This guide provides explanations of eigenvalues, eigenvectors, linear transformations, linear equations, vectors, and matrices.

    This book draws on material Michael created for his renowned Object Mentor seminars, techniques Michael has used in mentoring to help hundreds of developers, technical managers, and testers bring their legacy systems under control. The topics covered include: Understanding the mechanics of software change, adding features, fixing bugs, improving design, optimizing performance Getting legacy code into a test harness Writing tests that protect you against introducing new problems Techniques that can be used with any language or platform, with examples in Java, C++, C, and C# Accurately identifying where code changes need to be made Coping with legacy systems that aren't object-oriented Handling applications that don't seem to have any structureThis book also includes a catalog of twenty-four dependency-breaking techniques that help you work with program elements in isolation and make safer changes.

    It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

    Joining the professional web designers and programmers are new audiences who need to know a little bit of code at work (update a content management system or e-commerce store) and those who want to make their personal blogs more attractive. Many books teaching HTML and CSS are dry and only written for those who want to become programmers, which is why this book takes an entirely new approach. • Introduces HTML and CSS in a way that makes them accessible to everyone—hobbyists, students, and professionals—and it’s full-color throughout • Utilizes information graphics and lifestyle photography to explain the topics in a simple way that is engaging • Boasts a unique structure that allows you to progress through the chapters from beginning to end or just dip into topics of particular interest at your leisureThis educational book is one that you will enjoy picking up, reading, then referring back to. It will make you wish other technical topics were presented in such a simple, attractive and engaging way!

    These sections together make an appropriate one-term advanced/graduate level course (mathematical prerequisites: vector analysis and simple partial-differential equations). The book is printed to make it easy for readers to identify these sections.• The remaining Track 2 material provides a wealth of advanced topics instructors can draw from to flesh out a two-term course, with Track 1 sections serving as prerequisites.

    Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.