Matematikkens fundament

Taking an amusing and digestible look at the usually dry world of probability and statistics, this is the ultimate guide to how you can incorporate them into everyday life, from one of the world's most sought-after experts in game theory.This book reveals how statistics and probability are fundamental to our everyday life – from advertisements to public-opinion polls, weather forecasts to government policies, scientific research to stock market information. Haim Shapira then presents a myriad of anecdotes, riddles, case studies and practical exercises in his trademark witty voice to guide the reader through the importance of statistics and probability in everyday life. Some examples include:making sense of NBA stats – discover who is the greatest scorer of all timea beginner's guide to gambling successfullywhy events of very low probability have happened, are happening and will happenwhat role stats has to play in flat-earth conspiracy argumentsthe likelihood of winning the lotterymisconceptions about statistical findings surrounding COVID-19what "beyond reasonable doubt" really meansa case of misunderstood probabilities in the Sally Clarke and OJ Simpson trialsWith easy-to-follow explanations, tables and graphs of all the maths behind the statistics – averages, standard deviation, percentiles, logarithmic scales, correlation coefficient – this book provides everything you need to know to determine your options and calculate your chance of success, thereby learning to make better decisions.

Math Mammoth Grade 6 Tests & Cumulative Reviews (Canadian version) contains the end-of-chapter tests, the end-of-year test, and cumulative reviews lessons to match Math Mammoth Grade 6 curriculum (Canadian version).

Math Mammoth Grade 6-A worktext (Canadian version) is the first student book for sixth grade, and part of the Math Mammoth Grade 6 complete curriculum. In this book, students encounter the beginnings of algebra, learning about algebraic expressions, one-variable equations and inequalities, integers, and ratios. We also review and deepen the students' understanding of decimals, and study ratios and percent as new topics for 6th grade. The year starts out with a review of the four operations with whole numbers (including long division), place value, and rounding. Students are also introduced to exponents and do some problem solving.Chapter 2 starts the study of algebra topics, delving first into expressions and equations. Students practice writing expressions in many different ways, and use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. We also study briefly inequalities and using two variables. Chapter 3 has to do with decimals. This is a long chapter, as we review all of decimal arithmetic, just using more decimal digits than in 5th grade. Students also convert measuring units in this chapter. Ratios is a new topic (chapter 4). Students are already familiar with finding fractional parts from earlier grades, and now it is time to advance that knowledge into the study of ratios, which arise naturally from dividing a quantity into many equal parts. We study such topics as rates, unit rates, equivalent ratios, and problem solving using bar models.Percent (chapter 5) is an important topic to understand thoroughly, because of its many applications in real life. The goal of this chapter is to develop a basic understanding of percent, to see percentages as decimals, and to learn to calculate discounts. This curriculum is essentially the same as the U.S. version of Math Mammoth, only customized for the Canadian audience in these aspects:The curriculum uses the metric measurement units. Since Canadians do use imperial units, such as inches and pounds, in some contexts, the curriculum does mention them, but not often.The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.Page (paper) size is Letter.The US version of the curriculum is aligned to the Common Core Standards, which means this curriculum may not be properly aligned to the sixth grade standards in any Canadian province. However, you can probably find material for any missing topics in the neighbouring grade levels of Math Mammoth materials.Available separately, Math Mammoth Grade 6-B worktext covers the second half of 6th grade math. Also available are the answer keys and a book containing cumulative reviews and chapter tests.

This book includes answers for the Math Mammoth Grade 6-A and 6-B student worktexts (Canadian version), for all the chapter tests and end-of-year test, and for the cumulative reviews for grade 6. The other parts of the 6th grade curriculum (the 6-A and 6-B worktexts and the cumulative reviews & tests book) may be purchased separately.

Math Mammoth Grade 6-B worktext (Canadian version) is the second student book for sixth grade, and part of the Math Mammoth Grade 6 complete curriculum. This book contains chapters 6-10 of the curriculum.In chapter 6, we first review prime factorization, and then study the greatest common factor and the least common multiple.Chapter 7 first presents a thorough review of fraction operations from 5th grade (addition, subtraction, and multiplication). The topic of focus in the chapter is fraction division. Students also do some problem solving with fractions.In chapter 8, students are introduced to integers. They plot points in all four quadrants of the coordinate plane and learn to add and subtract with negative numbers. Multiplication and division of integers are studied in 7th grade.In geometry (chapter 9), the focus is on the area of polygons. This is studied in a logical progression: first, the area of right triangles, then the area of parallelograms, then, the area of triangles, and lastly the area of polygons. We also review some topics from earlier grades (quadrilaterals, perimeter, basic drawing). Other major topics in this chapter are calculating surface area of some solids using nets, and volume of rectangular prisms with fractional edge lengths.Lastly, in chapter 10, students study statistics. The focus idea is that of a statistical distribution. Students learn about measures of center and measures of variability, and how to summarize distributions using those. They learn how to make dot plots, histograms, boxplots, and stem-and-leaf plots.This curriculum is essentially the same as the U.S. version of Math Mammoth, only customized for the Canadian audience in these aspects:The curriculum uses the metric measurement units. Since Canadians do use imperial units, such as inches and pounds, in some contexts, the curriculum does mention them, but not often.The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.Page (paper) size is Letter.The US version of the curriculum is aligned to the Common Core Standards, which means this curriculum may not be properly aligned to the sixth grade standards in any Canadian province. However, you can probably find material for any missing topics in the neighbouring grade levels of Math Mammoth materials.Available separately, Math Mammoth Grade 6-A worktext covers the first half of 6th grade math. Also available are the answer keys and a book containing cumulative reviews and chapter tests.

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.

"Clinical Chemistry Instrumentation Principles and Essentials" is a concise textbook designed for 2nd-year undergraduate biomedical engineering students in Iraqi universities. It follows an objective-based approach, ensuring clear learning outcomes for each chapter. Question sheets aligned with Bloom's Taxonomy aid comprehension assessment. The initial chapters focus on lab safety, emphasizing the importance of a secure environment for accurate clinical chemistry analysis. Students learn safety protocols and quality control principles, enhancing their skills through practical examples. The book also covers spectrum instruments and their applications, providing a solid theoretical foundation. This engaging learning experience empowers students to apply clinical chemistry concepts effectively. With objective-based chapters and question sheets, it fosters a deep understanding of core principles, preparing students for successful academic progress and future careers in biomedical engineering and clinical chemistry instrumentation.

The Game of Logic is a book written by Lewis Carroll, the author best known for his famous works such as Alice's Adventures in Wonderland and Through the Looking-Glass. The Game of Logic is a treatise on logic and logical reasoning, written in the form of a game. The book was first published in 1887 and is still considered a valuable resource for those interested in logic and mathematics.In The Game of Logic, Carroll presents a series of logical problems and puzzles that are designed to be solved using a system he calls "diagrams." These diagrams are a visual tool that helps the reader to understand the relationships between different logical statements and propositions.Overall, The Game of Logic is a fascinating and engaging exploration of logical reasoning and is highly recommended for anyone interested in mathematics, philosophy or logic.

This book presents a new approach to computational musicology in which music becomes a computational entity based on human cognition, allowing us to calculate music like numbers. Does music have semantics? Can the meaning of music be revealed using symbols and described using language? The authors seek to answer these questions in order to reveal the essence of music. Chapter 1 addresses a very fundamental point, the meaning of music, while referring to semiotics, gestalt, Schenkerian analysis and cognitive reality. Chapter 2 considers why the 12-tone equal temperament came to be prevalent. This chapter serves as an introduction to the mathematical definition of harmony, which concerns the ratios of frequency in tonic waves. Chapter 3, "e;Music and Language,"e; explains the fundamentals of grammar theory and the compositionality principle, which states that the semantics of a sentence can be composed in parallel to its syntactic structure. In turn, Chapter 4 explains the most prevalent score notation - the Berklee method, which originated at the Berklee School of Music in Boston - from a different point of view, namely, symbolic computation based on music theory. Chapters 5 and 6 introduce readers to two important theories, the implication-realization model and generative theory of tonal music (GTTM), and explain the essence of these theories, also from a computational standpoint. The authors seek to reinterpret these theories, aiming at their formalization and implementation on a computer. Chapter 7 presents the outcomes of this attempt, describing the framework that the authors have developed, in which music is formalized and becomes computable. Chapters 8 and 9 are devoted to GTTM analyzers and the applications of GTTM. Lastly, Chapter 10 discusses the future of music in connection with computation and artificial intelligence.This book is intended both for general readers who are interested in music, and scientists whose research focuses on music information processing. In order to make the content as accessible as possible, each chapter is self-contained.

This book includes answers for Math Mammoth Grade 3-A and 3-B student worktexts (Canadian version), for all of the chapter tests, and for the cumulative reviews. The other parts of the curriculum may be purchased separately at Lulu.

This third volume of the book series shows R-calculus is a Gentzen-typed deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM postulates and the DP postulates. In this book, R-calculus is taken as Tableau-based/sequent-based/multisequent-based to preserve the satisfiability of the Theory/sequent/multisequent to revise, or sequent-based, to preserve the satisfiability of the sequent to revise. The R-calculi for Post and three-valued logic is given.  This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. 

Math Mammoth Grade 3 Tests and Cumulative Reviews (Canadian Version) contains the chapter tests, end-of-year test, and cumulative revision worksheets for Math Mammoth grade 3 curriculum. It does not contain answers; the answer key book may be purchased separately at Lulu.

Math Mammoth Grade 3-B Worktext (Canadian version) is the student book for the second half of third grade math. In this part B, the main areas of study are: place value (4-digit numbers)the concept of division and basic division facts; geometry (area and perimeter); measurement; fractions. The curriculum is essentially the same as the U.S. version of Math Mammoth Grade 3, only customized for the Canadian audience in these aspects:The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.Page (paper) size is Letter.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental math and number sense.It requires very little teacher preparation, which is a big help to most parents. The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations and further practice.For multiplication tables and division facts, you can use our online practice program (free).A companion to this book, Math Mammoth Grade 3-A worktext, covers the first half of 3rd grade math (available separately).

Math Mammoth Grade 3-A worktext (Light Blue Series) is the student book for the first half of third grade math. In this part A, the main areas of study are: addition and subtraction within 1,000 (including mental math); the concept of multiplication; the multiplication tables; telling time and working with time intervals; counting coins and solving problems related to money.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental math and number sense.It requires very little teacher preparation, which is a big help to most parents. The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations and further practice.For multiplication tables and division facts, you can use our online practice program (free).This curriculum is essentially the same as the U.S. version of Math Mammoth Grade 3, only customized for the Canadian audience in these aspects:The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.The currency used in the chapter on money is the Canadian dollar.Page (paper) size is Letter.

CSP-Rules is a generic pattern-based (or rule-based) solver of finite binary Constraint Satisfaction Problems (CSPs). This software is available on GitHub and it includes fully developed applications to various logic puzzles such as Sudoku, Latin Squares (allowing their Pandiagonal variant), Futoshiki, Kakuro, Numbrix, Hidato, Slitherlink and Map Colouring.CSP-Rules produces not only the solution to a CSP (as all the existing CSP solvers) but also a full "resolution path", i.e. a detailed justification for each step; this is a full mathematical proof of the solution. CSP-Rules and the present book are closely related to the author's book "Pattern Based Constraint Satisfaction and Logic Puzzles", where the fundamental theory underlying the approach is presented.This book includes an extended version of the original "Basic User Manual". But it also introduces new powerful generic rules (OR-chains) for taking advantage of almost-contradictory patterns. In particular, it applies these chains to the analysis of a newly discovered pattern (tridagon) and to the classification of a large database of extreme Sudoku puzzles that have it. It also adds the analyses of 630 impossible patterns and explains how to deal with such a large number of patterns. It shows that a handful of them provide almost the same resolution power as the full set. The long final two chapters are written as research notebooks on these very advanced topics.

This book is dedicated to V.A. Yankov's seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic.The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov's results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics.The book also contains an exposition of Yankov's revolutionary approach to constructive proof theory. The editors also include Yankov's contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.

Originally published in 1748, this comprehensive treatise on logic was designed to be a primer for young scholars entering the fields of philosophy and mathematics. With its clear and concise explanations of the principles of reasoning and argumentation, 'The Elements of Logic' remains a valuable resource for anyone seeking to enhance their critical thinking skills.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This classic text, written by philosopher and mathematician William Thomson, presents a systematic exposition of the laws of thought and their role in science, logic, and philosophy. The book is still widely used in philosophy and mathematics courses today.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.