Description The book has the material typically covered in the third semester of a mainstream calculus course for science, mathematics, and engineering students. There are 420 exercises grouped into easy, moderate, and challenging categories. There are answers and some hints for the odd-numbered problems and for some of the even-numbered problems. Some exercises require the student to write programs for numerical approximations with code samples given in Java, but any programming language could be used.
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 book is a well-organized text with carefully constructed examples, a full quota of exercises with solutions, and an emphasis that is algebraic rather than geometric. The book is Sage-enabled with approximately 90 examples of Sage code spread throughout. The book sections can be loaded into Sage as worksheets so that the code can be evaluated immediately; however, it is not necessary to use Sage in order to make use of this textbook.
Description This book has the standard content of a course for science, math, and engineering students that follows calculus. A semester of calculus is the explicit prerequisite, but most students would have three semesters of calculus and for them some of the beginning sections of the book can be skipped. Each chapter ends with three or four applications of that chapter’s subject.
Description Brown University has two introductory linear algebra courses. This text is used in the honors course that emphasizes proofs. The book’s title suggests that it is not the typical approach to linear algebra even among those books that are more theoretical.
Description From the author’s preface: 'This text is an expansion and refinement of lecture notes I developed while teaching proofs courses over the past ten years. It is written for an audience of mathematics majors at Virginia Commonwealth University, a large state university….However, I am mindful of a larger audience. I believe this book is suitable for almost any undergraduate mathematics program.' Designed for the typical bridge course that follows calculus and introduces the students to the language and style of more theoretical mathematics, Book of Proof has 13 chapters grouped into four sections: (I) Fundamentals, (II) How to Prove Conditional Statements, (III) More on Proof, (IV) Relations, Functions, and Cardinality. One math professor who has used the book writes: 'Hammack’s book is great. I’ve used the book twice now, will use it again, and have recommended it to other instructors. I have used it in a discrete math course which serves as a “transition” course for our majors.'
Description This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable.
Description This book emphasizes effective communication of mathematics through writing and it promotes active learning by the students. Notable features include preview activities for each section intended for students to do before class and progress checks within the text for the student to do on the spot, with answers at the end of the book.
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 open source textbook is being used at the University of Northern Colorado in a discrete mathematics course taken primarily by math majors, many of whom plan to become secondary teachers. This text can also be used in a bridge course or introduction to proofs. The major topics are introduced with Investigate! activities designed to get students more actively involved and which are suitable for inquiry based learning.
Description Parts I and II deal with two fundamental aspects of combinatorics: enumeration and graph theory. “Enumeration” can mean either counting or listing things. Mathematicians have generally limited their attention to counting, but listing plays an important role in computer science, so we discuss both aspects. After introducing the basic concepts of “graph theory” in Part II, we present a variety of applications of interest in computer science and mathematics. Induction and recursion play a fundamental role in mathematics. The usefulness of recursion in computer science and in its interaction with combinatorics is the subject of Part III. In Part IV we look at “generating functions,” a powerful tool for studying counting problems.
Description This book was designed for the junior level combinatorics course at Georgia Tech for students in computer science and in applied mathematics. The authors began writing the book in 2004 and has benefited from extensive classroom use. The source is now in MathBook XML, which serves as the common source for all three versions: HTML, PDF, and print, and so they are virtually identical. The HTML version does have the advantage of live Sage cells that the reader can evaluate and modify.
Description As the title suggests this book is designed for a “discovery method” course. The heart of the book is the hundreds of exercises that guide the student through the key ideas of enumerative combainatorics and a brief introduction to graph theory. The exercises are marked with special symbols to indicate their role in the course, for example, whether they are essential or motivational. The three supplmental sections deal with relations, mathematical induction, and exponential generating functions. This book is the result of an NSF project led by Ken Bogart and is currently maintained by the Mathematics Department of Dartmouth College.
Description This textbook serves admirably as an introduction for newcomers to Sage as well as a reference for those with some experience. It is written in an engaging and informal style and does an excellent job in explaining how Sage works. The book can be used profitably as an auxiliary text in any undergraduate mathematics class with a computational component, and it can be used in the mathematical software courses that are becoming more common, especially for math majors.
Description This book was developed as the text for a first course in numerical analysis at Southern Connecticut State University as an open source alternative to a classic text such as Burden and Faires. The first five chapters make up the content of a semester course. The style is engaging and conversational. As the author writes in the preface: “Much of the material will be presented as if it were being told to a student during tea time at University, but with the benefit of careful planning.” The exercises are plentiful and well-designed, and many of them have extensive solutions.
Description The content of this book is traditional for a first course in abstract algebra at the junior or senior level. It may be used for either one or two semesters. The exercises include both computational and theoretical and there are a number of applications. Hints or short answers are given to most problems but not fully written solutions.
Description This book is written with the author’s conviction that “it is easier to build a course from a base than to extract it from a big book.” The five chapters deal with fundamentals, groups, rings, matrix rings, and linear algebra. Despite the small size there is enough material for a full year. Many of the easy proofs are left as exercises. An instructor using this book should expect to add examples and build on the structure provided.
Description The writing style is informal and conversational. Examples appear before formal definitions. In addition to the usual material for a year long course on groups, rings, and fields, this book treats group actions, modules, and the Galois correspondence. The prerequisite is a good grasp of linear algebra, and overall the level of sophistication is above that of most undergraduate texts. There are appendices with background material in logic, set theory, induction, complex numbers, and linear algebra.
Description The approach in this 165 page book tends to be more sophisticated than other books for the first number theory course, but it motivates much of the material with public key cryptography. It also uses Sage in order to deal with more realistic examples—such as RSA codes based on primes with more than 30 digits. Although published commercially by Springer, the publisher has granted access to a free pdf version that individuals can download, use, and print.
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