By Ian Stewart
By Ian Stewart
This ebook explores aspects of Otto Neugebauer's profession, his influence at the heritage and perform of arithmetic, and the ways that his legacy has been preserved or reworked in fresh a long time, anticipating the instructions during which the research of the background of technology will head within the twenty-first century. Neugebauer, greater than the other student of modern occasions, formed the best way we understand premodern technology. via his scholarship and impact on scholars and collaborators, he inculcated either an method of old study on historical and medieval arithmetic and astronomy via distinct mathematical and philological research of texts, and a imaginative and prescient of those sciences as platforms of information and process that unfold outward from the traditional close to japanese civilizations, crossing cultural barriers and circulating over a huge geographical expanse of the previous global from the Atlantic to India.
By Michèle Audin, Mihai Damian
This ebook is an creation to fashionable tools of symplectic topology. it really is dedicated to explaining the answer of a massive challenge originating from classical mechanics: the 'Arnold conjecture', which asserts that the variety of 1-periodic trajectories of a non-degenerate Hamiltonian procedure is bounded under via the size of the homology of the underlying manifold.
The first half is an intensive advent to Morse concept, a basic device of differential topology. It defines the Morse complicated and the Morse homology, and develops a few of their applications.
Morse homology additionally serves an easy version for Floer homology, that's coated within the moment half. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been the most important within the fresh achievements in symplectic geometry and specifically within the evidence of the Arnold conjecture. The construction blocks of Floer homology are extra tricky and suggest using extra subtle analytical equipment, all of that are defined during this moment part.
The 3 appendices current a number of must haves in differential geometry, algebraic topology and analysis.
The ebook originated in a graduate direction given at Strasbourg college, and includes a huge diversity of figures and workouts. Morse thought and Floer Homology might be quite worthwhile for graduate and postgraduate students.
By Nathan Jacobson
By Rhonda HuettenmuellerYour way to getting to know ALGEBRA!
By Avishek Adhikari
The e-book is basically meant as a textbook on sleek algebra for undergraduate arithmetic scholars. it's also important if you happen to have an interest in supplementary studying at a better point. The textual content is designed in this type of method that it encourages self sufficient considering and motivates scholars in the direction of additional research. The e-book covers all significant subject matters in staff, ring, vector area and module concept which are often contained in a regular sleek algebra textual content.
In addition, it stories semigroup, crew motion, Hopf's crew, topological teams and Lie teams with their activities, purposes of ring idea to algebraic geometry, and defines Zariski topology, in addition to purposes of module conception to constitution idea of jewelry and homological algebra. Algebraic points of classical quantity concept and algebraic quantity conception also are mentioned with an eye fixed to constructing smooth cryptography. subject matters on purposes to algebraic topology, class idea, algebraic geometry, algebraic quantity idea, cryptography and theoretical laptop technological know-how interlink the topic with diversified parts. every one bankruptcy discusses person subject matters, ranging from the fundamentals, with assistance from illustrative examples. This entire textual content with a extensive number of ideas, functions, examples, routines and ancient notes represents a precious and targeted source.
By John Allen Paulos
By Luis Barreira
Over the final twenty years, the measurement concept of dynamical structures has steadily constructed into an self sufficient and intensely lively box of study. the most target of this quantity is to supply a unified, self-contained creation to the interaction of those 3 major components of analysis: ergodic idea, hyperbolic dynamics, and measurement thought. It begins with the fundamental notions of the 1st subject matters and ends with a sufficiently high-level creation to the 3rd. in addition, it comprises an creation to the thermodynamic formalism, that's a tremendous software in measurement concept.
The quantity is essentially meant for graduate scholars attracted to dynamical platforms, in addition to researchers in different parts who desire to know about ergodic concept, thermodynamic formalism, or size thought of hyperbolic dynamics at an intermediate point in a sufficiently targeted demeanour. specifically, it may be used as a foundation for graduate classes on any of those 3 matters. The textual content is usually used for self-study: it really is self-contained, and except for a few recognized easy proof from different components, all statements comprise precise proofs.