Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.
The Norton Anthology of Theory and Criticism presents a staggeringly varied collection of the most influential critical statements from the classical era to the present day. Edited by scholars and teachers whose interests range from the history of poetics to postmodernism, from classical rhetoric to ériture féminine, and from the social construction of gender to the machinery of academic superstardom, The Norton Anthology of Theory and Criticism promises to become the standard anthology in its field.
Measure theory is a classical area of mathematics born more than two thousand years ago. Nowadays it continues intensive development and has fruitful connections with most other fields of mathematics as well as important applications in physics. This book gives an exposition of the foundations of modern measure theory and offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course and, finally, more specialized topics partly covered by more than 850 exercises.
Integral Representation Theory: Applications to Convexity, Banach Spaces and Potential TheoryThis monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet´s theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book
Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers.
