A Treatise on the Binomial Theorem PDF Download
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Author: Craig Smorynski
Publisher: Texts in Mathematics
ISBN: 9781848900851
Category : Mathematics
Languages : en
Pages : 358
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Book Description
"The binomial theorem is usually quite rightly considered as one of the most important theorems in the whole of analysis." Thus wrote Bernard Bolzano in 1816 in introducing the first correct proof of Newton's generalisation of a century and a half earlier of a result familiar to us all from elementary algebra. Bolzano's appraisal may surprise the modern reader familiar only with the finite algebraic version of the Binomial Theorem involving positive integral exponents, and may also appear incongruous to one familiar with Newton's series for rational exponents. Yet his statement was a sound judgment back in the day. Here the story of the Binomial Theorem is presented in all its glory, from the early days in India, the Moslem world, and China as an essential tool for root extraction, through Newton's generalisation and its central role in infinite series expansions in the 17th and 18th centuries, and to its rigorous foundation in the 19th. The exposition is well-organised and fairly complete with all the necessary details, yet still readable and understandable for those with a limited mathematical background, say at the Calculus level or just below that. The present book, with its many citations from the literature, will be of interest to anyone concerned with the history or foundations of mathematics.
Author: Craig Smorynski
Publisher: Texts in Mathematics
ISBN: 9781848900851
Category : Mathematics
Languages : en
Pages : 358
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Book Description
"The binomial theorem is usually quite rightly considered as one of the most important theorems in the whole of analysis." Thus wrote Bernard Bolzano in 1816 in introducing the first correct proof of Newton's generalisation of a century and a half earlier of a result familiar to us all from elementary algebra. Bolzano's appraisal may surprise the modern reader familiar only with the finite algebraic version of the Binomial Theorem involving positive integral exponents, and may also appear incongruous to one familiar with Newton's series for rational exponents. Yet his statement was a sound judgment back in the day. Here the story of the Binomial Theorem is presented in all its glory, from the early days in India, the Moslem world, and China as an essential tool for root extraction, through Newton's generalisation and its central role in infinite series expansions in the 17th and 18th centuries, and to its rigorous foundation in the 19th. The exposition is well-organised and fairly complete with all the necessary details, yet still readable and understandable for those with a limited mathematical background, say at the Calculus level or just below that. The present book, with its many citations from the literature, will be of interest to anyone concerned with the history or foundations of mathematics.
Author: Jianlun Xu
Publisher: Createspace Independent Publishing Platform
ISBN: 9781545489642
Category :
Languages : en
Pages : 50
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Book Description
"The Binomial Theorem" is the book about binomial expansion and its applications. It is an important topic in algebra for high school and college students. As a self-study guide, the book provides plenty of examples and explanations to help readers to grasp math concepts.
Author: Paul A. Calter
Publisher: John Wiley & Sons
ISBN: 0470534923
Category : Mathematics
Languages : en
Pages : 836
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Book Description
This textbook has been in constant use since 1980, and this edition represents the first major revision of this text since the second edition. It was time to select, make hard choices of material, polish, refine, and fill in where needed. Much has been rewritten to be even cleaner and clearer, new features have been introduced, and some peripheral topics have been removed. The authors continue to provide real-world, technical applications that promote intuitive reader learning. Numerous fully worked examples and boxed and numbered formulas give students the essential practice they need to learn mathematics. Computer projects are given when appropriate, including BASIC, spreadsheets, computer algebra systems, and computer-assisted drafting. The graphing calculator has been fully integrated and calculator screens are given to introduce computations. Everything the technical student may need is included, with the emphasis always on clarity and practical applications.
Author: Edward Burger
Publisher:
ISBN: 9780967835723
Category : Mathematics
Languages : en
Pages :
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Book Description
Author: Lynn Marecek
Publisher:
ISBN: 9781951693848
Category :
Languages : en
Pages :
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Book Description
Author: Ken Levasseur
Publisher: Lulu.com
ISBN: 1105559297
Category : Computers
Languages : en
Pages : 574
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Book Description
''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).''--
Author: Michael Z. Spivey
Publisher: CRC Press
ISBN: 1351215809
Category : Mathematics
Languages : en
Pages : 277
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Book Description
The book has two goals: (1) Provide a unified treatment of the binomial coefficients, and (2) Bring together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton’s binomial series), differentiation (Leibniz’s generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics.
Author: Richard Forringer
Publisher:
ISBN: 9781935991373
Category : Mathematics
Languages : en
Pages : 122
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Book Description
While Symbolic Logic and the Binomial Expansion are subjects that are often mentioned in High School and College math courses, the two projects contained in this book have been carefully developed to help the student achieve a more in-depth understanding of these concepts. The projects are designed to be done independently or they can be incorporated into the curriculum of any math course from second semester algebra and beyond. Students who complete these projects will gain a stronger appreciation of what it means to think logically and they will see how two seemingly unrelated areas of study connect in ways that strengthen both. Areas of focus in these projects include: Truth Tables Compound Truth Tables Negations Conditionals Converse, Inverse, and Contrapositive Biconditionals Tautologies Symbolic logic (also known as Mathematical Logic) is foundational to many fields of study such as computer science and engineering. Those who have an understanding of symbolic logic and the binomial expansion will be better prepared for further courses of study in mathematics, science, and engineering. About the author: Dick Forringer received his Bachelors Degree from Kent State University, majoring in mathematics and he earned his Masters in Education from Fordham University. He retired after 42 years of being a teacher and administrator at Durham Academy, in Durham, North Carolina. He is a recipient of the F. Robertson Hershey Distinguished Faculty award and the Brumley Excellence in Teaching award. Dick has also had three feature articles published in Mathematics Teacher. This is his second published book.
Author: Jay P. Abramson
Publisher:
ISBN: 9781938168376
Category : Algebra
Languages : en
Pages : 1564
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Book Description
"The text is suitable for a typical introductory algebra course, and was developed to be used flexibly. While the breadth of topics may go beyond what an instructor would cover, the modular approach and the richness of content ensures that the book meets the needs of a variety of programs."--Page 1.
Author: Harris Kwong
Publisher: Open SUNY Textbooks
ISBN: 9781942341161
Category : Mathematics
Languages : en
Pages : 298
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Book Description
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.
