G繹del Forever: Through 90 Years of Foundational Claims
G繹del Forever takes a critical look at several foundation claims on G繹delian incompleteness that have appeared in the literature over the years, strictly adhering to mathematical details. Rephrasing the words from Torkel Franz矇n: Ken Williams presents a new book on G繹del's incompleteness theorem for a general audience since no existing book both explains the theorem from a mathematical point of view and reflects his experiences over the years of reading and commenting on references to the incompleteness theorem on the Internet. The range of critical review on the one hand and its elementary, if detailed, derivation of G繹del's Result (on which it is based) on the other makes G繹del Forever a must read for the serious study of the meaning and consequences of G繹del's Incompleteness.
Beyond the Learned Academy
The tremendous growth of the mathematical sciences in the early modern world was reflected contemporaneously in an increasingly sophisticated level of practical mathematics in fields such as merchants' accounts, instrument making, teaching, navigation, and gauging. In many ways, mathematics shaped the knowledge culture of the age, infiltrating workshops, dockyards, and warehouses, before extending through the factories of the Industrial Revolution to the trading companies and banks of the nineteenth century. While theoretical developments in the history of mathematics have been made the topic of numerous scholarly investigations, in many cases based around the work of key figures such as Descartes, Huygens, Leibniz, or Newton, practical mathematics, especially from the seventeenth century onwards, has been largely neglected. The present volume, comprising fifteen essays by leading authorities in the history of mathematics, seeks to fill this gap by exemplifying the richness, diversity, and breadth of mathematical practice from the seventeenth century through to the middle of the nineteenth century.
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.
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.
Lectures on Lagrangian Torus Fibrations
Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these fibrations encode the geometry of a symplectic 4-manifold in a simple 2-dimensional diagram. This text is a guide to interpreting these diagrams, aimed at graduate students and researchers in geometry and topology. First the theory is developed, and then studied in many examples, including fillings of lens spaces, resolutions of cusp singularities, non-toric blow-ups, and Vianna tori. In addition to the many examples, students will appreciate the exercises with full solutions throughout the text. The appendices explore select topics in more depth, including tropical Lagrangians and Markov triples, with a final appendix listing open problems. Prerequisites include familiarity with algebraic topology and differential geometry.
Linear Algebra for Data Science
This book serves as an introduction to linear algebra for undergraduate students in data science, statistics, computer science, economics, and engineering. The book presents all the essentials in rigorous (proof-based) manner, describes the intuition behind the results, while discussing some applications to data science along the way.The book comes with two parts, one on vectors, the other on matrices. The former consists of four chapters: vector algebra, linear independence and linear subspaces, orthonormal bases and the Gram-Schmidt process, linear functions. The latter comes with eight chapters: matrices and matrix operations, invertible matrices and matrix inversion, projections and regression, determinants, eigensystems and diagonalizability, symmetric matrices, singular value decomposition, and stochastic matrices. The book ends with the solution of exercises which appear throughout its twelve chapters.
Lectures on Lagrangian Torus Fibrations
Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these fibrations encode the geometry of a symplectic 4-manifold in a simple 2-dimensional diagram. This text is a guide to interpreting these diagrams, aimed at graduate students and researchers in geometry and topology. First the theory is developed, and then studied in many examples, including fillings of lens spaces, resolutions of cusp singularities, non-toric blow-ups, and Vianna tori. In addition to the many examples, students will appreciate the exercises with full solutions throughout the text. The appendices explore select topics in more depth, including tropical Lagrangians and Markov triples, with a final appendix listing open problems. Prerequisites include familiarity with algebraic topology and differential geometry.
Partial Differential Equations
Quite a number of phenomena in science and technology, industrial and/or agricultural production and transport, medical and/or biological flows and movements, social and/or economical developments, etc., depend on many variables, and are very much complicated. Although the detailed knowledge is accumulated in respective fields, it is meaningful to model and analyze the essential part of the phenomena in terms of smaller number of variables, which falls into partial differential equations. This book aims at providing students and researchers the basic ideas and the methods to solve problems in various fields. Particular attention is paid to bridge the gap between mathematics and the real world. To do this, we start from a simple system with intuitively understandable physical background, extract the essential part, formulate into mathematical tools, and then generalize for further application. Here logical thinking in depth and wide linking to various fields are sought to construct intellectual network.
Basic Topology 1
This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone-Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand-Kolmogoroff theorem. The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the conceptsleading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.
Partial Differential Equations
Quite a number of phenomena in science and technology, industrial and/or agricultural production and transport, medical and/or biological flows and movements, social and/or economical developments, etc., depend on many variables, and are very much complicated. Although the detailed knowledge is accumulated in respective fields, it is meaningful to model and analyze the essential part of the phenomena in terms of smaller number of variables, which falls into partial differential equations. This book aims at providing students and researchers the basic ideas and the methods to solve problems in various fields. Particular attention is paid to bridge the gap between mathematics and the real world. To do this, we start from a simple system with intuitively understandable physical background, extract the essential part, formulate into mathematical tools, and then generalize for further application. Here logical thinking in depth and wide linking to various fields are sought to construct intellectual network.
The Mathematical Papers of Sir William Rowan Hamilton: Volume 4
Pi
In this delightful layperson's introduction to one of math's most interesting phenomena, Drs. Posamentier and Lehmann review pi's history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating pi over the centuries, quirky examples of obsessing about pi, and useful applications of pi in everyday life, including statistics.
Mental Multiplication Volume 2
My goal in the educational arena is to cause students to realize their potential in this mathematical criteria. The free- thinking in this incredible journey that multiplication can take you to, will show the student how to find treasures in understanding. The higher and deeper depths that I have reached is so miraculous that I can achieve wonders without the use of a calculator except to confirm my answers. It is my desire that the student can reach such depths also! Prayer has caused such a methodology that I have never encountered in all my study of this mystery. In my many past years of hours and days and months of looking into this treasure of knowledge, many other areas of mathematics has increased. I invite you to try Mental Multiplication Volume 2, you will love it!
Fair Share
Kofi Annan, former Secretary General of the United Nations, argued that "We need to create a world that is equitable, that is stable and a world where we bear in mind the needs of others, and not only what we need immediately. We are all in the same boat."American businessman, John Landgraf stated: "I hope that most of us believe that we actually would all benefit from living in a more equitable society. If that's not happening, we're squandering human potential." For the world to be fair, one needs to know how to divide. Without the mathematics of division, humankind cannot function...Marie Antoinette, Queen of France (infamously) said "If people have no bread, let them eat cake," and while Ahmes ― the scribe of the Rhind Mathematical Papyrus ― dealt with loaves of bread, prosperous people in the twentieth century dealt with cake division, although bread is also uniformly available. You'll be surprised, but there are at least four books and over 200 scientific (not gastronomical!) papers on cake division. Those authors were not overly concerned with obesity, one can guess, but whether distributing loaves, cakes, chores, or dividends, one needs to master division.This book deals with a wide spectrum of division problems, and provides the historical background, giving a sense of how pervasive division is in our lives. In particular, the second part focuses on a problem that remained open until 1985, when Professor Robert John Aumann (Nobel laureate in Economics, 2005) and Professor Michael Maschler solved it using game-theoretic techniques. Simple alternative solutions are given, which are suitable for high schools and other educational institutions.
Tree successor algebra
Tree successor algebra: A new branch in mathematics is a book about a formal theory of tree generation with an axiomatic basis for a new object called collection space. The elements of this space, in other words collections, have a clear connection to rooted trees and are treated as variables in sum form equations, the application area of tree successor algebra. With connections to different branches of mathematics such as number theory, linear algebra and algebra, tree successor algebra shows a fundamental link between rooted tree generation and partition generation, establishing a well-defined order in which rooted trees are generated. This in turn makes it possible to define a successor operator, the unit of least action in tree generation, and generalize it in order to create a concept of tree sequences. Due to this, the concept of the infinite sequence of all rooted trees can be formed, and the notion of a rooted tree line, and thus the need for tools to solve sum form equations rises. The axiomatic system answers to this need.
Logic for Kids
Logic for Kids is intended to help parents take charge of the intellectual development of their children in a critical area: the acquisition of skills related to logical reasoning. Many other books, including math and science books, fail to treat logic as a subject in its own right, provide no special instruction, and expect students to figure out logic on their own. Without the corrective measures explained in this book, students will be ill-prepared to cope with increasing intellectual demands as they progress from grade to grade. These demands will become greater and more varied in college and once they embark on a professional career. Getting started in logic at the earliest opportunity is the answer.
Recent Advances in Mathematical Aspect in Engineering
The present text is an edited Special Issue in reprint form. This Special Issue took the opportunity to invite researchers to contribute their latest original research findings, which were either advances in the state-of-the-art of mathematical methods, theoretical studies, or experimental studies that extend the bounds of existing methodologies to new contributions, addressing current challenges and engineering problems on "Recent Advances in Mathematical Aspect in Engineering". Although this reprint is not a formal textbook, it will definitely be useful for university teachers, research students and industrial researchers, and will assist in overcoming difficulties while dealing with the nonlinear governing equations of fluid mechanics, energy, heat transfer, steady and unsteady flow problems, nanofluids, thermodynamics, magnetohydrodynamics, peristaltic and blood flow. For nonlinear and coupled differential equations, it is often more difficult to achieve an analytic solution or even a numerical one. This reprint has successfully handled this challenging task with the techniques reported within. In addition, the findings of the simulations are logically realistic and meet the standard of sufficient scientific value.
Topics in Graph Theory
The interplay between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences continues to grow.
Numerical Methods for Scientists and Engineers
The present shape of the book is based on my experience, extending over a long period of teaching Mathematics to under-graduate and post-graduate students of different colleges and universities. It is a self-contained textbook, designed for undergraduate students, who have mathematics as one of their subsidiary subjects. This book covers the different numerical methods, which are useful to solve algebraic and transcendental equations, systems of linear algebraic equations, and ordinary differential equations (initial value problems), and also covers the different strategies of numerical integration. This book contains various solved examples and a large number of standard unsolved questions that are given as exercise at the end of each chapter. In this book, each chapter contains the different MCQs, which are helpful for various competitive examinations of central and state services.
EZ Math Workbook
I HATE MATH.....There I said it! I bet thousands of students and parents have said it. When I was really having problems with Algebra in the 9th grade, my Grandmother ( who was a teacher) told me "math isn't hard if you understand it". When I started my career in teaching math in Jacksonville Florida I soon learned that all the math books we had were lacking really good easy to understand instructions on explaining specific areas. Most of the math books did have good parts i.e. one might have a really good section or chapter on fractions but lacked in explaining decimals etc. I taught 7 years plus both sessions of summer school for 5 years at several junior and senior high schools. Each school had "adopted" different math books to teach from. This is where the idea of creating my own math book self guide stated. Over several years I started writing and explaining the different areas of math. It is my hope that this workbook helps students and parents who my be frustrated with "new" math and "common core" principles. In this workbook you will find every area that is covered in math for secondary students. The chapter problems are specially designed to address several levels of a students skill sets. I found that most students would fall into various levels....advanced; standard; basic and remedial. Each chapter problems and chapter tests are designed with levels of "difficult", "moderate" and " easy" problems. As a former math teacher and a parent of three adult children I really hope this book helps.
Quantum Hydrodynamic Equation and Its Mathematical Theory
Quantum hydrodynamics comes from superfluid, superconductivity, semiconductor and so on. Quantum hydrodynamic model describes Helium II superfluid, Bose-Einstein condensation in inert gas, dissipative perturbation of Hamilton-Jacobi system, amplitude and dissipative perturbation of Eikonal quantum wave and so on. Owing to the broad application of quantum hydrodynamic equations, the study of the quantum hydrodynamic equations has aroused the concern of more and more scholars. Based on the above facts, we collected and collated the data of quantum hydrodynamic equations, and studied the concerning mathematical problems.The main contents of this book are: the derivation and mathematical models of quantum hydrodynamic equations, global existence of weak solutions to the compressible quantum hydrodynamic equations, existence of finite energy weak solutions of inviscid quantum hydrodynamic equations, non-isentropic quantum Navier-Stokes equations with cold pressure, boundary problem of compressible quantum Euler-Poisson equations, asymptotic limit to the bipolar quantum hydrodynamic equations.
Mathfatuated
Mathfatuated includes unique poems representing math topics associated with the lovable subject, making it the perfect gift for the math lover. Creating a poetry book about math can be a unique way of exploring mathematical concepts that may seem boringly challenging to some. Poetry can give a fresh perspective and bring an imaginative approach to learning about math. It can also help people remember mathematical concepts better. Moreover, it can bridge the gap between math and art and appeal to a larger audience. Overall, a poetry book about math can be an appealing and creative way to engage with the subject.
A new perspective on the determination of the prime numbers
Academic Paper from the year 2023 in the subject Mathematics - Number Theory, grade: 2.00, language: English, abstract: A procedure is developed for determining the primality of a number, N, but does not examine the number, rather a function of that number. The function has several properties, by means of which many of the non-primes may be identified and discarded without further investigation. Using the concept of cage numbers (defined in the text) a matrix of all of the counting numbers is produced, where, with the exception of the prime numbers 2 and 3, all of the prime numbers are embedded in one column of the matrix. Strings of consecutive numbers are extracted from the matrix, and it is seen that the only places within the whole of the range of the counting numbers where prime numbers can exist is at the positions of the second and penultimate numbers within a string By means of the function of N, all of the odd numbers may be generated and examined for primality.
The Geometry of Cubic Hypersurfaces
Cubic hypersurfaces are described by almost the simplest possible polynomial equations, yet their behaviour is rich enough to demonstrate many of the central challenges in algebraic geometry. With exercises and detailed references to the wider literature, this thorough text introduces cubic hypersurfaces and all the techniques needed to study them. The book starts by laying the foundations for the study of cubic hypersurfaces and of many other algebraic varieties, covering cohomology and Hodge theory of hypersurfaces, moduli spaces of those and Fano varieties of linear subspaces contained in hypersurfaces. The next three chapters examine the general machinery applied to cubic hypersurfaces of dimension two, three, and four. Finally, the author looks at cubic hypersurfaces from a categorical point of view and describes motivic features. Based on the author's lecture courses, this is an ideal text for graduate students as well as an invaluable reference for researchers in algebraic geometry.
The Navier-Stokes Problem in the 21st Century
This book provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics, now revised to include fresh examples, theorems, results, and references that have become relevant since the first edition published in 2016.
Outlier Detection Using Power Mean
Outliers have been regarded as the noisy data in statistics which have now turned out to be an important problem and are now been researched in diverse fields and application domains. Outlier detection has been in core interest of not only the statisticians but all the professionals who are working on a particular data set. Many outlier detection techniques have been developed specific to certain application domains, while some techniques are more generic. This work has added one more technique to the bucket list of all those professionals. Power mean which has been used as a general method to calculate various means like arithmetic mean (power mean with power 1), geometric mean (power mean with power 0), Lorentz mean (power mean with power 1/3) etc. can also be used to detect the sensitivity of the data towards being the outlier. This work studies various powers of power mean for outlier detection. It contains two different data sets, one containing fractions and the other integers. The results have been verified by the existing standard techniques of outlier detection. Thus this book contains description of detecting outliers using power mean with different types of data sets, graphs and figures for better understanding. The idea is to check the efficacy of the method using a data set in which the outlier or the anomaly is already known and then testing the same method for a data set in which the outliers are not known to us. The open research issues and challenges at the end will provide researchers a clear path for the future of outlier detection methods. The book would be useful for practitioners of applied statistics and data analysts.
Introduction to Proofs and Proof Strategies
Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof. The material revolves around possible strategies to approaching a problem without classifying 'types of proofs' or providing proof templates. Instead, it helps students develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow. Beginning by discussing familiar and fundamental topics from a more theoretical perspective, the book moves on to inequalities, induction, relations, cardinality, and elementary number theory. The final supplementary chapters allow students to apply these strategies to the topics they will learn in future courses. With its focus on 'doing mathematics' through 200 worked examples, over 370 problems, illustrations, discussions, and minimal prerequisites, this course will be indispensable to first- and second-year students in mathematics, statistics, and computer science. Instructor resources include solutions to select problems.
Four-Dimensional Manifolds and Projective Structure
This book may be considered first as an introduction to differential geometry and, in particular, to 4-dimensional manifolds, and secondly as an introduction to the study of projective structure and projective relatedness in manifolds.
Why Does Math Work ... If It's Not Real?
According to G. H. Hardy, the 'real' mathematics of the greats like Fermat and Euler is 'useless, ' and thus the work of mathematicians should not be judged on its applicability to real-world problems. Yet, mysteriously, much of mathematics used in modern science and technology was derived from this 'useless' mathematics. Mobile phone technology is based on trig functions, which were invented centuries ago. Newton observed that the Earth's orbit is an ellipse, a curve discovered by ancient Greeks in their futile attempt to double the cube. It is like some magic hand had guided the ancient mathematicians so their formulas were perfectly fitted for the sophisticated technology of today. Using anecdotes and witty storytelling, this book explores that mystery. Through a series of fascinating stories of mathematical effectiveness, including Planck's discovery of quanta, mathematically curious readers will get a sense of how mathematicians develop their concepts.
Introduction to Real Analysis
The emphasis of this now classic text is on sequences of real numbers, compact subsets of IR, as well as real-valued functions.
The Rule of Nine
"THE RULE OF NINE" IS A FASCINATING BOOK BY IYESIS MITCHELL-TIBERE THAT DELVES INTO THE MYSTICAL AND MATHEMATICAL SIGNIFICANCE OF THE NUMBER NINE. THE BOOK ARGUES THAT THE CREATOR'S SIGNATURE IS HIDDEN IN DIVINE MULTIPLICATION THROUGH THE RULE OF NINE, AND THAT BY UNDERSTANDING THE POWER OF THIS NUMBER, WE CAN UNLOCK LIMITLESS POTENTIAL WITHIN OURSELVES.IYESIS EXPLORES THE MANY WAYS IN WHICH THE NUMBER NINE APPEARS THROUGHOUT HISTORY AND OUR LIVES, FROM THE CYCLES OF NATURE TO THE STRUCTURE OF OUR BODIES. SHE ARGUES THAT THIS NUMBER IS NOT JUST A COINCIDENCE, BUT A FUNDAMENTAL ASPECT OF DESIGN.BY EXAMINING THE RULE OF NINE AND ITS VARIOUS MATHEMATICAL APPLICATIONS, THE AUTHOR SHOWS HOW WE CAN TAP INTO A DEEPER LEVEL OF UNDERSTANDING AND CONSCIOUSNESS. SHE EMPHASIZES THAT THIS UNDERSTANDING CAN HELP US ACHIEVE OUR FULL POTENTIAL AS INFINITE BEINGS AND RECOGNIZE THE LIMITLESS NATURE OF OUR OWN EXISTENCE.OVERALL, "THE RULE OF NINE" IS PROFOUNDLY INSPIRING AND THOUGHT-PROVOKING BOOK THAT ENCOURAGES READERS TO EXPLORE THE MYSTICAL AND MATHEMATICAL UNDERPINNINGS OF THE UNIVERSE. IT IS A MUST-READ FOR ANYONE INTERESTED IN THE INTERCONNECTION OF HISTORY, SCIENCE SPIRITUALITY, PERSONAL GROWTH, AND THE MYSTERIES OF THE COSMOS.
Multiplicative Differential Equations
Multiplicative Differential Equations: Volume 2 is the second part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics.
Multiplicative Differential Equations
Multiplicative Differential Equations: Volume I is the first part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics.
Graphs & Digraphs
Graphs & Digraphs masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory.
Why Does Math Work ... If It's Not Real?
According to G. H. Hardy, the 'real' mathematics of the greats like Fermat and Euler is 'useless, ' and thus the work of mathematicians should not be judged on its applicability to real-world problems. Yet, mysteriously, much of mathematics used in modern science and technology was derived from this 'useless' mathematics. Mobile phone technology is based on trig functions, which were invented centuries ago. Newton observed that the Earth's orbit is an ellipse, a curve discovered by ancient Greeks in their futile attempt to double the cube. It is like some magic hand had guided the ancient mathematicians so their formulas were perfectly fitted for the sophisticated technology of today. Using anecdotes and witty storytelling, this book explores that mystery. Through a series of fascinating stories of mathematical effectiveness, including Planck's discovery of quanta, mathematically curious readers will get a sense of how mathematicians develop their concepts.
Discrete Mathematics
Discrete Mathematics: A Gateway to the Mathematical Garden is an introduction to finite and discrete mathematics. This book includes all the important and foundational mathematics to support the student learning finite mathematics for the first time: logic, set theory, number theory, proofs, combinatorics, and graph theory. The exposition helps the student-reader learn to think logically and reasonably about mathematical structures. Discussions of cryptology, computer science, machine-readable codes, and operations research are used to give the student a sense of how the mathematics is applied. Throughout the book, examples illustrate the material and provide insight into the mathematical theory. The book is essentially self-contained. There are very few prerequistes aside from some mathematical maturity and familiarity with algebra. Problems to help the student master the concepts are included at the end of each section. Each chapter concludes with a set of supplementary problems and a set of sample test questions. Discrete Mathematics: A Gateway to the Mathematical Garden, Chuck Garner, paperback, color, first edition, 7.44in by 9.68 in, 217 pages, ISBN 978-1-312-71237-9, copyright 2023 Charles R. Garner Jr.
Computational Mathematics and Applied Statistics
Rapid advances in modelling research have created new challenges and opportunities for statisticians. Statistical inference in observational studies and many other emerging fields have motivated statisticians worldwide to develop cutting-edge methods and analytical strategies.The aim of this book is to showcase the applications and methodological research in all fields of computational statistics. This book will provide a forum for computer scientists, mathematicians, and statisticians working in a variety of areas in statistics, including biometrics, econometrics, data analysis, graphics, and simulation.
Special Functions with Applications to Mathematical Physics
This MDPI booklet lists the articles published in three Special Issues of the journal Mathematics devoted to special functions with applications in mathematical physics in the years 2020-2021.The call for papers considered theories and applications of high transcendental functions, including topics found mainly in the list of keywords: - Mittag-Leffler and related functions, and their applications in mathematical physics;- Wright and related functions and their applications in mathematical physics;- exponential integrals and their extensions with applications in mathematical physics;- generalized hypergeometric functions and their extensions with applicationsHowever, the Special Issues were not limited to the above list, for example, when the content of a paper was clearly related to some high transcendental functions and their applications.Special attention was reserved for distinct functions exhibiting some relevance in the framework of the theories and applications of the fractional calculus and in their visualization through illuminating plots.Both research and survey articles were included in this booklet, according to the content list.
Multivariate Calculus
This book is a compilation of all basic topics on functions of Several Variables and is primarily meant for undergraduate and post graduate students.
Differential Equations for Studies in Computational Electrophysiology
This open access text aims at giving you the simplest possible introduction to differential equations that are used in models of electrophysiology. It covers models at several spatial and temporal scales with associated numerical methods. The text demonstrates that a very limited number of fundamental techniques can be used to define numerical methods for equations ranging from ridiculously simple to extremely complex systems of partial differential equations. Every method is implemented in Matlab and the codes are freely available online. By using these codes, the reader becomes familiar with classical models of electrophysiology, like the cable equation, the monodomain model, and the bidomain model. But modern models that have just started to gain attention in the field of computational electrophysiology are also presented. If you just want to read one book, it should probably not be this one, but if you want a simple introduction to a complex field, it is worth considering the present text.
Computing and Analysing Energy Minimisation Problems in Liquid Crystals: Implementation Using Firedrake
How does one numerically analyse different phases of liquid crystals? With the help of some open-source libraries, what can we do in exploiting the mathematical models of liquid crystals and numerical aspects of their typical defects?There are many excellent books on liquid crystals, but none on their numerics to the knowledge of the author. This book presents some of the latest work on numerical investigations of liquid crystals, addressing some mathematical modelling and numerical problems. This book consists of three major parts, each of which focuses on different problems for different phases of liquid crystals: nematics and cholesterics, ferronematics and smectics. The associated topics include robust solvers for cholesterics, multiple solutions for ferronematics, and mathematical modelling theory for smectics, etc.This interdisciplinary book can be helpful in utilising the open-source libraries Firedrake (for solving problems using finite element methods) and Defcon (for computing multiple solutions) to solve general energy minimisation problems.
Temporal Logic: From Philosophy and Proof Theory to Artificial Intelligence and Quantum Computing
Calculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech applications, people are often not aware that temporal logic is deeply rooted in the philosophy of modalities. A deep understanding of these roots opens avenues to the modern calculi of temporal logic which have emerged by extension of modal logic with temporal operators. Computationally, temporal operators can be introduced in different formalisms with increasing complexity such as Basic Modal Logic (BML), Linear-Time Temporal Logic (LTL), Computation Tree Logic (CTL), and Full Computation Tree Logic (CTL*). Proof-theoretically, these formalisms of temporal logic can be interpreted by the sequent calculus of Gentzen, the tableau-based calculus, automata-based calculus, game-based calculus, and dialogue-based calculus with different advantages for different purposes, especially in computer science.The book culminates in an outlook on trendsetting applications of temporal logics in future technologies such as artificial intelligence and quantum technology. However, it will not be sufficient, as in traditional temporal logic, to start from the everyday understanding of time. Since the 20th century, physics has fundamentally changed the modern understanding of time, which now also determines technology. In temporal logic, we are only just beginning to grasp these differences in proof theory which needs interdisciplinary cooperation of proof theory, computer science, physics, technology, and philosophy.
Chatting with ChatGPT
This past April Ermes engaged ChatGPT in a wide variety of chats, ranging from philosophy to paradoxes to Canadian lit, to name just a few. Artificial intelligence is developing and improving very fast, so that no one should be surprised if a few years down the road one looks back at the ChatGPT responses given in this volume only to be amazed at the primitiveness and inaccuracy of some of the responses. For now, though, what stands out is ChatGPT's impressive ability to comment quickly and succinctly on any one of the given topics.
Of Men and Numbers
Of Men and Numbers, first published in 1963, is a fascinating look at the lives and works of history's greatest mathematicians. Beginning with the early Egyptians and Greeks such as Pythagoras, Euclid and Archimedes, author Jane Muir then describes, in non-technical terms, the discoveries and personal stories of math greats such as Descartes, Pascal, and Newton, and continues with the important work of more recent mathematicians such as Nicholas Lobatchevsky, ?variste Galois, and Georg Cantor. Illustrated throughout with line drawings and figures.
Mathfatuated
Mathfatuated includes unique poems representing math topics associated with the lovable subject, making it the perfect gift for the math lover. Creating a poetry book about math can be a unique way of exploring mathematical concepts that may seem boringly challenging to some. Poetry can give a fresh perspective and bring an imaginative approach to learning about math. It can also help people remember mathematical concepts better. Moreover, it can bridge the gap between math and art and appeal to a larger audience. Overall, a poetry book about math can be an appealing and creative way to engage with the subject.
A Textbook of Advanced Engineering Mathematics
Engineering is the practical application of science and technology. Mathematical models of these practical applications are obtained using various governing laws from science and technology. Most of the mathematical models lead to ordinary differential equations, partial differential equations or systems of partial or ordinary differential equations. The solution of these models plays a vital role in the analysis of the effect of parameters on the system. Solving the mathematical problem obtained by one of the many techniques covered in Engineering Mathematics. This book is a unique combination of differential equation theory and its fascinating application to "real-world" problems. The main aims of this book are: Elaborative discussion of the fundamental concepts of the relevant topicExtremely minute details have been addressed with sufficient justifications, and special care has been taken to make the explanation adequate, straightforward, and methodicalA large number of worked-out examples have been provided to aid in swiftly comprehending the subject matter and increasing self-confidence.Solution of engineering problem with detailed calculation.For more details, please visit https: //centralwestpublishing.com
