Topics in Complex Analysis
This graduate-level mathematics textbook provides an in-depth and readable exposition of selected topics in complex analysis. The material spans both the standard theory at a level suitable for a first-graduate class on the subject and several advanced topics delving deeper into the subject and applying the theory in different directions. The focus is on beautiful applications of complex analysis to geometry and number theory. The text is accompanied by beautiful figures illustrating many of the concepts and proofs. Among the topics covered are asymptotic analysis; conformal mapping and the Riemann mapping theory; the Euler gamma function, the Riemann zeta function, and a proof of the prime number theorem; elliptic functions, and modular forms. The final chapter gives the first detailed account in textbook format of the recent solution to the sphere packing problem in dimension 8, published by Maryna Viazovska in 2016 -- a groundbreaking proof for which Viazovska was awarded the Fields Medal in 2022. The book is suitable for self-study by graduate students or advanced undergraduates with an interest in complex analysis and its applications, or for use as a textbook for graduate mathematics classes, with enough material for 2-3 semester-long classes. Researchers in complex analysis, analytic number theory, modular forms, and the theory of sphere packing, will also find much to enjoy in the text, including new material not found in standard textbooks.
Flows on Compact Surfaces
This textbook offers a uniquely accessible introduction to flows on compact surfaces, filling a gap in the existing literature. The book can be used for a single semester course and/or for independent study. It demonstrates that covering spaces provide a suitable and modern setting for studying the structure of flows on compact surfaces. The thoughtful treatment of flows on surfaces uses topology (especially covering spaces), the classification of compact surfaces, and Euclidean and hyperbolic rigid motions to establish structural theorems that describe flows on surfaces generally. Several of the topics from dynamical systems that appear in this book (e.g., fixed points, invariant sets, orbits, almost periodic points) also appear in the many subareas of dynamical systems. The book successfully presents the reader with a self-contained introduction to dynamical systems or an expansion of one's existing knowledge of the field. Prerequisites include completion of a graduate-level topology course; a background in dynamical systems is not assumed.
Anova with Dependent Errors
This book presents the latest results related to one- and two-way models for time series data. Analysis of variance (ANOVA) is a classical statistical method for IID data proposed by R.A. Fisher to investigate factors and interactions of phenomena. In contrast, the methods developed in this book apply to time series data. Testing theory of the homogeneity of groups is presented under a wide variety of situations including uncorrelated and correlated groups, fixed and random effects, multi- and high-dimension, parametric and nonparametric spectral densities. These methods have applications in several scientific fields. A test for the existence of interactions is also proposed. The book deals with asymptotics when the number of groups is fixed and sample size diverges. This framework distinguishes the approach of the book from panel data and longitudinal analyses, which mostly deal with cases in which the number of groups is large. The usefulness of the theory in this book is illustratedby numerical simulation and real data analysis. This book is suitable for theoretical statisticians and economists as well as psychologists and data analysts.
Monogenic Functions in Spaces with Commutative Multiplication and Applications
This monograph develops a theory of continuous and differentiable functions, called monogenic functions, in the sense of Gateaux functions taking values in some vector spaces with commutative multiplication. The study of these monogenic functions in various commutative algebras leads to a discovery of new ways of solving boundary value problems in mathematical physics. The book consists of six parts: Part I presents some preliminary notions and introduces various concepts of differentiable mappings of vector spaces. Part II - V is devoted to the study of monogenic functions in various spaces with commutative multiplication, namely, three dimensional commutative algebras with two-dimensional radical, finite-dimensional commutative associative algebras, infinite-dimensional vector spaces associated with the three-dimensional Laplace equation and infinite-dimensional vector spaces associated with axial-symmetric potential fields. Part VI presents some boundary value problems for axial-symmetric potential fields and develops effective analytic methods of solving these boundary value problems with various applications in mathematical physics. Graduate students and researchers alike benefit from this book.
Tropical Circuit Complexity
This book presents an enticing introduction to tropical circuits and their use as a rigorous mathematical model for dynamic programming (DP), which is one of the most fundamental algorithmic paradigms for solving combinatorial, discrete optimization problems. In DP, an optimization problem is broken up into smaller subproblems that are solved recursively. Many classical DP algorithms are pure in that they only use the basic (min, +) or (max, +) operations in their recursion equations. In tropical circuits, these operations are used as gates. Thanks to the rigorous combinatorial nature of tropical circuits, elements from the Boolean and arithmetic circuit complexity can be used to obtain lower bounds for tropical circuits, which play a crucial role in understanding the limitations and capabilities of these computational models. This book aims to offer a toolbox for proving lower bounds on the size of tropical circuits.In this work, the reader will find lower-bound ideas and methods that have emerged in the last few years, with detailed proofs. Largely self-contained, this book is meant to be approachable by graduate students in mathematics and computer science with a special interest in circuit complexity.
Abstract Algebra
This book contains the basics of abstract algebra. In addition to elementary algebraic structures such as groups, rings and solids, Galois theory in particular is developed together with its applications to the cyclotomic fields, finite fields or the question of the resolution of polynomial equations. Special attention is paid to the natural development of the contents. Numerous intermediate explanations support this basic idea, show connections and help to better penetrate the underlying concepts. The book is therefore particularly suitable for learning algebra in self-study or accompanying online lectures.
Trends and Challenges in Cognitive Modeling
This book presents interdisciplinary research in the science of Human Cognition through mathematical and computational modeling and simulation. Featuring new approaches developed by leading experts in the field of cognitive science, it highlights the relevance and depth of this important area of social sciences and its expanding reach into the biological, physical, computational and mathematical sciences. This contributed volume compiles the most recent advancements and cutting-edge applications of cognitive modeling, employing a genuinely multidisciplinary approach to simulate thinking, memory, and decision-making. The topics covered encompass a wide range of subjects, such as Agent-based Modeling in psychological research, the Nyayasutra proof pattern, the utilization of the Pheromone Trail Algorithm for modeling Analog Memory, the theory and practical applications of Social Laser Theory, addressing the challenges of probabilistic learning in brain and behavior models, adopting a Physicalistic perspective to understand the emergence of cognition and computation, an in-depth analysis of the conjunction fallacy as a factual occurrence, exploring quantum modeling and causality in physics and its extensions, examining compositional vector semantics within spiking neural networks, delving into the realms of Optimality, Prototypes, and Bilingualism, and finally, investigating the intricate dimensionality of color perception. Given its scope and approach, the book will benefit researchers and students of computational social sciences, mathematics and its applications, quantum physics.
Extended Abstracts 2021/2022
This book offers an overview of the research results presented by group members and guests of the Ghent Analysis & PDE Center during the weekly seminar that took place from 2021 to 2022. It is an informal event of the Analysis & PDE Center and associated researchers, where everyone can present their work or relevant literature for about 20-30 minutes. The seminar aims to exchange ideas and foster effective learning and collaboration.In this book, group members and guests summarise their results presented during the seminar and provide outlooks for future work. In this way, the book also provides an overview of the recent developments in the Ghent Analysis & PDE Center. The main topics are functional analysis, Fourier analysis, noncommutative analysis, geometric analysis, partial differential equations of different types, harmonic analysis, functional inequalities, pseudo-differential operators, fractional derivatives, special functions, microlocal analysis, inverseproblems and imaging. The target audience of this book is any researcher working in the above fields.
Differential Heterogenesis
This book describes about unlike usual differential dynamics common in mathematical physics, heterogenesis is based on the assemblage of differential constraints that are different from point to point. The construction of differential assemblages will be introduced in the present study from the mathematical point of view, outlining the heterogeneity of the differential constraints and of the associated phase spaces, that are continuously changing in space and time. If homogeneous constraints well describe a form of swarm intelligence or crowd behaviour, it reduces dynamics to automatisms, by excluding any form of imaginative and creative aspect. With this study we aim to problematize the procedure of homogeneization that is dominant in life and social science and to outline the dynamical heterogeneity of life and its affective, semiotic, social, historical aspects. Particularly, the use of sub-Riemannian geometry instead of Riemannian one allows to introduce disjointed and autonomous areas in the virtual plane. Our purpose is to free up the dynamic becoming from any form of unitary and totalizing symmetry and to develop forms, action, thought by means of proliferation, juxtaposition, and disjunction devices. After stating the concept of differential heterogenesis with the language of contemporary mathematics, we will face the problem of the emergence of the semiotic function, recalling the limitation of classical approaches (Hjelmslev, Saussure, Husserl) and proposing a possible genesis of it from the heterogenetic flow previously defined. We consider the conditions under which this process can be polarized to constitute different planes of Content (C) and Expression (E), each one equipped with its own formed substances. A possible (but not unique) process of polarization is constructed by means of spectral analysis, that is introduced to individuate E/C planes and their evolution. The heterogenetic flow, solution of differential assemblages, gives rise to forms that are projected onto the planes, offering a first referring system for the flow, that constitutes a first degree of semiosis.
A First Course in Graph Theory and Combinatorics
This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick's theorem on areas of lattice polygons and Graham-Pollak's work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.
A Guide to Robust Statistical Methods
Robust statistical methods are now being used in a wide range of disciplines. The appeal of these methods is that they are designed to perform about as well as classic techniques when standard assumptions are true--but they continue to perform well in situations where classic methods perform poorly. This book provides a relatively non-technical guide to modern methods. The focus is on applying modern methods using R, understanding when and why classic methods can be unsatisfactory, and fostering a conceptual understanding of the relative merits of different techniques. A recurring theme is that no single method reveals everything one would like to know about the population under study. An appeal of robust methods is that under general conditions they provide much higher power than conventional techniques. Perhaps more importantly, they help provide a deeper and more nuanced understanding of data. The book is for readers who had at least one semester of statistics, aimed at non-statisticians.
Statistical Hypothesis Testing with Microsoft (R) Office Excel (R)
This book provides a comprehensive treatment of the logic behind hypothesis testing. Readers will learn to understand statistical hypothesis testing and how to interpret P-values under a variety of conditions including a single hypothesis test, a collection of hypothesis tests, and tests performed on accumulating data. The author explains how a hypothesis test can be interpreted to draw conclusions, and descriptions of the logic behind frequentist (classical) and Bayesian approaches to interpret the results of a statistical hypothesis test are provided. Both approaches have their own strengths and challenges, and a special challenge presents itself when hypothesis tests are repeatedly performed on accumulating data. Possible pitfalls and methods to interpret hypothesis tests when accumulating data are also analyzed. This book will be of interest to researchers, graduate students, and anyone who has to interpret the results of statistical analyses.
Multilevel and Longitudinal Modeling Using Stata, Volume II
Multilevel and Longitudinal Modeling Using Stata, Fourth Edition, is a complete resource for learning to model data in which observations are grouped. With comprehensive coverage, researchers who need to apply multilevel models will find this book to be the perfect companion. It is also the ideal text for courses in multilevel modeling because it provides examples from a variety of disciplines as well as end-of-chapter exercises that allow students to practice newly learned material. The book comprises two volumes. Volume II focuses on generalized linear models for binary, ordinal, count, and other types of outcomes.
Number Theory
This Book of Number Theory is a captivating exploration of one of the oldest branches of mathematics. From its ancient origins to modern-day breakthroughs, this book uncovers the patterns, properties, and relationships that lie at the heart of numbers. It delves into topics such as divisibility, prime numbers, modular arithmetic, Diophantine equations, prime number distribution, and sieve methods. With its comprehensive coverage and engaging explanations, The Book of Number Theory reveals the beauty and significance of this fascinating mathematical discipline.
Math Mammoth Foundational Word Problems
Math Mammoth Foundational Word Problems is a workbook intended for students in 3rd grade and above that need more practice with word problems. I especially aim to help students in 4th-7th grades who have trouble with word problems and who need to "go back to the beginning", so to speak, to learn to solve them.The problems are generally based on a knowledge of third grade math, such as regrouping in addition and subtraction, the multiplication tables, concept of division, and calculating change. The problems do not require long multiplication, long division, or calculations with fractions or decimals (with the exception of money amounts).The worksheets have examples and some instruction about common strategies for word problems. Students are often encouraged to write down the calculations they do. They are also encouraged to make a drawing or a sketch of the situation in the problem, to help them understand the situation and to see what math operation is involved.Overall, most of the problems require two or more steps; however, some problem sets focus on differentiating what math operation should be used, and those only require a single step.Several problem sets are designed to help students to master problems that involve equal-size groups. These questions either ask for the total (and are thus solved by multiplying), or they ask for the size of the group or for the quantity of the groups (one can write a missing number multiplication sentence, such as 3 ? ___ = 18 or use division).The book also includes word problems with fractions, with large numbers, with money, geometry word problems, and challenges in the form of puzzle corners.You can download sample pages from this link: https: //www.mathmammoth.com/word_problems/Foundational_Word_Problems_samples.pdf
The Algebrization of Mathematics during the 17th and 18th Centuries. Dwarfs and Giants, Centres and Peripheries
This book explores the major historical phenomenon of the algebraization of mathematics in the second half of the 17th and 18th centuries, offering a broader understanding of the consolidation of analytic geometry and infinitesimal calculus as disciplines. The authors examine the external (intellectual, geographical, and political) factors that influenced these transformations and shed light on the process of acquisition and integration of analytical mathematics into traditional curricula. Drawing on new trends in historiography of science, this book emphasizes the importance of "dwarfs", that is mathematicians but also technicians, artisans, military personnel, engineers, and architects, often ignored or marginalized in traditional histories, in the circulation of original mathematical knowledge, and of peripheral countries such as Italy and Spain as important sites for the appropriation and production of such knowledge.
Building Your Career as a Statistician
This book is intended for anyone who is considering a career in statistics or a related field, or those at any point in their career with sufficient work time remaining such that investing in additional learning could be beneficial. As such, the book would be suitable for anyone pursing an MS or PhD in statistics or those already working in statistics. The book focuses on the non-statistical aspects of being a statistician that are crucial for success. These factors include 1) productivity and prioritization, 2) innovation and creativity, 3) communication, 4) critical thinking and decisions under uncertainty, 5) influence and leadership, 6) working relationships, and 7) career planning and continued learning. Each of these chapters includes sections on foundational principles and a section on putting those principles into practice. Connections between these individual skills are emphasized such that the reader can appreciate how the skills build upon each other leading to a whole that is greater than the sum of its parts. By including the individual perspectives from other experts on the fundamental principles and their application, readers will have a well-rounded view on how to build upon and fully leverage their technical skills in statistics. The primary audience for the book is large and diverse. It will be useful for self-study by virtually any statistician, but could also be used as a text in a graduate program that includes a course on careers and career development. Key Features: Takes principles proven to be useful in other settings and applies them to statisticians and statistical settings. Focused Concise Accessible to all levels, from grad students to mid-later career statisticians.
Compact Matrix Quantum Groups and Their Combinatorics
An organised step-by-step introduction to the theory of compact quantum groups, starting with examples coming from quantum physics, which stems from the basic undergraduate mathematics curriculum. Introducing more abstract concepts along the way when needed, the reader is led from the fundamentals of the theory to recent research results. The emphasis is put on the combinatorics underlying compact quantum groups, which is very elementary to describe but leads to profound results. This book includes many exercises to help students work through new concepts and ideas and consolidate their understanding. The theory itself is illustrated by an array of examples, some related to other fields of Mathematics such as free probability theory or graph theory. The book is intended for graduate students, motivated undergraduate students and researchers.
Mathematical Conundrums
Want to sharpen your mathematical wits? If so, then Mathematical Conundrums is for you. Daily Telegraph enigmatologist, Barry R. Clarke, presents over 120 fiendish problems that will test both your ingenuity and persistence. Between these covers are puzzles in geometry, arithmetic, and algebra (there is even a section for computer programmers). And, for the smartest readers who wish to stretch their mind to its limits, a selection of engaging logic and visual lateral puzzles is included. Although no puzzle requires a greater knowledge of mathematics than the high school curriculum, this collection will take you to the edge. But are you equal to the challenge? Features High-school level of mathematics is the only pre-requisite Variety of algebraic, route-drawing, and geometrical conundrums Hints section for the lateral puzzles Warm-up excercises to sharpen the wits Full solutions to every problem Barry R. Clarke has published over 1,500 puzzles in The Daily Telegraph and has contributed enigmas to New Scientist, The Sunday Times, Reader's Digest, The Sunday Telegraph, and Prospect magazine. His book Challenging Logic Puzzles Mensa has sold over 100,000 copies. As well as a PhD in Shakespeare Studies, Barry has a master's degree and academic publications in quantum physics. He is now working on a revised theory of the hydrogen atom. Other skills include mathematics tutor, filmmaker, comedy-sketch writer, cartoonist, computer programmer, and blues guitarist! For more information please visit http: //barryispuzzled.com. 　 　
The Life and Work of James Bradley
The Life and Work of James Bradley: The New Foundations of 18th Century Astronomy is the first major work on the life and achievements of James Bradley for 190 years. This book offers a new perspective and new interpretations of previously published materials, together with various insights about recently researched sources. This book is a complete account of the life and work of Bradley as discerned from surviving documents of his working archive, as well as other documents and records. In addition, it offers a new interpretation of Bradley's work as an astronomer, not merely from his observations of Jupiter and Saturn and their satellites and annual aberration and the nutation of the Earth's axis, but also his corroborative work with pendulums and other horological work with George Graham. It also explores the little amount documented about his private life including a degree of speculation about his personal relationships. This work on 18th century astronomy is intended for students of the history of science, astronomy and 18th century English society, and for scholars seeking new lines of inquiry. It contains an extensive bibliography and a detailed chronology, both of which offer support for further reading and research.
Building Your Career as a Statistician
This book is intended for anyone who is considering a career in statistics or a related field, or those at any point in their career with sufficient work time remaining such that investing in additional learning could be beneficial. As such, the book would be suitable for anyone pursing an MS or PhD in statistics or those already working in statistics. The book focuses on the non-statistical aspects of being a statistician that are crucial for success. These factors include 1) productivity and prioritization, 2) innovation and creativity, 3) communication, 4) critical thinking and decisions under uncertainty, 5) influence and leadership, 6) working relationships, and 7) career planning and continued learning. Each of these chapters includes sections on foundational principles and a section on putting those principles into practice. Connections between these individual skills are emphasized such that the reader can appreciate how the skills build upon each other leading to a whole that is greater than the sum of its parts. By including the individual perspectives from other experts on the fundamental principles and their application, readers will have a well-rounded view on how to build upon and fully leverage their technical skills in statistics. The primary audience for the book is large and diverse. It will be useful for self-study by virtually any statistician, but could also be used as a text in a graduate program that includes a course on careers and career development. Key Features: Takes principles proven to be useful in other settings and applies them to statisticians and statistical settings. Focused Concise Accessible to all levels, from grad students to mid-later career statisticians.
Compact Matrix Quantum Groups and Their Combinatorics
An organised step-by-step introduction to the theory of compact quantum groups, starting with examples coming from quantum physics, which stems from the basic undergraduate mathematics curriculum. Introducing more abstract concepts along the way when needed, the reader is led from the fundamentals of the theory to recent research results. The emphasis is put on the combinatorics underlying compact quantum groups, which is very elementary to describe but leads to profound results. This book includes many exercises to help students work through new concepts and ideas and consolidate their understanding. The theory itself is illustrated by an array of examples, some related to other fields of Mathematics such as free probability theory or graph theory. The book is intended for graduate students, motivated undergraduate students and researchers.
Mathematical Conundrums
Daily Telegraph enigmatologist, Barry R. Clarke, presents over 120 fiendish problems that will test both your ingenuity and persistence. Between these covers are puzzles in geometry, arithmetic, and algebra (there is even a section for computer programmers).
Introduction to Probability Models
*Textbook and Academic Authors Association (TAA) McGuffey Longevity Award Winner, 2024* A trusted market leader for four decades, Sheldon Ross's Introduction to Probability Models offers a comprehensive foundation of this key subject with applications across engineering, computer science, management science, the physical and social sciences and operations research. Through its hallmark exercises and real examples, this valuable course text Introduction to Probability Models provides the reader with a comprehensive course in the subject, from foundations to advanced topics.
Machine Learning for Factor Investing
Machine learning (ML) is progressively reshaping the fields of quantitative finance and algorithmic trading. ML tools are increasingly adopted by hedge funds and asset managers, notably for alpha signal generation and stocks selection. The technicality of the subject can make it hard for non-specialists to join the bandwagon, as the jargon and coding requirements may seem out-of-reach. Machine learning for factor investing: Python version bridges this gap. It provides a comprehensive tour of modern ML-based investment strategies that rely on firm characteristics. The book covers a wide array of subjects which range from economic rationales to rigorous portfolio back-testing and encompass both data processing and model interpretability. Common supervised learning algorithms such as tree models and neural networks are explained in the context of style investing and the reader can also dig into more complex techniques like autoencoder asset returns, Bayesian additive trees and causal models. All topics are illustrated with self-contained Python code samples and snippets that are applied to a large public dataset that contains over 90 predictors. The material, along with the content of the book, is available online so that readers can reproduce and enhance the examples at their convenience. If you have even a basic knowledge of quantitative finance, this combination of theoretical concepts and practical illustrations will help you learn quickly and deepen your financial and technical expertise.
Rediscovering L矇on Brunschvicg’s Critical Idealism
L矇on Brunschvicg's contribution to philosophical thought in fin-de-si癡cle France receives full explication in the first English-language study on his work. Arguing that Brunschvicg is crucial to understanding the philosophical schools which took root in 20th-century France, Pietro Terzi locates Brunschvicg alongside his contemporary Henri Bergson, as well as the range of thinkers he taught and influenced, including L矇vinas, Merleau-Ponty, de Beauvoir, and Sartre. Brunschvicg's deep engagement with debates concerning spiritualism and rationalism, neo-Kantian philosophy, and the role of mathematics in philosophy made him the perfect supervisor for a whole host of nascent philosophical ideas which were forming in the work of his students. Terzi outlines Brunchvicg's defence of neo-Kantian judgement, historical analysis and the inextricability of the natural and humanist sciences to any rigorous system of philosophy, with wide-ranging implications for contemporary scholarship.
Elliptic Integrals and Elliptic Functions
This book gives a comprehensive introduction to those parts of the theory of elliptic integrals and elliptic functions which provide illuminating examples in complex analysis, but which are not often covered in regular university courses. These examples form prototypes of major ideas in modern mathematics and were a driving force of the subject in the eighteenth and nineteenth centuries. In addition to giving an account of the main topics of the theory, the book also describes many applications, both in mathematics and in physics. For the reader's convenience, all necessary preliminaries on basic notions such as Riemann surfaces are explained to a level sufficient to read the book.For each notion a clear motivation is given for its study, answering the question 'Why do we consider such objects?', and the theory is developed in a natural way that mirrors its historical development (e.g., 'If there is such and such an object, then you would surely expect this one'). This feature sets this text apart from other books on the same theme, which are usually presented in a different order. Throughout, the concepts are augmented and clarified by numerous illustrations. Suitable for undergraduate and graduate students of mathematics, the book will also be of interest to researchers who are not familiar with elliptic functions and integrals, as well as math enthusiasts.
The Calabi Problem for Fano Threefolds
Algebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds are a fundamental subclass that can be thought of as higher-dimensional generalizations of ordinary spheres. They belong to 105 irreducible deformation families. This book determines whether the general element of each family admits a K瓣hler-Einstein metric (and for many families, for all elements), addressing a question going back to Calabi 70 years ago. The book's solution exploits the relation between these metrics and the algebraic notion of K-stability. Moreover, the book presents many different techniques to prove the existence of a K瓣hler-Einstein metric, containing many additional relevant results such as the classification of all K瓣hler-Einstein smooth Fano threefolds with infinite automorphism groups and computations of delta-invariants of all smooth del Pezzo surfaces. This book will be essential reading for researchers and graduate students working on algebraic geometry and complex geometry.
Comparative Genomics
This book constitutes the refereed proceedings of the 20th Annual RECOMB Satellite Workshop on Comparative Genomics, RECOMB-CG 2023 which took place in Istanbul, Turkey, in April 2023. The 15 full papers included in this book were carefully reviewed and selected from 25 submissions. The papers present cutting edge research in comparative genomics, with an emphasis on computational approaches and novel experimental results.Chapters "Inferring Clusters of Orthologous and Paralogous Transcripts" and "Gene Order Phylogeny via Ancestral Genome Reconstruction under Dollo" are published Open Access under Creative Commons Attribution license (CC BY 4.0).
Uncomplicated Calculus
Embark on a guided journey with Uncomplicated Calculus!Starting with the very basics of functions and limits, you'll explore the landscape of derivatives and integrals, and journey into the realms of sequences, series, and differential equations. Advanced topics such as multivariable calculus, vectors, and line and surface integrals, once daunting, become comprehensible under clear explanations and practical examples.Interwoven throughout are real-world applications demonstrating the relevance of calculus in fields as diverse as physics, economics, and computer science. The book also offers ample exercises and problem-solving techniques to strengthen your understanding, allowing you to master calculus concepts at your own pace.Whether you're a student, a teacher, or a lifelong learner, this book illuminates the elegance of calculus, propelling your mathematical journey forward.
Attractors, Shadowing, and Approximation of Abstract Semilinear Differential Equations
The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.
Model Risk Management
This book provides the first systematic treatment of model risk, outlining the tools needed to quantify model uncertainty, to study its effects, and, in particular, to determine the best upper and lower risk bounds for various risk aggregation functionals of interest. Drawing on both numerical and analytical examples, this is a thorough reference work for actuaries, risk managers, and regulators. Supervisory authorities can use the methods discussed to challenge the models used by banks and insurers, and banks and insurers can use them to prioritize the activities on model development, identifying which ones require more attention than others. In sum, it is essential reading for all those working in portfolio theory and the theory of financial and engineering risk, as well as for practitioners in these areas. It can also be used as a textbook for graduate courses on risk bounds and model uncertainty.
Well-Posed Nonlinear Problems
This monograph presents an original method to unify the mathematical theories of well-posed problems and contact mechanics. The author uses a new concept called the Tykhonov triple to develop a well-posedness theory in which every convergence result can be interpreted as a well-posedness result. This will be useful for studying a wide class of nonlinear problems, including fixed-point problems, inequality problems, and optimal control problems. Another unique feature of the manuscript is the unitary treatment of mathematical models of contact, for which new variational formulations and convergence results are presented. Well-Posed Nonlinear Problems will be a valuable resource for PhD students and researchers studying contact problems. It will also be accessible to interested researchers in related fields, such as physics, mechanics, engineering, and operations research.
Local Systems in Algebraic-Arithmetic Geometry
The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is, its complex local systems. A fundamental problem is then to single out the complex points of such moduli spaces which correspond to geometric systems, and more generally to identify geometric subloci of the moduli space of local systems with special arithmetic properties. Deep conjectures have been made in relation to these problems. This book studies some consequences of these conjectures, notably density, integrality and crystallinity properties of some special loci.This monograph provides a unique compelling and concise overview of an active area of research and is useful to students looking to get into this area. It is of interest to a wide range of researchers and is a useful reference for newcomers and experts alike.
A Friendly Approach to Complex Analysis
The book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text.The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained.
The Fundamentals of People Analytics
This open access book prepares current and aspiring analytics professionals to effectively address this need by curating key concepts spanning the entire analytics lifecycle, along with step-by-step instructions for their applications to real-world problems, using ubiquitous and freely available open-source software. This book does not assume prior knowledge of statistics, how to query databases, or how to write performant code; early chapters include an introduction to R and SQL as well as an overview of statistical foundations. Human capital is an organization's most important asset. Without the knowledge and skills of people, an organization can accomplish nothing. The acquisition, development, and retention of critical talent has become increasingly more complex and challenging, and organizations are making significant investments to gain a deeper, data-informed understanding of organizational phenomena impacting the bottom line. By the end of this book, readers will be able to: - Design and conduct empirical research - Query and wrangle data using SQL - Profile, clean, and analyze data using R - Apply appropriate statistical and ML models to a range of people analytics use cases - Package and present analyses to communicate impactful insights to stakeholders
A Friendly Approach to Complex Analysis
The book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text.The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained.
Optimal Control
This book may serve as a basis for students and teachers. The text should provide the reader with a quick overview of the basics for Optimal Control and the link with some important conceptes of applied mathematical, where an agent controls underlying dynamics to find the strategy optimizing some quantity. There are broad applications for optimal control across the natural and social sciences, and the finale to this text is an invitation to read current research on one such application. The balance of the text will prepare the reader to gain a solid understanding of the current research they read.
Commutative Algebra
The primary audience for this book is students and the young researchers interested in the core of the discipline. Commutative algebra is by and large a self-contained discipline, which makes it quite dry for the beginner with a basic training in elementary algebra and calculus. A stable mathematical discipline such as this enshrines a vital number of topics to be learned at an early stage, more or less universally accepted and practiced. Naturally, authors tend to turn these topics into an increasingly short and elegant list of basic facts of the theory. So, the shorter the better. However, there is a subtle watershed between elegance and usefulness, especially if the target is the beginner. From my experience throughout years of teaching, elegance and terseness do not do it, except much later in the carrier. To become useful, the material ought to carry quite a bit of motivation through justification and usefulness pointers. On the other hand, it is difficult to contemplate these teaching devices in the writing of a short book. I have divided the material in three parts. starting with more elementary sections, then carrying an intermezzo on more difficult themes to make up for a smooth crescendo with additional tools and, finally, the more advanced part, versing on a reasonable chunk of present-day steering of commutative algebra. Historic notes at the end of each chapter provide insight into the original sources and background information on a particular subject or theorem. Exercises are provided and propose problems that apply the theory to solve concrete questions (yes, with concrete polynomials, and so forth).
The Fundamentals of People Analytics
This open access book prepares current and aspiring analytics professionals to effectively address this need by curating key concepts spanning the entire analytics lifecycle, along with step-by-step instructions for their applications to real-world problems, using ubiquitous and freely available open-source software. This book does not assume prior knowledge of statistics, how to query databases, or how to write performant code; early chapters include an introduction to R and SQL as well as an overview of statistical foundations. Human capital is an organization's most important asset. Without the knowledge and skills of people, an organization can accomplish nothing. The acquisition, development, and retention of critical talent has become increasingly more complex and challenging, and organizations are making significant investments to gain a deeper, data-informed understanding of organizational phenomena impacting the bottom line. By the end of this book, readers will be able to: - Design and conduct empirical research - Query and wrangle data using SQL - Profile, clean, and analyze data using R - Apply appropriate statistical and ML models to a range of people analytics use cases - Package and present analyses to communicate impactful insights to stakeholders
Polyhedra and Beyond
This volume collects papers based on talks given at the conference "Geometrias'19: Polyhedra and Beyond", held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal. These papers explore the conference's theme from an interdisciplinary standpoint, all the while emphasizing the relevance of polyhedral geometry in contemporary academic research and professional practice. They also investigate how this topic connects to mathematics, art, architecture, computer science, and the science of representation. Polyhedra and Beyond will help inspire scholars, researchers, professionals, and students of any of these disciplines to develop a more thorough understanding of polyhedra.
A Course on Holomorphic Discs
This textbook, based on a one-semester course taught several times by the authors, provides a self-contained, comprehensive yet concise introduction to the theory of pseudoholomorphic curves. Gromov's nonsqueezing theorem in symplectic topology is taken as a motivating example, and a complete proof using pseudoholomorphic discs is presented. A sketch of the proof is discussed in the first chapter, with succeeding chapters guiding the reader through the details of the mathematical methods required to establish compactness, regularity, and transversality results. Concrete examples illustrate many of the more complicated concepts, and well over 100 exercises are distributed throughout the text. This approach helps the reader to gain a thorough understanding of the powerful analytical tools needed for the study of more advanced topics in symplectic topology.This text can be used as the basis for a graduate course, and it is also immensely suitable for independentstudy. Prerequisites include complex analysis, differential topology, and basic linear functional analysis; no prior knowledge of symplectic geometry is assumed.This book is also part of the Virtual Series on Symplectic Geometry.
Set, Measure and Probability Theory
This book introduces the basic concepts of set theory, measure theory, the axiomatic theory of probability, random variables and multidimensional random variables, functions of random variables, convergence theorems, laws of large numbers, and fundamental inequalities.
Advances in Image Enhancement
In the era of the Internet of Things, images have played important roles in human-computer interactions, and with the arrival of big data technology, people have higher requirements regarding image quality, especially for images collected in dark light. This can be addressed through the development of camera hardware quality, i.e., the resolution and exposure time of cameras, which may require high computational costs. As an alternative, image enhancement techniques can exact salient features to improve the quality of captured images according to the differences in diverse features, although they suffer from some challenges, i.e., a low contrast, artifacts, and overexposure, thus making it decidedly necessary to determine how to use advanced image enhancement techniques. The topic of advances in the image enhancement of electronics is presented in this reprint, which brings together the research accomplishments of researchers from academia and industry. The secondary goal of this reprint is to display the latest research results of advances in image enhancement.
Knowledge Structures: Recent Developments in Theory and Application
Founded in 1985 by Jean-Claude Falmagne and Jean-Paul Doignon, Knowledge Structure Theory (KST) constitutes a rigorous and current mathematical theory for the representation and the assessment of human knowledge. The seminal work of these authors initiated a highly active research strand with an ever-growing literature, mostly scattered across various technical journals.Starting from a concise but comprehensive introduction to its foundations, this volume provides a state-of-the-art review of KST. For the first time the volume brings together the most important theoretical developments and extensions of the last decade and presents new areas of application beyond education, with contributions by key researchers in the field.Among the important advances covered by this book are (1) a comprehensive treatment of probabilistic models in KST; (2) polytomous extensions of the theory; (3) KST-based psychological diagnostics and neuropsychological assessment; (4) the representation and assessment of cognitive skills in problem solving, as well as procedural skills. In addition, this book also includes an overview of available software for the application of KST.
Next-Generation Sequencing Data Analysis
Next-Generation Sequencing Data Analysis walks readers through NGS data analysis step-by-step for a wide range of NGS applications.
Oxford's Sedleian Professors of Natural Philosophy
Established in the early seventeenth century following a bequest to the university by Sir William Sedley, Oxford's Sedleian Professorship of Natural Philosophy is one of the university's oldest professorships. In common with other such positions established around this time, such as the Savilian Professorships of Geometry and Astronomy, for example, its purpose was to provide centrally organised lectures on a specific subject. While the Professorship is now a high-profile research post in applied mathematics, it has previously been held by physicians, an astronomer, and several people in the eighteenth century whose credentials in natural philosophy are much less clear. This edited volume traces the varied history of the chair through the first four centuries of its existence, combining specialised contributions from historians of medicine, of science, of mathematics, and of universities, together with personal reminiscences of some of the more recent holders of the post.
