Description The authors are instructors at large community colleges in Ohio, and the book has now been adopted at several other locations. Those who have used the book expect to continue using it. One community college instructor now using it for the fourth time says he highly recommends the book to other colleagues and that his students often make positive comments about the book. He has found the authors “very approachable and helpful when I had questions or concerns.” Send email to the authors for more information about course adoptions of their books.
Description From the MAA review of this book: 'The discussions and explanations are succinct and to the point, in a way that pleases mathematicians who don’t like calculus books to go on and on.' The book covers the standard material in a calculus course for science and engineering. The size of the book is such that an instructor does not have to skip sections in order to fit the material into the typical course schedule. The single variable material is contained in eleven chapters beginning with analytic geometry and ending with sequences and series. The multivariable material consists of five chapters and includes with the vector calculus of in two and three dimensions through the divergence theorem. The book ends with a final chapter on differential equations. There are sufficiently many exercises at the end of each sections, but not as many as the much bigger commercial texts. Also available are WeBWorK problem sets keyed to the sections of the text. Some students and instructors may want to use something like a Schaum’s outline for additional problems.
Description Rather than detailed explanations and worked out examples, this book uses activities intended to be completed by the students in order to develop the standard concepts and computational techniques of calculus. The student activities offer structure so that instructors can interactively engage students during class; it’s also possible to assign select activities as homework. In addition to a modest number of more routine anonymous WeBWorK exercises in each section, the text includes 3-4 challenging problems per section. Instructors wanting a more extensive collection of exercises will need to supply their own or use an online homework system such as WeBWork. Active Calculus makes it possible to teach an inquiry-oriented or active learning course without severely restricting the material considered. The book has been publicly available since 2012 and has been used throughout that time at Grand Valley State (the authors’ institution) and for several years at numerous other colleges and universities.
Description The book is subtitled “Differential Equations for Engineers” and is suitable for the typical one term course for science and engineering students that follows calculus. The book lends itself to a variety of course designs. Beyond the first two chapters there is not a strict linear dependency for the remaining chapters. The book stands on its own but can also be used with IODE, a free software package developed at the University of Illinois for experimenting with differential equations.
Description These texts are appropriate for a first course in differential equations for one or two semesters. There are more than 2000 exercises, and the student manual has solutions for most of the even numbered ones.
Description This textbook contains the content of a two semester course in discrete structures, which is typically a second-year course for students in computer science or mathematics, but it does not have a calculus prerequisite. The material for the first semester is in chapters 1-10 and includes logic, set theory, functions, relations, recursion, graphs, trees, and elementary combinatorics. The second semester material in chapters 11-16 deals with algebraic structures: binary operations, groups, matrix algebra, Boolean algebra, monoids and automata, rings and fields.
Description This book originated in 2009 as lecture notes for the undergraduate analysis course at the University of Illinois, whose syllabus was based on the text of Bartle and Sherbert, but it is now a mature textbook. It has been used by a number of instructors at other institutions and they report that they recommend the book and will continue to use it. There is now a second volume, Basic Analysis 2, written for the second semester of a year long course.
Description From an instructor who recently used this book: “I found it mathematically sound, well organized and very instructive for a good upper division undergraduate class. In particular, the exercise sets are well thought out and both the proofs and the narrative speak well to that level of student without sacrificing any rigor.”
Description This text for a semester course portrays real analysis in the context of its historical development. It is written in a direct style aimed at students and not instructors. A student using the book is guided to understand and prove much of the actual mathematical content through the more than 200 problems that are embedded within the narrative and not placed at the end of sections as in most textbooks. For a course taught in the inquiry based learning mode this book should work better than standard texts. On the other hand, with the instructor offering more guidance it should also work well with a more traditional classroom style.
Description This book is written for upper division mathematics students with the aim of getting to and understanding the incompleteness theorems in a single semester. The authors outline two paths to this goal as described in the preface to the second edition: 'This has allowed us to chart two paths to the incompleteness theorems, splitting after the material in Chapter 4. Readers of the first edition will find that the exposition in Chapters 5 and 6 follows a familiar route, although the material there has been pretty thoroughly reworked. It is also possible, if you choose, to move directly from Chapter 4 to Chapter 7 and see a development of computability theory that covers the Entschei- dungsproblem, Hilbert’s 10th Problem, and Gödel’s First Incompleteness Theorem.'
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