Taking The Oof Out Of Proofs
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Taking The Oof Out Of Proofs
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Author : Alexandr Draganov
language : en
Publisher: CRC Press
Release Date : 2024-04-08
Taking The Oof Out Of Proofs written by Alexandr Draganov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-08 with Mathematics categories.
This book introduces readers to the art of doing mathematical proofs. Proofs are the glue that holds mathematics together. They make connections between math concepts and show why things work the way they do. This book teaches the art of proofs using familiar high-school concepts, such as numbers, polynomials, functions, and trigonometry. It retells math as a story, where the next chapter follows from the previous one. Readers will see how various mathematical concepts are tied and will see that mathematics is not a pile of formulas and facts; rather, it has an orderly and beautiful edifice. The author begins with basic rules of logic and then progresses through the topics already familiar to the students: numbers, inequalities, functions, polynomials, exponents, and trigonometric functions. There are also beautiful proofs for conic sections, sequences, and Fibonacci numbers. Each chapter has exercises for the reader. Reviewer Comments: I find the book very impressive. The choice and sequence of topics is excellent, and it is wonderful to have all of these things together in one volume. Theorems are clearly stated, and proofs are accurate. – Michael Comenetz The thoroughness of the narrative is one of the main strengths of the book. The book provides a perfect illustration of mathematical thinking. Each step of a given derivation is precise and clear. – Julie Gershunskaya Draganov’s book stands out from the many competing books. Draganov’s goal is to show that mathematics depends on the notion of proof. Unlike other transition books, he addresses mathematical topics at an accessible level, rather than topics studied later in the university curriculum. – Ken Rosen
Taking The Oof Out Of Proofs
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Author : ALEXANDR. DRAGANOV
language : en
Publisher:
Release Date : 2024-03-04
Taking The Oof Out Of Proofs written by ALEXANDR. DRAGANOV and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-04 with categories.
This book introduces readers to the art of doing mathematical proofs. Proofs are the glue that holds mathematics together. They make connections between math concepts and show why things work the way they do. This book teaches the art of proofs using familiar high school concepts, such as numbers, polynomials, functions, and trigonometry. It retells math as a story, where the next chapter follows from the previous one. Readers will see how various mathematical concepts are tied, will see mathematics is not a pile of formulas and facts, but has an orderlyandbeautifuledifice. The author begins with basic rules of logic, and then progresses through the topics already familiar to the students: numbers, inequalities, functions, polynomials, exponents, and trigonometric functions. There are also beautiful proofs for conic sections, sequences, and Fibonacci numbers. Each chapter has exercises for the reader. Reviewer Comments: "I find the book very impressive. The choice and sequence of topics is excellent, and it is wonderful to have all of these things together in one volume. Theorems are clearly stated, and proofs are accurate." -- Michael Comenetz The thoroughness of the narrative is one of the main strengths of the book. The book provides a perfect illustration of mathematical thinking. Each step of a given derivation is precise and clear.-- Julie Gershunskaya Draganov's book stands out from the many competing books. Draganov's goal is to show that mathematics depends on the notion of proof. Unlike other transitions books, he addresses mathematical topics at an accessible level rather than topics studied later in the university curriculum. -Ken Rosen
Contemporary Abstract Algebra
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Author : Joseph Gallian
language : en
Publisher: CRC Press
Release Date : 2025-06-20
Contemporary Abstract Algebra written by Joseph Gallian and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-20 with Mathematics categories.
Contemporary Abstract Algebra, Eleventh Edition is intended for a course whose main purpose is to enable students to do computations and write proofs. This text stresses the importance of obtaining a solid introduction to the traditional topics, while at the same time presenting abstract algebra as a contemporary and very much active subject, which is currently being used by working physicists, chemists, and computer scientists. For nearly four decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics presented. It is comprehensive, lively, and engaging. Students will learn how to do computations and write proofs. A unique feature of the book are exercises that build the skill of generalizing, a skill that students should develop, but rarely do. Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The hallmark features of previous editions of the book are enhanced in this edition. These include: A good mixture of approximately 1900 computational and theoretical exercises appearing in each chapter that synthesizes concepts from multiple chapters Back-of-the-book skeleton solutions and hints to odd-numbered exercises Over 300 worked-out examples ranging from routine computations to the more challenging Links to interactive True/False questions with comments Links to computer exercises that utilize interactive software available on the author's website, stressing guessing and making conjectures Many applications from scientific and computing fields, as well as some from everyday life Numerous historical notes and biographies that spotlight the people and events behind the mathematics Motivational and humorous quotations Hundreds of figures, photographs, and tables Changes to the eleventh edition include new exercises, examples, biographies, and quotes, and an enrichment of the discussion portions. These changes accentuate and enhance the hallmark features that have made previous editions of the book a comprehensive, lively, and engaging introduction to the subject. While many partial solutions and sketches for the odd-numbered exercises appear in the book, an Instructor’s Solutions Manual offers solutions for all the exercises. A Student's Solution Manual has comprehensive solutions for all odd-numbered exercises, many even-numbered exercises, and numerous alternative solutions as well.
American State Papers
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Author : USA
language : en
Publisher:
Release Date : 1861
American State Papers written by USA and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1861 with categories.
Numerical Methods And Analysis With Mathematical Modelling
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Author : William P. Fox
language : en
Publisher: CRC Press
Release Date : 2024-08-07
Numerical Methods And Analysis With Mathematical Modelling written by William P. Fox and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-07 with Mathematics categories.
What sets Numerical Methods and Analysis with Mathematical Modelling apart are the modelling aspects utilizing numerical analysis (methods) to obtain solutions. The authors cover first the basic numerical analysis methods with simple examples to illustrate the techniques and discuss possible errors. The modelling prospective reveals the practical relevance of the numerical methods in context to real-world problems. At the core of this text are the real-world modelling projects. Chapters are introduced and techniques are discussed with common examples. A modelling scenario is introduced that will be solved with these techniques later in the chapter. Often, the modelling problems require more than one previously covered technique presented in the book. Fundamental exercises to practice the techniques are included. Multiple modelling scenarios per numerical methods illustrate the applications of the techniques introduced. Each chapter has several modelling examples that are solved by the methods described within the chapter. The use of technology is instrumental in numerical analysis and numerical methods. In this text, Maple, Excel, R, and Python are illustrated. The goal is not to teach technology but to illustrate its power and limitations to perform algorithms and reach conclusions. This book fulfills a need in the education of all students who plan to use technology to solve problems whether using physical models or true creative mathematical modeling, like discrete dynamical systems.
Functional Analysis For The Applied Mathematician
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Author : Todd Arbogast
language : en
Publisher: CRC Press
Release Date : 2025-02-20
Functional Analysis For The Applied Mathematician written by Todd Arbogast and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Mathematics categories.
Functional Analysis for the Applied Mathematician is a self-contained volume providing a rigorous introduction to functional analysis and its applications. Students from mathematics, science, engineering, and certain social science and interdisciplinary programs will benefit from the material. It is accessible to graduate and advanced undergraduate students with a solid background in undergraduate mathematics and an appreciation of mathematical rigor. Students are called upon to actively engage with the material, to the point of proving some of the basic results or their straightforward generalizations, both within the text and within the generous set of exercises. Features: Replete with exercises and examples Suitable for graduate students and advanced undergraduates Develops the basics of functional analysis, exploring the interplay between algebraic linear space theory and topology Presents a variety of applications, often dealing with partial differential equations and their numerical approximation Doubles as a reference book with an extensive index listing the concepts and results
Fundamentals Of Abstract Algebra
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Author : Mark J. DeBonis
language : en
Publisher: CRC Press
Release Date : 2024-04-11
Fundamentals Of Abstract Algebra written by Mark J. DeBonis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-11 with Mathematics categories.
Fundamentals of Abstract Algebra is a primary textbook for a one year first course in Abstract Algebra, but it has much more to offer besides this. The book is full of opportunities for further, deeper reading, including explorations of interesting applications and more advanced topics, such as Galois theory. Replete with exercises and examples, the book is geared towards careful pedagogy and accessibility, and requires only minimal prerequisites. The book includes a primer on some basic mathematical concepts that will be useful for readers to understand, and in this sense the book is self-contained. Features Self-contained treatments of all topics Everything required for a one-year first course in Abstract Algebra, and could also be used as supplementary reading for a second course Copious exercises and examples Mark DeBonis received his PhD in Mathematics from the University of California, Irvine, USA. He began his career as a theoretical mathematician in the field of group theory and model theory, but in later years switched to applied mathematics, in particular to machine learning. He spent some time working for the US Department of Energy at Los Alamos National Lab as well as the US Department of Defense at the Defense Intelligence Agency, both as an applied mathematician of machine learning. He held a position as Associate Professor of Mathematics at Manhattan College in New York City, but later left to pursue research working for the US Department of Energy at Sandia National Laboratory as a Principal Data Analyst. His research interests include machine learning, statistics and computational algebra.
Vector Calculus
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Author : Steven G. Krantz
language : en
Publisher: CRC Press
Release Date : 2024-05-28
Vector Calculus written by Steven G. Krantz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-28 with Mathematics categories.
Using meaningful examples, credible applications, and incisive technology, Vector Calculus strives to empower students, enhance their critical thinking skills, and equip them with the knowledge and skills to succeed in the major or discipline they ultimately choose to study. This text is intended to be a cornerstone of that process. An engaging style and clear writing make the language of mathematics accessible, understandable, and enjoyable, with a high standard for mathematical rigor. A calculus book must tell the truth. This book is carefully written in the accepted language of mathematics in a readable exposition. It includes useful and fascinating applications, acquaints students with the history of the subject, and offers a sense of what mathematics is all about. Technique is presented, yet so are ideas. The authors help students to master basic methods and discover and build their own concepts in a scientific subject. There is an emphasis on using modeling and numerical calculation. Additional features include: A Quick Quiz and Problems for Practice, Further Theory and Practice, and Calculator/Computer Exercises appear at the end of each section All exercise sets are step laddered A Look Back and A Look Forward help students put the ideas in context Every chapter ends with a Genesis and Development section, giving history and perspective on key topics in the evolution of calculus Boxed Insights clear up points or answer commonly asked questions The text has an extra-large offering of examples Examples are illustrated with meaningful and useful graphics The pedagogical features make the subject more interesting and accessible to students than other texts, while maintaining an appropriate rigor. —Daniel Cunningham, CSU-Fresno This text is truly well written and organized. I do like the fact the book is quite rigorous, yet full of illustrative examples. —Bob Devaney, Boston University
Mathematical Biology
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Author : Christina Alvey
language : en
Publisher: CRC Press
Release Date : 2024-08-09
Mathematical Biology written by Christina Alvey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-09 with Mathematics categories.
This text serves as an exploration of the beautiful topic of mathematical biology through the lens of discrete and differential equations. Intended for students who have completed differential and integral calculus, Mathematical Biology: Discrete and Differential Equations allows students to explore topics such as bifurcation diagrams, nullclines, discrete dynamics, and SIR models for disease spread, which are often reserved for more advanced undergraduate or graduate courses. These exciting topics are sprinkled throughout the book alongside the more typical first- and second-order linear differential equations and systems of linear differential equations. This class-tested text is written in a conversational, welcoming voice, which should help invite students along as they discover the magic of mathematical biology and both discrete and differential equations. A focus is placed on examples with solutions written out step by step, including computational steps, with the goal of being as easy as possible for students to independently follow along. Rich in applications, this book can be used for a semester-long course in either differential equations or mathematical biology. Alternatively, it can serve as a companion text for a two-semester sequence beginning with discrete-time systems, extending through a wide array of topics in differential equations, and culminating in systems, SIR models, and other applications.
Algebra
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Author : Louis Halle Rowen
language : en
Publisher: CRC Press
Release Date : 2025-02-21
Algebra written by Louis Halle Rowen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-21 with Mathematics categories.
Algebra is a subject we have become acquainted with during most of our mathematical education, often in connection with the solution of equations. Algebra: Groups, Rings, and Fields, Second Edition deals with developments related to their solutions. The principle at the heart of abstract algebra, a subject that enables one to deduce sweeping conclusions from elementary premises, is that the process of abstraction enables us to solve a variety of such problems with economy of effort. This leads to the glorious world of mathematical discovery. This second edition follows the original three-pronged approach: the theory of finite groups, number theory, and Galois’ amazing theory of field extensions tying solvability of equations to group theory. As algebra has branched out in many directions, the authors strive to keep the text manageable while at the same time introducing the student to exciting new paths. In order to support this approach, the authors broadened the first edition, giving monoids a greater role, and relying more on matrices. Hundreds of new exercises were added. A course in abstract algebra, properly presented, could treat mathematics as an art as well as a science. In this exposition, we try to present underlying ideas, as well as the results they yield.