Mathematical Recurrence Relations: Visual Mathematics Series PDF Download
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Author: Kiran R. Desai, Ph.d.
Publisher: CreateSpace
ISBN: 9781481219273
Category : Mathematics
Languages : en
Pages : 100
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Book Description
This book is about arranging numbers in a two dimensional space. It illustrates that it is possible to create many different regular patterns of numbers on a grid that represent meaningful summations. It uses a color coding scheme to enhance the detection of the underlying pattern for the numbers. Almost all arrangements presented are scalable or extensible, in that the matrix can be extended to larger size without the need to change existing number placements. The emphasis in this book is about the placement and summation of all the numbers for recursive embeddings. In many cases, visual charts are used to provide a higher level view of the topography, and to make the recurrence relations come alive. Number arrangements are represented for many well known multi-dimensional numbers, polygonal numbers, and various polynomials defined by recurrence relations based on equations that are a function of an integer variable n. The solutions for the recurrence relations can also be checked by adding the numbers in the arrangements presented. It is also possible to create a recurrence relation by starting with any polynomial equation using induction principles. Studying the terms in the recurrence relation helps design of the matrix and the number arrangement. This book has shown arrangements for exact powers of two, three, four, and five. Higher powers are indeed conceivable in two or three dimensional space and could be a topic for further study. Number arrangements for equations with different polynomial degree are seen to differ in the rate of change between values at adjacent levels. These have been elaborated at various places in the book. The study of recurrence relations is then steered towards arrangements for multiplication tables and linear equations in two variables. When enumerated on a coordinate graph, linear equations are seen as planar surfaces in space, and also allow solving a system of such equations visually. Although intended for college or advanced high school level students, for the majority audience this book serves as a treatise on the beauty inherent in numbers.
Author: Kiran R. Desai, Ph.d.
Publisher: CreateSpace
ISBN: 9781481219273
Category : Mathematics
Languages : en
Pages : 100
Get Book
Book Description
This book is about arranging numbers in a two dimensional space. It illustrates that it is possible to create many different regular patterns of numbers on a grid that represent meaningful summations. It uses a color coding scheme to enhance the detection of the underlying pattern for the numbers. Almost all arrangements presented are scalable or extensible, in that the matrix can be extended to larger size without the need to change existing number placements. The emphasis in this book is about the placement and summation of all the numbers for recursive embeddings. In many cases, visual charts are used to provide a higher level view of the topography, and to make the recurrence relations come alive. Number arrangements are represented for many well known multi-dimensional numbers, polygonal numbers, and various polynomials defined by recurrence relations based on equations that are a function of an integer variable n. The solutions for the recurrence relations can also be checked by adding the numbers in the arrangements presented. It is also possible to create a recurrence relation by starting with any polynomial equation using induction principles. Studying the terms in the recurrence relation helps design of the matrix and the number arrangement. This book has shown arrangements for exact powers of two, three, four, and five. Higher powers are indeed conceivable in two or three dimensional space and could be a topic for further study. Number arrangements for equations with different polynomial degree are seen to differ in the rate of change between values at adjacent levels. These have been elaborated at various places in the book. The study of recurrence relations is then steered towards arrangements for multiplication tables and linear equations in two variables. When enumerated on a coordinate graph, linear equations are seen as planar surfaces in space, and also allow solving a system of such equations visually. Although intended for college or advanced high school level students, for the majority audience this book serves as a treatise on the beauty inherent in numbers.
Author: Kiran R. Desai
Publisher:
ISBN:
Category : Arithmetic
Languages : en
Pages : 100
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Book Description
Author: Claudi Alsina
Publisher: American Mathematical Soc.
ISBN: 1614441006
Category : Mathematics
Languages : en
Pages : 173
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Book Description
Is it possible to make mathematical drawings that help to understand mathematical ideas, proofs, and arguments? The [Author];s of this book are convinced that the answer is yes and the objective of this book is to show how some visualization techniques may be employed to produce pictures that have both mathematical and pedagogical interest. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece, and India, but only in the last thirty years has there been a growing interest in so-called ``proofs without words''. Hundreds of these have been published in Mathematics Magazine and The College Mathematics Journal, as well as in other journals, books, and on the internet. Often a person encountering a ``proof without words'' may have the feeling that the pictures involved are the result of a serendipitous discovery or the consequence of an exceptional ingenuity on the part of the picture's creator. In this book, the [Author];s show that behind most of the pictures, ``proving'' mathematical relations are some well-understood methods. As the reader shall see, a given mathematical idea or relation may have many different images that justify it, so that depending on the teaching level or the objectives for producing the pictures, one can choose the best alternative.
Author: Kiran R. Desai, Ph.d.
Publisher: Createspace Independent Publishing Platform
ISBN: 9781466290785
Category : Mathematics
Languages : en
Pages : 58
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Book Description
The problems in this book are suggested for Intermediate Level students in grades 7 and 8. All the problems are presented in full color and in a visual manner in order to keep it fun and interesting. They are meant to be challenging and reinforce problem solving for algebra problems.The problems presented in this book include:* Reinforcing algebra concepts based on color, visuals, and diagrams* Visual representation of problems for one variable algebra* Visual charts and related equations* Visual problems based on linear equations for lines and triangles* Determining area of objects constructed from circles, squares, and triangles* Two variable algebra problems depicted pictorially* Introduction to three and four variable algebra* Multiple visual representations for single and two variable algebra problems* Pictorial representations for polynomial addition and multiplication* Visual depictions of quadratic equations* Visual solutions to various algebraic summation problems* Algebra problems related to area and volume* Visual mathematical problems to improve deduction skills using algebraAlso available at CreateSpace eStore: https://www.createspace.com/3682162
Author: Graham Everest
Publisher: American Mathematical Soc.
ISBN: 1470423154
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
Author: Kiran R. Desai
Publisher: CreateSpace
ISBN: 9781490325767
Category : Mathematics
Languages : en
Pages : 50
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Book Description
This book is about creating artistic pictures based on mathematical equations and principles. The focus of this book is identification of some of the mathematical principles that can be used to represent pictorially. Some of the figures are used to elaborate principles of elementary mathematics such as properties of associativity, commutativity, and distributivity. Some of them are meant to serve as a pictorial proof for algebraic equations. There are a couple of drawings to elaborate cases where the area and perimeter of different shapes are the same, even though not apparent at first. The underlying theme in many figures is the use of shapes with equal area. A variety of such shapes of equal area are then used in the visual pictures. There are quite a few figures that are based on principles of recursion. One such painting provides a visual representation for the algebraic constant, 'e'. The latter part of the book has paintings based on properties of symmetry, reflection, and replication. All the images in this book are the original work of the author.
Author: Kiran Desai
Publisher: Createspace Independent Publishing Platform
ISBN: 9781463519285
Category :
Languages : en
Pages : 0
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Book Description
The problems in this book are suggested for Intermediate Level students in grades 6 and 7. All the problems are presented in a visual manner in order to keep it fun and interesting.The problems presented in this book include:* Reinforcing mathematical concepts based on shape and color* Mathematics puzzle style problems related to addition-subtraction facts* Mathematics puzzle style problems related to multiplication-division facts* Partitioning of squared numbers as a summation of series* Visual representations for factorization problems* Determination of averages based on identifying patterns in a data set* Combining distributed multiplication terms to get larger factors* Visual representation of least common multiple (LCM) problems* Generalization of concept of LCM to the fractions domain* Visual problems based on laws of distributivity, associativity, and commutativity* Problems related to volume and area based on 2D views of solid objects* Visual mathematical problems to improve deduction skills* Graph representations for simple and compound interest and their inter-relationship* Introduction to equations, right triangles, and intersection of lines* Solving algebra number problems represented pictoriallyAlso available at CreateSpace eStore: https://www.createspace.com/3618457
Author: Open University
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 56
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Book Description
Author: J. Wimp
Publisher: Halsted Press
ISBN: 9780470206171
Category :
Languages : en
Pages : 336
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Book Description
Author: Krassimir T. Atanassov
Publisher: World Scientific
ISBN: 9789812381347
Category : Mathematics
Languages : en
Pages : 334
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Book Description
Discusses new ground on Fibonacci sequences and the well-known Fibonacci numbers. There is a continuing emphasis on diagrams, both geometric and combinatorial, which helps to tie disparate topics together, weaving around the unifying themes of the golden mean and various generalizations of the Fibonacci recurrence relation.
