From Counting To Calculus
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From Counting To Calculus
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Author : Michael F. Petras
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2016-12-27
From Counting To Calculus written by Michael F. Petras and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-27 with categories.
A unified approach to mathematics covering all of the major topics from simple counting through calculus, including an introduction to differential equations. Starting with counting, all of the operations of arithmetic and the corresponding systems of numbers are developed as a single, interconnected framework. This framework is then used as a foundation for the construction of algebra and calculus. Each new topic is introduced as a logical extension of the topics that came before it, and is developed thoroughly and rigorously with the reader as if it was being invented for the first time. Although it is assumed that the reader is familiar with arithmetic and has had some exposure to algebra, proficiency with mathematics is not required. The conversational style and step-by-step approach make it easy to follow the flow of ideas, and numerous exercises sprinkled throughout allow readers to test their understanding before proceeding to the next topic. Among the topics covered are the additive and positional number systems, the operations of arithmetic, integer and non-integer exponents, fractions, rational and irrational numbers, real and complex numbers, algebraic solutions of equations, simultaneous equations, graphs and graphical solutions of equations, constructing polynomial equations from data, finding roots of polynomial equations, functions and inverse functions, differential calculus including the sum, product, and chain rules, integral calculus including proper and improper integrals, and an introduction to ordinary and partial differential equations, with applications to the physical sciences. Problems at the ends of the chapters, along with their solutions, provide the opportunity to practice methods discussed in the text, and explore important topics in more depth. The choice of subject matter and method of presentation makes this an ideal text for a high school or college level course, or as a self-teaching guide for the general reader interested in developing a deeper understanding of mathematics.
Understanding Mathematics
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Author : Keith Kressin
language : en
Publisher:
Release Date : 1997-03
Understanding Mathematics written by Keith Kressin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03 with Mathematics categories.
A comprehensive overview of elementary, middle, and high-school mathematics. Intended as a supplement to any math program, this book provides additional math explanation from basic to advanced levels. Emphasis is placed on why problems are solved in a certain manner. Tailored for those who need simplified, easy-to-read additional explanations of math concepts.
The Teaching Of Mathematics From Counting To Calculus
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Author : Harold Pascoe Fawcett
language : en
Publisher: C.E. Merill Publishing Company
Release Date : 1970
The Teaching Of Mathematics From Counting To Calculus written by Harold Pascoe Fawcett and has been published by C.E. Merill Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
Discrete Calculus
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Author : Carlo Mariconda
language : en
Publisher: Springer
Release Date : 2016-12-01
Discrete Calculus written by Carlo Mariconda and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-01 with Mathematics categories.
This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet user-friendly approach. This is particularly useful in combinatorics, a field where, all too often, exercises are solved by means of ad hoc tricks. The book contains more than 400 examples and about 300 problems, and the reader will be able to find the proof of every result. To further assist students and teachers, important matters and comments are highlighted, and parts that can be omitted, at least during a first and perhaps second reading, are identified.
Mathematics For The Million
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Author : Lancelot Thomas Hogben
language : en
Publisher:
Release Date : 1993
Mathematics For The Million written by Lancelot Thomas Hogben and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Explains mathematics from counting to calculus in the light of man's changing social achievements.
Mathematics For The Million
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Author : Lancelot Hogben
language : en
Publisher: W. W. Norton & Company
Release Date : 1968
Mathematics For The Million written by Lancelot Hogben and has been published by W. W. Norton & Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Explains mathematics from counting to calculus in the light of man's changing social achievements.
Calculus
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Author : Ivan Niven
language : en
Publisher:
Release Date : 1961
Calculus written by Ivan Niven and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with categories.
Counting With Symmetric Functions
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Author : Jeffrey Remmel
language : en
Publisher: Birkhäuser
Release Date : 2015-11-28
Counting With Symmetric Functions written by Jeffrey Remmel and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-28 with Mathematics categories.
This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties. Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.
First Year Calculus
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Author : Einar Hille
language : en
Publisher:
Release Date : 1968-06
First Year Calculus written by Einar Hille and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968-06 with Calculus categories.
Elliptic Tales
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Author : Avner Ash
language : en
Publisher: Princeton University Press
Release Date : 2014-10-19
Elliptic Tales written by Avner Ash and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-19 with Mathematics categories.
Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profoundmay appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.