Steven Schlicker - Böcker

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 ringsIntroducing the ideas behind definitions and theorems to help students develop intuitionHelping students understand how mathematics is done. Students will experiment through examples, make conjectures, and then refine or prove their conjecturesAssisting students in developing their abilities to effectively communicate mathematical ideasActively involving students in realizing each of these goals through in-class and out-of-class activities, common in-class intellectual experiences, and challenging problem setsChanges in the Second EditionStreamlining of introductory material with a quicker transition to the material on rings and groupsNew investigations on extensions of fields and Galois theoryNew exercises added and some sections reworked for clarityMore online Special Topics investigations and additional Appendices, including new appendices on other methods of proof and complex roots of unityEncouraging 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 accessible and practical introduction to wavelets With applications in image processing, audio restoration, seismology, and elsewhere, wavelets have been the subject of growing excitement and interest over the past several years. Unfortunately, most books on wavelets are accessible primarily to research mathematicians. Discovering Wavelets presents basic and advanced concepts of wavelets in a way that is accessible to anyone with only a fundamental knowledge of linear algebra. The basic concepts of wavelet theory are introduced in the context of an explanation of how the FBI uses wavelets to compress fingerprint images. Wavelet theory is further developed in the setting of function spaces. The book then moves on to present more advanced topics such as filters, multiresolution analysis, Daubechies' wavelets, and further applications. The book concludes with a series of projects and problems that introduce advanced topics and offer starting points for research. Sample projects that demonstrate real wavelet applications include image compression, a wavelet-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 wavelet applications* A companion Web site containing Pixel Images software and Maple files to be used with the projects in the book* Challenging problems that reinforce and expand on the ideas being developed* An appendix containing the linear algebra needed to understand wavelets as presented in the book