A Compact Capstone Course In Classical Calculus
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A Compact Capstone Course In Classical Calculus
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Author : Peter R. Mercer
language : en
Publisher: Springer Nature
Release Date : 2023-11-20
A Compact Capstone Course In Classical Calculus written by Peter R. Mercer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-20 with Mathematics categories.
This textbook offers undergraduates a self-contained introduction to advanced topics not covered in a standard calculus sequence. The author’s enthusiastic and engaging style makes this material, which typically requires a substantial amount of study, accessible to students with minimal prerequisites. Readers will gain a broad knowledge of the area, with approaches based on those found in recent literature, as well as historical remarks that deepen the exposition. Specific topics covered include the binomial theorem, the harmonic series, Euler's constant, geometric probability, and much more. Over the fifteen chapters, readers will discover the elegance of calculus and the pivotal role it plays within mathematics. A Compact Capstone Course in Classical Calculus is ideal for exploring interesting topics in mathematics beyond the standard calculus sequence, particularly for undergraduates who may not be taking more advanced math courses. It would also serve as a useful supplement for a calculus course and a valuable resource for self-study. Readers are expected to have completed two one-semester college calculus courses.
The Calculus Of Complex Functions
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Author : William Johnston
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-01
The Calculus Of Complex Functions written by William Johnston and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-01 with Mathematics categories.
The book introduces complex analysis as a natural extension of the calculus of real-valued functions. The mechanism for doing so is the extension theorem, which states that any real analytic function extends to an analytic function defined in a region of the complex plane. The connection to real functions and calculus is then natural. The introduction to analytic functions feels intuitive and their fundamental properties are covered quickly. As a result, the book allows a surprisingly large coverage of the classical analysis topics of analytic and meromorphic functions, harmonic functions, contour integrals and series representations, conformal maps, and the Dirichlet problem. It also introduces several more advanced notions, including the Riemann hypothesis and operator theory, in a manner accessible to undergraduates. The last chapter describes bounded linear operators on Hilbert and Banach spaces, including the spectral theory of compact operators, in a way that also provides an excellent review of important topics in linear algebra and provides a pathway to undergraduate research topics in analysis. The book allows flexible use in a single semester, full-year, or capstone course in complex analysis. Prerequisites can range from only multivariate calculus to a transition course or to linear algebra or real analysis. There are over one thousand exercises of a variety of types and levels. Every chapter contains an essay describing a part of the history of the subject and at least one connected collection of exercises that together comprise a project-level exploration.
Elementary Analysis
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Author : Kenneth A. Ross
language : en
Publisher: CUP Archive
Release Date : 2014-01-15
Elementary Analysis written by Kenneth A. Ross and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with Mathematics categories.
Connecting Abstract Algebra To Secondary Mathematics For Secondary Mathematics Teachers
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Author : Nicholas H. Wasserman
language : en
Publisher: Springer
Release Date : 2018-12-12
Connecting Abstract Algebra To Secondary Mathematics For Secondary Mathematics Teachers written by Nicholas H. Wasserman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Education categories.
Secondary mathematics teachers are frequently required to take a large number of mathematics courses – including advanced mathematics courses such as abstract algebra – as part of their initial teacher preparation program and/or their continuing professional development. The content areas of advanced and secondary mathematics are closely connected. Yet, despite this connection many secondary teachers insist that such advanced mathematics is unrelated to their future professional work in the classroom. This edited volume elaborates on some of the connections between abstract algebra and secondary mathematics, including why and in what ways they may be important for secondary teachers. Notably, the volume disseminates research findings about how secondary teachers engage with, and make sense of, abstract algebra ideas, both in general and in relation to their own teaching, as well as offers itself as a place to share practical ideas and resources for secondary mathematics teacher preparation and professional development. Contributors to the book are scholars who have both experience in the mathematical preparation of secondary teachers, especially in relation to abstract algebra, as well as those who have engaged in related educational research. The volume addresses some of the persistent issues in secondary mathematics teacher education in connection to advanced mathematics courses, as well as situates and conceptualizes different ways in which abstract algebra might be influential for teachers of algebra. Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers is a productive resource for mathematics teacher educators who teach capstone courses or content-focused methods courses, as well as for abstract algebra instructors interested in making connections to secondary mathematics.
Early Fourier Analysis
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Author : Hugh L. Montgomery
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-10
Early Fourier Analysis written by Hugh L. Montgomery 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 2014-12-10 with Mathematics categories.
Fourier Analysis is an important area of mathematics, especially in light of its importance in physics, chemistry, and engineering. Yet it seems that this subject is rarely offered to undergraduates. This book introduces Fourier Analysis in its three most classical settings: The Discrete Fourier Transform for periodic sequences, Fourier Series for periodic functions, and the Fourier Transform for functions on the real line. The presentation is accessible for students with just three or four terms of calculus, but the book is also intended to be suitable for a junior-senior course, for a capstone undergraduate course, or for beginning graduate students. Material needed from real analysis is quoted without proof, and issues of Lebesgue measure theory are treated rather informally. Included are a number of applications of Fourier Series, and Fourier Analysis in higher dimensions is briefly sketched. A student may eventually want to move on to Fourier Analysis discussed in a more advanced way, either by way of more general orthogonal systems, or in the language of Banach spaces, or of locally compact commutative groups, but the experience of the classical setting provides a mental image of what is going on in an abstract setting.
Calculus For The Ambitious
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Author : T. W. Körner
language : en
Publisher: Cambridge University Press
Release Date : 2014-05-29
Calculus For The Ambitious written by T. W. Körner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-29 with Mathematics categories.
From the author of The Pleasures of Counting and Naïve Decision Making comes a calculus book perfect for self-study. It will open up the ideas of the calculus for any 16- to 18-year-old, about to begin studies in mathematics, and will be useful for anyone who would like to see a different account of the calculus from that given in the standard texts. In a lively and easy-to-read style, Professor Körner uses approximation and estimates in a way that will easily merge into the standard development of analysis. By using Taylor's theorem with error bounds he is able to discuss topics that are rarely covered at this introductory level. This book describes important and interesting ideas in a way that will enthuse a new generation of mathematicians.
Beginning Functional Analysis
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Author : Karen Saxe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Beginning Functional Analysis written by Karen Saxe 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 2013-04-17 with Mathematics categories.
This book is designed as a text for a first course on functional analysis for ad vanced undergraduates or for beginning graduate students. It can be used in the undergraduate curriculum for an honors seminar, or for a "capstone" course. It can also be used for self-study or independent study. The course prerequisites are few, but a certain degree of mathematical sophistication is required. A reader must have had the equivalent of a first real analysis course, as might be taught using [25] or [109], and a first linear algebra course. Knowledge of the Lebesgue integral is not a prerequisite. Throughout the book we use elementary facts about the complex numbers; these are gathered in Appendix A. In one spe cific place (Section 5.3) we require a few properties of analytic functions. These are usually taught in the first half of an undergraduate complex analysis course. Because we want this book to be accessible to students who have not taken a course on complex function theory, a complete description of the needed results is given. However, we do not prove these results.
Introduction To Infinity Categories
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Author : Markus Land
language : en
Publisher: Springer Nature
Release Date : 2021-04-21
Introduction To Infinity Categories written by Markus Land and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-21 with Mathematics categories.
This textbook is an introduction to the theory of infinity-categories, a tool used in many aspects of modern pure mathematics. It treats the basics of the theory and supplies all the necessary details while leading the reader along a streamlined path from the basic definitions to more advanced results such as the very important adjoint functor theorems. The book is based on lectures given by the author on the topic. While the material itself is well-known to experts, the presentation of the material is, in parts, novel and accessible to non-experts. Exercises complement this textbook that can be used both in a classroom setting at the graduate level and as an introductory text for the interested reader.
Early Fourier Analysis
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Author : Hugh L. Montgomery
language : en
Publisher:
Release Date : 2015
Early Fourier Analysis written by Hugh L. Montgomery and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
In a more advanced way, either by way of more general orthogonal systems, or in the language of Banach spaces, or of locally compact commutative groups, but the experience of the classical setting provides a mental image of what is going on in an abstract setting
Abstracts Of Papers Presented To The American Mathematical Society
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Author : American Mathematical Society
language : en
Publisher:
Release Date : 1993
Abstracts Of Papers Presented To The American Mathematical Society written by American Mathematical Society 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.