A Transition To Mathematics With Proofs PDF Download
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| Author | : Michael J. Cullinane |
| Publisher | : Jones & Bartlett Publishers |
| Total Pages | : 367 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 1449627781 |
Download A Transition to Mathematics with Proofs Book in PDF, ePub and Kindle
Developed for the "transition" course for mathematics majors moving beyond the primarily procedural methods of their calculus courses toward a more abstract and conceptual environment found in more advanced courses, A Transition to Mathematics with Proofs emphasizes mathematical rigor and helps students learn how to develop and write mathematical proofs. The author takes great care to develop a text that is accessible and readable for students at all levels. It addresses standard topics such as set theory, number system, logic, relations, functions, and induction in at a pace appropriate for a wide range of readers. Throughout early chapters students gradually become aware of the need for rigor, proof, and precision, and mathematical ideas are motivated through examples.
| Author | : Gary Chartrand |
| Publisher | : Pearson |
| Total Pages | : 0 |
| Release | : 2013 |
| Genre | : Proof theory |
| ISBN | : 9780321797094 |
Download Mathematical Proofs Book in PDF, ePub and Kindle
This book prepares students for the more abstract mathematics courses that follow calculus. The author introduces students to proof techniques, analyzing proofs, and writing proofs of their own. It also provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory.
| Author | : Neil R. Nicholson |
| Publisher | : CRC Press |
| Total Pages | : 323 |
| Release | : 2019-03-21 |
| Genre | : Mathematics |
| ISBN | : 0429535473 |
Download A Transition to Proof Book in PDF, ePub and Kindle
A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology
| Author | : Douglas Smith |
| Publisher | : Cengage Learning |
| Total Pages | : 416 |
| Release | : 2010-06-01 |
| Genre | : Mathematics |
| ISBN | : 9780495562023 |
Download A Transition to Advanced Mathematics Book in PDF, ePub and Kindle
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.
| Author | : Bob A. Dumas |
| Publisher | : McGraw-Hill Education |
| Total Pages | : 0 |
| Release | : 2007 |
| Genre | : Logic, Symbolic and mathematical |
| ISBN | : 9780071106474 |
Download Transition to Higher Mathematics Book in PDF, ePub and Kindle
This book is written for students who have taken calculus and want to learn what "real mathematics" is.
| Author | : B. Sethuraman |
| Publisher | : American Mathematical Society |
| Total Pages | : 334 |
| Release | : 2021-12-02 |
| Genre | : Mathematics |
| ISBN | : 1470465140 |
Download Proofs and Ideas Book in PDF, ePub and Kindle
Proofs and Ideas serves as a gentle introduction to advanced mathematics for students who previously have not had extensive exposure to proofs. It is intended to ease the student's transition from algorithmic mathematics to the world of mathematics that is built around proofs and concepts. The spirit of the book is that the basic tools of abstract mathematics are best developed in context and that creativity and imagination are at the core of mathematics. So, while the book has chapters on statements and sets and functions and induction, the bulk of the book focuses on core mathematical ideas and on developing intuition. Along with chapters on elementary combinatorics and beginning number theory, this book contains introductory chapters on real analysis, group theory, and graph theory that serve as gentle first exposures to their respective areas. The book contains hundreds of exercises, both routine and non-routine. This book has been used for a transition to advanced mathematics courses at California State University, Northridge, as well as for a general education course on mathematical reasoning at Krea University, India.
| Author | : Ethan D. Bloch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461221307 |
Download Proofs and Fundamentals Book in PDF, ePub and Kindle
The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.
| Author | : Larry Gerstein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 355 |
| Release | : 2013-11-21 |
| Genre | : Science |
| ISBN | : 1468467085 |
Download Introduction · to Mathematical Structures and · Proofs Book in PDF, ePub and Kindle
This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.
| Author | : Donald E. Knuth |
| Publisher | : Cambridge University Press |
| Total Pages | : 132 |
| Release | : 1989 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9780883850633 |
Download Mathematical Writing Book in PDF, ePub and Kindle
This book will help those wishing to teach a course in technical writing, or who wish to write themselves.
| Author | : Daniel J. Velleman |
| Publisher | : Cambridge University Press |
| Total Pages | : 401 |
| Release | : 2006-01-16 |
| Genre | : Mathematics |
| ISBN | : 0521861241 |
Download How to Prove It Book in PDF, ePub and Kindle
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.
