Grid Homology for Knots and Links


Book Description

Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.




The Preparation of the Novel


Book Description

Completed just weeks before his death, the lectures in this volume mark a critical juncture in the career of Roland Barthes, in which he declared the intention, deeply felt, to write a novel. Unfolding over the course of two years, Barthes engaged in a unique pedagogical experiment: he combined teaching and writing to "simulate" the trial of novel-writing, exploring every step of the creative process along the way. Barthes's lectures move from the desire to write to the actual decision making, planning, and material act of producing a novel. He meets the difficulty of transitioning from short, concise notations (exemplified by his favorite literary form, haiku) to longer, uninterrupted flows of narrative, and he encounters a number of setbacks. Barthes takes solace in a diverse group of writers, including Dante, whose La Vita Nuova was similarly inspired by the death of a loved one, and he turns to classical philosophy, Taoism, and the works of François-René Chateaubriand, Gustave Flaubert, Franz Kafka, and Marcel Proust. This book uniquely includes eight elliptical plans for Barthes's unwritten novel, which he titled Vita Nova, and lecture notes that sketch the critic's views on photography. Following on The Neutral: Lecture Course at the Collège de France (1977-1978) and a third forthcoming collection of Barthes lectures, this volume provides an intensely personal account of the labor and love of writing.




Residues and Duality


Book Description




Differential Geometry in the Large


Book Description

These notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J.W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases. In the phenomena through special the central idea the of a or difficulty problem simplest background is becomes clear. in this fashion a crystal Doing geometry usually lead serious allows this to to - joy. Hopf's great insight approach for most of the in these notes have become the st- thematics, topics I will to mention a of further try ting-points important developments. few. It is clear from these notes that laid the on Hopf emphasis po- differential Most of the results in smooth differ- hedral geometry. whose is both t1al have understanding geometry polyhedral counterparts, works I wish to mention and recent important challenging. Among those of Robert on which is much in the Connelly rigidity, very spirit R. and in - of these notes (cf. Connelly, Conjectures questions open International of Mathematicians, H- of gidity, Proceedings Congress sinki vol. 1, 407-414) 1978, .




Lecture Notes In State And Local Public Finance (Parts I And Ii)


Book Description

This book is based on lectures conducted for two classes at the Maxwell School, Syracuse University: A Public Finance Seminar for PhD students in public administration and State and Local Public Finance for master's students in public administration.Topics covered include the role of voters in a federal system, the sorting of different households into different communities, the determinants of public service costs, the property tax and other sources of local (and state) revenue, fiscal aspects of economic development, and intergovernmental aid (especially for education).The notes for the Ph.D. class also cover several more advanced topics, such as the estimation of education production and cost functions, the capitalization of school quality into house values, and tax competition among jurisdictions. The focus in these notes is on the highly decentralized federal system in the United States, but many of the principles and much of the behavioral analysis in the class apply to other countries as well.These notes draw on Professor Yinger's extensive teaching experience and publication record in state and local public finance. They should prove useful to many teachers, scholars, and students who find topics in state and local public finance that they wish to pursue.




The Notes on Notes


Book Description

Fast-track your way to better Note Taking & Study Skills that are finally quick, easy, and a whole lot more fun! This visual book helps you tackle your material with an essential step-by-step action plan filled with how-to's and "Aha!" moments, taking you from day 1 to test day... and beyond! 15+ styles of note taking for every situation, a guide to reading textbooks in active mode, a cure for over highlighting, tips for margin notes, text and lecture notes, a learning styles quiz and guide, memory aids to make info stick, study schedules, assignment tracking, calendar setups, acclaimed methods including Cornell Notes, SQ3R, Feynman's Technique, Spaced Repetition and more. All in ways that work WITH your brain! Includes fun, easy to follow, visual examples and samples to practice. All from ShowMeTheNotes.com




Effective Notetaking


Book Description

You can predict how well a student will do simply on the basis of their use of effective study strategies. This book is for college students who are serious about being successful in study, and teachers who want to know how best to help their students learn. Being a successful student is far more about being a smart user of effective strategies than about being 'smart'. Research has shown it is possible to predict how well a student will do simply on the basis of their use of study strategies. This workbook looks at the most important group of study strategies – how to take notes (with advice on how to read a textbook and how to prepare for a lecture). You’ll be shown how to: * format your notes * use headings and highlighting * how to write different types of text summaries and pictorial ones, including concept maps and mind maps (you'll find out the difference, and the pros and cons of each) * ask the right questions * make the right connections * review your notes * evaluate text to work out which strategy is appropriate. There's advice on individual differences and learning styles, and on how to choose the strategies that are right for both you and the situation. Using effective notetaking strategies will help you remember what you read. It will help you understand more, and set you on the road to becoming an expert (or at least getting good grades!). Successful studying isn’t about hours put in, it’s about spending your time wisely. You want to study smarter not harder. As always with the Mempowered books, this thorough (and fully referenced) workbook doesn't re-hash the same tired advice that's been peddled for so long. Rather, Effective Notetaking builds on the latest cognitive and educational research to help you study for success. This 3rd edition has advance organizers and multi-choice review questions for each chapter, plus some additional material on multimedia learning, and taking notes in lectures. Keywords: best study strategies for college students, how to improve note taking skills, study skills, college study, taking notes




Local Cohomology


Book Description




Sets and Extensions in the Twentieth Century


Book Description

Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration - Serves as a singular contribution to the intellectual history of the 20th century - Contains the latest scholarly discoveries and interpretative insights