From the reviews: Serious graduate students ... would profit from reading the book for the mathematical maturity they would gain in the process. The conversational, almost Socratic, style of exposition is well suited to giving students some insight into the process of doing mathematics as well as to the importance of asking the right questions ... ......
Discovering Abstract Algebra takes an Inquiry-Based Learning approach to the subject, leading students to discover for themselves its main themes and techniques. Concepts are introduced conversationally through extensive examples and student investigation before being formally defined. Students will develop skills in carefully making statements ......
Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the ......
This book features plane curves-the simplest objects in differential geometry-to illustrate many deep and inspiring results in the field in an elementary and accessible way. After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of ......
This volume contains the proceedings of the AMS Special Session on Differential Geometry and Global Analysis, Honoring the Memory of Tadashi Nagano (1930-2017), held January 16, 2020, in Denver, Colorado. Tadashi Nagano was one of the great Japanese differential geometers, whose fundamental and seminal work still attracts much interest today. ......
A Dynamical Systems Approach to Theory and Practice
This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincare's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our ......
This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum field theory and knot theory. The text is replete with figures, diagrams, and ......
The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All ......
