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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.
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.
Many mathematics students have trouble the first time they take a course, such as linear algebra, abstract algebra, introductory analysis, or discrete mathematics, in which they are asked to prove various theorems. This textbook 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 "scratchwork" sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. Numerous exercises give students the opportunity to construct their own proofs. 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.
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
No More Pretending. No More Performing. No More Fighting to Prove Yourself. Are you tired, inside and out? Are you trying your best to measure up--yet you still feel as if you're losing ground and missing out on the best parts of life? You are not alone. Jennie Allen understands the daily struggle so many of us face with inadequacy and insecurity and the fear that we are not enough. And she invites us into a different experience, one in which our souls overflow with contentment and joy. In Nothing to Prove she calls us to... * Find freedom from self-induced pressure by admitting we're not enough--but Jesus is. * Stop doing things for God, and start doing things with Him. * Admit our greatest needs and watch them be filled by the only One who can meet them. * Discover how God moves wildly through those who have nothing to protect and nothing to prove. * Make it our goal to know and love Jesus, then watch what He does in and through us. As you wade into the refreshing truth of the more-than-enough life Jesus offers, you'll experience the joyous freedom that comes to those who are determined to discover what God can do through a soul completely in love with Him. Discover the answer to your soul-deep thirst Too many of us have bought into the lie that our cravings will be satisfied if we are enough and if we have enough. So we chase image, answers, things, and people--and we wonder all the while, Why am I still thirsty? My single goal with this book is to lead your thirsty soul to the only source of lasting fulfillment: Jesus. He is the living water, a limitless supply that will not only quench your thirst but will fill you and then come pouring out of you into a thirsty world. Because of Him, you are loved. You are known. You can take a deep breath. Because you have nothing to prove. --Jennie
This examination of the interaction between fictional representations of the Civil War and the memoirs and autobiographies of Civil War soldiers argues that veterans' accounts taught later generations to represent the conflict in terms of individual experiences, revealing how national identity developed according to written records of the past. Author Craig A. Warren explores seven popular novels about the Civil War--The Red Badge of Courage, Gone with the Wind, None Shall Look Back, The Judas Field, The Unvanquished, The Killer Angels, and Absalom, Absalom! His study reveals that the war owes much of its cultural power to a large but overlooked genre of writing: postwar memoirs, regimental histories, and other narratives authored by Union and Confederate veterans. Warren contends that literary scholars and historians took seriously the influence that veterans' narratives had on the shape and character of Civil War fiction. Scars to Prove It fills a gap in the study of Civil War literature and will appeal to those interested in the literature, military writing, and literary studies related to the Civil War.

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