Mathematical foundations Books
World Scientific Publishing Co Pte Ltd Mathematics That Power Our World, The: How Is It
Book SynopsisThe Mathematics That Power Our World: How Is It Made? is an attempt to unveil the hidden mathematics behind the functioning of many of the devices we use on a daily basis. For the past years, discussions on the best approach in teaching and learning mathematics have shown how much the world is divided on this issue. The one reality we seem to agree on globally is the fact that our new generation is lacking interest and passion for the subject. One has the impression that the vast majority of young students finishing high school or in their early post-secondary studies are more and more divided into two main groups when it comes to the perception of mathematics. The first group looks at mathematics as a pure academic subject with little connection to the real world. The second group considers mathematics as a set of tools that a computer can be programmed to use and thus, a basic knowledge of the subject is sufficient. This book serves as a middle ground between these two views. Many of the elegant and seemingly theoretical concepts of mathematics are linked to state-of-the-art technologies. The topics of the book are selected carefully to make that link more relevant. They include: digital calculators, basics of data compression and the Huffman coding, the JPEG standard for data compression, the GPS system studied both from the receiver and the satellite ends, image processing and face recognition.This book is a great resource for mathematics educators in high schools, colleges and universities who want to engage their students in advanced readings that go beyond the classroom discussions. It is also a solid foundation for anyone thinking of pursuing a career in science or engineering. All efforts were made so that the exposition of each topic is as clear and self-contained as possible and thus, appealing to anyone trying to broaden his mathematical horizons.
£21.85
World Scientific Publishing Co Pte Ltd Theoretical Foundations For Quantitative Finance
Book SynopsisThis book provides simple introduction to quantitative finance for students and junior quants who want to approach the typical industry problems with practical but rigorous ambition. It shows a simple link between theoretical technicalities and practical solutions. Mathematical aspects are discussed from a practitioner perspective, with a deep focus on practical implications, favoring the intuition and the imagination. In addition, the new post-crisis paradigms, like multi-curves, x-value adjustments (xVA) and Counterparty Credit Risk are also discussed in a very simple framework. Finally, real world data and numerical simulations are compared in order to provide a reader with a simple and handy insight on the actual model performances.
£61.75
World Scientific Publishing Co Pte Ltd Digital And The Real World, The: Computational
Book SynopsisIn the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy.Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT).
£135.00
World Scientific Publishing Co Pte Ltd Perspectives In Mathematical Science Ii: Pure
Book SynopsisThis book presents a collection of invited articles by distinguished Mathematicians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute, during the year 2007. These articles provide a current perspective of different areas of research, emphasizing the major challenging issues. Given the very significant record of the Institute in research in the areas of Statistics, Probability and Mathematics, distinguished authors have very admirably responded to the invitation. Some of the articles are written keeping students and potential new entrants to an area of mathematics in mind. This volume is thus very unique and gives a perspective of several important aspects of mathematics.Table of ContentsUse of Resultants and Approximate Roots for Doing the Jacobian Problem (S S Abhyankar); Monodromy of Principal Bundles (I Biswas); Oligomorphic Permutation Groups (P J Cameron); Factors, Roots and Embeddings of Measures on Lie Groups (S G Dani); Descriptive Set Theory and the Geometry of Banach Spaces (G Godefroy); Multiplicity-Free Homogeneous Operators in the Cowen-Douglas Class (A Koranyi & G Misra); Standard Conjectures on Algebraic Cycles (M S Narasimhan); Symmetric and Quasi-Symmetric and Strongly Regular Graphs (S S Sane); Perturbation Determinant, Krein's Shift Function and Index Theorem (K B Sinha); Zero Cycles and Complete Intersection Points on Affine Varieties (V Srinivas); Root Numbers and Rational Points on Elliptic Curves (R Sujatha); von Neumann Algebras and Ergodic Theory (V S Sunder); Gutzmer's Formula and the Segal-Bargmann Transform (S Thangavelu); Finite Translation Generalized Quadrangles (J A Thas); Super Geometry as the Basis for Super Symmetry (V S Varadarajan).
£80.75
Pan Stanford Publishing Pte Ltd Self-Field Theory: A New Mathematical Description
Book SynopsisThis is the first text to be written on the topic of Self-Field Theory (SFT), a new mathematical description of physics distinct from quantum field theory, the physical theory of choice by physicists at the present time. SFT is a recent development that has evolved from the classical electromagnetics of the electron’s self-fields that were studied by Abraham and Lorentz in 1903-04. Due to its bi-spinorial motions for particles and fields that obviate uncertainty, SFT is capable of obtaining closed-form solution for all atomic structures rather than the probabilistic solutions of QFT. Table of ContentsIntroduction. Self-Field Theory. The Photon. The Phonon. Self-Field Theory: A Mathematical Model of Physics. Appendices: Mathematical Preliminaries. Comments on Physical Constants, Equations, and Standards. Self-Field Theory: New Photonic Insights. Frequently Asked Questions. The Search for a General Physical Mathematics.
£103.50
World Scientific Publishing Co Pte Ltd Mathematical Applications And Modelling: Yearbook
Book SynopsisMathematical Applications and Modelling is the second in the series of the yearbooks of the Association of Mathematics Educators in Singapore. The book is unique as it addresses a focused theme on mathematics education. The objective is to illustrate the diversity within the theme and present research that translates into classroom pedagogies.The book, comprising of 17 chapters, illuminates how application and modelling tasks may help develop the capacity of students to use mathematics in their present and future lives. Several renowned international researchers in the field of mathematical modelling have published their work in the book. The chapters are comprehensive and laden with evidence-based examples for both mathematics educators and classroom teachers. The book is an invaluable contribution towards the emerging field of research in mathematical applications and modelling. It is a must-read for graduate research students and mathematics educators.Table of ContentsMathematical Applications and Modelling in Singapore Schools; Communities of Mathematical Inquiry to Support Engagement in Rich Tasks; Using ICT in Applications of Primary School Mathematics; Applications of Mathematical Application Problems in Primary School Mathematics; Collaborative Problem Solving as Modelling in the Primary Years of Schooling; Word Problems and Modelling in Primary School Mathematics; Mathematical Modelling in a PBL Setting for Pupils: Features and Task Design; Initial Experiences of Primary School Teachers with Mathematical Modelling; Why Study Mathematics?; Applications of Mathematics in Our Daily Life; Using ICT in Applications of Secondary School Mathematics; Developing Pupils' Analysis and Interpretation of Graphs and Tables Using a Five Step Framework; Theoretical Approaches and Examples for Modelling in Mathematics Education; Mathematical Modelling in the Singapore Secondary School Mathematics Curriculum; Making Decisions with Mathematics: From Mathematical Problem Solving to Modelling; The Cable Drum - Description of a Challenging Mathematical Modelling Example and a Few Experiences; Implementing Applications and Modelling in Secondary School: Issues for Teaching and Learning; What's Next.
£99.00
World Scientific Publishing Co Pte Ltd Reasoning, Communication And Connections In
Book SynopsisThis fourth volume in the series of yearbooks by the Association of Mathematics Educators in Singapore entitled Reasoning, Communication and Connections in Mathematics is unique in that it focuses on a single theme in mathematics education. The objective is to encourage teachers and researchers to advance reasoning, communication and connections in mathematics classrooms.Several renowned international researchers in the field have published their work in this volume. The fifteen chapters of the book illustrate evidence-based practices that school teachers and researchers can experiment with in their own classrooms to bring about meaningful learning outcomes. Three major themes: mathematical tasks, classroom discourse, and connectivity within and beyond mathematics, shape the ideas underpinning reasoning, communication and connections in these chapters. The book makes a significant contribution towards mathematical processes essential for learners of mathematics. It is a good resource for mathematics educators and research students.Table of ContentsReasoning, Communication and Connections in the School Mathematics Curriculum; The Epistemic Framing of Mathematical Tasks in Secondary 3 Mathematics Lessons in Singapore; Modifying Textbook Exercises to Incorporate Reasoning and Communication into the Primary Mathematics Classroom; Some "What Strategies" Strategies that Advance Reasoning and Communication in Primary School Mathematics Classrooms; Reasoning and Justification in the Secondary Mathematics Classroom; LOGO Project-Based Mathematics Learning for Communication, Reasoning and Connection; Reasoning, Communication and Connections in A-Level Mathematics; Visual and Spatial Reasoning: The Changing Form of Mathematics Representation and Communication; Understanding Classroom Talk in Secondary 3 Mathematics Classes in Singapore; Mathematics Classroom Discourse Through Analogical Reasoning; Students' Reasoning Errors in Writing Proof by Mathematical Induction; Numeracy: Connecting Mathematics; Presenting Mathematics as Connected in the Secondary Classroom; Making Connections Between School Mathematics and the Everyday World: The Example of Health; Mathematics, Astronomy and Culture: Helping Students See Connections.
£94.50
World Scientific Publishing Co Pte Ltd Spanning Tree Results For Graphs And Multigraphs:
Book SynopsisThis book is concerned with the optimization problem of maximizing the number of spanning trees of a multigraph. Since a spanning tree is a minimally connected subgraph, graphs and multigraphs having more of these are, in some sense, immune to disconnection by edge failure. We employ a matrix-theoretic approach to the calculation of the number of spanning trees.The authors envision this as a research aid that is of particular interest to graduate students or advanced undergraduate students and researchers in the area of network reliability theory. This would encompass graph theorists of all stripes, including mathematicians, computer scientists, electrical and computer engineers, and operations researchers.Table of ContentsGraph Theory Background; Matrix Theory Background, including Kroenecker Products, and Proofs of the Binet - Cauchy and Courant - Fischer Theorems; Spanning Tree Results for a Host of Graphs as well as Multigraphs; Node-Arc Incidence Matrix; Temperley's B Matrix. Multigraphs; Eigenvalues and Eigenvalue Bounds; A Lagrange Multiplier Approach to the Spanning Tree Problem.
£67.45
World Scientific Publishing Co Pte Ltd Truth And Assertibility
Book SynopsisThe book is a research monograph on the notions of truth and assertibility as they relate to the foundations of mathematics. It is aimed at a general mathematical and philosophical audience. The central novelty is an axiomatic treatment of the concept of assertibility. This provides us with a device that can be used to handle difficulties that have plagued philosophical logic for over a century. Two examples relate to Frege's formulation of second-order logic and Tarski's characterization of truth predicates for formal languages. Both are widely recognized as fundamental advances, but both are also seen as being seriously flawed: Frege's system, as Russell showed, is inconsistent, and Tarski's definition fails to capture the compositionality of truth. A formal assertibility predicate can be used to repair both problems. The repairs are technically interesting and conceptually compelling. The approach in this book will be of interest not only for the uses the author has put it to, but also as a flexible tool that may have many more applications in logic and the foundations of mathematics.Table of ContentsTruth; Concepts; Deduction; Assertibility; Formalization; Arithmetic; Surveyability;
£76.95
World Scientific Publishing Co Pte Ltd Problem-solving Strategies In Mathematics: From
Book SynopsisThis book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.Table of ContentsIntroduction; Working Backwards; Adopting a Different Point of View; Finding a Pattern; Solving a Simpler Analogous Problem; Accounting for All Possibilities; Considering Extreme Cases; Making a Drawing; Intelligent Guessing and Testing; Accounting for all Possibilities; Organizing Data; Logical Reasoning;
£42.75
World Scientific Publishing Co Pte Ltd Problem-solving Strategies In Mathematics: From
Book SynopsisThis book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.Table of ContentsIntroduction; Working Backwards; Adopting a Different Point of View; Finding a Pattern; Solving a Simpler Analogous Problem; Accounting for All Possibilities; Considering Extreme Cases; Making a Drawing; Intelligent Guessing and Testing; Accounting for all Possibilities; Organizing Data; Logical Reasoning;
£19.00
World Scientific Publishing Co Pte Ltd Mathematics That Power Our World, The: How Is It
Book SynopsisThe Mathematics That Power Our World: How Is It Made? is an attempt to unveil the hidden mathematics behind the functioning of many of the devices we use on a daily basis. For the past years, discussions on the best approach in teaching and learning mathematics have shown how much the world is divided on this issue. The one reality we seem to agree on globally is the fact that our new generation is lacking interest and passion for the subject. One has the impression that the vast majority of young students finishing high school or in their early post-secondary studies are more and more divided into two main groups when it comes to the perception of mathematics. The first group looks at mathematics as a pure academic subject with little connection to the real world. The second group considers mathematics as a set of tools that a computer can be programmed to use and thus, a basic knowledge of the subject is sufficient. This book serves as a middle ground between these two views. Many of the elegant and seemingly theoretical concepts of mathematics are linked to state-of-the-art technologies. The topics of the book are selected carefully to make that link more relevant. They include: digital calculators, basics of data compression and the Huffman coding, the JPEG standard for data compression, the GPS system studied both from the receiver and the satellite ends, image processing and face recognition.This book is a great resource for mathematics educators in high schools, colleges and universities who want to engage their students in advanced readings that go beyond the classroom discussions. It is also a solid foundation for anyone thinking of pursuing a career in science or engineering. All efforts were made so that the exposition of each topic is as clear and self-contained as possible and thus, appealing to anyone trying to broaden his mathematical horizons.
£43.70
Pan Stanford Publishing Pte Ltd Why Are We Conscious?: A Scientist’s Take on
Book SynopsisThere are two huge gaps in scientific theory. One, the contradiction between classical and quantum mechanics, is discussed in many publications. The other, the total failure to explain why anything made of atoms (such as ourselves) can be conscious, has little acknowledgement. The main thesis of this book is that to be conscious at all, you need an unconscious mind. The author explores the idea that this mind sometimes makes contact with a whole unknown world, sporadically revealed by paranormal effects, but perhaps discoverable by hitherto uninvented scientific instruments.The book looks at the notion of the unconscious mind, one of the most important hypotheses of the twentieth century. Psychiatrists often deploy it rather informally, but there is no accepted theory of it. No region of the human brain seems to hold it. The author delves into the notion that the unknown world exists and is very weakly coupled to the physical world. He ponders the properties it may have to allow this coupling, looks at several paranormal effects scientifically and points out that many of them seem to imply brief but dramatic changes of the forces between atoms—a possible effect of the unknown world, unexamined by physical science.No existing publication seeks to talk both about paranormal mysteries and scientific theory. If scientists know about the gaps in existing knowledge, they might initiate research into such gaps, or notice experimental oddities they now gloss over. If the general public was aware of the gaps in physical theory, they would be less overwhelmed by the intellectual diktats of some scientists.Table of ContentsIntroduction. The Physical World. Life and Its Information. The Unconscious Mind. Methods in Physical Science: Feelings Don’t Matter. Methods in Paranormal Science: Feelings Do Matter. The Physical Properties of the Unknown World Outside Our Diving Bell. Physical Effects of the Unconscious Mind and the Unknown World 1. Observed Effects of the Unconscious Mind and the Unknown World 2. Observed Effects of the Unconscious Mind and the Unknown World 3. Observed Effects of the Unconscious Mind and the Unknown World 4. Unscientific but Widespread Human Beliefs. Organizations and Unusual People Mediumship, the Societies for Psychical Research, and Star Guessers. Getting Information from the Unknown World by Insight and by Writing. Getting Information from AI. Technical Questions from AI. Concluding Remarks.
£25.64
Jenny Stanford Publishing The Math of Body, Soul, and the Universe
Book SynopsisThis book digs deeper and shows not only that quantum gravity is more than just a physical theory—describing physical aspects—but also that, in fact, it covers "it all."Table of ContentsPersonal Motivation Some Fundamental Motivation Seven Days The First Day: Let There Be Nothing 1. Making Contact with Quantum Gravity The Second Day: Let There Be Photons 2. Societons and Ecotons 3. Humanitons—The Intrinsic Photons of the Human Body Understand Them and Cure Yourself 4. Social Distancing 5. Mastering Human Crises with Quantum Gravity-Based but Still Practicable Models The Third Day: Let There Be Mass and Inertia 6. Masses and the Infinity Options Principle 7. The Three Generations of Elementary Particles The Fourth Day: Let There Be Quantum Gravity 8. Toward Quantum Einstein Field Equations The Fifth Day: Let There Be a Dirac Equation 9. The Metric Dirac Equation Revisited and the Geometry of Spinors 10. The Dirac Miracle The Sixth Day: A Math for Body, Soul, and Universe 11. A Curvy Math to Salvation 12. About the Flatness Problem in Cosmology 13. Mathematical Tools for Socioeconomic and Psychological Simulations The Seventh Day: Give It Some Rest 14. About the Origin of the Minimum Principle
£73.14
World Scientific Publishing Co Pte Ltd Mathematical Physics And Matrix Representations
Book Synopsis
£130.50
