through geometry, algebra, and beyond. He reveals the secret lives of real and imaginary numbers, teaches them to play abstract games with real-world applications, discovers unexpected patterns that connect humble lifeforms to enormous galaxies, and explores mathematical underpinnings for randomness and beauty. With evocative examples ranging from multidimensional crochet to the Mona Lisa's asymmetrical smile, as well as ingenious storytelling that helps illuminate complex concepts like infinity and relativity, The Big Bang of Numbers charts a playful, inventive course to existence. Mathematics, Suri shows, might best be understood not as something we invent to explain Nature, but as the source of all creation, whose directives Nature tries to obey as best she can.Offering both striking new perspectives for math aficionados and an accessible introduction for anyone daunted by calculation, The Big Bang of Numbers proves that we can all fall in love with math.
Games Businesses Play
Game theory has come to dominate industrial organization economics, but business strategists continue to debate its usefulness. So far, empirical work on the application of game theory to business strategy has been too limited to force a consensus. As a (partial) remedy, Games Businesses Play uses detailed case studies of competitive interaction to explore the uses and limits of game theory as a tool for business strategists. Because they are analytical rather than descriptive, the case studies are not typical teaching cases. The cases are paired with customized game-theoretic models that cover a wide range of commitment decisions, from short-run commitments such as price to longer-run commitments such as capacity expansion and reduction, product and process innovation, and battles for market share. A variety of quantitative and qualitative techniques are used to test the models' predictions on case data. In addition the book sheds light on a number of other issues important to strategic management, including the resource-based view of the firm and the emergent theory of dynamic capabilities.
Real Analysis
This book provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems.
Computational Genomics with R
This book has fundamental theoretical and practical aspects of data analysis, useful for beginners and experienced researchers that are looking for a recipe or an analysis approach. Since R has many packages, even experienced researchers look for how particular functions are used in an analysis workflow.
Stochastic Processes in Cell Biology
Sensing the environment.- Intracellular pattern formation and reaction-diffusion processes.- Statistical mechanics and dynamics of polymers and membranes.- Self-organization and assembly of cellular structures.- Dynamics and regulation of the cytoskeleton.- Bacterial population growth and collective behavior.- Stochastic reaction-diffusion processes.
Neural Networks are Homeomorphisms
This book is an introductory guide for data scientists to learn the mathematical principles behind the most well-known AI algorithms. The author proposes two original theoretical concepts: the accordion theory and the recurrent third iteration theory. He then applies them to real cases. This work covers topics of higher mathematics from algebraic topology and spectral theory to functional analysis and ergodic theory. These concepts are fundamental to understanding AI concepts and algorithms. This deepens both practitioners' and managers' knowledge of mathematical modeling and assists them to engage with specialized literature. More importantly this book will help them to formally write their own ideas and research.
Spatial Dynamics Models in the Life Sciences and the Role of Feedback in Robust Developments
Basic mathematical techniques for partial differential equations (PDE) with applications to the life sciences form an integral part of the core curriculum for programs in mathematical biology. Yet, students in such a program with an undergraduate training in biology are typically deficient in any exposure to PDE. This volume starts with simple first order PDE and progresses through higher order equations and systems but with interesting applications, even at the level of a single first order PDE with constant coefficients.Similar to the two previous volumes by the author, another unique feature of the book is highlighting the scientific theme(s) of interest for the biological phenomena being modelled and analysed. In addition to temporal evolution of a biological phenomenon, its limiting equilibrium states and their stability, the possibility of locational variations leads to a study of additional themes such as (signal and wave) propagation, spatial patterning and robustness. The requirement that biological developments are relatively insensitive to sustained environmental changes provides an opportunity to examine the issue of feedback and robustness not encountered in the previous two volumes of this series.
Study of Linear and Nonlinear Models with Mathematica
The book is devoted to the problems of modeling physical systems and fields using the tools and capabilities of the 'Mathematica' software package. In the process of teaching classical courses in mechanics and mathematical physics, one often has to overcome significant difficulties associated with the cumbersomeness of the mathematical apparatus, which more than once distracts from the essence of the problems under consideration. The use of the 'Mathematica' package, which has a rich set of analytical and graphic tools, makes the presentation of classic issues related to modeling and interpretation of physical processes much more transparent. This package enables the visualization of both analytical solutions of nonlinear differential equations and solutions obtained in the form of infinite series or special functions.The textbook consists of two parts that can be studied independently of each other. The first part deals with the issues of nonlinear mechanics and the theory of oscillations. The second part covers linear problems of classical mathematical physics and nonlinear evolution models describing, inter alia, transport phenomena and propagation of waves. The book contains the codes of programs written in the 'Mathematica' package environment. Supplementary materials of programs illustrating and often complementing the presented material are available on the publisher's website.
Classical Lie Algebras at Infinity
Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension.The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Cofinally Complete Metric Spaces and Related Functions
The monograph targets a huge variety of characterizations of cofinally complete metric spaces. These spaces are studied in terms of several properties of some classes of functions between metric spaces that are stronger than the continuous functions such as Cauchy-regular, uniformly continuous, strongly uniformly continuous, and various Lipschitz-type functions. There is one chapter that is dedicated to studying cofinally complete metric spaces in terms of hyperspace and function space topologies. Along with that, various characterizations are studied in terms of geometric functionals, sequences, Cantor-type conditions, etc. The study of such spaces is interesting as well as it has nice connections with various other branches of mathematics such as convex analysis, optimization theory, fixed point theory, functional analysis and approximation theory. But until now, there has been no textbook or research monograph which presents the entire theory of these spaces in a comprehensive way. The study of the aforesaid spaces and their variants is still a vibrant area of research, and many prominent researchers are working in this area.The book is targeted at researchers as well as graduate students interested in real functions, analysis on metric spaces, topology, and the aforementioned. Since the monograph often discusses various properties of Lipschitz-type functions, it would be of interest to people interested in PDEs as well.
Geometry of Deep Learning
The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems.Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.
Stochastic Processes in Cell Biology
Introduction.- Random walks and Brownian motion.- Protein receptors and ion channels.- Molecular motors.- Stochastic gene expression and regulatory networks.- Diffusive transport.- Active transport.- The WKB method, path integrals, and large deviations.- Probability theory and martingales.
Numerical Methods and Optimization
This text, covering a very large span of numerical methods and optimization, is primarily aimed at advanced undergraduate and graduate students. A background in calculus and linear algebra are the only mathematical requirements. The abundance of advanced methods and practical applications will be attractive to scientists and researchers working in different branches of engineering. The reader is progressively introduced to general numerical methods and optimization algorithms in each chapter. Examples accompany the various methods and guide the students to a better understanding of the applications. The user is often provided with the opportunity to verify their results with complex programming code. Each chapter ends with graduated exercises which furnish the student with new cases to study as well as ideas for exam/homework problems for the instructor. A set of programs made in Matlab(TM) is available on the author's personal website and presents both numerical and optimization methods.
Protecting Privacy Through Homomorphic Encryption
This book summarizes recent inventions, provides guidelines and recommendations, and demonstrates many practical applications of homomorphic encryption. This collection of papers represents the combined wisdom of the community of leading experts on Homomorphic Encryption. In the past 3 years, a global community consisting of researchers in academia, industry, and government, has been working closely to standardize homomorphic encryption. This is the first publication of whitepapers created by these experts that comprehensively describes the scientific inventions, presents a concrete security analysis, and broadly discusses applicable use scenarios and markets. This book also features a collection of privacy-preserving machine learning applications powered by homomorphic encryption designed by groups of top graduate students worldwide at the Private AI Bootcamp hosted by Microsoft Research.The volume aims to connect non-expert readers with thisimportant new cryptographic technology in an accessible and actionable way. Readers who have heard good things about homomorphic encryption but are not familiar with the details will find this book full of inspiration. Readers who have preconceived biases based on out-of-date knowledge will see the recent progress made by industrial and academic pioneers on optimizing and standardizing this technology. A clear picture of how homomorphic encryption works, how to use it to solve real-world problems, and how to efficiently strengthen privacy protection, will naturally become clear.
The Elements of Hawkes Processes
Hawkes processes are studied and used in a wide range of disciplines: mathematics, social sciences, and earthquake modelling, to name a few. This book presents a selective coverage of the core and recent topics in the broad field of Hawkes processes. It consists of three parts. Parts I and II summarise and provide an overview of core theory (including key simulation methods) and inference methods, complemented by a selection of recent research developments and applications. Part III is devoted to case studies in seismology and finance that connect the core theory and inference methods to practical scenarios. This book is designed primarily for applied probabilists, statisticians, and machine learners. However, the mathematical prerequisites have been kept to a minimum so that the content will also be of interest to undergraduates in advanced mathematics and statistics, as well as machine learning practitioners. Knowledge of matrix theory with basics of probability theory, including Poisson processes, is considered a prerequisite. Colour-blind-friendly illustrations are included.
Fundamentals of Statistical Thinking
Written for students with basic experience in college algebra and applied calculus, Fundamentals of Statistical Thinking: Tools and Applications familiarizes readers with fundamental concepts in statistical thinking in order to prepare them for specialized management courses such as econometrics and quantitative analysis. The book is organized into four sections, each of which focuses on a common tool used in application. Chapters 1 through 4 discuss data analysis and summaries, with an emphasis on descriptive statistics and visualization. In Chapters 5 through 8 students learn about probability models and sampling distributions. Chapters 9 and 10 deal with statistical inferences, while Chapters 11 and 12 provide further applications for categorical data and simple linear regression models. Graphical illustrations support the written text and each chapter concludes with a visual summary. Rooted in over ten years of classroom experience at both the undergraduate and graduate levels, Fundamentals of Statistical Thinking helps readers understand the importance of the main technical tools of statistical decision making, and explains when they can most appropriately be used for applied studies.
Foundations of Quantitative Finance Book II: Probability Spaces and Random Variables
Every financial professional wants and needs an advantage. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not-and that is the advantage these books offer the astute reader.
Fuzzy Natural Logic in IFSA-EUSFLAT 2021
The present book contains five papers accepted and published in the Special Issue, "Fuzzy Natural Logic in IFSA-EUSFLAT 2021", of the journal Mathematics (MDPI). These papers are extended versions of the contributions presented in the conference "The 19th World Congress of the International Fuzzy Systems Association and the 12th Conference of the European Society for Fuzzy Logic and Technology jointly with the AGOP, IJCRS, and FQAS conferences", which took place in Bratislava (Slovakia) from September 19 to September 24, 2021.Fuzzy Natural Logic (FNL) is a system of mathematical fuzzy logic theories that enables us to model natural language terms and rules while accounting for their inherent vagueness and allows us to reason and argue using the tools developed in them. FNL includes, among others, the theory of evaluative linguistic expressions (e.g., small, very large, etc.), the theory of fuzzy and intermediate quantifiers (e.g., most, few, many, etc.), and the theory of fuzzy/linguistic IF-THEN rules and logical inference. The papers in this Special Issue use the various aspects and concepts of FNL mentioned above and apply them to a wide range of problems both theoretically and practically oriented.This book will be of interest for researchers working in the areas of fuzzy logic, applied linguistics, generalized quantifiers, and their applications.
Mathematical Puzzle Tales from Mount Olympus
This book uses fascinating tales from Greek Mythology as the background for introducing mathematics puzzles to the general public. A background in high school mathematics will be ample preparation for using this book, and it should appeal to anyone who enjoys puzzles and recreational mathematics.
Lectures on the Theory of Elliptic Functions; Volume I
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An Elementary Course of Infinitesimal Calculus
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A History of Mechanics
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The Continuum, and Other Types of Serial Order, With an Introduction to Cantor's Transfinite Numbers
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Census of England and Wales, 1911 (10 Edward 7 and 1 George 5, ch. 27); Volume 1
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Census of Prairie Provinces. Population and Agriculture. Manitoba, Saskatchewan, Alberta. 1916
The Bible Reader's Aids ..
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Report On The Census Of Porto Rico, 1899
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Sir Isaac Newton's Two Treatises
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Census of Prairie Provinces. Population and Agriculture. Manitoba, Saskatchewan, Alberta. 1916
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A Treatise Of The System Of The World
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The Adjustment of Observations by the Method of Least Squares With Applications to Geodetic Work
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Lectures on the Theory of Elliptic Functions; Volume I
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Canada Year Book
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Fundamenta Nova Theoriae Functionum Ellipticarum
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Lectures on the Theory of Elliptic Functions
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A Treatise On The Dynamics Of A System Of Rigid Bodies. With Numerous Examples
Calculus
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Annual Report of the Commissioner of Indian Affairs for the Year 1883
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Report On the Census of Cuba, 1899
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Exponential Families in Theory and Practice
During the past half-century, exponential families have attained a position at the center of parametric statistical inference. Theoretical advances have been matched, and more than matched, in the world of applications, where logistic regression by itself has become the go-to methodology in medical statistics, computer-based prediction algorithms, and the social sciences. This book is based on a one-semester graduate course for first year Ph.D. and advanced master's students. After presenting the basic structure of univariate and multivariate exponential families, their application to generalized linear models including logistic and Poisson regression is described in detail, emphasizing geometrical ideas, computational practice, and the analogy with ordinary linear regression. Connections are made with a variety of current statistical methodologies: missing data, survival analysis and proportional hazards, false discovery rates, bootstrapping, and empirical Bayes analysis. The book connects exponential family theory with its applications in a way that doesn't require advanced mathematical preparation.
Knowledge is Power
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Newton's Interpolation Formulas
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Linear and Nonlinear Non-Fredholm Operators
This book is devoted to a new aspect of linear and nonlinear non-Fredholm operators and its applications. The domain of applications of theory developed here is potentially much wider than that presented in the book. Therefore, a goal of this book is to invite readers to make contributions to this fascinating area of mathematics.First, it is worth noting that linear Fredholm operators, one of the most important classes of linear maps in mathematics, were introduced around 1900 in the study of integral operators. These linear Fredholm operators between Banach spaces share, in some sense, many properties with linear maps between finite dimensional spaces. Since the end of the previous century there has been renewed interest in linear - nonlinear Fredholm maps from a topological degree point of view and its applications, following a period of "stagnation" in the mid-1960s. Now, linear and nonlinear Fredholm operator theory and the solvability of corresponding equations both from the analytical and topological points of view are quite well understood.Also noteworthy is, that as a by-product of our results, we have obtained an important tool for modelers working in mathematical biology and mathematical medicine, namely, the necessary conditions for preserving positive cones for systems of equations without Fredholm property containing local - nonlocal diffusion as well as terms for transport and nonlinear interactions.
Wavelet Analysis on Local Fields of Positive Characteristic
Local Fields.- Multiresolution Analysis on Local Fields.- Affine, Quasi-Affine and Co-Affine Frames.- Characterizations in Wavelet Analysis.- Biorthogonal Wavelets.- Wavelet Packets and Frame Packets.- Wavelets as Unconditional Bases.- Shift-Invariant Spaces and Wavelets.
Complex Symmetries
This volume is a collection of essays on complex symmetries. It is curated, emphasizing the analysis of the symmetries, not the various phenomena that display those symmetries themselves. With this, the volume provides insight to nonspecialist readers into how individual simple symmetries constitute complex symmetry. The authors and the topics cover many different disciplines in various sciences and arts. Simple symmetries, such as reflection, rotation, translation, similitude, and a few other simple manifestations of the phenomenon, are all around, and we are aware of them in our everyday lives. However, there are myriads of complex symmetries (composed of a bulk of simple symmetries) as well. For example, the well-known helix represents the combination of translational and rotational symmetry. Nature produces a great variety of such complex symmetries. So do the arts. The contributions in this volume analyse selected examples (not limited to geometric symmetries).These include physical symmetries, functional (meaning not morphological) symmetries, such as symmetries in the construction of the genetic code, symmetries in human perception (e.g., in geometry education as well as in constructing physical theories), symmetries in fractal structures and structural morphology, including quasicrystal and fullerene structures in stable bindings and their applications in crystallography and architectural design, as well as color symmetries in the arts. The volume is rounded of with beautiful illustrations and presents a fascinating panorama of this interdisciplinary topic.
Preliminary Report On the Eighth Census. 1860
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