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A Course in the Calculus of Variations
This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present.Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical H繹lder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality andthe Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence.While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.
Magic Multiplication
65 x 39 = 2535108 x 312 = 3369627 x 84 = 2268Can you work out these calculations in your head? Many of us would say "No way!" For anyone who reads this book and learns the tricks it contains, it won't be difficult anymore.This book aims to stimulate enthusiasm for math through rapid calculation, thereby creating a solid mathematical foundation for further learning. The goal is to express profound mathematical ideas in simple language, conveying the magic and mystery of calculation. As long as you can multiply two-digit numbers, do addition and subtraction, and understand simple negative numbers, you can handle the basics of this book.
The Joy of Statistics
The vast majority of statistics books delineate techniques used to analyze collected data. The Joy of Statistics is not one of these books. It consists of a series of 42 "short stories", each illustrating how statistical methods applied to data produce insight and solutions to the questions the data were collected to answer. Real-life and sometimes artificial data are used to demonstrate the often painless method and magic of statistics. In addition, the text contains brief histories of the evolution of statistical methods and a number of brief biographies of the most famous statisticians of the 20th century. Sprinkled throughout are statistical jokes, puzzles and traditional stories. The levels of statistical texts span a spectrum, from elementary to introductory to application to theoretical to advanced mathematical. The Joy of Statistics explores a variety of statistical applications using graphs and plots, along with detailed and intuitive descriptions, and occasionally a bit of 10th grade mathematics. Examples of a few of the topics included among these "short stories" are pet ownership, gambling games such as roulette, blackjack and lotteries, as well as more serious subjects such as comparison of African-American and white infant mortality risk, infant birth weight and maternal age, estimation of coronary heart disease risk and racial differences in Hodgkin disease. The statistical descriptions of these topics are in many cases accompanied by easy to understand explanations labelled "How It Works."
Modeling Reality with Mathematics
Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.
Applied Numerical Analysis with Matlab(r)/Simulink(r)
This textbook provides a compact but comprehensive treatment that guides students through applied numerical analysis, using MATLAB(R)/Simulink(R). Ideal as a hands-on source for courses in Numerical Analysis, this text focuses on solving problems using market-standard software, corresponding to all key concepts covered in the classroom. The author uses his extensive classroom experience to guide students toward deeper understanding of key concepts, while they gain facility with software they will need to master for later studies and practical use in their engineering careers.
AP Pre-Calculus for Beginners
AP Pre-Calculus Breakthrough: 2024 Comprehensive Guide with Online CourseAP Pre-Calculus for Beginners is a meticulously crafted textbook designed for students preparing for the 2024 AP Pre-Calculus examination. This book stands out for its comprehensive coverage, high complexity, and alignment with the latest test guidelines. It's an indispensable resource for both beginners and those seeking to solidify their pre-calculus foundations.Key Features: In-Depth Coverage: Each chapter delves into pre-calculus concepts with clarity and depth, ensuring thorough understanding. Topics range from fundamental principles to advanced applications, catering to a wide spectrum of learning needs.2024 Test Guidelines Alignment: The content is updated and aligned with the 2024 AP Pre-Calculus test guidelines, providing students with relevant and current material for effective exam preparation.Interactive Learning Approach: Unique to this textbook is the integration of QR codes and web links in each section. These codes lead to an online platform that offers a rich array of learning tools: Detailed Online Lessons: Each topic is accompanied by a comprehensive online lesson, providing a more in-depth exploration of the subject matter.Illustrative Examples and Exercises: The online resource includes numerous examples and exercises that reinforce learning and provide practical applications of theoretical concepts.Engaging Video Lessons: For auditory and visual learners, the book offers access to high-quality video lessons that complement the written content.Downloadable Worksheets: Students can test their knowledge with a variety of worksheets, which are available for download and print.Answer Key: A complete answer key is provided for all questions and exercises, both in the book and online. This feature enables students to self-assess and understand their areas of strength and improvement.Complementary Online Course: The textbook is paired with a full-fledged online course, mirroring the book's structure. This course offers a learning experience, featuring quizzes, additional resources, and feedback to enhance understanding.AP Pre-Calculus for Beginners is not just a textbook; it's a comprehensive learning ecosystem. It's tailored for the modern student, integrating traditional and digital learning methods to offer a well-rounded educational experience. This book is a valuable tool for anyone aiming to excel in the AP Pre-Calculus exam and build a strong foundation for future mathematical endeavors. Ideal for self-study and classroom usage!
Advances in Optimization and Applications
This book constitutes the refereed proceedings of the 14th International Conference on Advances in Optimization and Applications, OPTIMA 2023, held in Petrovac, Montenegro, during September 18-22, 2023.The 21 full papers included in this book were carefully reviewed and selected from 68 submissions. They were organized in topical sections as follows: ​mathematical programming; global optimization; continuous optimization; discrete and combinatorial optimization; optimal control; game theory and mathematical economics; optimization in economics and finance; and applications.
Practical Guide to Applied Conformal Prediction in Python
Elevate your machine learning skills using the Conformal Prediction framework for uncertainty quantification. Dive into unique strategies, overcome real-world challenges, and become confident and precise with forecasting.Key Features: Master Conformal Prediction, a fast-growing ML framework, with Python applicationsExplore cutting-edge methods to measure and manage uncertainty in industry applicationsUnderstand how Conformal Prediction differs from traditional machine learningBook Description: In the rapidly evolving landscape of machine learning, the ability to accurately quantify uncertainty is pivotal. The book addresses this need by offering an in-depth exploration of Conformal Prediction, a cutting-edge framework to manage uncertainty in various ML applications.Learn how Conformal Prediction excels in calibrating classification models, produces well-calibrated prediction intervals for regression, and resolves challenges in time series forecasting and imbalanced data. Discover specialised applications of conformal prediction in cutting-edge domains like computer vision and NLP. Each chapter delves into specific aspects, offering hands-on insights and best practices for enhancing prediction reliability. The book concludes with a focus on multi-class classification nuances, providing expert-level proficiency to seamlessly integrate Conformal Prediction into diverse industries. With practical examples in Python using real-world datasets, expert insights, and open-source library applications, you will gain a solid understanding of this modern framework for uncertainty quantification.By the end of this book, you will be able to master Conformal Prediction in Python with a blend of theory and practical application, enabling you to confidently apply this powerful framework to quantify uncertainty in diverse fields.What You Will Learn: The fundamental concepts and principles of conformal predictionLearn how conformal prediction differs from traditional ML methodsApply real-world examples to your own industry applicationsExplore advanced topics - imbalanced data and multi-class CPDive into the details of the conformal prediction frameworkBoost your career as a data scientist, ML engineer, or researcherLearn to apply conformal prediction to forecasting and NLPWho this book is for: Ideal for readers with a basic understanding of machine learning concepts and Python programming, this book caters to data scientists, ML engineers, academics, and anyone keen on advancing their skills in uncertainty quantification in ML.
Crowd Dynamics, Volume 4
This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. The volume begins with an overview of analytical problems related to crowd modeling. Attention is then given to the importance of considering the social and psychological factors that influence crowd behavior - such as emotions, communication, and decision-making processes - in order to create reliable models. Finally, specific features of crowd behavior are explored, including single-file traffic, passenger movement, modeling multiple groups in crowds, and the interplay between crowd dynamics and the spread of disease.Crowd Dynamics, Volume 4 is ideal for mathematicians, engineers, physicists, and other researchers working in the rapidly growing field of modeling and simulation of human crowds.
Affine Algebraic Geometry
Algebraic geometry is more advanced with the completeness condition for projective or complete varieties. Many geometric properties are well described by the finiteness or the vanishing of sheaf cohomologies on such varieties. For non-complete varieties like affine algebraic varieties, sheaf cohomology does not work well and research progress used to be slow, although affine spaces and polynomial rings are fundamental building blocks of algebraic geometry. Progress was rapid since the Abhyankar-Moh-Suzuki Theorem of embedded affine line was proved, and logarithmic geometry was introduced by Iitaka and Kawamata.Readers will find the book covers vast basic material on an extremely rigorous level:
Spin/Pin-Structures and Real Enumerative Geometry
Spin/Pin-structures on vector bundles have long featured prominently in differential geometry, in particular providing part of the foundation for the original proof of the renowned Atiyah-Singer Index Theory. More recently, they have underpinned the symplectic topology foundations of the so-called real sector of the mirror symmetry of string theory.This semi-expository three-part monograph provides an accessible introduction to Spin- and Pin-structures in general, demonstrates their role in the orientability considerations in symplectic topology, and presents their applications in enumerative geometry.Part I contains a systematic treatment of Spin/Pin-structures from different topological perspectives and may be suitable for an advanced undergraduate reading seminar. This leads to Part II, which systematically studies orientability problems for the determinants of real Cauchy-Riemann operators on vector bundles. Part III introduces enumerative geometry of curves in complex projective varieties and in symplectic manifolds, demonstrating some applications of the first two parts in the process. Two appendices review the Čech cohomology perspective on fiber bundles and Lie group covering spaces.
A Pen and Paper Introduction to Statistics
This book proposes to reverse the way statistics is taught, by starting with the introduction of linear models. Today, many statisticians know that the one unifying principle of statistical tests is that most of them are instances of linear models.
Parabolic Problems
This book collects the very best of the almost 1800 problems and puzzles published in Parabola magazine into a single volume. Many of the problems have been re-mastered, and new illustrations have been added. Topics covered range across geometry, number theory, combinatorics, logic, and algebra.
Solitons, Instantons, and Twistors
Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well-behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topologically different from vacuum. While integrable equations in lower space-time dimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yang-Mills and Einstein equations require twistor theory. Both techniques rely on an ability to represent nonlinear equations as compatibility conditions for overdetermined systems of linear differential equations. The book provides a self-contained and accessible introduction to the subject. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, vortices, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system.
K羹nneth Geometry
This clear and elegant text introduces K羹nneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic development of the foundations of Lagrangian foliations. The latter half of the text discusses K羹nneth geometry from the point of view of basic differential topology, featuring both new expositions of standard material and new material that has not previously appeared in book form. This subject, which has many interesting uses and applications in physics, is developed ab initio, without assuming any previous knowledge of pseudo-Riemannian or para-complex geometry. This book will serve both as a reference work for researchers, and as an invitation for graduate students to explore this field, with open problems included as inspiration for future research.
Tales of the Tail
"Tales of the Tail: Legendary Cats Throughout History" is an enchanting exploration into the feline realm, delving into the captivating stories of extraordinary cats that have left an indelible mark on human history. This whimsical tome unveils the rich tapestry of legends, folklore, and real-life anecdotes surrounding these enigmatic creatures, celebrating their mystique and the profound impact they have had on various cultures.Within the pages of "Tales of the Tail," readers will embark on a journey through time, discovering mythical cats that have been revered as divine entities, guardians, and symbols of good fortune. From ancient civilizations to modern times, the book weaves together narratives of cats that have transcended the ordinary, earning their place as revered beings in the annals of history.The tales within this collection are not limited to mere whimsy; they are intertwined with historical events, cultural beliefs, and the evolving roles that cats have played in societies around the world. Whether exploring the sacred cats of ancient Egypt, the mischievous Cheshire Cat of Wonderland fame, or the famed literary cat companions of renowned authors, each story is a testament to the profound connections between humans and their feline counterparts.Each chapter unfolds like a storybook, with vivid descriptions and captivating illustrations bringing these legendary cats to life. From the graceful and regal to the cunning and magical, "Tales of the Tail" pays homage to the diverse personalities and qualities that have made cats such beloved companions throughout the ages.This enchanting collection is a celebration of the enduring fascination with cats and their timeless allure. "Tales of the Tail" invites readers to immerse themselves in the magical world of legendary felines, where history, mythology, and the timeless charm of cats converge in a purrfectly delightful tapestry of tales.
The Evolution of the Vehicle Routing Problem
This book presents state-of-the-art research and practice in optimization routing, specifically the vehicle routing problem (VRP). Since its introduction in the late 1950s, the VRP has been a very significant area of research and practice in operations research. Vehicles are used to make deliveries and for pick-ups every day and everywhere. Companies such as Amazon, UPS, FedEx, and DHL use route optimization to reduce mileage, fuel use, number of trucks on the road, and carbon dioxide emissions. The authors compile and analyze 135 survey and review articles on vehicle routing topics published between 2005 and 2022 in an effort to make key observations about publication and trend history, summarize the overall contributions in the field, and identify trends in VRP research and practice. The authors have compiled published research on models, algorithms, and applications for specific areas, including: alternative and multiple objectives; arc routing and general routing; drones, last-mile delivery, and urban distribution; dynamic and stochastic routing; green routing; inventory routing; loading constraints; location-routing; multiple depots; pickup and delivery and dial-a-ride problems; rich and multi-attribute routing; routing over time; shipping; two-echelon, collaborative, and inter-terminal problems; specific variants, benchmark datasets, and software; and exact algorithms and heuristics. In addition, the book discusses how vehicle routing problems are among the most widely studied problems in combinatorial optimization due to the mathematical complexity and practical significance.
Miracles, Mystics, Mathematicians
Miracles, Mystics, Mathematicians: Searching for Deep Reality focuses on the lives and writings of some of history's most influential mathematicians and the impact that their mystical beliefs had on their lives and on their mathematical work. Modern biographers often cleanse the lives of renowned scientists of any hint of mysticism or occultism. Such threads are sometimes regarded as relics of the superstitious past; flaws that need to be hushed up, marginalized, or reinterpreted. This book represents a minor attempt to push back against this tendency and to examine these aspects of the history of mathematics with seriousness and intellectual curiosity.Features A breadth of scope covering many centuries Suitable for anyone interested in mathematics, history, philosophy, paranormal phenomena, psi-research, mysticism, or in any combination of the above An almost unique account of known histories, examined from a new vantage point Sasho Kalajdzievski is a Senior Scholar in the Department of Mathematics at the University of Manitoba.
K羹nneth Geometry
This clear and elegant text introduces K羹nneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic development of the foundations of Lagrangian foliations. The latter half of the text discusses K羹nneth geometry from the point of view of basic differential topology, featuring both new expositions of standard material and new material that has not previously appeared in book form. This subject, which has many interesting uses and applications in physics, is developed ab initio, without assuming any previous knowledge of pseudo-Riemannian or para-complex geometry. This book will serve both as a reference work for researchers, and as an invitation for graduate students to explore this field, with open problems included as inspiration for future research.
Interactive Epistemology
Robert J Aumann has received numerous prizes, including the Nobel Memorial Prize in Economic Sciences for 2005.With his 1976 paper, 'Agreeing to Disagree', Robert Aumann pioneered the subject of interactive epistemology: the study of what people know, and what they know about what others know. Since then, the discipline has burgeoned enormously. This book documents Aumann's work leading to the 1976 paper and his subsequent contributions to the discipline. The scientific controversies emanating from his work are also included.
Probability and Stochastic Processes
The book collects papers on several topics in probability and stochastic processes. These papers have been presented at a conference organised in honour of Professor Rajeeva L. Karandikar who turned 65 in 2021. He was a distinguished researcher and a teacher at the Indian Statistical Institute (ISI), Delhi Centre, for many years. He has been a multi-faceted academician, interacting with the Government of India and the industry. He has left an indelible mark in every endeavour of his and in his several different avatars--be it in the ISI, in the industry or as Director of Chennai Mathematical Institute. This book will be useful to senior undergraduate and graduate students, as well as researchers in probability, statistics and related fields.
Twisted Logic
Draws upon an array of popular and novel puzzles, problems, and paradoxes, and uses these to help understand and navigate our everyday world. Addresses some of the big questions. Aimed at all those interested in learning about weird and wonderful problems and paradoxes.
Nested Simulations: Theory and Application
Maximilian Klein analyses nested Monte Carlo simulations for the approximation of conditional expected values. Thereby, the book deals with two general risk functional classes for conditional expected values, on the one hand the class of moment-based estimators (notable examples are the probability of a large loss or the lower partial moments) and on the other hand the class of quantile-based estimators. For both functional classes, the almost sure convergence of the respective estimator is proven and the underlying convergence speed is quantified. In particular, the class of quantile-based estimators has important practical consequences especially for life insurance companies since the Value-at-Risk falls into this class and thus covers the solvency capital requirement problem. Furthermore, a novel non parametric confidence interval method for quantiles is presented which takes the additional noise of the inner simulation into account.
Formal Aspects of Component Software
This book constitutes the refereed proceedings of the 19th International Conference on Formal Aspects of Component Software, FACS 2023, which took place virtually during October 19-20, 2023.The 11 full papers included in this book were carefully reviewed and selected from 23 submissions. They were organized in topical sections as follows: cloud computing, cyber-physical and critical systems, and the Internet of Things.
Women in Numbers Europe IV
This volume contains research and expository content based on a wide variety of topics within modern number theory and arithmetic geometry. Research in this volume arises from or is connected with the Women in Numbers Europe (WiNE) IV conference held in summer 2022 in Utrecht, The Netherlands. The contents of this volume are of interest to professional mathematicians, graduate students, and researchers working in number theory, arithmetic geometry, and related areas.
Optimal Transport and Applications to Geometric Optics
This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chapter on Monge-Amp癡re measures is included containing also exercises. A detailed analysis of the Wasserstein metric is also carried out. For the applications to optics, the book describes the necessary background concerning light refraction, solving both far-field and near-field refraction problems, and indicates lines of current research in this area. Researchers in the fields of mathematical analysis, optimal transport, partial differential equations (PDEs), optimization, and optics will find this book valuable. It is also suitable for graduate students studying mathematics, physics, and engineering. The prerequisites for this book include a solid understanding of measure theory and integration, as well as basic knowledge of functional analysis.
Elements of Discrete Mathematics
This book treats the elements of discrete mathematics that have important applications in computer science, thus providing the necessary tools for the reader to come to a competent mathematical judgement of modern developments in the age of information. Almost all assertions are shown with full proofs. Exercises are provided, with solutions presented in full detail.
Twisted Logic
Draws upon an array of popular and novel puzzles, problems, and paradoxes, and uses these to help understand and navigate our everyday world. Addresses some of the big questions. Aimed at all those interested in learning about weird and wonderful problems and paradoxes.
Fixed Point Theory in Generalized Metric Spaces
This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.
Discrete Variational Problems with Interfaces
Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task, especially for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems, and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.
Crucial Event Rehabilitation Therapy
This book describes a new strategy for rehabilitation from injury and/or disease using Crucial Event Therapy. Recent studies have shown that individuals can recuperate more rapidly from surgery and other invasive procedures intended to correct the negative effects of disease or injury through the use of life support systems that operate at the body's natural biofrequencies. The same observation has been clinically shown to reverse the degenerative effects of neurodegenerative diseases such as Parkinson's and Alzheimer's Disease. Crucial Event Therapy describes medicine as the operational control of the functions of the human body treated as a network-of-networks, with 1/f-variable crucial events coding the dynamic states of health and disease through information flow within a network and information exchange between biomedical networks. A new way of thinking based on the statistics of Cortical Events is presented and the relevant literature is suitably referenced. This is anideal book for biophysicists and data scientists seeking to understand the connection of complexity measures for the study of consciousness with the clinical aspects of designing a rehabilitation strategy.
Stochastic Versus Deterministic Systems of Iterative Processes
Continuous state dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend on mode of convergence. Second, the basic probabilistic and statistical properties, namely, the behavior of mean, variance, moments of solutions are described as qualitative/quantitative properties of solution process. We observe that the nature of probability distribution or density functions possess the qualitative/quantitative properties of iterative prosses as a special case. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focused on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the solutions outlined above and made slow progress in developing problems. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.
Mischief of Math, The: Short Stories of Clowns, Contortionists, and Court-Jesters
Embark on a whimsical odyssey through the realms of ethics in AI bots, logic, game theory, paradoxes, biases, fake data detection, graph theory, and so much more! Within these pages you'll find a collection of fictional short stories that weave together the intriguing, the counterintuitive and the downright quirky with bold characters from every walk of life.
Problems and Solutions in Mathematical Olympiad (Secondary 2)
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
Mischief of Math, The: Short Stories of Clowns, Contortionists, and Court-Jesters
Embark on a whimsical odyssey through the realms of ethics in AI bots, logic, game theory, paradoxes, biases, fake data detection, graph theory, and so much more! Within these pages you'll find a collection of fictional short stories that weave together the intriguing, the counterintuitive and the downright quirky with bold characters from every walk of life.Check out the book's website here!
Problems and Solutions in Mathematical Olympiad (Secondary 2)
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
Exercises in Applied Mathematics
This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections. It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels. The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning. Exercises are selected from a number of different domains, both theoretical and more applied. Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many. For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as theymove on to more advanced work.
Randomized Response Techniques
This book presents an up-to-date perspective on randomized response techniques (RRT). It discusses the most appropriate and efficient procedures of RRT for analysing data from queries dealing with sensitive and confidential issues, including the treatment of infinite and finite population setups. The book aims to spark a renewed interest among sampling experts who may have overlooked RRT. By addressing the missing topics and incorporating a wide range of contributors' works, it seeks to foster an appreciative academic environment and inspire a reformed and amended view of RRT. As the book unfolds, readers will gain valuable insights into the evolving landscape of RRT and its applications, positioning them at the forefront of this engaging field of study.On RRT, the literature has grown immensely since its inception in 1965 by S.L. Warner. Despite several books published on the subject, there are still two crucial topics missing from the existing RRT literature. This book aimsto address these gaps and provide valuable insights to curious readers in the field. The book is mandatory reading for statisticians and biostatisticians, market researchers, operations researchers, pollsters, sociologists, political scientists, economists and advanced undergraduate and graduate students in these areas.
A Spectral Theory of Noncommuting Operators
The main goal of this book is to describe various aspects of the theory of joint spectra for matrices and linear operators. It is suitable for a graduate-level topic course in spectral theory and/or representation theory. The first three chapters can also be adopted for an advanced course in linear algebra. Centered around the concept of projective spectrum, the book presents a coherent treatment of fundamental elements from a wide range of mathematical disciplines, such as complex analysis, complex dynamics, differential geometry, functional analysis, group theory, and Lie algebras. Researchers and students, particularly those who aspire to gain a bigger picture of mathematics, will find this book both informative and resourceful.
Lecture Notes on Geometry of Numbers
This book serves as an illuminating introduction to the intricacies of the geometry of numbers. It commences by exploring basic concepts of convex sets and lattices in Euclidean space and goes on to delve into Minkowski's fundamental theorem for convex bodies and its applications. It discusses critical determinants and successive minima before explaining the core results of packings and coverings. The text goes on to delve into the significance of renowned conjectures such as Minkowski's conjecture regarding the product of linear forms, Watson's conjecture, and the conjecture of Bambah, Dumir, and Hans-Gill concerning non-homogeneous minima of indefinite quadratic forms. Dedicated to Prof. R.P. Bambah on his 98th birthday, a living legend of number theory in India, this comprehensive book addresses both homogeneous and non-homogeneous problems, while sprinkling in historical insights and highlighting unresolved questions in the field. It is ideally suited for beginnersembarking on self-study as well as for use as a text for a one- or two-semester introductory course.
Journal of Applied Logics. IfCoLog Journal of Logics and their Applications. Volume 10, number 5, November 2023
The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.
Abstract Algebra
Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think.
A Pen and Paper Introduction to Statistics
This book proposes to reverse the way statistics is taught, by starting with the introduction of linear models. Today, many statisticians know that the one unifying principle of statistical tests is that most of them are instances of linear models.
Collected Papers in Honor of Yoshihiro Shibata
Yoshihiro Shibata has made many significant contributions to the area of mathematical fluid mechanics over the course of his illustrious career, including landmark work on the Navier-Stokes equations. The papers collected here -- on the occasion of his 70th birthday -- are written by world-renowned researchers and celebrate his decades of outstanding achievements.
The Mathematics of Finance for High Schoolers
It's never too early to start learning about finance. But the mathematics covered in this book is not the mathematics of balancing your check book, or splitting a restaurant bill among friends, some of whom had the set menu, and others the specials. The mathematics here is an introduction to the subject known as mathematical finance, quantitative finance or financial engineering. It's an introduction to the higher level of mathematics used in banks and hedge funds, in valuing complex financial instruments, in allocating money to different assets, and in measuring and managing risk.This book is for high-school children who are confident in their mathematics. They do not have to be advanced or even top of their class. But they do have to be comfortable with learning new concepts.The book starts with a chapter on the history of money, banks, bubbles and crashes. Then there's the jargon. Bankers do like their jargon, but it's all very straightforward. Then there's a chapter on careers in finance. There are jobs that just require familiarity with spreadsheets, then there are jobs that require a degree in mathematics or computer science. A chapter on the basic mathematics is next. That's a little bit, but only a little bit, about the exponential function, logarithms and simple ideas in probability. The last four chapters are on fixed income (that's just putting money in the bank), shares, portfolios, and finally the financial instruments known as options.
