Comparative Perspectives on Inquiry-Based Science Education
The core practice of professional scientists is inquiry, often referred to as research. If educators are to prepare students for a role in the professional scientific and technological community, exposing them to inquiry-based learning is essential. Despite this, inquiry-based teaching and learning (IBTL) remains relatively rare, possibly due to barriers that teachers face in deploying it or to a lack of belief in the teaching community that inquiry-based learning is effective. Comparative Perspectives on Inquiry-Based Science Education examines stories and experiences from members of an international science education project that delivered learning resources based around guided inquiry for students to a wide range of schools in 12 different countries in order to identify key themes that can provide useful insights for student learning, teacher support, and policy formulation at the continental level. The book provides case studies across these 12 different settings that enable readers to compare and contrast both practice and policy issues with their own contexts while accessing a cutting-edge model of professional development. It is designed for educators, instructional designers, administrators, principals, researchers, policymakers, practitioners, and students seeking current and relevant research on international education and education strategies for science courses.
Strategic Applications of Measurement Technologies and Instrumentation
Measurement techniques form the basis of scientific, engineering, and industrial innovations. The methods and instruments of measurement for different fields are constantly improving, and it's necessary to address not only their significance but also the challenges and issues associated with them. Strategic Applications of Measurement Technologies and Instrumentation is a collection of innovative research on the methods and applications of measurement techniques in medical and scientific discoveries, as well as modern industrial applications. The book is divided into two sections with the first focusing on the significance of measurement strategies in physics and biomedical applications and the second examining measurement strategies in industrial applications. Highlighting a range of topics including material assessment, measurement strategies, and nanoscale materials, this book is ideally designed for engineers, academicians, researchers, scientists, software developers, graduate students, and industry professionals.
Differential Equations
The book concerns with solving about 650 ordinary and partial differential equations. Each equation has at least one solution and each solution has at least one coloured graph. The coloured graphs reveal different features of the solutions. Some graphs are dynamical as for Clairaut differential equations. Thus, one can study the general and the singular solutions. All the equations are solved by Mathematica. The first chapter contains mathematical notions and results that are used later through the book. Thus, the book is self-contained that is an advantage for the reader. The ordinary differential equations are treated in Chapters 2 to 4, while the partial differential equations are discussed in Chapters 5 to 10. The book is useful for undergraduate and graduate students, for researchers in engineering, physics, chemistry, and others. Chapter 9 treats parabolic partial differential equations while Chapter 10 treats third and higher order nonlinear partial differential equations, both with modern methods. Chapter 10 discusses the Korteweg-de Vries, Dodd-Bullough-Mikhailov, Tzitzeica-Dodd-Bullough, Benjamin, Kadomtsev-Petviashvili, Sawada-Kotera, and Kaup-Kupershmidt equations.
C∞-Algebraic Geometry with Corners
Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C∞-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.
Analytic Combinatorics in Several Variables
Discrete structures model a vast array of objects ranging from DNA sequences to internet networks. The theory of generating functions provides an algebraic framework for discrete structures to be enumerated using mathematical tools. This book is the result of 25 years of work developing analytic machinery to recover asymptotics of multivariate sequences from their generating functions, using multivariate methods that rely on a combination of analytic, algebraic, and topological tools. The resulting theory of analytic combinatorics in several variables is put to use in diverse applications from mathematics, combinatorics, computer science, and the natural sciences. This new edition is even more accessible to graduate students, with many more exercises, computational examples with Sage worksheets to illustrate the main results, updated background material, additional illustrations, and a new chapter providing a conceptual overview.
A Course in Combinatorics and Graphs
This compact textbook consists of lecture notes given as a fourth-year undergraduate course of the mathematics degree at the Universitat Polit癡cnica de Catalunya, including topics in enumerative combinatorics, finite geometry, and graph theory. This text covers a single-semester course and is aimed at advanced undergraduates and masters-level students. Each chapter is intended to be covered in 6-8 hours of classes, which includes time to solve the exercises. The text is also ideally suited for independent study. Some hints are given to help solve the exercises and if the exercise has a numerical solution, then this is given. The material covered allows the reader with a rudimentary knowledge of discrete mathematics to acquire an advanced level on all aspects of combinatorics, from enumeration, through finite geometries to graph theory. The intended audience of this book assumes a mathematical background of third-year students in mathematics, allowing for a swifter useof mathematical tools in analysis, algebra, and other topics, as these tools are routinely incorporated in contemporary combinatorics. Some chapters take on more modern approaches such as Chapters 1, 2, and 9. The authors have also taken particular care in looking for clear concise proofs of well-known results matching the mathematical maturity of the intended audience.
From Computational Logic to Computational Biology
Alfredo Ferro's impact on information technology has traversed diverse domains, encompassing Computational Logic, Data Mining, Bioinformatics, and Complex Systems. After first studying Mathematics at the University of Catania, he received a Ph.D. in Computer Science from NYU in 1981, working under the supervision of Jacob Theodor (Jack) Schwartz. He returned to the University of Catania where he established the Computer Science undergraduate program, served as the coordinator of the Ph.D. program in Computer Science, cofounded the Ph.D. program in Biology, Human Genetics, and Bioinformatics, and retired as a full professor in 2021.Alfredo's academic career as a computer scientist is characterized by two distinct research phases: Computational Logic until approximately 1995, followed by a notable focus on Data Mining and Bioinformatics. The contributions in this volume reflect the quality and the scope of his personal and collaborative successes.He also taught andinspired many excellent scientists. A pioneering initiative was to establish summer schools for Ph.D. students in 1989, leading to the so-called Lipari School, now the J.T. Schwartz International School for Scientific Research, where Alfredo continues to serve as director. This prestigious series includes schools focused on Computer Science, Complex Systems, and Computational Biology, featuring world-class scientists as lecturers and mentors.
Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations
Real-world issues can be translated into the language and concepts of mathematics with the use of mathematical models. This book provides these real-world examples, explores research challenges in numerical treatment, and demonstrates how to create new numerical methods for resolving problems.
Engaging Young Students in Mathematics through Competitions - World Perspectives and Practices
Engaging Young Students in Mathematics through Competitions presents a wide range of topics relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment. Following the earlier two volumes, contributors explore a wide variety of fascinating problems of the type often presented at mathematics competitions. In this new third volume, many chapters are directly related to the challenges involved in organizing competitions under Covid-19, including many positive aspects resulting from the transition to online formats. There are also sections devoted to background information on connections between the mathematics of competitions and their organization, as well as the competitions' interplay with research, teaching and more.The various chapters are written by an international group of authors involved in problem development, many of whom were participants of the 9th Congress of the World Federation of National Mathematics Competitions in Bulgaria in 2022. Together, they provide a deep sense of the issues involved in creating such problems for competition mathematics and recreational mathematics.
Sharpening Everyday Mental/Thinking Skills Through Mathematics Problem Solving and Beyond
Mathematics is a subject taught from kindergarten through to high school, and yet it is the one subject that most adults are almost proud to admit to not having been very good at, and, therefore, tend to avoid it where they can. However, one of the key factors in mathematics is its ability to enable us to solve everyday problems. When we consider 'the worst-case scenario' of the situation, it is analogous to solving a mathematical problem by considering extremes. Or, we might consider the best path to take from point A to point B, where geometric relationships can be helpful. This book is intended to demonstrate a variety of neglected aspects of mathematics, in order to demonstrate the power and beauty of the field of mathematics beyond where most people, students, and teachers believe is possible.The chapters of the book explore a multitude of topics: unusual arithmetic calculations and shortcuts, entertaining and instructional problem-solving strategies, unusual applications of algebra, and how geometry allows us to better appreciate physical relationships. Only a basic mathematical knowledge is needed to understand these topics and problems; however, the book also demonstrates that, armed with even this level of understanding, our mathematical skills far exceed what we learned at school! The final chapter is the most challenging, and explores a curious problem-solving technique.
Methods of Geometry in the Theory of Partial Differential Equations
Mathematical models are used to describe the essence of the real world, and their analysis induces new predictions filled with unexpected phenomena.In spite of a huge number of insights derived from a variety of scientific fields in these five hundred years of the theory of differential equations, and its extensive developments in these one hundred years, several principles that ensure these successes are discovered very recently.This monograph focuses on one of them: cancellation of singularities derived from interactions of multiple species, which is described by the language of geometry, in particular, that of global analysis.Five objects of inquiry, scattered across different disciplines, are selected in this monograph: evolution of geometric quantities, models of multi-species in biology, interface vanishing of d - δ systems, the fundamental equation of electro-magnetic theory, and free boundaries arising in engineering.The relaxation of internal tensions in these systems, however, is described commonly by differential forms, and the reader will be convinced of further applications of this principle to other areas.
Sharpening Everyday Mental/Thinking Skills Through Mathematics Problem Solving and Beyond
Mathematics is a subject taught from kindergarten through to high school, and yet it is the one subject that most adults are almost proud to admit to not having been very good at, and, therefore, tend to avoid it where they can. However, one of the key factors in mathematics is its ability to enable us to solve everyday problems. When we consider 'the worst-case scenario' of the situation, it is analogous to solving a mathematical problem by considering extremes. Or, we might consider the best path to take from point A to point B, where geometric relationships can be helpful. This book is intended to demonstrate a variety of neglected aspects of mathematics, in order to demonstrate the power and beauty of the field of mathematics beyond where most people, students, and teachers believe is possible.The chapters of the book explore a multitude of topics: unusual arithmetic calculations and shortcuts, entertaining and instructional problem-solving strategies, unusual applications of algebra, and how geometry allows us to better appreciate physical relationships. Only a basic mathematical knowledge is needed to understand these topics and problems; however, the book also demonstrates that, armed with even this level of understanding, our mathematical skills far exceed what we learned at school! The final chapter is the most challenging, and explores a curious problem-solving technique.
Mathematics for Fisheries Economics
The institute (ICAR-CIFE) has continuously adopted itself to meet the current needs, methodological challenges, and quality enhancement in fisheries education with the advances in information technology. The increasing application of mathematics to various branches/courses of economics in the past decade has made it necessary for economists to have an elementary knowledge of mathematics. To this end, an attempt has been made to bring out a practical manual on mathematics for catering to needs of fisheries students, most of whom having a non-mathematical background during their tertiary education. This book has been structured to solve problems on a wide range of topics such as matrix, determinants, limit & continuity, differentiation, integration, partial differentiation, etc. It is hoped that the book brought out will serve as a useful source of knowledge to the students and also will help them in solving various types of mathematical problems.
Local Mathematics for Local Physics
The language of the universe is mathematics, but how exactly do you know that all parts of the universe 'speak' the same language? Benioff builds on the idea that the entity that gives substance to both mathematics and physics is the fundamental field, called the 'value field'. While exploring this idea, he notices the similarities that the value field shares with several mysterious phenomena in modern physics: the Higgs field, and dark energy.The author first introduces the concept of the value field and uses it to reformulate the basic framework of number theory, calculus, and vector spaces and bundles. The book moves on to find applications to classical field theory, quantum mechanics and gauge theory. The last two chapters address the relationship between theory and experiment, and the possible physical consequences of both the existence and non-existence of the value field. The book is open-ended, and the list of open questions is certainly longer than the set of proposed answers.Paul Benioff, a pioneer in the field of quantum computing and the author of the first quantum-mechanical description of the Turing machine, devoted the last few years of his life to developing a universal description in which mathematics and physics would be on equal footing. He died on March 29, 2022, his work nearly finished. The final editing was undertaken by Marek Czachor who, in the editorial afterword, attempts to place the author's work in the context of a shift in the scientific paradigm looming on the horizon.
Ancilla to the Pre-Socratic Philosophers
Dive into the intellectual origins of Western philosophy with "Ancilla to the Pre-Socratic Philosophers." This comprehensive translation brings to life the fragments of wisdom left by the ancient Greek thinkers, spanning from the enigmatic Orpheus to the brilliant minds of Thales, Pythagoras, Heracleitus, Zeno, and Democritus. Delve into the essence of their philosophies through meticulously translated quotations, discovering the lost books they authored and gaining insight into the perspectives of contemporaneous authors on their beliefs.This invaluable reference provides a window into the foundations of philosophical thought, offering not only the known but also the obscure and debated fragments. From brief biographies to spurious quotes, this book paints a vivid picture of the Pre-Socratic era, making it an essential companion for scholars and a captivating read for anyone intrigued by the roots of Western philosophical inquiry.
The World Through the Lens of Mathematics
This amazing book aims to shatter the barrier between students and mathematics. By encouraging students to look at mathematics from a different perspective, build a bridge between their surroundings and mathematics and, at the same time, enrich them with the culture, history, customs, and geography of different parts of the world.
Fractional Integrals and Derivatives
This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like "What are the fractional integrals and derivatives?", "What are their decisive mathematical properties?", "What fractional operators make sense in applications and why?'', etc. In particular, the "new fractional derivatives and integrals" and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue.
Logos and Alogon
This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book's title, an alogon in the logos of mathematics. The outcomeof this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields.
Elementary School Test Materials 2022-2023
This book contains one year of mathleague.org elementary school tests and answer keys: 7 qualifying-level test sets, one district-level test set, one state-level test set, one national-level test set, and one international-level test set. Each test set contains a Sprint, Target, Team, and Number Sense test.
2022-2023 High School Contest Materials
This book contains one year of mathleague.org high school tests and answer keys: 7 qualifying-level test sets, one state-level test set, one national-level test set, and one international-level test set. Each test set contains a Sprint, Target, Team, and Relay test; three of the sets contain a Power Question.
The Logica Yearbook 2022
This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2022, Tepl獺, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.
Introductory Differential Equations
**2025 Textbook and Academic Authors Association (TAA) McGuffey Longevity Award Winner** Introductory Differential Equations, Sixth Edition provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies. The book's accessible explanations and many robust sample problems are appropriate for a first semester course in introductory ordinary differential equations (including Laplace transforms), for a second course in Fourier series and boundary value problems, and for students with no background on the subject.
Partial Clones of Terms
Words are strings of letters from a fixed alphabet. Sets of words are said to be formal languages. Natural languages, but also programming languages, are examples of such formal languages. On the set of all words the concatenation is a binary associative operation which produces a new word from any two given words. Therefore, there is a semigroup defined on the set of all words on an alphabet. This semigroup is an algebra of type (2), i.e., it has one binary operation satisfying the associative identity. Many properties of words and formal languages can be described by the algebraic properties of the word semigroup. To get languages of more expressive power, words can be generalized to terms using one more alphabet consisting of operation symbols. The combination of n+1 terms to a new term can be described by an (n+1)-ary superposition operation. This superposition operation satisfies the superassociative identity, a generalization of the associative identity. A clone is a multi-based algebraic structure with (n+1)-ary superposition operations as fundamental operations and satisfying the superassociative itentity. Clones of terms take over the role of word semigroups and describe the properties of terms and sets of terms which are also called tree languages. In this book we generalize the superposition operations to partial many-sorted operations. If the superassociative law is satisfied as a weak identity we obtain partial clones. The properties of several important kinds of terms such as linear terms and linear tree languages can be described by partial clones.
A Promenade in Mathematical Proofs with Comprehensive Review of Proof Techniques
A Promenade in Mathematical Proofs with Comprehensive Review of Proof Techniques is designed to support students as they advance their mathematical knowledge, bridging the gap from basic arithmetic and calculus to a deeper understanding of mathematical concepts through proof writing. It emphasizes the importance of being able to articulate mathematical ideas and solutions effectively, asserting that proof writing is as crucial as the subject matter itself. The book is structured to build upon the reader's knowledge systematically, starting with mathematical writing and progressing through logic, set theory, proof techniques, and more advanced topics such as sequences, relations, and functions. Each chapter concludes with practice problems and solutions to reinforce learning. A Promenade in Mathematical Proofs with Comprehensive Review of Proof Techniques is suitable for upper-division undergraduate courses in mathematics, particularly those focusing on advanced mathematical concepts and proof-based learning. Courses in fields such as computer science that require a strong foundation in mathematical reasoning and proof techniques would also benefit from this material.
Documentary review of the Pythagorean Theorem throughout history
Geometry has two great treasures: one is the theorem of Pythagoras; the other is the division of a line into an extreme and an average proportion. We may compare the first to a measure of gold; the second we may call a precious jewel. Jonannes Kepler (1596)The Pythagorean theorem, as Kepler (1596) says, is one of the greatest treasures of Geometry, it states that "in every right triangle the measure of the hypotenuse squared is equal to the sum of the measures of the squares of the legs". Anyone who has attended high school has been in contact with this theorem, whether they remember it or not. The general objective of this work is to analyze the proofs and demonstrations of the Pythagorean Theorem throughout the History of Mathematics, with the purpose of creating didactic sequences for its teaching at the Middle Level.
Human and Artificial Intelligence
Although tremendous advances have been made in recent years, many real-world problems still cannot be solved by machines alone. Hence, the integration of Human Intelligence and Artificial Intelligence is needed. However, several challenges make this integration complex. The aim of this Special Issue was to provide a large and varied collection of high-level contributions presenting novel approaches and solutions to address the above issues. This Special Issue contains 14 papers (13 research papers and 1 review paper) that deal with various topics related to human-machine interactions and cooperation. Most of these works concern different aspects of recommender systems, which are among the most widespread decision support systems. The domains covered range from healthcare to movies and from biometrics to cultural heritage. However, there are also contributions on vocal assistants and smart interactive technologies. In summary, each paper included in this Special Issue represents a step towards a future with human-machine interactions and cooperation. We hope the readers enjoy reading these articles and may find inspiration for their research activities.
Proven Impossible
In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic - and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training - all you need is the discipline to follow logical arguments and a pen in your hand.
The Bertrand Russell Collection
Embark on an intellectual journey with "The Bertrand Russell Collection," a comprehensive anthology spanning the influential philosopher's groundbreaking works. From "The Analysis of Mind" to insightful essays on humanism, ethics, and society, this collection encapsulates Russell's brilliance and offers timeless reflections on reason, knowledge, and the complexities of the human experience. Explore the mind of one of the 20th century's greatest thinkers through his diverse and impactful writings.
Proven Impossible
In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic - and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training - all you need is the discipline to follow logical arguments and a pen in your hand.
Journal of Applied Logics, Volume 10, Number 6, December 2023. Special Issue
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.
Instability and Non-Uniqueness for the 2D Euler Equations, After M. Vishik
An essential companion to M. Vishik's groundbreaking work in fluid mechanics The incompressible Euler equations are a system of partial differential equations introduced by Leonhard Euler more than 250 years ago to describe the motion of an inviscid incompressible fluid. These equations can be derived from the classical conservations laws of mass and momentum under some very idealized assumptions. While they look simple compared to many other equations of mathematical physics, several fundamental mathematical questions about them are still unanswered. One is under which assumptions it can be rigorously proved that they determine the evolution of the fluid once we know its initial state and the forces acting on it. This book addresses a well-known case of this question in two space dimensions. Following the pioneering ideas of M. Vishik, the authors explain in detail the optimality of a celebrated theorem of V. Yudovich from the 1960s, which states that, in the vorticity formulation, the solution is unique if the initial vorticity and the acting force are bounded. In particular, the authors show that Yudovich's theorem cannot be generalized to the L^p setting.
Groups and Graphs, Designs and Dynamics
This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
Problem Posing and Problem Solving in Mathematics Education
This book presents both theoretical and empirical contributions from a global perspective on problem solving and posing (PS/PP) and their application, in relation to the teaching and learning of mathematics in schools. The chapters are derived from selected presentations in the PS/PP Topical Study Group in ICME14. Although mathematical problem posing is a much younger field of inquiry in mathematics education, this topic has grown rapidly. The mathematics curriculum frameworks in many parts of the world have incorporated problem posing as an instructional focus, building on problem solving as its foundation. The juxtaposition of problem solving and problem posing in mathematics presented in this book addresses the needs of the mathematics education research and practice communities at the present day. In particular, this book aims to address the three key points: to present an overview of research and development regarding students' mathematical problem solving and posing; to discuss new trends and developments in research and practice on these topics; and to provide insight into the future trends of mathematical problem solving and posing.
Modern FORTRAN Explained
Fortran remains one of the principal programming languages used in high-performance scientific, numerical, and engineering computing. A series of significant revisions to the standard versions of the language have progressively enhanced its capabilities, and the current standard - Fortran 2023 - brings with it further additions and improvements. The language as defined by its most recent standards, with their introduction of object-oriented programming and of coarrays, is often referred to generically as 'Modern Fortran', and this term is increasingly used in the literature. Thus, we see that Fortran's particular advantages as a high-end numerical language, especially where arrays are the main form of data object and/or where complex arithmetic is involved, are still to the fore. It is able to attain the highest achievable optimization, mainly because multi-dimensional arrays are 'natural' objects and because its pointers are highly constrained. There is every sign that Modern Fortran will continue to be used to tackle major scientific computing problems in the next decade and beyond and will long remain a living tribute to its early pioneers. This third edition of Modern Fortran Explained expands on the second. The material contained in the four final chapters of the second edition have been merged into the main text, thereby offering, in 20 chapters, a comprehensive and uniform description of Fortran 2018. The additional features now brought by the 2023 standard, which are mostly relatively minor in nature, are described in two final chapters, the first on generic programming and the second on the other features. This structure enables the reader to distinguish clearly between what is old and what is new. This new edition, written by experts in the field, three of whom have actively contributed to Fortran 2023, is thus a complete and authoritative description of Fortran in its latest form, with the intention that it remain the main reference work in the field.
The Bertrand Russell Collection
Embark on an intellectual journey with "The Bertrand Russell Collection," a comprehensive anthology spanning the influential philosopher's groundbreaking works. From "The Analysis of Mind" to insightful essays on humanism, ethics, and society, this collection encapsulates Russell's brilliance and offers timeless reflections on reason, knowledge, and the complexities of the human experience. Explore the mind of one of the 20th century's greatest thinkers through his diverse and impactful writings.
Equivariant Cohomology in Algebraic Geometry
Equivariant cohomology has become an indispensable tool in algebraic geometry and in related areas including representation theory, combinatorial and enumerative geometry, and algebraic combinatorics. This text introduces the main ideas of the subject for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics. The first six chapters cover the basics: definitions via finite-dimensional approximation spaces, computations in projective space, and the localization theorem. The rest of the text focuses on examples - toric varieties, Grassmannians, and homogeneous spaces - along with applications to Schubert calculus and degeneracy loci. Prerequisites are kept to a minimum, so that one-semester graduate-level courses in algebraic geometry and topology should be sufficient preparation. Featuring numerous exercises, examples, and material that has not previously appeared in textbook form, this book will be a must-have reference and resource for both students and researchers for years to come.
Introduction to Graph Theory
Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory.The book builds on the verity that graph theory even at high school level is a subject that lends itself well to the development of mathematical reasoning and proof.This is an updated edition of two books already published with World Scientific, i.e., Introduction to Graph Theory: H3 Mathematics & Introduction to Graph Theory: Solutions Manual. The new edition includes solutions and hints to selected problems. This combination allows the book to be used as a textbook for undergraduate students. Professors can select unanswered problems for tutorials while students have solutions for reference.
A Brief History of Mathematics for Curious Minds
This book offers a short and accessible account of the history of mathematics, written for the intelligent layman to gain a better appreciation of its beauty, relevance, and place in history. It traces the development of the subject throughout the centuries, starting with the so-called Lebombo bone, the oldest known mathematical object that was estimated to be at least 43,000 years old, and ending with the 21st century.The presentation is informal, and no prior knowledge of mathematics is needed to enjoy the systematic chronological insights. A collection of appendices is included for more technical material -- though still at the level of secondary school mathematics -- and is concerned with the historically important proofs and concepts that can be explained in a simple way.
Introduction to Graph Theory
Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory.The book builds on the verity that graph theory even at high school level is a subject that lends itself well to the development of mathematical reasoning and proof.This is an updated edition of two books already published with World Scientific, i.e., Introduction to Graph Theory: H3 Mathematics & Introduction to Graph Theory: Solutions Manual. The new edition includes solutions and hints to selected problems. This combination allows the book to be used as a textbook for undergraduate students. Professors can select unanswered problems for tutorials while students have solutions for reference.
Differential Calculus
This volume contains more than 900 problems in differential calculus, covering limits, continuity, derivatives, and their applications. The applications are comprised of a variety of approximations, growth and decay, optimization, curve sketching techniques, and analytical tools to investigate properties of parametrically given planar curves. The problems are sorted by topic, each opening with with a summary of the relevant mathematical notions and their properties. Through a careful selection of appropriate problems in each chapter, the book clearly communicates some of the big ideas and applications in calculus: the notion of a function, the notion of an infinitesimal, the notion of a differentiable function, and the notion of an approximation, among others. The book provides the answers to each problem, often with a detailed sketch of the solution process.With about 260 true-false and multiple-choice questions, the book provides its users with an accessible way to assess and practice their understanding of calculus related facts and nuances. More than 180 figures are included to help readers to visualize properties of functions, illustrate word problems, depict solutions, and provide an extensive bank of polar curves.The purpose of this problem collection is to serve as a supplementary learning resource for students who are studying university-level differential calculus. The book also acts as a teaching resource for calculus instructors.
A Brief History of Mathematics for Curious Minds
This book offers a short and accessible account of the history of mathematics, written for the intelligent layman to gain a better appreciation of its beauty, relevance, and place in history. It traces the development of the subject throughout the centuries, starting with the so-called Lebombo bone, the oldest known mathematical object that was estimated to be at least 43,000 years old, and ending with the 21st century.The presentation is informal, and no prior knowledge of mathematics is needed to enjoy the systematic chronological insights. A collection of appendices is included for more technical material - though still at the level of secondary school mathematics - and is concerned with the historically important proofs and concepts that can be explained in a simple way.
Differential Calculus
This volume contains more than 900 problems in differential calculus, covering limits, continuity, derivatives, and their applications. The applications are comprised of a variety of approximations, growth and decay, optimization, curve sketching techniques, and analytical tools to investigate properties of parametrically given planar curves. The problems are sorted by topic, each opening with with a summary of the relevant mathematical notions and their properties. Through a careful selection of appropriate problems in each chapter, the book clearly communicates some of the big ideas and applications in calculus: the notion of a function, the notion of an infinitesimal, the notion of a differentiable function, and the notion of an approximation, among others. The book provides the answers to each problem, often with a detailed sketch of the solution process.With about 260 true-false and multiple-choice questions, the book provides its users with an accessible way to assess and practice their understanding of calculus related facts and nuances. More than 180 figures are included to help readers to visualize properties of functions, illustrate word problems, depict solutions, and provide an extensive bank of polar curves.The purpose of this problem collection is to serve as a supplementary learning resource for students who are studying university-level differential calculus. The book also acts as a teaching resource for calculus instructors.
The Joy of Abstraction
Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life - from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material, learning everything needed to understand category theory, and then key concepts in category theory like natural transformations, duality, and even a glimpse of ongoing research in higher-dimensional category theory. For fans of How to Bake Pi, this will help you dig deeper into mathematical concepts and build your mathematical background.
And I Saw Sequences of Petals and Leaves
In this captivating historical novel, Daniele Struppa skillfully weaves a fictional autobiography, bringing Fibonacci to life with vivid details of his upbringing and adult years in Medieval Europe. As we explore the historical context of Fibonacci's time, we delve into the intriguing aspects of a bygone era, painting a compelling picture of a man whose contributions to mathematics continue to resonate today. From his groundbreaking work on congruent numbers to the famous numerical sequence that bears his name, the author invites readers to imagine the creative sparks that ignited Fibonacci's mathematical innovations. When historical evidence is elusive, accuracy and passion are seamlessly combined, offering plausible scenarios grounded in documented facts. A meticulously crafted apparatus of notes distinguishes fact from fiction, providing readers with a clear guide to navigate this enthralling reconstruction of Fibonacci's life. Step into the medieval world of Leonardo Fibonacci, one of the most celebrated mathematicians in history, and discover the man behind the mathematical genius. Mathematicians and curious readers alike will appreciate the allure of Fibonacci's mathematical brilliance.
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!
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.
