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| what is the law of detachment math: The Joy of Finite Mathematics Chris P. Tsokos, Rebecca D. Wooten, 2015-10-27 The Joy of Finite Mathematics: The Language and Art of Math teaches students basic finite mathematics through a foundational understanding of the underlying symbolic language and its many dialects, including logic, set theory, combinatorics (counting), probability, statistics, geometry, algebra, and finance. Through detailed explanations of the concepts, step-by-step procedures, and clearly defined formulae, readers learn to apply math to subjects ranging from reason (logic) to finance (personal budget), making this interactive and engaging book appropriate for non-science, undergraduate students in the liberal arts, social sciences, finance, economics, and other humanities areas. The authors utilize important historical facts, pose interesting and relevant questions, and reference real-world events to challenge, inspire, and motivate students to learn the subject of mathematical thinking and its relevance. The book is based on the authors' experience teaching Liberal Arts Math and other courses to students of various backgrounds and majors, and is also appropriate for preparing students for Florida's CLAST exam or similar core requirements. - Highlighted definitions, rules, methods, and procedures, and abundant tables, diagrams, and graphs, clearly illustrate important concepts and methods - Provides end-of-chapter vocabulary and concept reviews, as well as robust review exercises and a practice test - Contains information relevant to a wide range of topics, including symbolic language, contemporary math, liberal arts math, social sciences math, basic math for finance, math for humanities, probability, and the C.L.A.S.T. exam - Optional advanced sections and challenging problems are included for use at the discretion of the instructor - Online resources include PowerPoint Presentations for instructors and a useful student manual |
| what is the law of detachment math: Encyclopedia of Mathematics Education Louise Grinstein, Sally I. Lipsey, 2001-03-15 This single-volume reference is designed for readers and researchers investigating national and international aspects of mathematics education at the elementary, secondary, and post-secondary levels. It contains more than 400 entries, arranged alphabetically by headings of greatest pertinence to mathematics education. The scope is comprehensive, encompassing all major areas of mathematics education, including assessment, content and instructional procedures, curriculum, enrichment, international comparisons, and psychology of learning and instruction. |
| what is the law of detachment math: Applied Discrete Structures Ken Levasseur, Al Doerr, 2012-02-25 ''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the favorite examples that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''-- |
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| what is the law of detachment math: Finite Mathematics Michael Sullivan, 2010-03-29 This text is an unbound, binder-ready edition. Sullivan's Finite Mathematics: An Applied Approach, Binder Ready Version 11th Edition continues its rich tradition of demonstrating how mathematics applies to various fields of study through its engaging writing style and relevant applications. The purpose of the text is to provide a survey of mathematical analysis techniques used in the working world while also giving students practice in analytical thinking and the application of knowledge to their chosen fields of study. This edition is packed with real data and real-life applications to business, economics, and social and life sciences--thereby giving your students the confidence they need succeed in the classroom and beyond. WileyPLUS sold separately from text. |
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| what is the law of detachment math: Discrete Mathematics with Proof Eric Gossett, 2009-06-22 A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distribution Important examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theorem Extensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercises Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics. |
| what is the law of detachment math: A Survey of Finite Mathematics Marvin Marcus, 1993-01-01 Outstanding undergraduate text, suitable for non-mathematics majors, introduces fundamentals of linear algebra and theory of convex sets. Includes 150 worked examples and over 1,200 exercises. Answers to selected exercises. Bibliography. 1969 edition. |
| what is the law of detachment math: The Math Book Nancy Myers, 1975 |
| what is the law of detachment math: Becoming a Reflective Mathematics Teacher Alice F. Artzt, Eleanor Armour-Thomas, Frances R. Curcio, Theresa J. Gurl, Mara Markinson, 2015-06-05 Ideal for preservice mathematics teachers who are taking methods courses or are student teaching, this research-based, activity-oriented guide offers a highly effective framework for teacher reflection and self-assessment. Highlighting inquiry-based, learner-centered teaching and grounded in a cognitive perspective, Becoming a Reflective Teacher of Mathematics, Third Edition features: Detailed observation instruments for observing other teachers Reflective activities that provide a structure for beginning teachers to think about their teaching Guidelines and instruments for supervisors to use when observing, conferencing with, and assessing beginning or student teachers The Third Edition of Becoming a Reflective Teacher of Mathematics is aligned with the latest standards for teaching mathematics including the Common Core State Standards-Mathematics, and the latest assessments for mathematics teacher certification which place a high priority on reflective practice. Thoroughly revised and updated throughout, the Third Edition continues to provide preservice and in-service mathematics teachers with practical ideas for developing and honing reflective and self-analytical skills needed to advance and improve instruction. |
| what is the law of detachment math: Discovering Geometry Michael Serra, Key Curriculum Press Staff, 2003-03-01 |
| what is the law of detachment math: The Nature and Growth of Modern Mathematics Edna Ernestine Kramer, 1982 Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful ideals of Dedekind and Emmy Noether; and the importance of purifying mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail. |
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| what is the law of detachment math: Mathematics, the Alphabet of Science Margaret F. Willerding, Ruth A. Hayward, 1972 This book is intended for liberal arts students and other students who wish to know what mathematics is about, but who have no desire to be mathematicians. The presentation is designed so that even persons who have little or no high school mathematics, or those whose mathematics study is so far in the past that it is completely forgotten, will have no trouble following the explanations. |
| what is the law of detachment math: Principia Mathematica Alfred North Whitehead, Bertrand Russell, 1927 The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century. |
| what is the law of detachment math: Sequential Mathematics Lawrence S. Leff, 1988 |
| what is the law of detachment math: Mathematics All Around Thomas L. Pirnot, 2001 * Problem-solving principles and strategies are introduced in chapter one and are used consistently throughout the text. * Of Further Interest sections appear at the end the chapter, and cover current topics that are exciting for students but are not typically part of the standard curriculum. * Statement Headings provide the students with a clear idea of the concept being discussed and are useful when reviewing for exams. * Applications motivate the discussion of the mathematics and increase student interest in the material. * Quiz Yourself questions are found throughout each section, and allow students to gauge their level of understanding before moving on to the next concept. * Some Good Advice is a feature that provides students with timely hints, tips, cautions and warnings about the material being covered. * Highlights are boxed features that consist of historical notes or biographical vignettes, uses of technology, and interesting applications. |
| what is the law of detachment math: Mathematics for Elementary Teachers Albert B. Bennett, Leonard T. Nelson, 2001 Emphasizing conceptual understanding through the use of models and visuals, this text helps students connect ideas and concepts while providing them with useful methods for teaching math to elementary school children. Mathematics for Elementary Teachers: A Conceptual Approach addresses the NCTM standards by encouraging active student participation through features such as Math Activities and Math Investigations. The Math Investigations now appear on the companion website. |
| what is the law of detachment math: Mathematics for Elementary Teachers Mhhe, Albert B. Bennett, Ted Nelson, 2003-04 |
| what is the law of detachment math: A Spiral Workbook for Discrete Mathematics Harris Kwong, 2015-11-06 A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills. |
| what is the law of detachment math: Mathematics Joseph M. Scandura, 1971 Booklet inserted: Answers to even-numbered exercises for Mathematics, comcnrete behavioral foundatin / Joseph M. Scandura, Rev. ed., harper & Row, 1971. |
| what is the law of detachment math: Mathematics B Edward P. Keenan, Ann Xavier Gantert, Isidore Dressler, 2001-12-19 This paperback textbook provides coverage in the NY State Core Curriculum Key Ideas and Performance Indicators. |
| what is the law of detachment math: Experiencing Mathematics James R. Breunlin, Timothy A. Kasper, Michelle Kolet, 2006 Experiencing Mathematics: Activities to Engage the High School Student is the result of the collaborative effort of nine Adolescent Young Adult (AYA) National Board Certified Teachers in mathematics. This teacher edition is a compilation of successful activities that prompt high school students to explore, conjecture, and reflect on their mathematical adventures--thus experience mathematics. The relevant nature of the activities will motivate students to pursue their investigations with vigor and take the intellectual risk necessary to construct knowledge and improve problem-solving competence. This edition will educate teachers regarding tenets of cognitive science, motivation theory, and the NCTM/NBCT standards. It will dispel the myth that the crowded curriculum does not have room for such activities and, in fact, will convince teachers that using such activities increases teacher and student motivation and achievement. The resources provide detailed instructions for each activity, along with student prompts and reflective questions for the teacher. |
| what is the law of detachment math: A Problem Solving Approach to Mathematics for Elementary School Teachers Rick Billstein, Shlomo Libeskind, Johnny W. Lott, 1993 A VARIETY OF APPROACHES TO TEACHING MATH AND MATHEMATICAL REASONING. |
| what is the law of detachment math: The Nature of Modern Mathematics Karl J. Smith, 1973 |
| what is the law of detachment math: Math in Society David Lippman, 2022-07-14 Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course. This book is an open textbook; it can be read free online at http://www.opentextbookstore.com/mathinsociety/. Editable versions of the chapters are available as well. |
| what is the law of detachment math: Elements of Discrete Mathematics Ronald E. Prather, 1986 |
| what is the law of detachment math: Metamath: A Computer Language for Mathematical Proofs Norman Megill, David A. Wheeler, 2019 Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor. While simple, it is also powerful; the Metamath Proof Explorer (MPE) database has over 23,000 proven theorems and is one of the top systems in the Formalizing 100 Theorems challenge. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database. |
| what is the law of detachment math: Advanced Mathematical Methods Francesco Mainardi, Andrea Giusti, 2020-02-05 The many technical and computational problems that appear to be constantly emerging in various branches of physics and engineering beg for a more detailed understanding of the fundamental mathematics that serves as the cornerstone of our way of understanding natural phenomena. The purpose of this Special Issue was to establish a brief collection of carefully selected articles authored by promising young scientists and the world's leading experts in pure and applied mathematics, highlighting the state-of-the-art of the various research lines focusing on the study of analytical and numerical mathematical methods for pure and applied sciences. |
| what is the law of detachment math: Mathematics for Sustainable Industry Ahmad Fadillah Embong, Zaitul Marlizawati Zainuddin, Ani Shabri, Fatin Nadiah Mohamed Yussof, 2025-05-29 This volume gathers selected, peer-reviewed contributions presented at the 5th International Seminar on Mathematics in Industry – ISMI2024, held on September 9-11, 2024 in Kuala Lumpur, Malaysia. Articles in this volume touch on fields such as applied mathematics, applied probability theory and stochastic modeling, statistical modeling, operations research, biomathematics, optimization, inventory management, supply chain, and computational mathematics, all with an emphasis on solutions to real-world problems. Many of the studies contained here closely relate to the United Nations’ Sustainable Development Goals, namely SDG 9 (Industry) and SDG 3 (Health), potentially inspiring practitioners and scholars to deploy these findings and pursue similar avenues of research. Since its inception in 2013, ISMI has been organized by the Centre for Industrial and Applied Mathematics (UTM-CIAM) and the Department of Mathematical Sciences, Universiti Teknologi Malaysia (UTM) with the aims of disseminating knowledge, sharing experiences in research on various aspects of industrial mathematics and statistics and fostering collaboration among academia, government agencies, industry, and community. |
| what is the law of detachment math: 2000 Solved Problems in Discrete Mathematics Seymour Lipschutz, Marc Lipson, 1992 Master discrete mathematics with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, use this book to: Brush up before tests Study quickly and more effectively Learn the best strategies for solving tough problems in step-by-step detail Review what you've learned in class by solving thousands of relevant problems that test your skill Compatible with any classroom text, Schaum's Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to remember--fast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams. Inside you will find: 2,000 solved problems with complete solutions--the largest selection of solved problems yet published on this subject An index to help you quickly locate the types of problems you want to solve Problems like those you'll find on your exams Techniques for choosing the correct approach to problems Guidance toward the quickest, most efficient solutions If you want top grades and thorough understanding of discrete mathematics, this powerful study tool is the best tutor you can have! |
| what is the law of detachment math: Glencoe Math, Course 1, Student Edition McGraw-Hill Education, 2014-06-06 The Glencoe Math Student Edition is an interactive text that engages students and assist with learning and organization. It personalizes the learning experience for every student. The write-in text, 3-hole punched, perfed pages allow students to organize while they are learning. |
| what is the law of detachment math: Introduction to Modern Mathematics Helena Rasiowa, 2014-05-12 Introduction to Modern Mathematics focuses on the operations, principles, and methodologies involved in modern mathematics. The monograph first tackles the algebra of sets, natural numbers, and functions. Discussions focus on groups of transformations, composition of functions, an axiomatic approach to natural numbers, intersection of sets, axioms of the algebra of sets, fields of sets, prepositional functions of one variable, and difference of sets. The text then takes a look at generalized unions and intersections of sets, Cartesian products of sets, and equivalence relations. The book ponders on powers of sets, ordered sets, and linearly ordered sets. Topics include isomorphism of linearly ordered sets, dense linear ordering, maximal and minimal elements, quasi-ordering relations, inequalities for cardinal numbers, sets of the power of the continuum, and Cantor's theorem. The manuscript then examines elementary concepts of abstract algebras, functional calculus and its applications in mathematical proofs, and propositional calculus and its applications in mathematical proofs. The publication is a valuable reference for mathematicians and researchers interested in modern mathematics. |
| what is the law of detachment math: Test Bank to Accompany Finite Mathematics Mizrahi, 1999-11 |
| what is the law of detachment math: The World of Mathematics James Roy Newman, 2000-09-18 Presents 33 essays on such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the mathematical way of thinking, the unreasonableness of mathematics, and mathematics as an art. A reprint of volume 3 of the four-volume edition originally published by Simon and Schuster in 1956. Annotation c. Book News, Inc., Portland, OR (booknews.com). |
| what is the law of detachment math: Mathematical Logic in Asia S. S. Goncharov, Rod G. Downey, H. Ono, 2006 This volume is devoted to the main areas of mathematical logic and applications to computer science. There are articles on weakly o-minimal theories, algorithmic complexity of relations, models within the computable model theory, hierarchies of randomness tests, computable numberings, and complexity problems of minimal unsatisfiable formulas. The problems of characterization of the deduction-detachment theorem, o 1 -induction, completeness of Leoniewski''s systems, and reduction calculus for the satisfiability problem are also discussed. The coverage includes the answer to Kanovei''s question about the upper bound for the complexity of equivalence relations by convergence at infinity for continuous functions. The volume also gives some applications to computer science such as solving the problems of inductive interference of languages from the full collection of positive examples and some negative data, the effects of random negative data, methods of formal specification and verification on the basis of model theory and multiple-valued logics, interval fuzzy algebraic systems, the problems of information exchange among agents on the base topological structures, and the predictions provided by inductive theories. Sample Chapter(s). Chapter 1: Another Characterization of the Deduction-Detachment Theorem (535 KB). Contents: Another Characterization of the Deduction-Detachment Theorem (S V Babyonyshev); On Behavior of 2-Formulas in Weakly o-Minimal Theories (B S Baizhanov & B Sh Kulpeshov); Arithmetic Turing Degrees and Categorical Theories of Computable Models (E Fokina); Negative Data in Learning Languages (S Jain & E Kinber); Effective Cardinals in the Nonstandard Universe (V Kanovei & M Reeken); Model-Theoretic Methods of Analysis of Computer Arithmetic (S P Kovalyov); The Functional Completeness of Leoniewski''s Systems (F Lepage); Hierarchies of Randomness Tests (J Reimann & F Stephan); Intransitive Linear Temporal Logic Based on Integer Numbers, Decidability, Admissible Logical Consecutions (V V Rybakov); The Logic of Prediction (E Vityaev); Conceptual Semantic Systems Theory and Applications (K E Wolff); Complexity Results on Minimal Unsatisfiable Formulas (X Zhao); and other papers. Readership: Researchers in mathematical logic and algebra, computer scientists in artificial intelligence and fuzzy logic. |
| what is the law of detachment math: After the Flood A. H. Hay, 2016-03-01 When disaster strikes, the amount of planning done ahead of time will dictate how quickly a system can recover and return to normal. Even the largest and most complex organizations can experience upset and disruption, whether by flood, fire, power failure, earthquake, or anything else that life can throw at us. Resiliency, like any other performance measure, can be designed into businesses, institutions, communities, cities, and even countries. This is a book about implementing that planning before it’s too late, and about learning to pick up and get going after a fall. Join Marianne as she explores the world of modern infrastructure technology within the context of a job with real threats, exciting opportunities, and throbbing headaches. With her, we learn what resilience means to a city or company, how to assess hazards and plan for continuity, and how effective system design can reduce the impact of disasters. From the basic concepts and terms to how they fit into real systems, After the Flood is a clear and engaging introduction to resilience planning for students, industry practitioners, or anyone interested in infrastructure, business continuity, and emergency and risk management. |
| what is the law of detachment math: The Little Blue Reasoning Book Brandon Royal, 2013-01-01 The Little Blue Reasoning Book helps readers build essential critical thinking, creative thinking, and decision-making skills and is suitable for the everyday student, test-prep candidate, or working professional in need of a refresher course. Interwoven within the book's five chapters -Perception & Mindset, Decision Making, Creative Thinking, Analyzing Arguments, and Mastering Logic - are 50 reasoning tips that summarize the common themes behind classic reasoning problems and situations. Appendixes contain summaries of fallacious reasoning, analogies, trade-offs, and a review of critical reading. |
| what is the law of detachment math: Introduction to Logic Alfred Tarski, 2013-07-04 This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout. |
| what is the law of detachment math: An Introduction to Mathematics Alfred North Whitehead, 1958 This distinguished little 'book' is a brisk introduction to a series of mathematical concepts, a history of their development, and a concise summary of how the contemporary reader may use them.- Publisher |
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