Thirty years ago mathematical, as opposed to applied numerical, computation was difficult to perform and so relatively little used. Three threads changed that: the emergence of the personal computer; the discovery of fiber-optics and the consequent development of the modern internet; and the building of the Three “M’s” Maple, Mathematica and Matlab. We intend to persuade that Mathematica and other similar tools are worth knowing, assuming only that one wishes to be a mathematician, a mathematics educator, a computer scientist, an engineer or scientist, or anyone else who wishes/needs to use mathematics better. We also hope to explain how to become an "experimental mathematician" while learning to be better at proving things. To accomplish this our material is divided into three main chapters followed by a postscript. These cover elementary number theory, calculus of one and several variables, introductory linear algebra, and visualization and interactive geometric computation.

As the open-source and free competitor to expensive software like MapleTM, Mathematica®, Magma, and MATLAB®, Sage offers anyone with access to a web browser the ability to use cutting-edge mathematical software and display his or her results for others, often with stunning graphics. This book is a gentle introduction to Sage for undergraduate students toward the end of Calculus II (single-variable integral calculus) or higher-level course work such as Multivariate Calculus, Differential Equations, Linear Algebra, or Math Modeling. The book assumes no background in computer science, but the reader who finishes the book will have learned about half of a first semester Computer Science I course, including large parts of the Python programming language. The audience of the book is not only math majors, but also physics, engineering, finance, statistics, chemistry, and computer science majors.

"One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration." "In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide."--BOOK JACKET.

This book constitutes the refereed proceedings of the third Maple Conference, MC 2019, held in Waterloo, Ontario, Canada, in October 2019. The 21 revised full papers and 9 short papers were carefully reviewed and selected out of 37 submissions, one invited paper is also presented in the volume. The papers included in this book cover topics in education, algorithms, and applciations of the mathematical software Maple.

This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author. This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. - See more at: http://bookstore.ams.org/CHEL-376-H/#sthash.wHQ1vpdk.dpuf This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author. This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. - See more at: http://bookstore.ams.org/CHEL-376-H/#sthash.wHQ1vpdk.dpuf

Modern computing tools like Maple (symbolic computation) and Matlab (a numeric computation and visualization program) make it possible to easily solve realistic nontrivial problems in scientific computing. In education, traditionally, complicated problems were avoided, since the amount of work for obtaining the solutions was not feasible for the students. This situation has changed now, and the students can be taught real-life problems that they can actually solve using the new powerful software. The reader will improve his knowledge through learning by examples and he will learn how both systems, MATLAB and MAPLE, may be used to solve problems interactively in an elegant way. Readers will learn to solve similar problems by understanding and applying the techniques presented in the book. All programs used in the book are available to the reader in electronic form.