This text aims to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. Anti-self duality is rather special to 4-dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics. The book reviews some basic geometry, but it assumes that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah,...
This text aims to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. Anti-self duali...
Suitable for readers who want to learn about the Newtonian $N$-body problem, this book contains simple explanations of the apparent 'looping' orbit of Mars and the unexpected 'Sunrise, Sunset' behavior as viewed from Mercury. It also covers the weird dynam
Suitable for readers who want to learn about the Newtonian $N$-body problem, this book contains simple explanations of the apparent 'looping' orbit of...
Based on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, this work presents fresh perspectives in graph theory and helps to contribute to a sound scientific foundation for our understanding of discrete networks that permeat
Based on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, this work presents fresh perspectives in graph theory and he...
Modular forms appear in many ways in number theory. This book details various roles that modular forms and $q$-series play in number theory, such as applications and connections to basic hypergeometric functions, Gaussian hypergeometric functions, super-congruences, Weierstrass points on modular curves, singular moduli, and class numbers.
Modular forms appear in many ways in number theory. This book details various roles that modular forms and $q$-series play in number theory, such as a...
The concept of 'wave packet analysis' originates in Carleson's famous proof of almost everywhere convergence of Fourier series of $L^2$ functions. This work emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main devel
The concept of 'wave packet analysis' originates in Carleson's famous proof of almost everywhere convergence of Fourier series of $L^2$ functions. Thi...
Among nonlinear PDEs, dispersive and wave equations form an important class of equations, including the nonlinear Schrodinger equation, nonlinear wave equation, Korteweg de Vries equation, and the wave maps equation. This book offers an introduction to the
Among nonlinear PDEs, dispersive and wave equations form an important class of equations, including the nonlinear Schrodinger equation, nonlinear wave...
Includes an analytic solution to the Busemann-Petty problem, which asks whether bodies with smaller areas of central hyperplane sections necessarily have smaller volume, characterizations of intersection bodies, extremal sections of certain classes of bodi
Includes an analytic solution to the Busemann-Petty problem, which asks whether bodies with smaller areas of central hyperplane sections necessarily h...
Although division algebras are a very classical object, this book presents this 'classical' material in a new way, highlighting various approaches and fresh theorems, and illuminating the connections with a variety of areas in mathematics. It is based on lectures on division algebras given at a conference held at Colorado State University.
Although division algebras are a very classical object, this book presents this 'classical' material in a new way, highlighting various approaches and...
The geometrical study of differential equations has a long and distinguished history, dating back to the classical investigations of Sophus Lie, Gaston Darboux, and Elie Cartan. These ideas occupy a central position in several areas of pure and applied mathematics, including the theory of completely integrable evolution equations, the calculus of variations, and the study of conservation laws.
The geometrical study of differential equations has a long and distinguished history, dating back to the classical investigations of Sophus Lie, Gasto...
This fourth volume of Research in Collegiate Mathematics Education (RCME IV) reflects the themes of student learning and calculus. Included are overviews of calculus reform in France and in the US and large-scale and small-scale longitudinal comparisons of students enrolled in first-year reform courses and in traditional courses. The work continues with detailed studies relating students' understanding of calculus and associated topics. Direct focus is then placed on instruction and student comprehension of courses other than calculus, namely abstract algebra and number theory. The volume...
This fourth volume of Research in Collegiate Mathematics Education (RCME IV) reflects the themes of student learning and calculus. Included are overvi...