Steven Schlicker

Ted Sundstrom

Jonathan K. Hodge

Abstract Algebra: An Inquiry-Based Approach, Second Edition not only teaches abstract algebra, but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think. The second edition of this unique, flexible approach builds on the success of the first edition. The authors offer an emphasis on active learning, helping students learn algebra by gradually building both their intuition and their ability to write coherent proofs in context. The goals for this text include: Allowing the flexibility to begin the course with either groups or rings. Introducing the ideas behind definitions and theorems to help students develop intuition. Helping students understand how mathematics is done. Students will experiment through examples, make conjectures, and then refine or prove their conjectures. Assisting students in developing their abilities to effectively communicate mathematical ideas. Actively involving students in realizing each of these goals through in-class and out-of-class activities, common in-class intellectual experiences, and challenging problem sets. Changes in the Second Edition Streamlining of introductory material with a quicker transition to the material on rings and groups. New investigations on extensions of fields and Galois theory. New exercises added and some sections reworked for clarity. More online Special Topics investigations and additional Appendices, including new appendices on other methods of proof and complex roots of unity. Encouraging students to do mathematics and be more than passive learners, this text shows students the way mathematics is developed is often different than how it is presented; definitions, theorems, and proofs do not simply appear fully formed; mathematical ideas are highly interconnected; and in abstract algebra, there is a considerable amount of intuition to be found.

An Inquiry-Based Approach

Abstract Algebra

Edward Aboufadel

An accessible and practical introduction to wavelets With applications in image processing, audio restoration,seismology, and elsewhere, wavelets have been the subject ofgrowing excitement and interest over the past several years.Unfortunately, most books on wavelets are accessible primarily toresearch mathematicians. Discovering Wavelets presents basic andadvanced concepts of wavelets in a way that is accessible to anyonewith only a fundamental knowledge of linear algebra. The basic concepts of wavelet theory are introduced in the contextof an explanation of how the FBI uses wavelets to compressfingerprint images. Wavelet theory is further developed in thesetting of function spaces. The book then moves on to present moreadvanced topics such as filters, multiresolution analysis,Daubechies' wavelets, and further applications. The book concludeswith a series of projects and problems that introduce advancedtopics and offer starting points for research. Sample projects thatdemonstrate real wavelet applications include image compression, awavelet-based search engine, processing with Daubechies' wavelets,and more. Among the special features of Discovering Wavelets are: * Real-life, hands-on examples that involve actual waveletapplications * A companion Web site containing Pixel Images software and Maplefiles to be used with the projects in the book * Challenging problems that reinforce and expand on the ideas beingdeveloped * An appendix containing the linear algebra needed to understandwavelets as presented in the book

Discovering Wavelets

This college level trigonometry text may be different than most other trigonometry textbooks. In this book, the reader is expected to do more than read the book but is expected to study the material in the book by working out examples rather than just reading about them. So the book is not just about mathematical content (although it does contain important topics in trigonometry needed for further study in mathematics), but it is also about the process of learning and doing mathematics and is designed not to be just casually read but rather to be engaged. Recognizing that actively studying a mathematics book is often not easy, several features of the textbook have been designed to help students become more engaged as they study the material. Some of the features are: Beginning activities in each section that engage students with the material to be introduced, focus questions that help students stay focused on what is important in the section, progress checks that are short exercises or activities that replace the standard examples in most textbooks, a section summary, and appendices with answers for the progress checks and selected exercises.

Trigonometry

David Austin

Matthew Boelkins

Active Calculus is different from most existing texts in that: the text is free to read online in .html or via download by users in .pdf format; in the electronic format, graphics are in full color and there are live .html links to java applets; the text is open source, so interested instructor can gain access to the original source files via GitHub; the style of the text requires students to be active learners ... there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus ideas; each section begins with motivating questions, a brief introduction, and a preview activity; each section concludes (in .html) with live WeBWorK exercises for immediate feedback, followed by a few challenging problems.

Steven Schlicker

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