Part of Cambridge Studies in Advanced Mathematics
Date Published: January 2017
format: Paperback
isbn: 9781316614105
With roots in the nineteenth century, Lie theory has since found many and varied applications in mathematics and mathematical physics, to the point where it is now regarded as a classical branch of mathematics in its own right. This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York, Stony Brook, the book includes numerous exercises and worked examples, and is ideal for graduate courses on Lie groups and Lie algebras.
The exposition emphasizes the main concepts rather than technical details of the proofs, making it possible to cover a lot of material in relatively concise work
Numerous exercises and worked examples, as well as a sample syllabus, make this an ideal text for a graduate course on Lie groups and Lie algebras
Focusses on semisimple Lie algebras and their representations; contains material rarely included in standard textbooks such as BGG resolution
October 1, 2017 Forthcoming
Textbook - 316 Pages - 453 B/W Illustrations
ISBN 9781138197800
Series: Textbooks in Mathematics
Employs graph theory to teach mathematical reasoning
Written for non-mathematics students
Promotes critical thinking and problem solving
Rich examples
Does not present proofs
This book introduces graph theory to students who are not mathematics majors. The primary use of this book is for furthering mathematical reasoning through the subject of graph theory. Concepts are introduced through relatable real-world examples modeled mathematically. The book is written with no proofs, but rather explanations so students understand where the results come from. Each chapter attempts to answer three main questions--existence (does a solution exist?), construction (how do we find a solution?), and optimization (how do we find the best answer or dind one quickly?). Ample examples and exercises are provided to help students better understand the concepts.
Preface: 1. Euelrian Tours; 2. Hamiltonian Cycles; 3. Paths; 4. Trees and Networks; 5. Matching; 6. Graph Coloring; 7. Additional Topics; Selected Answers and Solutions; Bibliography; Index
Surveys of Modern Mathematics, Volume 11
To Be Published: 28 April 2017
Paperback
238 pages
Description
This volume presents a set of never-before-published notes from lectures given by S.-S. Chern in 1951 on the topic of “Minimal Submanifolds in a Riemannian Manifold.”
Also presented are five of Chern’s expository papers which complement the lecture notes and provide an overview of the scope and power of differential geometry: “From Triangles to Manifolds,” “Curves and Surfaces in Euclidean Space,” “Characteristic Classes and Characteristic Forms,” “Geometry and Physics,” and “The Geometry of G-Structures.”
Surveys of Modern Mathematics, Volume 12
To Be Published: 28 April 2017
Paperback
258 pages
This volume presents two sets of never-before-published notes from lectures given by S.-S. Chern. The set entitled “Differential Manifolds” gives a smooth and rapid introduction to differential manifolds and differential geometry, while the set entitled “Lectures on Integral Geometry” is an accessible introduction to that subject.
Also presented is a paper by Chern that serves as a gentle introduction to differential geometry, and reviews the status of global differential geometry in 1971.
Surveys of Modern Mathematics, Volume 13
To Be Published: 28 April 2017
Paperback
200 pages
This book intends to construct a theory of modular forms for families of Calabi?Yau threefolds with Hodge numbers of the third cohomology equal to one. It discusses many differences and similarities between the new theory and the classical theory of modular forms defined on the upper half plane. The main examples of the new theory are topological string partition functions which encode the Gromov?Witten invariants of the mirror Calabi?Yau threefolds. It is mainly written for two primary target audiences: researchers in classical modular and automorphic forms who wish to understand the q-expansions of physicists derived from Calabi?Yau threefolds, and mathematicians in enumerative algebraic geometry who want to understand how mirror symmetry counts rational curves in compact Calabi?Yau threefolds. This book is also recommended for mathematicians who work with automorphic forms and their role in algebraic geometry, in particular for those who have noticed that the class of algebraic varieties involved in their study is limited: for instance, it does not include compact non-rigid Calabi?Yau threefolds. A basic knowledge of complex analysis, differential equations, algebraic topology and algebraic geometry is required for a smooth reading of the book.
About the Author
Hossein Movasati is an Iranian-Brazilian mathematician who since 2006 has worked at the Instituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro. He began his mathematical career working on holomorphic foliations and differential equations on complex manifolds, and gradually moved to study Hodge theory and modular forms and the role of these in mathematical physics, and in particular mirror symmetry.