Solving Spatial Metric Geometry Problems
The aim of this work is to propose an activity aimed at second-year high school students, with the aim of teaching some concepts of Spatial Metric Geometry, specifically calculating the areas and volumes of geometric solids such as cones, cylinders, spheres, pyramids and prisms, with the help of technology, using the GeoGebra software. In order to develop this activity, we looked at some trends in teaching and learning mathematics, focusing mainly on Problem Solving and Information and Communication Technology.
New Advances in Audio Signal Processing
In the era of digitalization, audio signal processing is gaining peculiar relevance as an automation and remote analysis means, also considering its enhancement by novel artificial intelligence (AI) techniques.This Reprint aims to offer an overview of the current developments in all fields that revolve around audio processing: from advancements in the acoustic domain to deep learning architectures for the audio-based analysis of real-world problems such as pitch detection or pathology identification.
Advances in Radar Systems for Target Detection and Tracking
Radar systems can provide the all-weather and all-time detection and tracking of targets of interest, and they have been extensively applied by the remote sensing community, in applications such as geological exploration, disaster forecasting, traffic monitoring, urban planning, environmental sciences, hydrology, littoral zones, oceans, etc. This reprint contains the several advance research studies on radar systems for target detection and tracking. It includes multipath ghost suppression, maneuvering target tracking, target detection, and other topics.
Applied Statistical Modeling and Data Mining
This reprint comprises a compilation of 15 insightful research papers published in the Special Issue "Applied Statistical Modeling and Data Mining" within the Mathematics journal. Spanning multiple domains at the intersection of statistics, machine learning, and real-world applications, the collection presents diverse perspectives and innovative approaches in the field of applied statistical modeling and data mining. These selected papers explore diverse and important topics, including predictive modeling in healthcare, cybersecurity in transportation systems, data quality assessment, emergency call modeling, and innovative crime prevention strategies, among others. By covering a wide spectrum of subjects, this reprint serves as a valuable resource for researchers, academics, and practitioners interested in addressing contemporary challenges across diverse domains through statistical modeling, data mining, and machine learning applications.
Real Analysis
This is a classical Real Analysis/Calculus problem book. This volume contains a huge number of engaging problems and solutions, as well as detailed explanations of how to achieve these solutions. This latter quality is something that many problem books lack, and it is hoped that this feature will be useful to students and instructors alike.
Numerical Approaches to Optimal Control
Optimal control has been widely applied to modern control systems design and has drawn great attention for decades. In the optimal control theory, the control problem is formulated as an optimization problem, and the control law is calculated by solv-ing the optimal control problem (OCP). Comparing with traditional control methods like PID control, optimal control is capable of providing an optimal control law in a systematic way. However, optimal control can achieve an analytic expression of the optimal control law only for some relatively simpler cases, for instance, unconstrained linear systems. Specifically, the optimal feedback control law for unconstrained linear systems with a quadratic cost function is in a simple linear form, and the optimal control gain is obtained by solving a Riccati equation. In practical systems, most of the physical plants are essentially nonlinear systems subject to physical constraints. For these cases, it is difficult to obtain an analytical solution to the optimal control problems. In order to find the optimum to an intractable optimization problem, ap-proximate solutions have to be taken into account.
Make: Math Teacher's Supplement
Make: Math Teacher's Supplement is the essential guide for teachers, parents, and other educators wanting to supplement their curriculum with Joan Horvath and Rich Cameron's Make: Geometry, Make: Trigonometry, and Make: Calculus books. This book is a companion to the three math books, and does not duplicate the content in them. Drawing on the authors' experience guiding both students and teachers, it covers: The philosophy behind the Make: math book series, including the key inclusion of universal design principles to make the material accessible to those who learn differently A list of topics, projects, and needed maker skills, tied to the math book chapters Key learning objectives and associated assessment ideas A practical primer on 3D printing in an educational environment Helpful tips to manage student 3D printed workflow Five specific examples of ways to use content from the math books, including studying geometry with castles and using LEGO bricks to demonstrate calculus concepts Packed with tips and links to online resources, Make: Math Teacher's Supplement will let you see how to build math intuition to create a solid base for your learner's future.
Optimization Problems in Transportation and Logistics
This educational guide will help students and practitioners seeking to understand the fundamentals and practice of linear programming. The exercises contained within demonstrate how to solve classical optimization problems with an emphasis on spatial analysis in supply chain management and transport logistics. All exercises describe the Python programs and optimization libraries that can be used to solve them. The first chapter introduces key concepts in linear programming and establishes a new cognitive framework to help students and practitioners set up each optimization problem. This cognitive framework organizes the decision variables, constraints, objective function, and variable bounds in a format that allows for direct application to optimization software. The second chapter introduces two types of mobility optimization problems (shortest path in a network and minimum cost tour) in the context of delivery and service planning logistics. The third chapter introduces four types of spatial optimization problems (neighborhood coverage, flow capturing, zone heterogeneity, service coverage) and provides a workflow for visualizing the optimized solutions in maps. The workflow creates decision variables from maps by using the free geographic information systems (GIS) programs QGIS and GeoDA. The fourth chapter introduces three types of spatial logisticsproblems (spatial distribution, flow maximization, warehouse location optimization) and demonstrates how to scale the cognitive framework in software to reach solutions. The final chapter summarizes lessons learned and provides insights about how students and practitioners can modify the Python programs and GIS workflows to solve their own optimization problem andvisualize the results.
Computational Methods for Coupled Problems in Science and Engineering
The ninth edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2021) was organized to take place on 13-16 June 2021. Due to the pandemic, COUPLED 2021 was a fully online and completely synchronous conference. The previous eight editions of this conference were held on the islands of Santorini (Greece) on 25-28 May 2005; Ibiza (Spain) on 21-23 May 2007; Ischia (Italy) on 8-11 June 2009; Kos (Greece) on 20-22 June 2011; Ibiza (Spain) on 17-19 June 2013; San Servolo, Venice (Italy), on 18-20 May 2015; Rhodes Island (Greece) on 12-14 June 2017; and Sitges (Spain) on 3-5 June 2019. The objectives of COUPLED PROBLEMS 2021 were to present and discuss the state of the art in mathematical models, numerical methods and computational techniques for solving coupling problems of a multidisciplinary character in science and engineering. The conference's goal was to make advances in the formulation and solution of real-life problems with a multidisciplinary perspective, accounting for all the complex couplings involved in the physical description of the problem. The conference was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS) and a Special Interest Conference of the International Association for Computational Mechanics (IACM). It was also supported by other scientific organizations in Europe and across the globe.
Risk Revealed
Explore the concept of risk through numerous examples and their statistical modeling, traveling from a historical perspective all the way to an up-to-date technical analysis. Written with a wide readership in mind, this book begins with accounts of a selection of major historical disasters, such as the North Sea flood of 1953 and the L'Aquila earthquake. These tales serve to set the scene and to motivate the second part of the book, which describes the mathematical tools required to analyze these events, and how to use them. The focus is on the basic understanding of the mathematical modeling of risk and what types of questions the methods allow one to answer. The text offers a bridge between the world of science and that of everyday experience. It is written to be accessible to readers with only a basic background in mathematics and statistics. Even the more technical discussions are interspersed with historical comments and plentiful examples.
The families of prime numbers
The book introduces innovative approaches to conjectures and established knowledge in the realm of prime numbers. It explores how famous mathematicians like Sophie Germain and Mersenne, among others, conceptualized prime numbers Not only does the text clarify Fermat's Little Theorem, but it also offers an explanation for the existence of pseudoprimes. Furthermore, it sheds light on the effectiveness of the Lucas-Lehmer algorithm in discovering Mersenne Primes. By elucidating fundamental concepts, the book provides fresh insights into the study of prime numbers within Number Theory. While its primary audience consists of enthusiasts and mathematicians in search of new patterns and analytical methodologies for prime numbers, the book is designed to be accessible to a broader audience. With over 70 explanatory figures and clear prose, it appeals to anyone intrigued by the intricate world of prime numbers.
Tangles
Tangles offer a precise way to identify structure in imprecise data. By grouping qualities that often occur together, they not only reveal clusters of things but also types of their qualities: types of political views, of texts, of health conditions, or of proteins. Tangles offer a new, structural, approach to artificial intelligence that can help us understand, classify, and predict complex phenomena. This has become possible by the recent axiomatization of the mathematical theory of tangles, which has made it applicable far beyond its origin in graph theory: from clustering in data science and machine learning to predicting customer behaviour in economics; from DNA sequencing and drug development to text and image analysis. Such applications are explored here for the first time. Assuming only basic undergraduate mathematics, the theory of tangles and its potential implications are made accessible to scientists, computer scientists, and social scientists.
Higher Special Functions
Higher special functions emerge from boundary eigenvalue problems of Fuchsian differential equations with more than three singularities. This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order, exploring previously unknown methods for finding higher special functions. Starting from the fact that it is the singularities of a differential equation that determine the local, as well as the global, behaviour of its solutions, the author develops methods that are both new and efficient and lead to functional relationships that were previously unknown. All the developments discussed are placed within their historical context, allowing the reader to trace the roots of the theory back through the work of many generations of great mathematicians. Particular attention is given to the work of George Cecil Jaff矇, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.
Linear Partial Differential and Difference Equations and Simultaneous Systems with Constant or Homogeneous Coefficients
Linear Partial Differential and Difference Equations and Simultaneous Systems: With Constant or Homogeneous Coefficients is part of the series "Mathematics and Physics for Science and Technology," which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. Volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to: acoustic, elastic, water, electromagnetic and other waves; the diffusion of heat, mass, and electricity; and their interactions. This is the third book of the volume.The book starts with six different methods of solution of linear partial differential equations (p.d.e.) with constant coefficients. One of the methods, namely characteristic polynomial, is then extended to a further five classes, including linear p.d.e. with homogeneous power coefficients and finite difference equations and simultaneous systems of both (simultaneous partial differential equations [s.p.d.e.] and simultaneous finite difference equations [s.f.d.e.]). The applications include detailed solutions of the most important p.d.e. in physics and engineering, including the Laplace, heat, diffusion, telegraph, bar, and beam equations. The free and forced solutions are considered together with boundary, initial, asymptotic, starting, and other conditions.The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical, and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics.
Vector Calculus
A calculus book must tell the truth. This book is carefully written in the accepted language of mathematics in a readable exposition. It includes useful and fascinating applications, acquaints students with the history of the subject and offers a sense of what mathematics is all about.
Current topics in Logic and the Philosophy of Science. Papers from SILFS 2022 postgraduate conference
Logic and the Philosophy of Science are disciplines that avoid stopping and wandering around in circles on the same topics. Their role in dedicating themselves to scientific and applicative subjects always makes them extraordinarily fruitful and productive, in step with the developments of scientific and technological knowledge. The writings contained in this volume are proof of this. The set of research selected for this publication, starting from the 2022 Postgraduate Conference of SILFS (the Italian Society for Logic and the Philosophy of Science), testifies to a lively and rich knowledge widespread among young scholars of this area who combine pure logic and philosophy to the analysis of cutting-edge knowledge produced by current scientific and technological disciplines. The result is a kaleidoscope of research on updated logical and philosophical-scientific topics, which gives rise to promising developments on the part of young scholars who are contributing today to the logic and philosophy of science to create further perspectives in the future.
The Code of Mathematics
Inspired by recent developments in dependent type theory and infinity categories, this book presents a history of ideas around the topics of truth, proof, equality and equivalence. Besides selected ideas of Platon, Aristoteles, Leibniz, Kant, Frege and others, the results of G繹del and Tarski on incompleteness, undecidability and truth in deductive systems and their semantic models are covered. The main focus of this textbook is on dependent type theory and its recent variant homotopy type theory. Such theories contain identity types, which give a new understanding of equality, symmetry, equivalence and isomorphism in a conceptual way. The interaction of type theory and infinity category theory yields a new paradigm for a structural view on mathematics. This supports the tendencies towards formalising mathematics with the help of proof assistants. This book was first published in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Bridging Gaps In Elementary Mathematics
Bridging Gaps in Elementary Mathematics is a Mathematics study supplement created to improve upon the appreciation and fundamental understanding of Mathematics by employing the "why" of Mathematics approach. It was also created to ensure that those who did not have an opportunity in their earlier years to study Mathematics, or those who did but need better understanding, would be able to "bridge" the gaps formed in their education. The material covers topics found in the curriculum at the Primary to the pre-Junior High School level. It is not intended to substitute for formally prescribed schooling study materials and textbooks. Still, it is a supplement that provides a more profound understanding, real-life applications and different perspectives of the universal elements of the Mathematics curriculum. It effectively approaches the subject from the root to help make it less abstract.
Inverse Gravity Cosmology
The book is about the inverse gravity cosmology hypothesis which is based on three of the author's published papers which past peer review. Hence, the book presents the inverse gravity concept, its mathematical structure, and its incorporation to established and proven aspects of physics. New developments and mathematics of the theoretical concept are expressed. Moreover, the book cites mistakes/deficiencies and omissions in previous publications. Lastly, the book's introduction includes information about the author's background that inspired the inception of the theoretical concept.
Partitions, Objective Indefiniteness, and Quantum Reality
This book presents a new 'partitional' approach to understanding or interpreting the math of standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set and, conversely, the math of partitions is a skeletonized set level version of the math of QM. Since at the set level, partitions are the mathematical tool to represent distinctions and indistinctions (or definiteness and indefiniteness), this approach shows how to interpret the key non-classical QM notion of superposition in terms of (objective) indefiniteness between definite alternatives (as opposed to seeing it as the sum of 'waves'). Thus, the book develops a new mathematical, or indeed, logical, approach to the century-old problem of interpreting quantum mechanics, ensure it is of interest to philosophers of science as well as mathematicians and physicists.
Risk Revealed
Explore the concept of risk through numerous examples and their statistical modeling, traveling from a historical perspective all the way to an up-to-date technical analysis. Written with a wide readership in mind, this book begins with accounts of a selection of major historical disasters, such as the North Sea flood of 1953 and the L'Aquila earthquake. These tales serve to set the scene and to motivate the second part of the book, which describes the mathematical tools required to analyze these events, and how to use them. The focus is on the basic understanding of the mathematical modeling of risk and what types of questions the methods allow one to answer. The text offers a bridge between the world of science and that of everyday experience. It is written to be accessible to readers with only a basic background in mathematics and statistics. Even the more technical discussions are interspersed with historical comments and plentiful examples.
Integrated Computer Technologies in Mechanical Engineering - Synergetic Engineering Ⅱ
The best works were selected after the conference titled "Integrated Computer Technologies in Mechanical Engineering"-Synergetic Engineering (ICTM) II. The conference provided technical exchange between the scientific community in the form of keynote addresses, panel discussions, and a special session. In addition, participants were treated to a series of techniques that facilitated collaboration among fellow researchers. Moreover, ICTM 2021 received 110 applications from different countries.
Integrated Computer Technologies in Mechanical Engineering - Synergetic Engineering
The best works were selected after the conference "Integrated Computer Technologies in Mechanical Engineering"-Synergetic Engineering (ICTM). The conference provided technical exchange between the scientific community in the form of keynote addresses, panel discussions, and a special session. In addition, participants were treated to a series of techniques that facilitated collaboration among fellow researchers. Moreover, ICTM 2021 received 110 applications from different countries.
The Power of Probability
"The Power of Probability: Making Sense of Uncertainty" is a comprehensive exploration of probability theory and probabilistic reasoning. From its historical origins to its practical applications in diverse domains, the book delves into the fundamental concepts, methodologies, and implications of understanding uncertainty. Through engaging discussions and practical examples, readers are empowered to embrace probabilistic thinking, make informed decisions, and navigate complexities in an uncertain world.
Combinatorics Problems and Solutions
This book will help you learn combinatorics in the most effective way possible - through problem solving. It contains 263 combinatorics problems with detailed solutions. Combinatorics is the part of mathematics that involves counting. It is therefore an essential part of anyone's mathematical toolkit. The applications of combinatorics include probability, cryptography, error correcting, games, music and visual art. In this new edition we have expanded the introductory section by more than twice the original size, and the number of problems has grown by over 30%. There are new sections on the pigeon hole principle and integer partitions with accompanying problems. Many of the new problems are application oriented. There are also new combinatorial geometry problems. Someone with no prior exposure to combinatorics will find enough introductory material to quickly get a grasp of what combinatorics is all about and acquire the confidence to start tackling problems.
Shrinkage for Stabilizing the Detection of Changepoints in Covariances for High-Dimensional Data
Diploma Thesis from the year 2012 in the subject Mathematics, grade: 1,0, University of Kaiserslautern (Fakult瓣t f羹r Mathematik), language: English, abstract: In mathematical statistics, detecting changes in parameters of real-life data series, known as change-point problems, is crucial. Originating in quality control during the 1950s, these problems have widespread applications today, spanning fields like economics, finance, medicine, and geology. In finance, fluctuations in asset returns can violate assumptions of constant variance, leading to inaccurate forecasts. Chapter 2 briefly discusses the univariate case, focusing on detecting changes in mean and variance parameters over time. The Cumulative Sums (CUSUM) test statistics, derived from likelihood ratios, serve as change-point estimators. However, their asymptotic distribution complexity and slow convergence limit applicability to small sample sizes. Nevertheless, asymptotic quantiles help determine if changes have occurred. Chapter 3 extends this analysis to the multivariate case, specifically addressing changes in covariance matrices. Estimating the covariance matrix, particularly in scenarios with many variables and few observations, poses challenges. Shrinkage estimators, like the Ledoit-Wolf (LW) estimator, offer improvements over sample covariance matrices, especially in small sample sizes. The Rao-Blackwell theorem leads to the development of the Rao-Blackwellized Ledoit-Wolf (RBLW) estimator, enhancing performance under Gaussian assumptions. A simulation study in Chapter 5 demonstrates the effectiveness of using these shrinkage estimators in detecting change-points, resulting in improved test power and accuracy. However, due to the absence of an asymptotic distribution for the test statistics, quantiles must be obtained through simulation.
General Combination Theorem and Selected Combinations
Document from the year 2024 in the subject Mathematics - Algebra, language: English, abstract: So for combinations are discussed with different theorems in algebra. In this chapter I apply assembly analysis to get the theorems easy and memorable. After assembly analysis applied there becomes a lot of new theorems and all the theorems get a new face by summation methods. We have a full idea about combination. It indicates the outcome of arandom experiment. That is combination is the selection of M different components taken V at a time what is called usually a random experiment where order is not taken into account and repetitions are not allowed.
General Permutation Theorem and Selected Permutations
Document in the subject Mathematics - Algebra, language: English, abstract: We have permutations are discussed with different theorems in algebra. In this chapter I apply B system analysis to get the theorems easy and memorable. After B system analysis applied there becomes a lot of new theorems and all the theorems get a new face by summation methods. One usual theorem described with summation method and face new looks.
Exploring Unique Expressions of Positive Integers through Partitions and Theorems
Research Paper (postgraduate) from the year 2024 in the subject Mathematics - Algebra, language: English, abstract: This paper delves into the realm of natural numbers and their expression as sums of other natural numbers, a concept known as partitions. Focusing on partitions originating from a positive integer and comprising positive integers, a systematic analysis is presented. Essential terms are defined to lay the groundwork, followed by the introduction of three key theorems and a consequential corollary. These theorems elucidate the uniqueness of expressions formed through arithmetic addition operations on such partitions, offering valuable insights into the structure and properties of positive integers. This exploration not only contributes to the theory of numbers but also holds implications for various mathematical and computational applications.
Analyzing Repartition Numbers of Parent Partitions. Theorems and their Implications
Research Paper (postgraduate) from the year 2024 in the subject Mathematics - Algebra, language: English, abstract: This paper delves into the intricate realm of partition theory, specifically focusing on the repartition numbers of parent partitions. Through a systematic development of six theorems, insights into the distribution of repartitions, delineating distinct patterns for two separate parent partitions, are unveiled. Theorems are structured to elucidate the occurrences of repartitions based on the number of components involved, providing a comprehensive understanding of the repartition phenomena. The findings contribute to a deeper comprehension of partition theory and its implications across various domains.
Holy Trinity & Inverted Holy Trinity
The Trinities are all over the place!There is the positive Holy Trinity turned upwords... and there is the negative or Inverted Holy Trinity, turned upside down. From a Mathematical perspective. Applied Math to Life, Research. Bridge/Fusion between Mathematical Science & Spirituality.
Once Upon a Prime
A New York Times Book Review Editors' Choice "Wide-ranging and thoroughly winning." --Jordan Ellenberg, The New York Times Book Review "An absolute joy to read!" --Steven Levitt, New York Times bestselling author of Freakonomics For fans of Seven Brief Lessons in Physics, an exploration of the many ways mathematics can transform our understanding of literature and vice versa, by the first woman to hold England's oldest mathematical chair. We often think of mathematics and literature as polar opposites. But what if, instead, they were fundamentally linked? In her clear, insightful, laugh-out-loud funny debut, Once Upon a Prime, Professor Sarah Hart shows us the myriad connections between math and literature, and how understanding those connections can enhance our enjoyment of both. Did you know, for instance, that Moby-Dick is full of sophisticated geometry? That James Joyce's stream-of-consciousness novels are deliberately checkered with mathematical references? That George Eliot was obsessed with statistics? That Jurassic Park is undergirded by fractal patterns? That Sir Arthur Conan Doyle and Chimamanda Ngozi Adichie wrote mathematician characters? From sonnets to fairytales to experimental French literature, Professor Hart shows how math and literature are complementary parts of the same quest, to understand human life and our place in the universe. As the first woman to hold England's oldest mathematical chair, Professor Hart is the ideal tour guide, taking us on an unforgettable journey through the books we thought we knew, revealing new layers of beauty and wonder. As she promises, you're going to need a bigger bookcase.
Probability and Statistics
Probability and Statistics: Theory and Exercises is a textbook focused on practical examples of probability theory and statistics, with the goal of giving readers a thorough understanding of mathematical relationships in these subjects. The book is designed for basic courses in probability and statistics, and is aimed primarily at non-specialists and beginner level students. The book is divided into 2 sections, respectively. Probability: Includes a primer on set theory, basic probability theory definitions and calculations, combinatorial analysis, random variables and distribution laws Statistics: Covers basic concepts of descriptive statistics Key features - Simple, clear language for easy comprehension of key concepts - Carefully chosen exercises with solutions for self-learning - Over 40 Illustrations for clear explanations - References for further reading and tutorials
Tensor Analysis
Tensor calculus is a prerequisite for many tasks in physics and engineering. This book introduces the symbolic and the index notation side by side and offers easy access to techniques in the field by focusing on algorithms in index notation. It explains the required algebraic tools and contains numerous exercises with answers, making it suitable for self study for students and researchers in areas such as solid mechanics, fluid mechanics, and electrodynamics. ContentsAlgebraic ToolsTensor Analysis in Symbolic Notation and in Cartesian CoordinatesAlgebra of Second Order TensorsTensor Analysis in Curvilinear CoordinatesRepresentation of Tensor FunctionsAppendices: Solutions to the Problems; Cylindrical Coordinates and Spherical Coordinates
Philosophy of Mathematics
The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today's mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally - First nonstandard steps Retrospection
Sudoku for beginners - 50 puzzles from Mio - think for yourself
The playing field is a 9x9 square, divided into smaller squares with a side length of 3 fields. The main goal of the game is to fill the empty cells with numbers from 1 to 9 so that each number appears only once in each row, column and 3x3 square. Can you fill in all the cells correctly?
Single Variable Calculus
The book is a comprehensive yet compressed entry-level introduction on single variable calculus, focusing on the concepts and applications of limits, continuity, derivative, defi nite integral, series, sequences and approximations. Chapters are arranged to outline the essence of each topic and to address learning diffi culties, making it suitable for students and lecturers in mathematics, physics and engineering. ContentsPrerequisites for calculusLimits and continuityThe derivativeApplications of the derivativeThe definite integralTechniques for integration and improper integralsApplications of the definite integralInfinite series, sequences, and approximations
Foundations of Information and Knowledge Systems
This LNCS conference volume constitutes the proceedings of the 13th International Symposium, FoIKS 2024, in Sheffield, UK, in April 2024. The 18 full papers together with 3 short papers included in this volume were carefully reviewed and selected from 42 submissions.The Symposium focuses on fundamental aspect of information and knowledge systems, including submissions that apply ideas, theories, or methods from specific disciplines to information and knowledge systems. Examples of such disciplines are discrete mathematics, logic and algebra, model theory, databases, information theory, complexity theory, algorithmics and computation, statistics, and optimization.
The Land Between
The Land Between is the first concise history of Slovenia and Slovenes written in English by leading scholars from the country. The authors base their arguments on Slovenian, former Yugoslav, and Western sources to provide a comprehensive account of Slovenes' political, social, economic and cultural history, from early Slav settlements to the present day. The authors focus on Slovenian history but, to their credit, manage to place it in a wider context of empires and states to which Slovenian lands had belonged throughout history. The book will be of use to students of Slovenia and East-Central Europe, to diplomats, journalists, tourists, and anyone interested in this part of the world. It represents a welcome addition to the historiography of Slovenia and former Yugoslavia as well as a unique insight into the state of scholarship in post-1991 Slovenia. Dejan Djokic, historian, National University of Ireland, Maynooth A study which makes the reader feel and understand that since the end of the Cold War there is a new lease of life for Central Europe. The former borderlands between East and West construct their new identities. Slovenia is one of the most successful new democratic societies in the middle of Europe. This book is an excellent history of Slovenia which maps the narrative of a small European people without falling into the traps of national mythmaking. Writing about a small European country with two million inhabitants which crave for Central European, Mediterranean and Balkan traditions at the same time is no simple task. The book makes fine reading for everybody interested in understanding the fascinating and creative complexities in the heart of Europe. Highly recommendable for history lovers and historians alike! Emil Brix, historian and ambassador, Director of the Diplomatische Akademie Wien - Vienna School of International Studies The book presents a concise and intelligible history of the Slovenes. The authors take into due consideration the history of the territory between the Eastern Alps and the Pannonian Plain, starting with the period that began long before the first Slavic settlements. Thus, they wish to emphasize that the Slovenes' ancestors did not settle an empty territory, but rather coexisted with other peoples and cultures ever since their arrival in the Eastern Alps. This has enabled them to build a community shaped by countless influences stemming from a long period of living alongside German, Romance, and South Slav neighbors in a melting pot of languages, cultures, and landscapes. The same reasons have most probably also contributed to the perception of their land as a "land in between." Constituting a link between Eastern and Western Europe, Slovenia has recently also been increasingly perceived as the meeting point of Central Europe and the Balkans. Today, history still occupies the central position in the life of the Slovenes. The heroic period of emancipation has been completed and the Slovenes will be bracing themselves for a no less turbulent period of challenging "essentialist" notions of identity in order to create a thoroughly open society.
Origins and Varieties of Logicism
This book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism.
Mathematicians Don't Work with Numbers
This book answers, in the form of short and entertaining vignettes, the question: "What do mathematicians really do?" Readers will learn that mathematicians use numbers in the same way that novelists use letters. The individual letters are typed while the author thinks on a much grander scale, invisible to the observer. Requiring only familiarity with the multiplication table (and that for only one vignette), the book makes accessible a variety of mathematical concepts, such as game theory, chaos, and traffic flow modelling. The author accomplishes this with a light, engaging style, and a range of real-world examples that includes everything from barbershops to President James Garfield. Mathematicians Don't Work With Numbers will be of interest to the large audience of people who have always assumed that mathematicians do, in fact, work with numbers.
Journal of Applied Logics, Volume 11, Number 1, January 2024. 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.
Cambridge IGCSE Complete Mathematics Core Student Book 6th E
Cambridge IGCSE Complete Mathematics Extended Student Book 6
The Fourth Coming
In a time of dire need, as climate change, conflict, and economic upheaval imperil our existence and our mental well-being deteriorates from not utilising our minds as God intended, Francis Keith Robins introduces a groundbreaking approach to saving humanity - reshaping our thought processes through mathematics. In his book, The Fourth Coming, Robins provides a detailed, step-by-step guide to unlocking our inherent mathematical potential. His vision is to create a society that is inclusive, equal, and peaceful - one that aligns with God's desire for us. He advocates for a paradigm shift where shared mathematical models and systematic thinking supplant the ineffective classes of governments and institutions currently jeopardizing our planet. This revolutionary approach aims to alter the trajectory of human history in a manner that aligns with divine intentions. Robins' theories, described as a work of mathematical brilliance, offer a refreshingly simple yet profound solution to consciousness - which, as noted by 'New Scientist', remains one of the most elusive and significant mysteries in science and philosophy. Furthermore, he concludes that the introduction of religion by God was a response to humanity's failure to use their brains as He intended.
The Fourth Coming
In a time of dire need, as climate change, conflict, and economic upheaval imperil our existence and our mental well-being deteriorates from not utilising our minds as God intended, Francis Keith Robins introduces a groundbreaking approach to saving humanity - reshaping our thought processes through mathematics. In his book, The Fourth Coming, Robins provides a detailed, step-by-step guide to unlocking our inherent mathematical potential. His vision is to create a society that is inclusive, equal, and peaceful - one that aligns with God's desire for us. He advocates for a paradigm shift where shared mathematical models and systematic thinking supplant the ineffective classes of governments and institutions currently jeopardizing our planet. This revolutionary approach aims to alter the trajectory of human history in a manner that aligns with divine intentions. Robins' theories, described as a work of mathematical brilliance, offer a refreshingly simple yet profound solution to consciousness - which, as noted by 'New Scientist', remains one of the most elusive and significant mysteries in science and philosophy. Furthermore, he concludes that the introduction of religion by God was a response to humanity's failure to use their brains as He intended.
Persistent Homology and Persistent Cohomology
Persistent homology has become an important tool in non-linear data reduction. Its sister theory, Persistent cohomology, has attracted less attention in the past eventhough it has many advantages. We surveyed several literatures and present a summary of the status quo in persistent (co)homology covering the theory, computations, representations in terms of cycles (for persistent homology) and cocycles (for persistent cohomology), lens (quotient) space and their equivalence. Moreover, we computed the persistent homology and persistent cohomology for the 2 - sphere both manually and computationally (Using Ripserer). In both cases, same result was obtained, particularly in the computation of their barcodes much more that persistent cohomology is not only faster in computation than persistent homology, but also uses less memory in a little time.
Paradoxes and Inconsistent Mathematics
Logical paradoxes - like the Liar, Russell's, and the Sorites - are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses "dialetheic paraconsistency" - a formal framework where some contradictions can be true without absurdity - as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.
