The book is a self-contained introduction to the results and computational methods in classical invariant theory. It relies on minimal mathematical prerequisites, and can be read by advanced undergraduate or graduate students. A variety of innovations will also make the book of interest to specialists and researchers.
This textbook develops essential tools of linear algebra, aiming to impart both technique and contextual understanding. Applications and theory are intertwined, reinforcing each other to help students gain technical proficiency and an appreciation for the use of linear algebra in modern applied mathematics. It covers key topics such as Gaussian elimination, inner products, norms, eigenvalues, and singular values, suitable for both an in-depth first course or an application-driven second course. The second edition features updated and expanded applications, including numerical methods, dynamical systems, data analysis, and signal processing, while enhancing the pedagogical flow of core material. The text emphasizes conceptual connections between applications and underlying linear algebra techniques, enabling students to apply mathematical tools in routine contexts and adapt to unique problems. No prior knowledge of linear algebra is required, with single-variable calculus as the only prerequisite. However, some mathematical maturity is necessary to engage with the increasing abstraction of the subject. Equipped with the tools and concepts from this book, students will be prepared for further studies in differential equations, numerical analysis, data science, and statistics. The first author’s text on partial differential equations serves as an ideal companion, extending the linear mathematical methods developed here.
A solid introduction to applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented such that graduates and researchers can readily learn to use them. Following an exposition of the applications, the book develops the underlying theory, with many of the topics presented in a novel way, emphasising explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at the end of each chapter.
Focusing on the fundamentals of partial differential equations, this textbook is tailored for advanced undergraduates and beginning graduate students across various disciplines. It expertly combines solution techniques with mathematical rigor and practical applications, supported by numerous examples. Each subsection features extensive exercises, ranging from computational problems to theoretical proofs and challenging projects, encouraging deeper exploration of the subject.
This book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. It will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and related fields.
"Comprises some of the key work presented at two IMA Wokshops on Computer Vision during fall of 2000."--Pref.