Lectures in Nonlinear Functional Analysis
This book is a systematic presentation of basic notions, facts, and ideas of nonlinear functional analysis and their applications to nonlinear partial differential equations. It begins from a brief introduction to linear functional analysis, including various types of convergence and functional spaces. The main part of the book is devoted to the theory of nonlinear operators. Various methods of the study of nonlinear differential equations based on the facts of nonlinear analysis are presented in detail. This book may serve as an introductory textbook for students and undergraduates specializing in modern mathematical physics.
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.
The Complete Pre 11+ Maths Course Book (Year 4)
This book covers the complete Pre 11+ Mathematics syllabus aimed at children working to attend selective independent and state schools. By working through this book, children will grasp the firm foundations for 11+ Maths and gain confidence. Parents can use this book to teach their children in year 4 in a structured and coherent format and getting them prepared for year 5.This book tackles each 11+ topic by: - Explaining the mathematical concepts- Providing questions for consolidation- Detailed mark schemes ( separate booklet available )- Termly tests This unique Pre 11+ Maths book ensures the highest results in the exams; every year over 8 out of 10 children completing the course obtain a place in the school of their choice and a majority of the children obtain multiple offers.
Space-Time Geometries for Motion and Perception in the Brain and the Arts
Introduction.- Perception and Memory.- Action and Emotion.- Music.- Drawing and Painting.- Performing arts.- Digital Arts.
Turnpike Theory for the Robinson-Solow-Srinivasan Model
This book is devoted to the study of a class of optimal control problems arising in mathematical economics, related to the Robinson-Solow-Srinivasan (RSS) model. It will be useful for researches interested in the turnpike theory, infinite horizon optimal control and their applications, and mathematical economists. The RSS is a well-known model of economic dynamics that was introduced in the 1960s and as many other models of economic dynamics, the RSS model is determined by an objective function (a utility function) and a set-valued mapping (a technology map). The set-valued map generates a dynamical system whose trajectories are under consideration and the objective function determines an optimality criterion. The goal is to find optimal trajectories of the dynamical system, using the optimality criterion. Chapter 1 discusses turnpike properties for some classes of discrete time optimal control problems. Chapter 2 present the description of the RSS model and discuss its basic properties. Infinite horizon optimal control problems, related to the RSS model are studied in Chapter 3. Turnpike properties for the RSS model are analyzed in Chapter 4. Chapter 5 studies infinite horizon optimal control problems related to the RSS model with a nonconcave utility function. Chapter 6 focuses on infinite horizon optimal control problems with nonautonomous optimality criterions. Chapter 7 contains turnpike results for a class of discrete-time optimal control problems. Chapter 8 discusses the RSS model and compares different optimality criterions. Chapter 9 is devoted to the study of the turnpike properties for the RSS model. In Chapter 10 the one-dimensional autonomous RSS model is considered and the continuous time RSS model is studied in Chapter 11.
Polarized Light and the Mueller Matrix Approach
This revised compendium integrates basic concepts of polarization phenomena from the dual viewpoints of polarization of electromagnetic waves and transformations by the action of material media. Through selected examples, it illustrates actual and potential applications in materials science, biology, and optics technology.
Algebraic Topology
Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation.This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites - basic general topology and little else - and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions.It can be used as a textbook for a semester course or self-study, and a guidebook for further study.
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.
Tree generation and enumeration
I believe in inspiring and connecting people with mathematics. I also believe in sharing knowledge and passing it on to further generations. By making books and building a community for graph theory and treespeak enthusiasts, I can show people that mathematics is a form of art, a pinnacle of creativity, and a competitive game as well. Whether you are a mathematician, student, teacher, enthusiast or hobbyist, I think this book can awaken your curiosity, and help you in your mathematical journeys. Especially if you would like to know about tree generation and enumeration, how trees are linked to partitions and what a Peano-like axiomatic system for rooted trees looks like. Treespeak is about the subtle cooperation between vertex edge algebra and the tree generation algorithm. Feel free to check out the Treespeak tool / game in my website www.matladpi.com.
Irrationality and Transcendence in Number Theory
This book tells the story of irrational numbers from their discovery in the days of Pythagoras to the ideas behind the work of Baker and Mahler on transcendence in the 20th century. It focuses on themes of irrationality, algebraic and transcendental numbers, continued fractions, approximation of real numbers by rationals, etc.
Theory of Statistical Inference
The purpose of applying mathematical theory to the theory of statistical inference is to make it simpler and more elegant. Theory of Statistical Inference is concerned with the development of a type of optimization theory which can be used to inform the choice of statistical methodology.
Richard Brauer
Richard Brauer (1901-1977) was one of the leading algebraists of this century. Although he contributed to a number of mathematical fields, Brauer devoted the major share of his efforts to the study of finite groups, a subject of considerable abstract interest and one that underlies many of the more recent advances in combinatorics and finite geometries.
Richard Brauer
Richard Brauer (1901-1977) was one of the leading algebraists of this century. Although he contributed to a number of mathematical fields, Brauer devoted the major share of his efforts to the study of finite groups, a subject of considerable abstract interest and one that underlies many of the more recent advances in combinatorics and finite geometries. The 120 papers collected in this volume were first published between 1926 and 1979. Brauer's mathematical impulse was remarkably steady, and his papers are equally distributed between those written before his fiftieth year and those written thereafter, including a number of contributions that were published after his formal retirement as Perkins Professor of Mathematics as Harvard in 1971. The papers are grouped into six sections following an autobiographical preface written for this collection. The first section contains twenty papers on the theory of algebras and is introduced by Oscar Goldman. The seventy-four papers on finite groups make up the second and largest section, which spans all three volumes. The final four sections complete the third volume and represent Brauer's contribution to Lie groups, number theory, polynomials and equations, geometries and biographies of Artin and Thompson.
Fundamentals of Mathematics, Volume 2
Fundamentals of Mathematics represents a new kind of mathematical publication. While excellent technical treatises have been written about specialized fields, they provide little help for the nonspecialist; and other books, some of them semipopular in nature, give an overview of mathematics while omitting some necessary details. Fundamentals of Mathematics strikes a unique balance, presenting an irreproachable treatment of specialized fields and at the same time providing a very clear view of their interrelations, a feature of great value to students, instructors, and those who use mathematics in applied and scientific endeavors. Moreover, as noted in a review of the German edition in Mathematical Reviews, the work is designed to acquaint [the student] with modern viewpoints and developments. The articles are well illustrated and supplied with references to the literature, both current and 'classical.' The outstanding pedagogical quality of this work was made possible only by the unique method by which it was written. There are, in general, two authors for each chapter: one a university researcher, the other a teacher of long experience in the German educational system. (In a few cases, more than two authors have collaborated.) And the whole book has been coordinated in repeated conferences, involving altogether about 150 authors and coordinators.Volume I opens with a section on mathematical foundations. It covers such topics as axiomatization, the concept of an algorithm, proofs, the theory of sets, the theory of relations, Boolean algebra, and antinomies. The closing section, on the real number system and algebra, takes up natural numbers, groups, linear algebra, polynomials, rings and ideals, the theory of numbers, algebraic extensions of a fields, complex numbers and quaternions, lattices, the theory of structure, and Zorn's lemma.Volume II begins with eight chapters on the foundations of geometry, followed by eight others on its analytic treatment. The latter include discussions of affine and Euclidean geometry, algebraic geometry, the Erlanger Program and higher geometry, group theory approaches, differential geometry, convex figures, and aspects of topology.Volume III, on analysis, covers convergence, functions, integral and measure, fundamental concepts of probability theory, alternating differential forms, complex numbers and variables, points at infinity, ordinary and partial differential equations, difference equations and definite integrals, functional analysis, real functions, and analytic number theory. An important concluding chapter examines The Changing Structure of Modern Mathematics.
Using Mathematics to Understand Biological Complexity
1. Collaborative Workshop for Women in Mathematical Biology (R. Segal, B. Shtylla, S. Sindi).- 2. Connecting Actin Polymer Dynamics Across Multiple Scales (C. Copos, B. Bannish, K. Gasior, R.L. Pinals, M.W. Rostami, A.T. Dawes).- 3. Modeling RNA: DNA Hybrids with Formal Grammars (N. Jonoska, N. Obatake, S. Poznanovic, C. Price, M. Riehl, M. Vazquez).- 4. Secondary Structure Ensemble Analysis via Community Detection (H. Du, M.M. Ferrari, C. Heitsch, F. Hurley, C.V. Mennicke, B.D. Sullivan, and B. Xu.)- 5. How Do Interventions Impact Malaria Dynamics Between Neighboring Countries? A Case Study with Botswana and Zimbabwe (F. Agusto, A. Goldberg, O. Ortega, Joan Ponce+, Sofya Zaytseva, S. Sindi, Sally Blower).- 6. Investigating the Impact of Combination Phage and Antibiotic Therapy (S. Banuelos, H. Gulbudak, M.A. Horn, Q. Huang, A. Nandi, H Ryu, R. Segal).- 7. Mathematical Modeling of Retinal Degeneration (E. Camacho, A. Dobreva, K. Larripa, A. Radulescu, D. Schmidt, I. Trejo).- 8. A Framework for Performing Data-Driven Modeling of Tumor Growth with Radiotherapy Treatment (H. Cho, A.L. Lewis, K.M. Storey, R. Jennings, B. Shtylla, A.M. Reynolds, H.M. Byrne).
Using Hard Problems to Create Pseudorandom Generators
Randomization is an important tool in the design of algorithms, and the ability of randomization to provide enhanced power is a major research topic in complexity theory. Noam Nisan continues the investigation into the power of randomization and the relationships between randomized and deterministic complexity classes by pursuing the idea of emulating randomness, or pseudorandom generation. Pseudorandom generators reduce the number of random bits required by randomized algorithms, enable the construction of certain cryptographic protocols, and shed light on the difficulty of simulating randomized algorithms by deterministic ones. The research described here deals with two methods of constructing pseudorandom generators from hard problems and demonstrates some surprising connections between pseudorandom generators and seemingly unrelated topics such as multiparty communication complexity and random oracles. Nisan first establishes a precise connection between computational complexity and pseudorandom number generation, revealing that efficient deterministic simulation of randomized algorithms is possible under much weaker assumptions than was previously known, and bringing to light new consequences concerning the power of random oracles. Using a remarkable argument based on multiparty communication complexity, Nisan then constructs a generator that is good against all tests computable in logarithmic space. A consequence of this result is a new construction of universal traversal sequences.ContentsIntroduction - Hardness vs. Randomness - Pseudorandom Generators for Logspace and Multiparty Protocols
Artificial Intelligence and Ambient Intelligence
This book includes a series of scientific papers published in the Special Issue on Artificial Intelligence and Ambient Intelligence at the journal Electronics MDPI. The book starts with an opinion paper on "Relations between Electronics, Artificial Intelligence and Information Society through Information Society Rules", presenting relations between information society, electronics and artificial intelligence mainly through twenty-four IS laws. After that, the book continues with a series of technical papers that present applications of Artificial Intelligence and Ambient Intelligence in a variety of fields including affective computing, privacy and security in smart environments, and robotics. More specifically, the first part presents usage of Artificial Intelligence (AI) methods in combination with wearable devices (e.g., smartphones and wristbands) for recognizing human psychological states (e.g., emotions and cognitive load). The second part presents usage of AI methods in combination with laser sensors or Wi-Fi signals for improving security in smart buildings by identifying and counting the number of visitors. The last part presents usage of AI methods in robotics for improving robots' ability for object gripping manipulation and perception. The language of the book is rather technical, thus the intended audience are scientists and researchers who have at least some basic knowledge in computer science.
Fundamentals of Data Science Part II
In Part II of this series, we cover the elements of statistical modeling, focusing on: validation methodologyprinciples of object-oriented designlinear and logistic regressiongeneralized linear modelscausalitytime series analysisBayesian statistics, including simulations in pymc3Modeling customer lifetime values, including a detailed study of the beta-Bernoulli/beta-binomial model, a discretized version of the classic Pareto/NBDan introduction to credibility theoryThe theory is illustrated with simulations in Python throughout the text.
Computational Fractional Dynamical Systems
Computational Fractional Dynamical Systems A rigorous presentation of different expansion and semi-analytical methods for fractional differential equations Fractional differential equations, differential and integral operators with non-integral powers, are used in various science and engineering applications. Over the past several decades, the popularity of the fractional derivative has increased significantly in diverse areas such as electromagnetics, financial mathematics, image processing, and materials science. Obtaining analytical and numerical solutions of nonlinear partial differential equations of fractional order can be challenging and involve the development and use of different methods of solution. Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications presents a variety of computationally efficient semi-analytical and expansion methods to solve different types of fractional models. Rather than focusing on a single computational method, this comprehensive volume brings together more than 25 methods for solving an array of fractional-order models. The authors employ a rigorous and systematic approach for addressing various physical problems in science and engineering. Covers various aspects of efficient methods regarding fractional-order systems Presents different numerical methods with detailed steps to handle basic and advanced equations in science and engineering Provides a systematic approach for handling fractional-order models arising in science and engineering Incorporates a wide range of methods with corresponding results and validation Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications is an invaluable resource for advanced undergraduate students, graduate students, postdoctoral researchers, university faculty, and other researchers and practitioners working with fractional and integer order differential equations.
Oxford's Savilian Professors of Geometry
The Savilian Professorships in Geometry and Astronomy at Oxford University were founded in 1619 by Sir Henry Savile, distinguished scholar and Warden of Merton College. The Geometry chair, in particular, is the earliest University-based mathematics professorship in England, predating the first Cambridge equivalent by about sixty years. To celebrate the 400th anniversary of the founding of the geometry chair, a meeting was held at the Bodleian Library in Oxford, and the talks presented at this meeting have formed the basis for this fully edited and lavishly illustrated book, which outlines the first 400 years of Oxford's Savilian Professors of Geometry. Starting with Henry Briggs, the co-inventor of logarithms, this volume proceeds via such figures as John Wallis, a founder member of the Royal Society, and Edmond Halley, via the 19th-century figures of Stephen Rigaud, Baden Powell, Henry Smith, and James Joseph Sylvester, to the 20th century and the present day. Oxford's Savilian Professors of Geometry: The First 400 Years assumes no mathematical background, and should therefore appeal to the interested general reader with an interest in mathematics and the sciences. It should also be of interest to anyone interested in the history of mathematics or of the development of Oxford and its namesake university. To all of these audiences it offers portraits of mathematicians at work and an accessible exposition of historical mathematics in the context of its times.
Geometry
The study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof - deductive reasoning from a set of axioms - first arose. To this day geometry remains a very active area of research in mathematics. This Very Short Introduction covers the areas of mathematics falling under geometry, starting with topics such as Euclidean and non-Euclidean geometries, and ranging to curved spaces, projective geometry in Renaissance art, and geometry of space-time inside a black hole. Starting from the basics, Maciej Dunajski proceeds from concrete examples (of mathematical objects like Platonic solids, or theorems like the Pythagorean theorem) to general principles. Throughout, he outlines the role geometry plays in the broader context of science and art. bVery Short Introductionsb: Brilliant, Sharp, Inspiring /b ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Graph Sampling
Graph Sampling can primarily be used as a resource for researchers working with sampling or graph problems, and as the basis of an advanced course for post-graduate students in statistics, mathematics and data science.
Statistical Data Modeling and Machine Learning with Applications
The modeling and processing of empirical data is one of the main subjects and goals of statistics. Nowadays, with the development of computer science, the extraction of useful and often hidden information and patterns from data sets of different volumes and complex data sets in warehouses has been added to these goals. New and powerful statistical techniques with machine learning (ML) and data mining paradigms have been developed. To one degree or another, all of these techniques and algorithms originate from a rigorous mathematical basis, including probability theory and mathematical statistics, operational research, mathematical analysis, numerical methods, etc. Popular ML methods, such as artificial neural networks (ANN), support vector machines (SVM), decision trees, random forest (RF), among others, have generated models that can be considered as straightforward applications of optimization theory and statistical estimation. The wide arsenal of classical statistical approaches combined with powerful ML techniques allows many challenging and practical problems to be solved.This Special Issue belongs to the section "Mathematics and Computer Science". Its aim is to establish a brief collection of carefully selected papers presenting new and original methods, data analyses, case studies, comparative studies, and other research on the topic of statistical data modeling and ML as well as their applications. Particular attention is given, but is not limited, to theories and applications in diverse areas such as computer science, medicine, engineering, banking, education, sociology, economics, among others.The resulting palette of methods, algorithms, and applications for statistical modeling and ML presented in this Special Issue is expected to contribute to the further development of research in this area. We also believe that the new knowledge acquired here as well as the applied results are attractive and useful for young scientists, doctoral students, and researchers from various scientific specialties.
Equivariant Topology and Derived Algebra
This volume contains eight research papers inspired by the 2019 'Equivariant Topology and Derived Algebra' conference, held at the Norwegian University of Science and Technology, Trondheim in honour of Professor J. P. C. Greenlees' 60th birthday. These papers, written by experts in the field, are intended to introduce complex topics from equivariant topology and derived algebra while also presenting novel research. As such this book is suitable for new researchers in the area and provides an excellent reference for established researchers. The inter-connected topics of the volume include: algebraic models for rational equivariant spectra; dualities and fracture theorems in chromatic homotopy theory; duality and stratification in tensor triangulated geometry; Mackey functors, Tambara functors and connections to axiomatic representation theory; homotopy limits and monoidal Bousfield localization of model categories.
Approximation and Online Algorithms
This book constitutes the thoroughly refereed workshop post-proceedings of the 19th International Workshop on Approximation and Online Algorithms, WAOA 2021, held in September 2021. Due to COVID-19 pandemic the conference was held virtually. The 16 revised full papers presented in this book were carefully reviewed and selected from 31 submissions. The papers focus on the design and analysis of algorithms for online and computationally hard problems.
Machine Learning in Biotechnology and Life Sciences
Explore all the tools and templates needed for data scientists to drive success in their biotechnology careers with this comprehensive guideKey Features: Learn the applications of machine learning in biotechnology and life science sectorsDiscover exciting real-world applications of deep learning and natural language processingUnderstand the general process of deploying models to cloud platforms such as AWS and GCPBook Description: The booming fields of biotechnology and life sciences have seen drastic changes over the last few years. With competition growing in every corner, companies around the globe are looking to data-driven methods such as machine learning to optimize processes and reduce costs. This book helps lab scientists, engineers, and managers to develop a data scientist's mindset by taking a hands-on approach to learning about the applications of machine learning to increase productivity and efficiency in no time.You'll start with a crash course in Python, SQL, and data science to develop and tune sophisticated models from scratch to automate processes and make predictions in the biotechnology and life sciences domain. As you advance, the book covers a number of advanced techniques in machine learning, deep learning, and natural language processing using real-world data.By the end of this machine learning book, you'll be able to build and deploy your own machine learning models to automate processes and make predictions using AWS and GCP.What You Will Learn: Get started with Python programming and Structured Query Language (SQL)Develop a machine learning predictive model from scratch using PythonFine-tune deep learning models to optimize their performance for various tasksFind out how to deploy, evaluate, and monitor a model in the cloudUnderstand how to apply advanced techniques to real-world dataDiscover how to use key deep learning methods such as LSTMs and transformersWho this book is for: This book is for data scientists and scientific professionals looking to transcend to the biotechnology domain. Scientific professionals who are already established within the pharmaceutical and biotechnology sectors will find this book useful. A basic understanding of Python programming and beginner-level background in data science conjunction is needed to get the most out of this book.
The Puzzles of Nobuyuki Yoshigahara
This book convenes a selection of 200 mathematical puzzles with original solutions, all celebrating the inquisitive and inspiring spirit of Nobuyuki "Nob" Yoshigahara - a legend in the worldwide community of mathematical and mechanical puzzles. A graduate from the Tokyo Institute of Technology, Yoshigahara invented numerous mechanical puzzles and published over 80 puzzle books. In 2003, he was honored with the Sam Loyd Award, given by the Association for Games & Puzzles International to individuals who have been made a significant contribution to the world of mechanical puzzles.In this work, the reader will find some of the most ingenious puzzles ever created, organized in ten categories: Logic, matchstick, maze, algorithmic, combinatorial, digital, number, geometric, dissection, and others. Some of them could rivalry with those found at Mathematical Olympiads tests around the globe; others will work as powerful brain teasers for those with an interest in problem-solving. Math teachers, curious students of any age and even experienced mathematicians with a taste for the fun in science can find in this book unconventional paths to develop their problem-solving skills in a creative way.
Theory of Games and Economic Behavior
John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.
Advances in Mathematical Optimization
No detailed description available for "Advances in Mathematical Optimization".
Multivariable Control
No detailed description available for "Multivariable Control".
An Invitation to Abstract Algebra
Studying abstract algebra can be an adventure of awe-inspiring discovery. The subject need not be watered down nor should it be presented as if all students will become mathematics instructors. This is a beautiful, profound, and useful field which is part of the shared language of many areas both within and outside of mathematics. To begin this journey of discovery, some experience with mathematical reasoning is beneficial. This text takes a fairly rigorous approach to its subject, and expects the reader to understand and create proofs as well as examples throughout.The book follows a single arc, starting from humble beginnings with arithmetic and high-school algebra, gradually introducing abstract structures and concepts, and culminating with Niels Henrik Abel and Evariste Galois' achievement in understanding how we can--and cannot--represent the roots of polynomials. The mathematically experienced reader may recognize a bias toward commutative algebra and fondness for number theory. The presentation includes the following features: Exercises are designed to support and extend the material in the chapter, as well as prepare for the succeeding chapters. The text can be used for a one, two, or three-term course. Each new topic is motivated with a question. A collection of projects appears in Chapter 23. Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks--period. This book is offered as a manual to a new way of thinking. The author's aim is to instill the desire to understand the material, to encourage more discovery, and to develop an appreciation of the subject for its own sake.
Engineering Design Optimization
Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments.
An Introduction to Complex Analysis and the Laplace Transform
The textbook is designed for university students studying science and engineering. I have aimed for a comparatively short book that would give a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications.
Math Without Numbers
An illustrated tour of the structures and patterns we call "math" The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math--topology, analysis, and algebra--which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject. Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world. The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.
Mathematics Numbers 1-10
The basic elements of mathematics are in many ways. The educators to understand and develop the early learners' mathematical skills. Numeracy is a very important part of basic mathematic. As I am an educator my responsibility is to develop the early learner's mathematical interest. Here are the different types of exercises for 4 - 5 years old children about numbers 1-10. These practices will give the concrete concept of numeracy independently.
Iamblichus: On the General Science of Mathematics
On the General Science of Mathematics is the third of four surviving works out of ten by Iamblichus (c. 245 CE-early 320s) on the Pythagoreans. He thought the Pythagoreans had treated mathematics as essential for drawing the human soul upwards to higher realms described by Plato, and downwards to understand the physical cosmos, the products of arts and crafts and the order required for an ethical life. His Pythagorean treatises use edited quotation to re-tell the history of philosophy, presenting Plato and Aristotle as passing on the ideas invented by Pythagoras and his early followers. Although his quotations tend to come instead from Plato and later Pythagoreanising Platonists, this re-interpretation had a huge impact on the Neoplatonist commentators in Athens. Iamblichus' cleverness, if not to the same extent his re-interpretation, was appreciated by the commentators in Alexandria.
USA Through the Lens of Mathematics
This unique book helps instructors in popularizing mathematics by uniting them in a unique multidisciplinary way. This cross-disciplinary approach contributes to innovative teaching strategies that not only improve students' critical and problem-solving skills, but also broaden their scientific vision and multidisciplinary knowledge.
Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields
This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners.
Wavelet Analysis on Local Fields of Positive Characteristic
Nonuniformly Hyperbolic Attractors
This monograph offers a coherent, self-contained account of the theory of Sinai-Ruelle-Bowen measures and decay of correlations for nonuniformly hyperbolic dynamical systems. A central topic in the statistical theory of dynamical systems, the book in particular provides a detailed exposition of the theory developed by L.-S. Young for systems admitting induced maps with certain analytic and geometric properties. After a brief introduction and preliminary results, Chapters 3, 4, 6 and 7 provide essentially the same pattern of results in increasingly interesting and complicated settings. Each chapter builds on the previous one, apart from Chapter 5 which presents a general abstract framework to bridge the more classical expanding and hyperbolic systems explored in Chapters 3 and 4 with the nonuniformly expanding and partially hyperbolic systems described in Chapters 6 and 7. Throughout the book, the theory is illustrated with applications. A clear and detailed account of topicsof current research interest, this monograph will be of interest to researchers in dynamical systems and ergodic theory. In particular, beginning researchers and graduate students will appreciate the accessible, self-contained presentation.
Kurt G繹del
G繹del's Functional Interpretation in Context.- Part I: Axiomatic Intuitionist Logic.- Part II: The Functional Interpretation.- References.- Name Index.
USA Through the Lens of Mathematics
This unique book helps instructors in popularizing mathematics by uniting them in a unique multidisciplinary way. This cross-disciplinary approach contributes to innovative teaching strategies that not only improve students' critical and problem-solving skills, but also broaden their scientific vision and multidisciplinary knowledge.
Formal Analysis by Abstract Interpretation
The book provides a gentle introduction and definition of the denotational-based abstract interpretation method. The book demonstrates how the above method of formal analysis can be used, not only to address the security of systems, but other more general and interesting properties related to the testing, mutating and semantic ambiguity resolution of protocols. The book presents three case studies, all related to current complex protocols and standards used in industry, particularly in the context of IoT and Industry 4.0.
The Thirteen Books of Euclid's Elements; 3
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Computational Cryptography
The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra-Lenstra-Lov獺sz lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.
Logical Foundations of Computer Science
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2022, held in Deerfield Beach, FL, USA, in January 2022. The 23 revised full papers were carefully reviewed and selected from 35 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.
A Mensuration For Indian Schools And Colleges Part II And Part III
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
