EQAO Grade 6 Math Test Prep!
Created to help Grade 6 students prepare for the EQAO Mathematics Assessment Test.The 10 practice tests were designed to be similar to the actual test the students will be taking. The questions are either multiple choice or open response so that students can get familiar with the question/answer format.The first 5 tests each feature a different key math skill for targeted practice: number sense & numeration, patterning & algebra, measurement, geometry & spatial sense, and data management & probability. Students struggling in any of these areas will benefit from this skill-specific practice.The following 5 tests feature mixed math skills with questions that are a combination of all the math skills. There is no particular sequence to the tests. They can be used in whatever order you choose to fit your student's needs.
Precalculus 2
The second half of the second edition of Precalculus: An Investigation of Functions. This is an open textbook, available free online. This second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisted more extensively in the third chapter. As with the first part of the book, an emphasis is placed on motivating the concepts and on modeling and interpretation.
Precalculus 1
The first half of the second edition of Precalculus: An Investigation of Functions. This is an open textbook, available free online. This first portion of the book (Chapters 1-4) is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.
Gamma Solution
The Gamma Function is a generalisation of the factorial for use with complex numbers. The plane of complex numbers subsumes fractions including transcendental numbers, some of which have especially elegant Gamma forms. The Gamma Function has a number of applications in advanced science including quantum physics, astrophysics and fluid dynamics An analytical and experimental study was undertaken to assess how theoretical and experimental code and performance metrics might assist the choice of published Complete Gamma Function ( CGF ) solution algorithms, or inform the development of new CGF methods. Accuracy, speed and component timing statistics were computed for thirteen methods or method variations, and new empirical metrics proposed. Empirical metrics and component time profiles disclosed significant algorithm properties and assisted coding optimisations. Halstead metrics did not apply, but code token ratios correlated with other CGF algorithm features. Further research could involve recently discovered Elliptic, Laplacian or Zeta Function avenues. Enjoy the work and I hope you find it useful as a starting point.Extensive equations and diagrams are included, as well as program code in Visual Basic
Teaching and Research in Mathematics
The author's goal is to help the transition from graduate studies and make it less diffcult and time-consuming. Part I covers techniques on teaching and conducting research and in Part II, the author has introduced some modern research in mathematics in various industries.
Teaching and Research in Mathematics
The author's goal is to help the transition from graduate studies and make it less diffcult and time-consuming. Part I covers techniques on teaching and conducting research and in Part II, the author has introduced some modern research in mathematics in various industries.
Precalculus
An open textbook covering pre-calculus including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisited more extensively in the third chapter. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.
Advances in Architectural Acoustics
Satisfactory acoustics is crucial for the ability of spaces such as auditoriums and lecture rooms to perform their primary function. The acoustics of dwellings and offices greatly affects the quality of our life, since we are all consciously or subconsciously aware of the sounds to which we are daily subjected. Architectural acoustics, which encompasses room and building acoustics, is the scientific field that deals with these topics and can be defined as the study of generation, propagation, and effects of sound in enclosures. Modeling techniques, as well as related acoustic theories for accurately calculating the sound field, have been the center of many major new developments. In addition, the image conveyed by a purely physical description of sound would be incomplete without regarding human perception; hence, the interrelation between objective stimuli and subjective sensations is a field of important investigations.A holistic approach in terms of research and practice is the optimum way for solving the perplexing problems which arise in the design or refurbishment of spaces, since current trends in contemporary architecture, such as transparency, openness, and preference for bare sound-reflecting surfaces are continuing pushing the very limits of functional acoustics. All the advances in architectural acoustics gathered in this Special Issue, we hope that inspire researchers and acousticians to explore new directions in this age of scientific convergence.
Miniaturized Transistors, Volume II
In this book, we aim to address the ever-advancing progress in microelectronic device scaling. Complementary Metal-Oxide-Semiconductor (CMOS) devices continue to endure miniaturization, irrespective of the seeming physical limitations, helped by advancing fabrication techniques. We observe that miniaturization does not always refer to the latest technology node for digital transistors. Rather, by applying novel materials and device geometries, a significant reduction in the size of microelectronic devices for a broad set of applications can be achieved. The achievements made in the scaling of devices for applications beyond digital logic (e.g., high power, optoelectronics, and sensors) are taking the forefront in microelectronic miniaturization. Furthermore, all these achievements are assisted by improvements in the simulation and modeling of the involved materials and device structures. In particular, process and device technology computer-aided design (TCAD) has become indispensable in the design cycle of novel devices and technologies.It is our sincere hope that the results provided in this Special Issue prove useful to scientists and engineers who find themselves at the forefront of this rapidly evolving and broadening field. Now, more than ever, it is essential to look for solutions to find the next disrupting technologies which will allow for transistor miniaturization well beyond silicon's physical limits and the current state-of-the-art. This requires a broad attack, including studies of novel and innovative designs as well as emerging materials which are becoming more application-specific than ever before.
Teaching the Essentials of Arithmetic (Yesterday's Classics)
A thoughtful discussion of best practices for teaching arithmetic processes and the order in which to teach them. The author urges that methods adopted early on smooth the way for more advanced calculations taught later. Lots of food for thought for home educators as well as classroom teachers.
Expanding Mathematical Toolbox: Interweaving Topics, Problems, and Solutions
Expanding Mathematical Toolbox: Interweaving Topics, Problems, and Solutions offers several topics from different mathematical disciplines and shows how closely they are related. The purpose of this book is to direct the attention of readers who have an interest in and talent for mathematics to engaging and thought-provoking problems that should help them change their ways of thinking, entice further exploration and possibly lead to independent research and projects in mathematics. In spite of the many challenging problems, most solutions require no more than a basic knowledge covered in a high-school math curriculum. To shed new light on a deeper appreciation for mathematical relationships, the problems are selected to demonstrate techniques involving a variety of mathematical ideas. Included are some interesting applications of trigonometry, vector algebra and Cartesian coordinate system techniques, and geometrical constructions and inversion in solving mechanical engineering problems and in studying models explaining non-Euclidean geometries. This book is primarily directed at secondary school teachers and college professors. It will be useful in teaching mathematical reasoning because it emphasizes how to teach students to think creatively and strategically and how to make connections between math disciplines. The text also can be used as a resource for preparing for mathematics Olympiads. In addition, it is aimed at all readers who want to study mathematics, gain deeper understanding and enhance their problem-solving abilities. Readers will find fresh ideas and topics offering unexpected insights, new skills to expand their horizons and an appreciation for the beauty of mathematics.
Advances in Artificial Intelligence
The present book contains all the articles accepted and published in the Special Issue "Advances in Artificial Intelligence: Models, Optimization, and Machine Learning" of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of artificial intelligence and its subfields. These topics include, among others, deep learning and classic machine learning algorithms, neural modelling, architectures and learning algorithms, biologically inspired optimization algorithms, algorithms for autonomous driving, probabilistic models and Bayesian reasoning, intelligent agents and multiagent systems. We hope that the scientific results presented in this book will serve as valuable sources of documentation and inspiration for anyone willing to pursue research in artificial intelligence, machine learning and their widespread applications.
Complex Variable Functions
The internationalization of mathematics education has become an inevitable trend, and bilingual education is the booster to realize the internationalization of mathematics education. For the freshmen majoring in science and engineering, it is not realistic to choose the first-year mathematics basic courses such as advanced mathematics and linear algebra as the bilingual teaching object; it is not the best choice for the bilingual teaching object compared with the senior mathematics courses, such as Function of Real Variables, Functional Analysis and Topology of Point Set, which are more difficult; "Complex Variable Functions" is a relatively easy mathematics course, which is the extension and supplement of higher mathematics. This book is divided into nine chapters, which systematically introduces the basic theory and methods of complex variable function, including complex number and complex variable function, analytic function, integral of complex variable function, power series representation of analytic function, Laurent expansion of analytic function and its isolated singularities, residue theory and its application, conformal mappings. This book is suitable for teachers and students of science and engineering major in colleges and universities all over the country, and can also be read and referenced by engineering and technical personnel.
tsixE toN oD srebmuN evitageN
.tsixe od sehsifrats tnegilletni tuB .tsixe ton od srebmun evitageN .evitisop si, gnirusaem era ew tahw, gnihtyrevE .tsixe ton od seititne evitageN .noitcerid rehtona otni secnatsid evitisop derusaem neht dna relur eht dnuora denrut ylno evah niaga dna niaga su fo llA .ecaps fo ecnatsid evitagen a derusaem reve sah, gnieb namuh on, ydobon dnA .emit fo htgnel evitagen a derusaem reve sah, gnieb namuh on, ydoboN .tsixe ton od srebmun evitageN
Jerome Cardan
This book has been considered important throughout the human history, and so that this work is never forgotten we have made efforts in its preservation by republishing this book in a modern format for present and future generations. This whole book has been reformatted, retyped and designed. These books are not made of scanned copies and hence the text is clear and readable.
Invariants of complex and p-adic origami-curves
Origamis (also known as square-tiled surfaces) are Riemann surfaces which are constructed by glueing together finitely many unit squares. By varying the complex structure of these squares one obtains easily accessible examples of Teichm羹ller curves in the moduli space of Riemann surfaces.Different Teichm羹ller curves can be distinguished by several invariants, which are explicitly computed. The results are then compared to a p-adic analogue where Riemann surfaces are replaced by Mumford curves.
On Length Spectra of Lattices
The aim of this work is to study Schmutz Schaller's conjecture that in dimensions 2 to 8 the lattices with the best sphere packings have maximal lengths. This means that the distinct norms which occur in these lattices are greater than those of any other lattice in the same dimension with the same covolume.Although the statement holds asymptotically we explicitly present a counter-example. However, it seems that there is nothing but this exception.
Strategic power plant investment planning under fuel and carbon price uncertainty
The profitability of power plant investments depends strongly on uncertain fuel and carbon prices. In this doctoral thesis, we combine fundamental electricity market models with stochastic dynamic programming to evaluate power plant investments under uncertainty. The application of interpolation-based stochastic dynamic programming and approximate dynamic programming allows us to consider a greater variety of stochastic fuel and carbon price scenarios compared to other approaches.
Coalgebraic Methods in Computer Science
This book constitutes the thoroughly refereed post-conference proceedings of the 16th International Workshop on Coalgebraic Methods in Computer Science, CMCS 2022, colocated with ETAPS 2022, held in Munich, Germany, in April 2022. The 9 revised full papers were carefully reviewed and selected from 12 submissions. The papers cover a wide range of topics in the theory, logics, and applications of coalgebras.
AI Age Knowledge
Peter Chew theorem is AI age knowledge because the theorem can help convert all Quadratic Surds . In addition, the theorem can help convert easier and faster than current method. Applying Peter Chew theorem in AI age calculator, PCET calculator can help the calculator solve all problem of Quadratic Surds. This will cause students to increase their interest in using PCET calculator and increase the promotion of effective mathematics learning. When the future epidemics such as Covid-19 occur in the future, it can effectively help mathematics teaching, especially for students studying at home. Presenting numbers in surd form is quite common in science and engineering especially where a calculator is either not allowed or unavailable, and the calculations to be undertaken involve irrational values. Therefore, the application of Peter Chew theorem in Mechanical Engineering can make the teaching and learning of Mechanical Engineering easier. About the Author: Peter Chew is Mathematician, Inventor and Biochemist from National University Of Malaysia (UKM). Global issue analyst and Reviewer for Eliva Press. Peter Chew also is CEO PCET, Malaysia, PCET is a long research associate of IMRF (International Multidisciplinary Research Foundation), Institute of higher Education & Research with its HQ at India and Academic Chapters all over the world.Peter Chew obtain the Certificate of appreciation from Malaysian Health Minister Datuk Seri Dr. Adam Baba(2021), PSB Singapore. National QC Convention STAR AWARD (2 STAR), IMRF Outstanding Analyst Award 2019, IMFR Inventor Award 2020, the Best Presentation Award ICEMP 2019 in Ningbo, China . Invited speaker at the ATCM 2019, China. iCon-MESSSH'20 and iCon-MESSSH'21 Special Talk Speaker the 100th CONF of the IMRF, Goa, India. Keynote Speaker of the ICCEMS 2019 and the ICPCE 2020.
The Art of Mathematics - Take Two
Lovers of mathematics, young and old, professional and amateur, will enjoy this book. It is mathematics with fun: a collection of attractive problems that will delight and test readers. Many of the problems are drawn from the large number that have entertained and challenged students, guests and colleagues over the years during afternoon tea. The problems have their roots in many areas of mathematics. They vary greatly in difficulty: some are very easy, but most are far from trivial, and quite a few rather hard. Many provide substantial and surprising results that form the tip of an iceberg, providing an introduction to an important topic. To enjoy and appreciate the problems, readers should browse the book choosing one that looks particularly enticing, and think about it on and off for a while before resorting to the hint or the solution. Follow threads for an enjoyable and enriching journey through mathematics.
Gradient Descent, Stochastic Optimization, and Other Tales
The goal of this book is to debunk and dispel the magic behind the black-box optimizers and stochastic optimizers. It aims to build a solid foundation on how and why the techniques work. This manuscript crystallizes this knowledge by deriving from simple intuitions, the mathematics behind the strategies. This book doesn't shy away from addressing both the formal and informal aspects of gradient descent and stochastic optimization methods. By doing so, it hopes to provide readers with a deeper understanding of these techniques as well as the when, the how and the why of applying these algorithms.Gradient descent is one of the most popular algorithms to perform optimization and by far the most common way to optimize machine learning tasks. Its stochastic version receives attention in recent years, and this is particularly true for optimizing deep neural networks. In deep neural networks, the gradient followed by a single sample or a batch of samples is employed to save computational resources and escape from saddle points. In 1951, Robbins and Monro published A stochastic approximation method, one of the first modern treatments on stochastic optimization that estimates local gradients with a new batch of samples. And now, stochastic optimization has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this article is to give a self-contained introduction to concepts and mathematical tools in gradient descent and stochastic optimization.
Solution Techniques for Elementary Partial Differential Equations
This book remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). It provides a streamlined, direct approach to developing students' competence in solving PDEs, and offers concise, easily understood explanations and worked examples that enable students to see the techniques in action.
Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval
Lattice Boltzmann methods are a promising approach for the numerical solution of fluid-dynamic problems. We consider the one-dimensional Goldstein-Taylor model with the aim to answer some of the questions concerning the numerical analysis of lattice Boltzmann schemes. Discretizations for the solution of the heat equation are presented for a selection of boundary conditions. Stability and convergence of the solutions are proved by employing energy estimates and explicit Fourier representations.
Mathematical Explorations
Mathematical Explorations can take an infinity offorms, at least as diverse as the explorations of space and time.Unlike explorations of space there is no need for expensiveequipment such as ice-axes, GPS systems or space rockets.Indeed, even the semi-invalid may pursue such adventureswithout leaving their desks, though admittedly it helps to have asmall computer to hand. ( Not essential ). In this further album of research reports Jim Warrenexplores inter alia the Re-Binning of Grouped Statistics; theMathematics of Ancient Pyramid Planning; ways of AssessingComputer Efficiency; the Mechanics of Planetary Flattening;Unusual Aspects of Algebraic Polynomials; and Testing theIntegrity of Decision Logic. Enjoy the work and I hope you find it useful as a starting point.Full algebraic developments and diagrams included
Partial Differential Equations
Designed for a one-semester course, this text provides a bridge between the standard PDE course for undergraduate students in science and engineering and the PDE course for graduate students in mathematics who are pursuing a research career in analysis.
Towards Deep Understanding of Elementary School Mathematics: A Brief Companion for Teacher Educators and Others
The book is intended to serve as a brief companion for mathematical educators of elementary teacher candidates who learn mathematics within a college of education both at the undergraduate and graduate levels. Being informed by mathematics teaching and learning standards of the United States, Australia, Canada, Chile, England, Japan, Korea, Singapore, and South Africa, the book can be used internationally.The teaching methods emphasize the power of visualization, the use of physical materials, and support of computer technology including spreadsheet, Wolfram Alpha, and the Geometer's Sketchpad.The basic ideas include the development of the concepts of number, base-ten system, problem solving and posing, the emergence of fractions in the context of simple real-life activities requiring the extension of whole number arithmetic, decimals, percent, ratio, geoboard geometry, elements of combinatorics, probability and data analysis.The book includes historical aspects of elementary school mathematics. For example, readers would be interested to know that two-sided counters stem from the binary system with its genesis in the 1st millennium BC China of which Leibnitz (17th century) was one of the first notable proponents. The genesis of the base-ten arithmetic is in the Egyptian mathematics of the 4th millennium BC, enriched with the positional notation with the advent of Hindu-Arabic numerals in the 12th century Europe.
Unreasonable Mathematics
Unreasonable mathematics constitutes a very diverse, some would say miscellaneous, congeries of topics: Merely those which excited the curiosity of this author. Notwithstanding, like any mathematics, these areas can be researched with the greatest rigor, as long as we retain a sense of humor and a flexible and workmanlike approach that integrates mathematical, statistical and computational devices in a practical way. Topics touched upon include: Calibrating a Pedometer; Iterating the Theorem of Pythagoras; Fitting Non-Linear Equations; Mineral Crystal Chemistry; The Types of Names that can be Pronounced; and the Quadrature of Irregular Polygons. Enjoy the work and I hope you find it useful as a starting point.Full algebraic derivations and diagrams included.
Fundamentals of Spread Spectrum Modulation
This lecture covers the fundamentals of spread spectrum modulation, which can be defined as any modulation technique that requires a transmission bandwidth much greater than the modulating signal bandwidth, independently of the bandwidth of the modulating signal. After reviewing basic digital modulation techniques, the principal forms of spread spectrum modulation are described. One of the most important components of a spread spectrum system is the spreading code, and several types and their characteristics are described. The most essential operation required at the receiver in a spread spectrum system is the code synchronization, which is usually broken down into the operations of acquisition and tracking. Means for performing these operations are discussed next. Finally, the performance of spread spectrum systems is of fundamental interest and the effect of jamming is considered, both without and with the use of forward error correction coding. The presentation ends with consideration of spread spectrum systems in the presence of other users. For more complete treatments of spread spectrum, the reader is referred to [1, 2, 3].
Automated Reasoning
This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving, Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems.This is an open access book.
Computational Fluid Dynamics 2020
This book presents a collection of works published in a recent Special Issue (SI) entitled "Computational Fluid Dynamics". These works address the development and validation of existent numerical solvers for fluid flow problems and their related applications. They present complex nonlinear, non-Newtonian fluid flow problems that are (in some cases) coupled with heat transfer, phase change, nanofluidic, and magnetohydrodynamics (MHD) phenomena. The applications are wide and range from aerodynamic drag and pressure waves to geometrical blade modification on aerodynamics characteristics of high-pressure gas turbines, hydromagnetic flow arising in porous regions, optimal design of isothermal sloshing vessels to evaluation of (hybrid) nanofluid properties, their control using MHD, and their effect on different modes of heat transfer. Recent advances in numerical, theoretical, and experimental methodologies, as well as new physics, new methodological developments, and their limitations are presented within the current book. Among others, in the presented works, special attention is paid to validating and improving the accuracy of the presented methodologies. This book brings together a collection of inter/multidisciplinary works on many engineering applications in a coherent manner.
Tree generation and enumeration
I believe in passing on knowledge to further generations, inspiring scientists and mathematicians of today and tomorrow. By making books about graph theory, I can make my vision happen and leave a mark in this world, and enrich the minds of curious individuals. The book Tree generation and enumeration: an extended model in graph theory, is about a formal system for tree generation, including such tree types as rooted trees, free trees, series-reduced rooted trees and series-reduced free trees. A link is made between positive integer partitions, natural numbers and trees, and the scope of tree generation is expanded to equations, a new branch in graph theory called advanced vertex edge algebra. With multiple various examples and results, this model, or theory, can be an insightful experience, and can improve intuition and expertise especially in rooted tree generation. The main focus of the book is in tree generation, but there are quite many examples of tree enumeration as well.
How to Predict Future Lottery Results Book 5
This book is designed for all lottery players around the world. The prediction in this book is based on understanding the behaviour and complexity of random systems. Understanding random systems is the best tool we have for predicting future lottery results. This book predicts higher returns when numbers 48 and 49 come out together in your chosen combination. Each combination in this book is affordable to individuals, families playing together as a syndicate, or syndicates set up in the workplace or community. The book includes a selection of lucky bonus combinations which can also be played in various countries around the world, including the UK. You can be the judge of this book by observing each combination over time, or you can choose from combinations 1 to 21 and start playing your chosen combination. You can also choose from one of the seven bonus combinations in this book. The following combination has already come out from the German lottery on Saturday, 15 January 2022: 5 34 42 43 48 49 This is evidence that the researched combinations in this book have the potential to guarantee winnings. After the prediction of two-, three-, and four-number combinations in previous volumes of the series, the author now publishes the prediction of five-number combinations that are affordable to lottery players around the globe.
Mathematical Methods, Modelling and Applications
This volume deals with novel high-quality research results of a wide class of mathematical models with applications in engineering, nature, and social sciences. Analytical and numeric, deterministic and uncertain dimensions are treated. Complex and multidisciplinary models are treated, including novel techniques of obtaining observation data and pattern recognition. Among the examples of treated problems, we encounter problems in engineering, social sciences, physics, biology, and health sciences. The novelty arises with respect to the mathematical treatment of the problem. Mathematical models are built, some of them under a deterministic approach, and other ones taking into account the uncertainty of the data, deriving random models. Several resulting mathematical representations of the models are shown as equations and systems of equations of different types: difference equations, ordinary differential equations, partial differential equations, integral equations, and algebraic equations. Across the chapters of the book, a wide class of approaches can be found to solve the displayed mathematical models, from analytical to numeric techniques, such as finite difference schemes, finite volume methods, iteration schemes, and numerical integration methods.
Threatcasting
Impending technological advances will widen an adversary's attack plane over the next decade. Visualizing what the future will hold, and what new threat vectors could emerge, is a task that traditional planning mechanisms struggle to accomplish given the wide range of potential issues. Understanding and preparing for the future operating environment is the basis of an analytical method known as Threatcasting. It is a method that gives researchers a structured way to envision and plan for risks ten years in the future. Threatcasting uses input from social science, technical research, cultural history, economics, trends, expert interviews, and even a little science fiction to recognize future threats and design potential futures. During this human-centric process, participants brainstorm what actions can be taken to identify, track, disrupt, mitigate, and recover from the possible threats. Specifically, groups explore how to transform the future they desire into reality while avoiding anundesired future. The Threatcasting method also exposes what events could happen that indicate the progression toward an increasingly possible threat landscape. This book begins with an overview of the Threatcasting method with examples and case studies to enhance the academic foundation. Along with end-of-chapter exercises to enhance the reader's understanding of the concepts, there is also a full project where the reader can conduct a mock Threatcasting on the topic of "the next biological public health crisis." The second half of the book is designed as a practitioner's handbook. It has three separate chapters (based on the general size of the Threatcasting group) that walk the reader through how to apply the knowledge from Part I to conduct an actual Threatcasting activity. This book will be useful for a wide audience (from student to practitioner) and will hopefully promote new dialogues across communities and novel developments in the area.
Foundations of Information and Knowledge Systems
This book constitutes the refereed proceedings of the 12th International Symposium on Foundations of Information and Knowledge Systems, FoIKS 2022, held in Helsinki, Finland, in June 2022. The 13 full papers presented were carefully reviewed and selected from 21 submissions. The papers address various topics such as 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.
Fast Track to Differential Equations
The second edition of this successful textbook includes a significantly extended chapter on Climate Change with an analysis of the CO2 budget. It also contains a completely new part on Epidemiology, treating the SEIR-model which describes the behavior and dynamics of epidemics. In particular, COVID-19 with actual data is discussed. This compact introduction to ordinary differential equations and their applications is aimed at anyone who in their studies is confronted voluntarily or involuntarily with this versatile subject. Numerous applications from physics, technology, biomathematics, cosmology, economy and optimization theory are given. Abstract proofs and unnecessary formalism are avoided as far as possible. The focus is on modelling ordinary differential equations of the first and second orders as well as their analytical and numerical solution methods, in which the theory is dealt with briefly before moving on to application examples. In addition, program codes show exemplarily how even more challenging questions can be tackled and represented meaningfully with the help of a computer algebra system. The first chapter deals with the necessary prior knowledge of integral and differential calculus. 103 motivating exercises together with their solutions round off the work. "I am happy to see such a book. It will serve as a support for many students, professors and faculty." Dr. Alessio Figalli, Professor at the ETH Z羹rich and Fields medalist 2018
A Million Nines
This is the sequel to A Million And One Random Digits. It contains 200 pages, each containing 50 lines that look like this: 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999.
Discovering Calculus
Learn Calculus, the easy way! This volume covers both differential and integral calculus, focusinging on conept, technique, and application: concept: a fresh perspective on the key concepts explained step-by-step in a way that students can understandtechnique: a few simple rules is all you need! A Calculus is a simple method for calculating, yet most other texts make it hopelessly confusing. It's actually meant to be easy. We state the key rules clearly and simply, do some examples, and carry on from there. application: this goes beyond any other text to prepare students for advanced courses in mathematics, science, and engineering. This book teaches the art of problem solving, covering a diverse range of interesting real-world applications.This text can be used as a two-semester applied calculus course for engineers, physicisits, and other students of the mathematical sciences. Be sure to check out our page Discovering Calculus on YouTube for free Calculus lectures and worked examples from the author. https: //bit.ly/3RfJ7QN
Stable Categories and Structured Ring Spectra
This comprehensive text focuses on the homotopical technology in use at the forefront of modern algebraic topology. Following on from a standard introductory algebraic topology sequence, it will provide students with a comprehensive background in spectra and structured ring spectra. Each chapter is an extended tutorial by a leader in the field, offering the first really accessible treatment of the modern construction of the stable category in terms of both model categories of point-set diagram spectra and infinity-categories. It is one of the only textbook sources for operadic algebras, structured ring spectra, and Bousfield localization, which are now basic techniques in the field, and the book provides a rare expository treatment of spectral algebraic geometry. Together the contributors -- Emily Riehl, Daniel Dugger, Clark Barwick, Michael A. Mandell, Birgit Richter, Tyler Lawson, and Charles Rezk -- offer a complete, authoritative source to learn the foundations of this vibrant area.
Seriously Fun Maths
In Seriously Fun Maths, Dr Laura Tuohilampi changes the narrative of mathematics education into something fascinating, intriguing and something that touches every human. Based on her cutting-edge research she challenges the outdated ways of motivating students around maths. This engaging book provides teachers with research, resources and activities to teach a lesson a month. The rich activities are accessible to young students and deep enough for secondary students. Even adults! This book will help mathematics educators reflect on their skills of orchestrating mathematical discussions and problem-solving. They will learn how to increase students' engagement in ways that reduce stress-inducing expectations around what a 'good' student in maths can and cannot do. Teachers will improve their grasp of what's important - making mathematics a meaningful experience.Everyone will have serious fun while learning maths!
Advances in Discrete Applied Mathematics and Graph Theory
The present reprint contains twelve papers published in the Special Issue "Advances in Discrete Applied Mathematics and Graph Theory, 2021" of the MDPI Mathematics journal, which cover a wide range of topics connected to the theory and applications of Graph Theory and Discrete Applied Mathematics. The focus of the majority of papers is on recent advances in graph theory and applications in chemical graph theory. In particular, the topics studied include bipartite and multipartite Ramsey numbers, graph coloring and chromatic numbers, several varieties of domination (Double Roman, Quasi-Total Roman, Total 3-Roman) and two graph indices of interest in chemical graph theory (Sombor index, generalized ABC index), as well as hyperspaces of graphs and local inclusive distance vertex irregular graphs.
Mathematics: Its Historical Aspects, Wonders and Beyond
Whenever the topic of mathematics is mentioned, people tend to indicate their weakness in the subject as a result of not having enjoyed its instruction during their school experience. Many students unfortunately do not have very positive experiences when learning mathematics, which can result from teachers who have a tendency 'to teach to the test'. This is truly unfortunate for several reasons. First, basic algebra and geometry, which are taken by almost all students, are not difficult subjects, and all students should be able to master them with the proper motivational instruction. Second, we live in a technical age, and being comfortable with basic mathematics can certainly help you deal with life's daily challenges. Other, less tangible reasons, are the pleasure one can experience from understanding the many intricacies of mathematics and its relation to the real world, experiencing the satisfaction of solving a mathematical problem, and discovering the intrinsic beauty and historical development of many mathematical expressions and relationships. These are some of the experiences that this book is designed to deliver to the reader.The book offers 101 mathematical gems, some of which may require a modicum of high school mathematics and others, just a desire to carefully apply oneself to the ideas. Many folks have spent years encountering mathematical terms, symbols, relationships and other esoteric expressions. Their origins and their meanings may never have been revealed, such as the symbols +, -, =, π. ꝏ, √, ∑, and many others. This book provides a delightful insight into the origin of mathematical symbols and popular theorems such as the Pythagorean Theorem and the Fibonacci Sequence, common mathematical mistakes and curiosities, intriguing number relationships, and some of the different mathematical procedures in various countries. The book uses a historical and cultural approach to the topics, which enhances the subject matter and greatly adds to its appeal. The mathematical material can, therefore, be more fully appreciated and understood by anyone who has a curiosity and interest in mathematics, especially if in their past experience they were expected to simply accept ideas and concepts without a clear understanding of their origins and meaning. It is hoped that this will cast a new and positive picture of mathematics and provide a more favorable impression of this most important subject and be a different experience than what many may have previously encountered. It is also our wish that some of the fascination and beauty of mathematics shines through in these presentations.
Mathematics: Its Historical Aspects, Wonders and Beyond
Whenever the topic of mathematics is mentioned, people tend to indicate their weakness in the subject as a result of not having enjoyed its instruction during their school experience. Many students unfortunately do not have very positive experiences when learning mathematics, which can result from teachers who have a tendency 'to teach to the test'. This is truly unfortunate for several reasons. First, basic algebra and geometry, which are taken by almost all students, are not difficult subjects, and all students should be able to master them with the proper motivational instruction. Second, we live in a technical age, and being comfortable with basic mathematics can certainly help you deal with life's daily challenges. Other, less tangible reasons, are the pleasure one can experience from understanding the many intricacies of mathematics and its relation to the real world, experiencing the satisfaction of solving a mathematical problem, and discovering the intrinsic beauty and historical development of many mathematical expressions and relationships. These are some of the experiences that this book is designed to deliver to the reader.The book offers 101 mathematical gems, some of which may require a modicum of high school mathematics and others, just a desire to carefully apply oneself to the ideas. Many folks have spent years encountering mathematical terms, symbols, relationships and other esoteric expressions. Their origins and their meanings may never have been revealed, such as the symbols +, -, =, π. ꝏ, √, ∑, and many others. This book provides a delightful insight into the origin of mathematical symbols and popular theorems such as the Pythagorean Theorem and the Fibonacci Sequence, common mathematical mistakes and curiosities, intriguing number relationships, and some of the different mathematical procedures in various countries. The book uses a historical and cultural approach to the topics, which enhances the subject matter and greatly adds to its appeal. The mathematical material can, therefore, be more fully appreciated and understood by anyone who has a curiosity and interest in mathematics, especially if in their past experience they were expected to simply accept ideas and concepts without a clear understanding of their origins and meaning. It is hoped that this will cast a new and positive picture of mathematics and provide a more favorable impression of this most important subject and be a different experience than what many may have previously encountered. It is also our wish that some of the fascination and beauty of mathematics shines through in these presentations.
The Art of Mathematics - Take Two
Lovers of mathematics, young and old, professional and amateur, will enjoy this book. It is mathematics with fun: a collection of attractive problems that will delight and test readers. Many of the problems are drawn from the large number that have entertained and challenged students, guests and colleagues over the years during afternoon tea. The problems have their roots in many areas of mathematics. They vary greatly in difficulty: some are very easy, but most are far from trivial, and quite a few rather hard. Many provide substantial and surprising results that form the tip of an iceberg, providing an introduction to an important topic. To enjoy and appreciate the problems, readers should browse the book choosing one that looks particularly enticing, and think about it on and off for a while before resorting to the hint or the solution. Follow threads for an enjoyable and enriching journey through mathematics.
Mathematical Olympiad in China (2015-2016): Problems and Solutions
In China, lots of excellent maths students takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results -- they have always been among the top 3, in fact in the first place most of the time.The authors of this book are coaches of the China national team. They are Xiong Bin, Yao Yijun, Qu Zhenhua, et al. The translator of this book is Chen Xiaomin.The materials of this book come from a series of two books (in Chinese) on Forward to IMO: A Collection of Mathematical Olympiad Problems (2015-2016). It is a collection of problems and solutions of the major mathematical competitions in China. It provides a glimpse of how the China national team is selected and formed.
Variational Convergence and Stochastic Homogenization of Nonlinear Reaction-Diffusion Problems
A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or population dynamics, they describe the density of some populations or species. In this book the state variable is a concentration, or a density according to the cases. The reaction function may be complex and include time delays terms that model various situations involving maturation periods, resource regeneration times, or incubation periods. The dynamics may occur in heterogeneous media and may depend upon a small or large parameter, as well as the reaction term. From a purely formal perspective, these parameters are indexed by n. Therefore, reaction-diffusion equations give rise to sequences of Cauchy problems.The first part of the book is devoted to the convergence of these sequences in a sense made precise in the book. The second part is dedicated to the specific case when the reaction-diffusion problems depend on a small parameter ∊ₙ intended to tend towards 0. This parameter accounts for the size of small spatial and randomly distributed heterogeneities. The convergence results obtained in the first part, with additionally some probabilistic tools, are applied to this specific situation. The limit problems are illustrated through biological invasion, food-limited or prey-predator models where the interplay between environment heterogeneities in the individual evolution of propagation species plays an essential role. They provide a description in terms of deterministic and homogeneous reaction-diffusion equations, for which numerical schemes are possible.
