Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a...
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or appl...
Geometric measure theory has roots going back to ancient Greek mathematics, for considerations of the isoperimetric problem (to ?nd the planar domain of given perimeter having greatest area) led naturally to questions about spatial regions and boundaries. In more modern times, the Plateau problem is considered to be the wellspring of questions in geometric measure theory. Named in honor of the nineteenth century Belgian physicist Joseph Plateau, who studied surface tension phenomena in general, andsoap?lmsandsoapbubblesinparticular, thequestion(initsoriginalformulation) was to show that a...
Geometric measure theory has roots going back to ancient Greek mathematics, for considerations of the isoperimetric problem (to ?nd the planar domain ...
Classical mechanics is one of those special occurrences in science where interdisciplinary contributions have come together in a perfect blend, providing a most elegant and penetrating example of "modeling" in science. Following Lagrangrian principles, the author employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries, such as the d'Alembert principle, complex systems dynamics, and Hamiltonian mechanics. Today, these same dynamics are now being focused to address other interdisciplinary areas of research in...
Classical mechanics is one of those special occurrences in science where interdisciplinary contributions have come together in a perfect blend, pro...
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole, presenting the subject matter in a forward-looking way that takes into account its historical development.
Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group...
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, wh...
This is a revised and extended version of my 1995 elementary introduction to partial di?erential equations. The material is essentially the same except for three new chapters. The ?rst (Chapter 8) is about non-linear equations of ?rst order and in particular Hamilton–Jacobi equations. It builds on the continuing idea that PDEs, although a branch of mathematical analysis, are closely related to models of physical phenomena. Such underlying physics in turn provides ideas of solvability. The Hopf variational approach to the Cauchy problem for Hamilton–Jacobi equations is one of the clearest...
This is a revised and extended version of my 1995 elementary introduction to partial di?erential equations. The material is essentially the same excep...
This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that of the previous editions by including five new chapters covering additional PDE topics relevant for current areas of active research. This includes coverage of linear parabolic equations with measurable coefficients, parabolic DeGiorgi classes,...
This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful...
