Advertisement
| 2 2 skills practice statements conditionals and biconditionals: How to Prove It Daniel J. Velleman, 2006-01-16 Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians. |
| 2 2 skills practice statements conditionals and biconditionals: Proofs and Fundamentals Ethan D. Bloch, 2011-02-15 “Proofs and Fundamentals: A First Course in Abstract Mathematics” 2nd edition is designed as a transition course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. The text serves as a bridge between computational courses such as calculus, and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra and real analysis. This 3-part work carefully balances Proofs, Fundamentals, and Extras. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. New to the second edition: 1) A new section about the foundations of set theory has been added at the end of the chapter about sets. This section includes a very informal discussion of the Zermelo– Fraenkel Axioms for set theory. We do not make use of these axioms subsequently in the text, but it is valuable for any mathematician to be aware that an axiomatic basis for set theory exists. Also included in this new section is a slightly expanded discussion of the Axiom of Choice, and new discussion of Zorn's Lemma, which is used later in the text. 2) The chapter about the cardinality of sets has been rearranged and expanded. There is a new section at the start of the chapter that summarizes various properties of the set of natural numbers; these properties play important roles subsequently in the chapter. The sections on induction and recursion have been slightly expanded, and have been relocated to an earlier place in the chapter (following the new section), both because they are more concrete than the material found in the other sections of the chapter, and because ideas from the sections on induction and recursion are used in the other sections. Next comes the section on the cardinality of sets (which was originally the first section of the chapter); this section gained proofs of the Schroeder–Bernstein theorem and the Trichotomy Law for Sets, and lost most of the material about finite and countable sets, which has now been moved to a new section devoted to those two types of sets. The chapter concludes with the section on the cardinality of the number systems. 3) The chapter on the construction of the natural numbers, integers and rational numbers from the Peano Postulates was removed entirely. That material was originally included to provide the needed background about the number systems, particularly for the discussion of the cardinality of sets, but it was always somewhat out of place given the level and scope of this text. The background material about the natural numbers needed for the cardinality of sets has now been summarized in a new section at the start of that chapter, making the chapter both self-contained and more accessible than it previously was. 4) The section on families of sets has been thoroughly revised, with the focus being on families of sets in general, not necessarily thought of as indexed. 5) A new section about the convergence of sequences has been added to the chapter on selected topics. This new section, which treats a topic from real analysis, adds some diversity to the chapter, which had hitherto contained selected topics of only an algebraic or combinatorial nature. 6) A new section called ``You Are the Professor'' has been added to the end of the last chapter. This new section, which includes a number of attempted proofs taken from actual homework exercises submitted by students, offers the reader the opportunity to solidify her facility for writing proofs by critiquing these submissions as if she were the instructor for the course. 7) All known errors have been corrected. 8) Many minor adjustments of wording have been made throughout the text, with the hope of improving the exposition. |
| 2 2 skills practice statements conditionals and biconditionals: Forall X P. D. Magnus, Tim Button, Robert Trueman, Richard Zach, 2023 |
| 2 2 skills practice statements conditionals and biconditionals: An Introduction to Abstract Mathematics Robert J. Bond, William J. Keane, 2007-08-24 Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments. |
| 2 2 skills practice statements conditionals and biconditionals: An Invitation to Abstract Mathematics Béla Bajnok, 2020-10-27 This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH |
| 2 2 skills practice statements conditionals and biconditionals: Proof, Logic, and Conjecture Robert S. Wolf, 1997-12-15 This text is designed to teach students how to read and write proofs in mathematics and to acquaint them with how mathematicians investigate problems and formulate conjecture. |
| 2 2 skills practice statements conditionals and biconditionals: Thinking Skills John Butterworth, Geoff Thwaites, 2013-04-18 Thinking Skills, second edition, is the only endorsed book offering complete coverage of the Cambridge International AS and A Level syllabus. |
| 2 2 skills practice statements conditionals and biconditionals: The Logic of Our Language Rodger L. Jackson, Melanie L. McLeod, 2014-11-04 The Logic of Our Language teaches the practical and everyday application of formal logic. Rather than overwhelming the reader with abstract theory, Jackson and McLeod show how the skills developed through the practice of logic can help us to better understand our own language and reasoning processes. The authors’ goal is to draw attention to the patterns and logical structures inherent in our spoken and written language by teaching the reader how to translate English sentences into formal symbols. Other logical tools, including truth tables, truth trees, and natural deduction, are then introduced as techniques for examining the properties of symbolized sentences and assessing the validity of arguments. A substantial number of practice questions are offered both within the book itself and as interactive activities on a companion website. |
| 2 2 skills practice statements conditionals and biconditionals: The Power of Logic 6e Frances Howard-Snyder, HOWARD-SNYDER, Ryan Wasserman, 2019-07-25 This edition of The Power of Logic offers an introduction to informal logic, traditional categorical logic, and modern symbolic logic. The authors' direct and accessible writing style, along with a wealth of engaging examples and challenging exercises, makes this an ideal text for today's logic classes. Instructors and students can now access their course content through the Connect digital learning platform by purchasing either standalone Connect access or a bundle of print and Connect access. McGraw-Hill Connect® is a subscription-based learning service accessible online through your personal computer or tablet. Choose this option if your instructor will require Connect to be used in the course. Your subscription to Connect includes the following: * SmartBook® - an adaptive digital version of the course textbook that personalizes your reading experience based on how well you are learning the content. * Access to your instructor's homework assignments, quizzes, syllabus, notes, reminders, and other important files for the course. * Progress dashboards that quickly show how you are performing on your assignments and tips for improvement. * The option to purchase (for a small fee) a print version of the book. This binder-ready, loose-leaf version includes free shipping. Complete system requirements to use Connect can be found here: http://www.mheducation.com/highered/platforms/connect/training-support-students.html |
| 2 2 skills practice statements conditionals and biconditionals: On What We Know We Don't Know Sylvain Bromberger, 1992 In this collection of essays, Bromberger explores the centrality of questions and predicaments they create in scientific research. He discusses the nature of explanation, theory, and the foundations of linguistics. |
| 2 2 skills practice statements conditionals and biconditionals: Autonomy Platonism and the Indispensability Argument Russell Marcus, 2015-06-11 Mathematical platonism is the view that mathematical statements are true of real mathematical objects like numbers, shapes, and sets. One central problem with platonism is that numbers, shapes, sets, and the like are not perceivable by our senses. In contemporary philosophy, the most common defense of platonism uses what is known as the indispensability argument. According to the indispensabilist, we can know about mathematics because mathematics is essential to science. Platonism is among the most persistent philosophical views. Our mathematical beliefs are among our most entrenched. They have survived the demise of millennia of failed scientific theories. Once established, mathematical theories are rarely rejected, and never for reasons of their inapplicability to empirical science. Autonomy Platonism and the Indispensability Argument is a defense of an alternative to indispensability platonism. The autonomy platonist believes that mathematics is independent of empirical science: there is purely mathematical evidence for purely mathematical theories which are even more compelling to believe than empirical science. Russell Marcus begins by contrasting autonomy platonism and indispensability platonism. He then argues against a variety of indispensability arguments in the first half of the book. In the latter half, he defends a new approach to a traditional platonistic view, one which includes appeals to a priori but fallible methods of belief acquisition, including mathematical intuition, and a natural adoption of ordinary mathematical methods. In the end, Marcus defends his intuition-based autonomy platonism against charges that the autonomy of mathematics is viciously circular. This book will be useful to researchers, graduate students, and advanced undergraduates with interests in the philosophy of mathematics or in the connection between science and mathematics. |
| 2 2 skills practice statements conditionals and biconditionals: Dissertation Abstracts International , 2001 |
| 2 2 skills practice statements conditionals and biconditionals: An Introduction to Discrete Mathematics Steven Roman, 1989 Intended for a one-term course in discrete mathematics, to prepare freshmen and sophomores for further work in computer science as well as mathematics. Sets, proof techniques, logic, combinatorics, and graph theory are covered in concise form. All topics are motivated by concrete examples, often emphasizing the interplay between computer science and mathematics. Examples also illustrate all definitions. Applications and references cover a wide variety of realistic situations. Coverage of mathematical induction includes the stroung form of induction, and new sections have been added on nonhomogeneous recurrence relations and the essentials of probability. |
| 2 2 skills practice statements conditionals and biconditionals: Logic and Critical Reasoning Anand Vaidya, Andrew Erickson, 2011 |
| 2 2 skills practice statements conditionals and biconditionals: Discrete Mathematics with Applications, Metric Edition Susanna Epp, 2019 DISCRETE MATHEMATICS WITH APPLICATIONS, 5th Edition, Metric Edition explains complex, abstract concepts with clarity and precision and provides a strong foundation for computer science and upper-level mathematics courses of the computer age. Author Susanna Epp presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to today's science and technology. |
| 2 2 skills practice statements conditionals and biconditionals: Clear and Present Thinking Brendan Myers, Charlene Elsby, Kimberly Baltzer-Jaray, 2013-05 The product of a Kickstarter fundraising campaign, Clear and Present Thinking is a college-level textbook in logic and critical thinking. Chapters: 1. Questions, Problems, and World Views 2. Good and Bad Thinking Habits 3. Basics of Argumentation 4. Fallacies 5. Reasonable Doubt 6. Moral Reasoning In an effort to reduce the cost of education for students, this textbook was funded by over 700 people through the Kickstarter online crowd-funding platform. This softcover edition is available here for the lowest reasonable price. All profits from the sale of this print edition will go towards funding future free or nearly-free college textbook projects. |
| 2 2 skills practice statements conditionals and biconditionals: The Critical Thinking Toolkit Galen A. Foresman, Peter S. Fosl, Jamie C. Watson, 2016-08-29 The Critical Thinking Toolkit is a comprehensive compendium that equips readers with the essential knowledge and methods for clear, analytical, logical thinking and critique in a range of scholarly contexts and everyday situations. Takes an expansive approach to critical thinking by exploring concepts from other disciplines, including evidence and justification from philosophy, cognitive biases and errors from psychology, race and gender from sociology and political science, and tropes and symbols from rhetoric Follows the proven format of The Philosopher’s Toolkit and The Ethics Toolkit with concise, easily digestible entries, “see also” recommendations that connect topics, and recommended reading lists Allows readers to apply new critical thinking and reasoning skills with exercises and real life examples at the end of each chapter Written in an accessible way, it leads readers through terrain too often cluttered with jargon Ideal for beginning to advanced students, as well as general readers, looking for a sophisticated yet accessible introduction to critical thinking |
| 2 2 skills practice statements conditionals and biconditionals: Knowledge Representation and Reasoning Ronald Brachman, Hector Levesque, 2004-05-19 Knowledge representation is at the very core of a radical idea for understanding intelligence. This book talks about the central concepts of knowledge representation developed over the years. It is suitable for researchers and practitioners in database management, information retrieval, object-oriented systems and artificial intelligence. |
| 2 2 skills practice statements conditionals and biconditionals: Teleosemantics Graham Macdonald, David Papineau, 2006-09-28 Teleosemantics seeks to explain meaning and other intentional phenomena in terms of their function in the life of the species. This volume of new essays from an impressive line-up of well-known contributors offers a valuable summary of the current state of the teleosemantics debate. |
| 2 2 skills practice statements conditionals and biconditionals: Art, Emotion and Ethics Berys Gaut, 2007-05-24 Can a good work of art be evil? 'Art, Ethics, and Emotion' explores this issue, arguing that artworks are always aesthetically flawed insofar as they have a moral defect that is aesthetically relevant. This book will be of interest to anyone who wants to understand the relation of art to morality. |
| 2 2 skills practice statements conditionals and biconditionals: The Power of Logic Ryan Wasserman, Dr., Daniel Howard-Snyder, Professsor, Frances Howard-Snyder, Dr., 2012-03-22 This fifth edition of The Power of Logic offers an introduction to informal logic, traditional categorical logic, and modern symbolic logic. The authors’ direct and accessible writing style, along with a wealth of engaging examples and challenging exercises, makes this an ideal text for today’s logic classes. Instructors and students can now access their course content through the Connect digital learning platform by purchasing either standalone Connect access or a bundle of print and Connect access. McGraw-Hill Connect® is a subscription-based learning service accessible online through your personal computer or tablet. Choose this option if your instructor will require Connect to be used in the course. Your subscription to Connect includes the following: • SmartBook® - an adaptive digital version of the course textbook that personalizes your reading experience based on how well you are learning the content. • Access to your instructor’s homework assignments, quizzes, syllabus, notes, reminders, and other important files for the course. • Progress dashboards that quickly show how you are performing on your assignments and tips for improvement. • The option to purchase (for a small fee) a print version of the book. This binder-ready, loose-leaf version includes free shipping. Complete system requirements to use Connect can be found here: http://www.mheducation.com/highered/platforms/connect/training-support-students.html |
| 2 2 skills practice statements conditionals and biconditionals: International Perspectives on the Teaching and Learning of Geometry in Secondary Schools Patricio Herbst, Ui Hock Cheah, Philippe R. Richard, Keith Jones, 2018-04-27 This book presents current perspectives on theoretical and empirical issues related to the teaching and learning of geometry at secondary schools. It contains chapters contributing to three main areas. A first set of chapters examines mathematical, epistemological, and curricular perspectives. A second set of chapters presents studies on geometry instruction and teacher knowledge, and a third set of chapters offers studies on geometry thinking and learning. Specific research topics addressed also include teaching practice, learning trajectories, learning difficulties, technological resources, instructional design, assessments, textbook analyses, and teacher education in geometry. Geometry remains an essential and critical topic in school mathematics. As they learn geometry, students develop essential mathematical thinking and visualization skills and learn a language that helps them relate to and interact with the physical world. Geometry has traditionally been included as a subject of study in secondary mathematics curricula, but it has also featured as a resource in out-of-school problem solving, and has been connected to various human activities such as sports, games, and artwork. Furthermore, geometry often plays a role in teacher preparation, undergraduate mathematics, and at the workplace. New technologies, including dynamic geometry software, computer-assisted design software, and geometric positioning systems, have provided more resources for teachers to design environments and tasks in which students can learn and use geometry. In this context, research on the teaching and learning of geometry will continue to be a key element on the research agendas of mathematics educators, as researchers continue to look for ways to enhance student learning and to understand student thinking and teachers’ decision making. |
| 2 2 skills practice statements conditionals and biconditionals: Discrete Mathematics with Ducks Sarah-marie Belcastro, 2018-11-15 Discrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels. The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they’ve learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. The author’s lively and friendly writing style is appealing to both instructors and students alike and encourages readers to learn. The book’s light-hearted approach to the subject is a guiding principle and helps students learn mathematical abstraction. Features: The book’s Try This! sections encourage students to construct components of discussed concepts, theorems, and proofs Provided sets of discovery problems and illustrative examples reinforce learning Bonus sections can be used by instructors as part of their regular curriculum, for projects, or for further study |
| 2 2 skills practice statements conditionals and biconditionals: Becoming a Mathematics Teacher Tony Brown, Olwen McNamara, 2011-02-08 The book is centered on how major curriculum reform shapes mathematics and the professional practices of teachers. This book documents in real time the implementation of a major government numeracy programme and its receipt by trainee and new teachers. It documents the complete life span of that initiative. The account is targeted at an international readership in terms of how curriculum reform more generally shapes mathematics in schools and the practices of teachers. A key dimension of the book is an alternative view of mathematics education research in which the task of teacher development is understood at policy level where large numbers of teachers were interviewed to assess how policies were being processed through individuals. The book provides an easy and accessible commentary utilising contemporary theory to describe how such teachers reconcile their personal aspirations with the external demands they encounter in negotiating their identities as professional teachers. |
| 2 2 skills practice statements conditionals and biconditionals: An Introduction to Criminological Theory and the Problem of Causation Jason Warr, 2017-01-24 This text offers a novel contribution to the literature on core criminological theory by introducing the complex issues relating to the structuring and analysing of causation. This text traces the paradigm shift, or drift, that has occurred in the history of criminology and shows how the problem of causation has been a leading factor in these theoretical developments. This short book is the first of its kind and is an introductory text designed to introduce both seasoned criminologists as well as students of criminology to the interesting intersections between the fields of criminology and the philosophy of the social sciences. The problem of causation is notoriously difficult and has plagued philosophers and scientists for centuries. Warr highlights the importance of grappling with this problem and demonstrates how it can lead to unsuccessful theorising and can prevent students from fully appreciating the development of thinking in criminology. This accessible account will prove to be a must-read for scholars of criminal justice, penology and philosophy of social science. |
| 2 2 skills practice statements conditionals and biconditionals: Essentials of Logic Irving Copi, Carl Cohen, Daniel Flage, 2016-12-08 Rendered from the 11th Edition of Copi/Cohen, Introduction to Logic, the most respected introductory logic book on the market, this concise version presents a simplified yet rigorous introduction to the study of logic. It covers all major topics and approaches, using a three-part organization that outlines specific topics under logic and language, deduction, and induction. For individuals intrigued by the formal study of logic. |
| 2 2 skills practice statements conditionals and biconditionals: A Transition to Advanced Mathematics Douglas Smith, Maurice Eggen, Richard St. Andre, 2010-06-01 A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. |
| 2 2 skills practice statements conditionals and biconditionals: Aspects of Teaching Secondary Mathematics Linda Haggarty, 2003-09-02 If learners in the classroom are to be excited by mathematics, teachers need to be both well informed about current initiatives and able to see how what is expected of them can be translated into rich and stimulating classroom strategies. The book examines current initiatives that affect teaching mathematics and identifies pointers for action in the classroom. Divided into three major sections, it looks at: the changing mathematics classroom at primary, secondary and tertiary level major components of the secondary curriculum practical pedagogical issues of particular concern to mathematics teachers. Each issue is explores in terms of major underpinnings and research in that area, and practical ideas can be drawn from the text and implemented in the reader's classroom practice. Each chapter has been written by a well-respected writer, researcher and practitioner in their field and all share a common goal: to look thoughtfully and intelligently at some of the practical issues facing mathematics teachers and offer their perspectives on those issues. |
| 2 2 skills practice statements conditionals and biconditionals: The Logic Book Merrie Bergmann, James Moor, Jack Nelson, 2008-07-30 This leading text for symbolic or formal logic courses presents all techniques and concepts with clear, comprehensive explanations, and includes a wealth of carefully constructed examples. Its flexible organization (with all chapters complete and self-contained) allows instructors the freedom to cover the topics they want in the order they choose. |
| 2 2 skills practice statements conditionals and biconditionals: Language, Proof, and Logic Dave Barker-Plummer, Jon Barwise, John Etchemendy, 2011 Rev. ed. of: Language, proof, and logic / Jon Barwise & John Etchemendy. |
| 2 2 skills practice statements conditionals and biconditionals: Logic Paul Tomassi, 2013-05-13 Bringing elementary logic out of the academic darkness into the light of day, Paul Tomassi makes logic fully accessible for anyone attempting to come to grips with the complexities of this challenging subject. Including student-friendly exercises, illustrations, summaries and a glossary of terms, Logic introduces and explains: * The Theory of Validity * The Language of Propositional Logic * Proof-Theory for Propositional Logic * Formal Semantics for Propositional Logic including the Truth-Tree Method * The Language of Quantificational Logic including the Theory of Descriptions. Logic is an ideal textbook for any logic student: perfect for revision, staying on top of coursework or for anyone wanting to learn about the subject. Related downloadable software for Macs and PCs is available for this title at www.logic.routledge.com. |
| 2 2 skills practice statements conditionals and biconditionals: The Art of Proof Matthias Beck, Ross Geoghegan, 2010-08-17 The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions. |
| 2 2 skills practice statements conditionals and biconditionals: Patty Paper Geometry Michael Serra, 1994 |
| 2 2 skills practice statements conditionals and biconditionals: The Twenty-First Century Mechanistic Theory of Human Cognition Diego Azevedo Leite, 2020-11-30 This book presents a theoretical critical appraisal of the Mechanistic Theory of Human Cognition (MTHC), which is one of the most popular major theories in the contemporary field of cognitive science. It analyses and evaluates whether MTHC provides a unifying account of human cognition and its explanation. The book presents a systematic investigation of the internal and external consistency of the theory, as well as a systematic comparison with other contemporary major theories in the field. In this sense, it provides a fresh look at more recent major theoretical debates in this area of scientific research and a rigorous analysis of one of its most central major theories. Rigorous theoretical work is integrated with objective consideration of relevant empirical evidence, making the discussions robust and clear. As a result, the book shows that MTHC provides a significant theoretical contribution for the field of cognitive science. The content is useful for those interested in theoretical and empirical issues concerning major theories in the contemporary field of cognitive science. |
| 2 2 skills practice statements conditionals and biconditionals: Truth, Politics, Morality Cheryl Misak, 2002-02-07 Cheryl Misak argues that truth ought to be reinstated to a central position in moral and political philosophy. She argues that the correct account of truth is one found in a certain kind of pragmatism: a true belief is one upon which inquiry could not improve, a belief which would not be defeated by experience and argument. This account is not only an improvement on the views of central figures such as Rawls and Habermas, but it can also make sense of the idea that, despite conflict, pluralism, and the expression of difference, our moral and political beliefs aim at truth and can be subject to criticism. Anyone interested in a fresh discussion of political theory and philosophy will find this a fascinating read. |
| 2 2 skills practice statements conditionals and biconditionals: Mathematical Excursions Richard N. Aufmann, Richard D. Nation, Joanne Lockwood, Daniel K. Clegg, 2003-03-01 Developed for the liberal arts math course by a seasoned author team,Mathematical Excursions,is uniquely designed to help students see math at work in the contemporary world. Using the proven Aufmann Interactive Method, students learn to master problem-solving in meaningful contexts. In addition, multi-partExcursionexercises emphasize collaborative learning. The text's extensive topical coverage offers instructors flexibility in designing a course that meets their students' needs and curriculum requirements. TheExcursionsactivity and correspondingExcursion Exercises,denoted by an icon, conclude each section, providing opportunities for in-class cooperative work, hands-on learning, and development of critical-thinking skills. These activities are also ideal for projects or extra credit assignments. TheExcursionsare designed to reinforce the material that has just been covered in the section in a fun and engaging manner that will enhance a student's journey and discovery of mathematics. The proven Aufmann Interactive Method ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains at least one set of matched-pair examples. The method begins with a worked-out example with a solution in numerical and verbal formats to address different learning styles. The matched problem, calledCheck Your Progress,is left for the student to try. Each problem includes a reference to a fully worked out solution in an appendix to which the student can refer for immediate feedback, concept reinforcement, identification of problem areas, and prevention of frustration. Eduspace, powered by Blackboard, for the Aufmann/Lockwood/Nation/CleggMath Excursionscourse features algorithmic exercises and test bank content in question pools. |
| 2 2 skills practice statements conditionals and biconditionals: Clear and Present Thinking, Second Edition Charlene Elsby, Alex Zieba, 2019-01-10 This is the second edition of the popular, low-cost, college-level textbook in logic and critical thinking. Covering topics like worldviews, formal and informal logic, science, reasonable doubt, propaganda, fake news, and the history of logic, Clear and Present Thinking aims to make philosophy in general, and critical thinking skills in particular, unmysterious, and widely available for the general public.Contents: Chapter 1: An Outline History of LogicChapter 2: Informal Logic: Questions, Problems, and World ViewsChapter 3: Informal Logic: Habits of ThinkingChapter 4: Basics of Formal LogicChapter 5: ArgumentsChapter 6: Science and Scientific ReasoningChapter 7: FallaciesChapter 8: Reasonable DoubtChapter 9: Moral ReasoningChapter 10: ActivitiesEpilogue: Why Can't We All Get Along?Glossary of Terms in Logic and Philosophy |
| 2 2 skills practice statements conditionals and biconditionals: Computational Logic and Human Thinking Robert Kowalski, 2011 The practical benefits of computational logic need not be limited to mathematics and computing. As this book shows, ordinary people in their everyday lives can profit from the recent advances that have been developed for artificial intelligence. The book draws upon related developments in various fields from philosophy to psychology and law. It pays special attention to the integration of logic with decision theory, and the use of logic to improve the clarity and coherence of communication in natural languages such as English. This book is essential reading for teachers and researchers who may be out of touch with the latest developments in computational logic. It will also be useful in any undergraduate course that teaches practical thinking, problem solving or communication skills. Its informal presentation makes the book accessible to readers from any background, but optional, more formal, chapters are also included for those who are more technically oriented-- |
| 2 2 skills practice statements conditionals and biconditionals: Logic Stan Baronett, 2008 |
| 2 2 skills practice statements conditionals and biconditionals: Prolog Programming in Depth Michael A. Covington, Donald Nute, André Vellino, 1997 Appropriate for courses in artificial intelligence, computer science, logic programming, and expert systems. Can be used as supplemental text in courses in computational linguistics (natural language processing). This text covers the Prolog programming language thoroughly with an emphasis on building practical application software, not just theory. Working through this book, students build several types of expert systems, as well as natural language processing software and utilities to read foreign file formats. This is the first book to cover ISO Standard Prolog, but the programs are compatible with earlier dialects of the language. Program files are available by FTP from The University of Georgia. |
2 - Wikipedia
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and the only even prime number. Because it forms the basis of a duality, it has …
2 Player Games - TwoPlayerGames.org
World's 2 player games platform. Daily updated best two player games in different categories are published for you.
2 PLAYER GAMES - Play Online for Free! - Poki
We offer all sorts of two-player games including 1 v 1 Fighting Games, work together in two-player Co-op Games, play with 2 or more players in our Board Games, play Basketball, Soccer, …
The Number 2 for kids - Learning to Count - YouTube
How many wheels are there on a bike? How about twin brothers? Besides, at the end of the video children will be able to enjoy singing a song. How about learning to count all together? This …
2 Player Games Play on CrazyGames
Our 2-player games include fierce sports games such as Basketball Stars, calm board games, and everything in between. Play the Best Online 2 Player Games for Free on CrazyGames, No …
2 (number) - Simple English Wikipedia, the free encyclopedia
2 (Two; / ˈ t uː / ) is a number, numeral, and glyph. It is the number after 1 and the number before 3 . In Roman numerals, it is II.
2 (number) - New World Encyclopedia
2 (two) is a number, numeral, and glyph that represents the number. It is the natural number [1] that follows 1 and precedes 3. It is an integer and a cardinal number, that is, a number that is …
23 Fun Facts About The Number 2 That Will Surprise You
Mar 13, 2023 · The number 2 is generally considered a positive and harmonious number in numerology. It is associated with balance, cooperation, and diplomacy. The number 2 is often …
Number 2 - Facts about the integer - Numbermatics
Your guide to the number 2, the only even prime number. Mathematical info, prime factorization, fun facts and numerical data for STEM, education and fun.
10 Fantastic Facts About The Number 2 - The Fact Site
Feb 2, 2021 · Today let’s take a look at 10 fun facts about the number 2. The number two is the first prime number. There are only eight prime numbers under 20, and two is the only even …
2 - Wikipedia
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and the only even prime number. Because it forms the basis of a duality, it has …
2 Player Games - TwoPlayerGames.org
World's 2 player games platform. Daily updated best two player games in different categories are published for you.
2 PLAYER GAMES - Play Online for Free! - Poki
We offer all sorts of two-player games including 1 v 1 Fighting Games, work together in two-player Co-op Games, play with 2 or more players in our Board Games, play Basketball, Soccer, …
The Number 2 for kids - Learning to Count - YouTube
How many wheels are there on a bike? How about twin brothers? Besides, at the end of the video children will be able to enjoy singing a song. How about learning to count all together? This …
2 Player Games Play on CrazyGames
Our 2-player games include fierce sports games such as Basketball Stars, calm board games, and everything in between. Play the Best Online 2 Player Games for Free on CrazyGames, No …
2 (number) - Simple English Wikipedia, the free encyclopedia
2 (Two; / ˈ t uː / ) is a number, numeral, and glyph. It is the number after 1 and the number before 3 . In Roman numerals, it is II.
2 (number) - New World Encyclopedia
2 (two) is a number, numeral, and glyph that represents the number. It is the natural number [1] that follows 1 and precedes 3. It is an integer and a cardinal number, that is, a number that is …
23 Fun Facts About The Number 2 That Will Surprise You
Mar 13, 2023 · The number 2 is generally considered a positive and harmonious number in numerology. It is associated with balance, cooperation, and diplomacy. The number 2 is often …
Number 2 - Facts about the integer - Numbermatics
Your guide to the number 2, the only even prime number. Mathematical info, prime factorization, fun facts and numerical data for STEM, education and fun.
10 Fantastic Facts About The Number 2 - The Fact Site
Feb 2, 2021 · Today let’s take a look at 10 fun facts about the number 2. The number two is the first prime number. There are only eight prime numbers under 20, and two is the only even …
