Calculus A New Approach For Schools That Starts With Simple Algebra
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Calculus A New Approach For Schools That Starts With Simple Algebra
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Author : R Michael Range
language : en
Publisher: World Scientific
Release Date : 2025-06-13
Calculus A New Approach For Schools That Starts With Simple Algebra written by R Michael Range and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-13 with Mathematics categories.
Unlock the mysteries of Calculus with a fresh approach rooted in simplicity and historical insight. This book reintroduces a nearly forgotten idea from René Descartes (1596-1650), showing how the fundamental concepts of Calculus can be understood using just basic algebra. Starting with rational functions — the core of early Calculus — this method allows the reader to grasp the rules for derivatives without the intimidating concepts of limits or real numbers, making the subject more accessible than ever.But the journey doesn't stop there. While attempting to apply this algebraic approach to exponential functions, the reader will encounter the limitations of simple methods, revealing the necessity for more advanced mathematical tools. This natural progression leads to the discovery of continuity, the approximation process, and ultimately, the introduction of real numbers and limits. These deeper concepts pave the way for understanding differentiable functions, seamlessly bridging the gap between elementary algebra and the profound ideas that underpin Calculus.Whether you're a student, educator, or math enthusiast, this book offers a unique pathway to mastering Calculus. By connecting historical context with modern mathematical practice, it provides a richer, more motivating learning experience. For those looking to dive even deeper, the author's 2015 book, What is Calculus? From Simple Algebra to Deep Analysis, is the perfect next step.
Calculus A New Approach For Schools That Starts With Simple Algebra
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Author : R MICHAEL. RANGE
language : en
Publisher: World Scientific Publishing Company
Release Date : 2025-07-13
Calculus A New Approach For Schools That Starts With Simple Algebra written by R MICHAEL. RANGE and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-13 with Mathematics categories.
Unlock the mysteries of Calculus with a fresh approach rooted in simplicity and historical insight. This book reintroduces a nearly forgotten idea from René Descartes (1596-1650), showing how the fundamental concepts of Calculus can be understood using just basic algebra. Starting with rational functions -- the core of early Calculus -- this method allows the reader to grasp the rules for derivatives without the intimidating concepts of limits or real numbers, making the subject more accessible than ever.But the journey doesn't stop there. While attempting to apply this algebraic approach to exponential functions, the reader will encounter the limitations of simple methods, revealing the necessity for more advanced mathematical tools. This natural progression leads to the discovery of continuity, the approximation process, and ultimately, the introduction of real numbers and limits. These deeper concepts pave the way for understanding differentiable functions, seamlessly bridging the gap between elementary algebra and the profound ideas that underpin Calculus.Whether you're a student, educator, or math enthusiast, this book offers a unique pathway to mastering Calculus. By connecting historical context with modern mathematical practice, it provides a richer, more motivating learning experience. For those looking to dive even deeper, the author's 2015 book, What is Calculus? From Simple Algebra to Deep Analysis, is the perfect next step.
A New Approach To Differential Geometry Using Clifford S Geometric Algebra
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Author : John Snygg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-08
A New Approach To Differential Geometry Using Clifford S Geometric Algebra written by John Snygg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-08 with Mathematics categories.
Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.
The Power In The Room
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Author : Jay Gillen
language : en
Publisher: Beacon Press
Release Date : 2019-09-24
The Power In The Room written by Jay Gillen and has been published by Beacon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-24 with Education categories.
How community-centered, peer-to-peer, youth knowledge exchanges are evolving into a strong economic and political foundation on which to build radical public education. Following in the rich traditions in African American cooperative economic and educational thought, teacher-organizer Jay Gillen describes the Baltimore Algebra Project (BAP) as a youth-run cooperative enterprise in which young people direct their peers’ and their own learning for a wage. BAP and similar enterprises are creating an educational network of empowered, employed students. Gillen argues that this is a proactive political, economic, and educational structure that builds relationships among and between students and their communities. It’s a structure that meets communal needs—material and social, economic and political—both now and in the future. Through the story of the Baltimore Algebra Project, readers will learn why youth employment is a priority, how to develop democratic norms and cultures, how to foster positive community roles for 20–30 year-olds, and how to implement educational accountability from below.
Classical And Quantum Mechanics With Lie Algebras
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Author : Yair Shapira
language : en
Publisher: World Scientific
Release Date : 2021-07-19
Classical And Quantum Mechanics With Lie Algebras written by Yair Shapira and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-19 with Science categories.
How to see physics in its full picture? This book offers a new approach: start from math, in its simple and elegant tools: discrete math, geometry, and algebra, avoiding heavy analysis that might obscure the true picture. This will get you ready to master a few fundamental topics in physics: from Newtonian mechanics, through relativity, towards quantum mechanics.Thanks to simple math, both classical and modern physics follow and make a complete vivid picture of physics. This is an original and unified point of view to highlighting physics from a fresh pedagogical angle.Each chapter ends with a lot of relevant exercises. The exercises are an integral part of the chapter: they teach new material and are followed by complete solutions. This is a new pedagogical style: the reader takes an active part in discovering the new material, step by step, exercise by exercise.The book could be used as a textbook in undergraduate courses such as Introduction to Newtonian mechanics and special relativity, Introduction to Hamiltonian mechanics and stability, Introduction to quantum physics and chemistry, and Introduction to Lie algebras with applications in physics.
Algebraic Calculus
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Author : Dr Roderick Lumsden
language : en
Publisher: Eusephany Publishing
Release Date : 2016-06-29
Algebraic Calculus written by Dr Roderick Lumsden and has been published by Eusephany Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-29 with categories.
From the Preface of the First Edition: This book advocates a radically new approach to the introduction of Higher Mathematics at Freshman level. I adopt a slightly polemical tone because I'm aiming to stimulate debate. The methods, and some of the terminology, that I propose may appear unconventional, but they have sound roots in mathematical history and translate exceptionally well into digital practice, so I'll start by reviewing this background. The mathematical methods introduced by Elie Cartan the better part of a hundred years ago are now widespread in research-level work. But what is not fully acknowledged is that they can revolutionize the teaching of the subject too. All that is needed is a readable, informal account of them. Bringing in these methods, suitably simplified, right at the start, in a simple, engaging style, transforms the clarity and comprehensibility of the subject. The true meaning of so many aspects of intermediate mathematics falls naturally into place. So I'm doing two things: I'm showing that the idea of differential forms, which crystallised around a hundred years ago, allied to the concept of simplexes, suffices as a foundation to develop the entire body of the calculus easily and quickly, and gives a much more coherent line of development. I'm putting it in a way that is clear, readable and, hopefully, entertaining. So I have preferred English readability to mathematical formality wherever reasonably possible. Along the way, I cover in some depth various supporting fields such as vector algebra, with an introduction to the up and coming area of geometric algebra, and I also give a good, but more critical, introduction to the subject of generalised functions, which were more the fashion in Europe in the fifties. And to enrich the readability of the text, there are digressions into fields that are not obviously mathematical, especially if they relate to computer graphics or are particularly relevant to digital practice. I would hope the book's groundbreaking approach will be especially interesting to teachers working in digital applications at this level. So for those teaching the subject, I'll first give a brief summary of what I see as the salient original features of the book. 1)I introduce differentiation using the exterior derivative on a scalar function to generate a 1-form, so making it multivariate from the start. 2)I define integration as a product between a differential form and a simplex. 3)I use the axioms of a group to show that the addition of angles in the circle leads naturally to the idea of complex numbers. 4)The book incorporates geometric algebra into the presentation of vector algebra and analysis from an early stage. 5)Generalised Functions are introduced fully based on differential forms, and this treatment prepares the way for an advanced coverage of Fourier and Laplace transforms."
A Brief On Tensor Analysis
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Author : James G. Simmonds
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-31
A Brief On Tensor Analysis written by James G. Simmonds and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-31 with Mathematics categories.
In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.
Research In Collegiate Mathematics Education Ii
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Author : James J. Kaput
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Research In Collegiate Mathematics Education Ii written by James J. Kaput and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
The field of research in collegiate mathematics education has grown rapidly over the past 25 years. Many people are convinced that improvement in mathematics education can only come with a greater understanding of what is involved when a student tries to learn mathematics and how pedagogy can be more directly related to the learning process. Today there is a substantial body of work and a growing group of researchers addressing both basic and applied issues of mathematics education at the collegiate level. This second volume in Research in Collegiate Mathematics Education begins with a paper that attends to methodology and closes with a list of questions. The lead-off paper describes a distinctive approach to research on key concepts in the undergraduate mathematics curriculum. This approach is distinguished from others in several ways, especially its integration of research and instruction. The papers in this volume exhibit a large diversity in methods and purposes, ranging from historical studies, to theoretical examinations of the role of gender in mathematics education, to practical evaluations of particular practices and circumstances. As in RCME I, this volume poses a list of questions to the reader related to undergraduate mathematics education. The eighteen questions were raised at the first Oberwolfach Conference in Undergraduate Mathematics Education, which was held in the Fall of 1995, and are related to both research and curriculum. This series is published in cooperation with the Mathematical Association of America.
Companion Encyclopedia Of The History And Philosophy Of The Mathematical Sciences
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Author : Ivor Grattan-Guinness
language : en
Publisher: Routledge
Release Date : 2002-09-11
Companion Encyclopedia Of The History And Philosophy Of The Mathematical Sciences written by Ivor Grattan-Guinness and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-11 with Philosophy categories.
* Examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century * 176 articles contributed by authors of 18 nationalities * Chronological table of main events in the development of mathematics * Fully integrated index of people, events and topics * Annotated bibliographies of both classic and contemporary sources * Unique coverage of Ancient and non-Western traditions of mathematics
Economic And Financial Modeling With Mathematica
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Author : Hal R. Varian
language : en
Publisher: Springer
Release Date : 2013-11-21
Economic And Financial Modeling With Mathematica written by Hal R. Varian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Business & Economics categories.
Mathematica is a computer program (software) for doing symbolic, numeric and graphical analysis of mathematical problems. In the hands of economists, financial analysts and other professionals in econometrics and the quantitative sector of economic and financial modeling, it can be an invaluable tool for modeling and simulation on a large number of issues and problems, besides easily grinding out numbers, doing statistical estimations and rendering graphical plots and visuals. Mathematica enables these individuals to do all of this in a unified environment. This book's main use is that of an applications handbook. Modeling in Economics and Finance with Mathematica is a compilation of contributed papers prepared by experienced, "hands on" users of the Mathematica program. They come from a broad spectrum of Mathematica devotees in the econometric and financial/investment community on both the professional and academic fronts. Each paper provides a set of tools and examples of Mathematica in action. These tools will also be made accessible to users via a DOS-based floppy disk which will contain Mathematica Notebooks and Packages, and be packaged with the book.