A Scrapbook of Complex Curve Theory PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download A Scrapbook of Complex Curve Theory PDF full book. Access full book title A Scrapbook of Complex Curve Theory by Charles Herbert Clemens. Download full books in PDF and EPUB format.
Author: Charles Herbert Clemens
Publisher: American Mathematical Soc.
ISBN: 0821833073
Category : Mathematics
Languages : en
Pages : 202
Get Book Here
Book Description
This fine book by Herb Clemens quickly became a favorite of many algebraic geometers when it was first published in 1980. It has been popular with novices and experts ever since. It is written as a book of ``impressions'' of a journey through the theory of complex algebraic curves. Many topics of compelling beauty occur along the way. A cursory glance at the subjects visited reveals a wonderfully eclectic selection, from conics and cubics to theta functions, Jacobians, and questions of moduli. By the end of the book, the theme of theta functions becomes clear, culminating in the Schottky problem. The author's intent was to motivate further study and to stimulate mathematical activity. The attentive reader will learn much about complex algebraic curves and the tools used to study them. The book can be especially useful to anyone preparing a course on the topic of complex curves or anyone interested in supplementing his/her reading.
Author: Charles Herbert Clemens
Publisher: American Mathematical Soc.
ISBN: 0821833073
Category : Mathematics
Languages : en
Pages : 202
Get Book Here
Book Description
This fine book by Herb Clemens quickly became a favorite of many algebraic geometers when it was first published in 1980. It has been popular with novices and experts ever since. It is written as a book of ``impressions'' of a journey through the theory of complex algebraic curves. Many topics of compelling beauty occur along the way. A cursory glance at the subjects visited reveals a wonderfully eclectic selection, from conics and cubics to theta functions, Jacobians, and questions of moduli. By the end of the book, the theme of theta functions becomes clear, culminating in the Schottky problem. The author's intent was to motivate further study and to stimulate mathematical activity. The attentive reader will learn much about complex algebraic curves and the tools used to study them. The book can be especially useful to anyone preparing a course on the topic of complex curves or anyone interested in supplementing his/her reading.
Author: C. Herbert Clemens
Publisher: Springer Science & Business Media
ISBN: 1468470000
Category : Mathematics
Languages : en
Pages : 191
Get Book Here
Book Description
This is a book of "impressions" of a journey through the theory of com plex algebraic curves. It is neither self-contained, balanced, nor particularly tightly organized. As with any notebook made on a journey, what appears is that which strikes the writer's fancy. Some topics appear because of their compelling intrinsic beauty. Others are left out because, for all their impor tance, the traveler found them boring or was too dull or lazy to give them their due. Looking back at the end of the journey, one can see that a common theme in fact does emerge, as is so often the case; that theme is the theory of theta functions. In fact very much of the material in the book is prepara tion for our study of the final topic, the so-called Schottky problem. More than once, in fact, we tear ourselves away from interesting topics leading elsewhere and return to our main route.
Author: C. Herbert Clemens
Publisher: Springer
ISBN: 9781468470024
Category : Mathematics
Languages : en
Pages : 196
Get Book Here
Book Description
This is a book of "impressions" of a journey through the theory of com plex algebraic curves. It is neither self-contained, balanced, nor particularly tightly organized. As with any notebook made on a journey, what appears is that which strikes the writer's fancy. Some topics appear because of their compelling intrinsic beauty. Others are left out because, for all their impor tance, the traveler found them boring or was too dull or lazy to give them their due. Looking back at the end of the journey, one can see that a common theme in fact does emerge, as is so often the case; that theme is the theory of theta functions. In fact very much of the material in the book is prepara tion for our study of the final topic, the so-called Schottky problem. More than once, in fact, we tear ourselves away from interesting topics leading elsewhere and return to our main route.
Author: Krishnaswami Alladi
Publisher: Springer Science & Business Media
ISBN: 0387785108
Category : Mathematics
Languages : en
Pages : 193
Get Book Here
Book Description
Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt).
Author: Heinz-dietrich Doebner
Publisher: World Scientific
ISBN: 9814544655
Category :
Languages : en
Pages : 402
Get Book Here
Book Description
This book consists of about 20 lectures on theoretical and observational aspects of astrophysical black holes, by experts in the field. The basic principles and astrophysical applications of the black hole magnetosphere and the Blandford-Znajek process are reviewed in detail, as well as accretion by black holes, black hole X-Ray binaries, black holes with cosmic strings, and so on. Recent advances in X-Ray observations of galactic black holes and new understanding of supermassive black holes in AGNs and normal galaxies are also discussed.
Author: David V. Chudnovsky
Publisher: Springer
ISBN: 3540395350
Category : Mathematics
Languages : en
Pages : 287
Get Book Here
Book Description
a
Author: Matthias Kreck
Publisher: American Mathematical Soc.
ISBN: 0821848984
Category : Mathematics
Languages : en
Pages : 234
Get Book Here
Book Description
This book presents a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. The author introduces a new class of stratified spaces, so-called stratifolds. He derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality. Based on this, homology groups are constructed in the framework of stratifolds and the homology axioms are proved. This implies that for nice spaces these homology groups agree with ordinary singular homology. Besides the standard computations of homology groups using the axioms, straightforward constructions of important homology classes are given. The author also defines stratifold cohomology groups following an idea of Quillen. Again, certain important cohomology classes occur very naturally in this description, for example, the characteristic classes which are constructed in the book and applied later on. One of the most fundamental results, Poincare duality, is almost a triviality in this approach. Some fundamental invariants, such as the Euler characteristic and the signature, are derived from (co)homology groups. These invariants play a significant role in some of the most spectacular results in differential topology. In particular, the author proves a special case of Hirzebruch's signature theorem and presents as a highlight Milnor's exotic 7-spheres. This book is based on courses the author taught in Mainz and Heidelberg. Readers should be familiar with the basic notions of point-set topology and differential topology. The book can be used for a combined introduction to differential and algebraic topology, as well as for a quick presentation of (co)homology in a course about differential geometry.
Author: Сергей Петрович Новиков
Publisher: American Mathematical Soc.
ISBN: 0821839292
Category : Mathematics
Languages : en
Pages : 658
Get Book Here
Book Description
Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.
Author: R. J. Williams
Publisher: American Mathematical Society
ISBN: 1470460386
Category : Mathematics
Languages : en
Pages : 162
Get Book Here
Book Description
The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Scholes appeared a third of a century ago. This book is intended as an introduction to some elements of the theory that will enable students and researchers to go on to read more advanced texts and research papers. The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in the discrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale, equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for a continuous market model that generalizes the simple Black-Scholes model in several directions.
Author: Bennett Chow
Publisher: American Mathematical Society, Science Press
ISBN: 1470473690
Category : Mathematics
Languages : en
Pages : 648
Get Book Here
Book Description
Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.
