Tag: Algebraic

Free Download Hodge Theory and Complex Algebraic Geometry II by Claire Voisin, Leila Schneps
English | 2008 | ISBN: 0521718023 | 362 Pages | PDF | 3.0 MB
The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties.

Free Download Algebraic Approaches to Program Semantics by Ernest G. Manes , Michael A. Arbib
English | PDF | 1986 | 358 Pages | ISBN : 1461293774 | 23.4 MB
In the 1930s, mathematical logicians studied the notion of "effective comput ability" using such notions as recursive functions, A-calculus, and Turing machines. The 1940s saw the construction of the first electronic computers, and the next 20 years saw the evolution of higher-level programming languages in which programs could be written in a convenient fashion independent (thanks to compilers and interpreters) of the architecture of any specific machine. The development of such languages led in turn to the general analysis of questions of syntax, structuring strings of symbols which could count as legal programs, and semantics, determining the "meaning" of a program, for example, as the function it computes in transforming input data to output results. An important approach to semantics, pioneered by Floyd, Hoare, and Wirth, is called assertion semantics: given a specification of which assertions (preconditions) on input data should guarantee that the results satisfy desired assertions (postconditions) on output data, one seeks a logical proof that the program satisfies its specification. An alternative approach, pioneered by Scott and Strachey, is called denotational semantics: it offers algebraic techniques for characterizing the denotation of (i. e. , the function computed by) a program-the properties of the program can then be checked by direct comparison of the denotation with the specification. This book is an introduction to denotational semantics. More specifically, we introduce the reader to two approaches to denotational semantics: the order semantics of Scott and Strachey and our own partially additive semantics.

Free Download C∞-Algebraic Geometry with Corners
English | 2024 | ISBN: 1009400169 | 223 Pages | PDF | 3 MB
Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, ‘C∞-schemes’, which allow differential geometers to study a huge range of singular spaces, including ‘infinitesimals’ and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of ‘derived manifolds’. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces ‘C∞-schemes with corners’, singular spaces in differential geometry with good notions of boundary and corners. They can be used to define ‘derived manifolds with corners’ and ‘derived orbifolds with corners’. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.

Free Download Algebraic Foundations for Applied Topology and Data Analysis (Mathematics of Data) by Hal Schenck
English | November 22, 2022 | ISBN: 3031066634 | 236 pages | MOBI | 25 Mb
This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA). Covering a wide range of topics at levels of sophistication varying from elementary (matrix algebra) to esoteric (Grothendieck spectral sequence), it offers a mirror of data science aimed at a general mathematical audience.

Free Download Algebraic Structures and Operator Calculus Volume II: Special Functions and Computer Science by Philip Feinsilver , René Schott
English | PDF | 1994 | 151 Pages | ISBN : 079232921X | 6 MB
In this volume we will present some applications of special functions in computer science. This largely consists of adaptations of articles that have appeared in the literature . Here they are presented in a format made accessible for the non-expert by providing some context. The material on group representations and Young tableaux is introductory in nature. However, the algebraic approach of Chapter 2 is original to the authors and has not appeared previously . Similarly, the material and approach based on Appell states, so formulated, is presented here for the first time . As in all volumes of this series, this one is suitable for self-study by researchers . It is as well appropriate as a text for a course or advanced seminar . The solutions are tackled with the help of various analytical techniques, such as g- erating functions, and probabilistic methods/insights appear regularly . An interesting feature is that, as has been the case in classical applications to physics, special functions arise- here in complexity analysis. And, as in physics, their appearance indicates an underlying Lie structure. Our primary audience is applied mathematicians and theoretical computer scientists . We are quite sure that pure mathematicians will find this volume interesting and useful as well .

Free Download Algebraic Aspects of Cryptography by Neal Koblitz
English | PDF | 1998 | 214 Pages | ISBN : 3540634460 | 20.2 MB
This book is intended as a text for a course on cryptography with emphasis on algebraic methods. It is written so as to be accessible to graduate or advanced undergraduate students, as well as to scientists in other fields. The first three chapters form a self-contained introduction to basic concepts and techniques. Here my approach is intuitive and informal. For example, the treatment of computational complexity in Chapter 2, while lacking formalistic rigor, emphasizes the aspects of the subject that are most important in cryptography. Chapters 4-6 and the Appendix contain material that for the most part has not previously appeared in textbook form. A novel feature is the inclusion of three types of cryptography – "hidden monomial" systems, combinatorial-algebraic sys tems, and hyperelliptic systems – that are at an early stage of development. It is too soon to know which, if any, of these cryptosystems will ultimately be of practical use. But in the rapidly growing field of cryptography it is worthwhile to continually explore new one-way constructions coming from different areas of mathematics. Perhaps some of the readers will contribute to the research that still needs to be done. This book is designed not as a comprehensive reference work, but rather as a selective textbook. The many exercises (with answers at the back of the book) make it suitable for use in a math or computer science course or in a program of independent study.

Free Download Paul R. Halmos, "Algebraic Logic"
English | 2016 | pages: 274 | ISBN: 161427634X, 1258373629 | EPUB | 28,0 mb
Beginning with an introduction to the concepts of algebraic logic, this concise volume features ten articles by a prominent mathematician that originally appeared in journals from 1954 to 1959. Covering monadic and polyadic algebras, these articles are essentially self-contained and accessible to a general mathematical audience, requiring no specialized knowledge of algebra or logic.

Free Download Algebraic Geometry II: Cohomology of Schemes With Examples and Exercises
English | 2023 | ISBN: 3658430303 | 877 Pages | PDF (True) | 10 MB
It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck’s algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously.

Free Download Algebraic Equations (Quick Study Academic)
English | 2014 | ISBN: 14232238X | 6 Pages | PDF (True) | 3 MB
This guide outlines basic algebraic equations, formulas, properties & operations

Free Download Learn to Solve Algebraic Equations Recursively in Python
Published 12/2023
Created by Bonaventure Ogeto
MP4 | Video: h264, 1280×720 | Audio: AAC, 44.1 KHz, 2 Ch
Genre: eLearning | Language: English | Duration: 5 Lectures ( 1h 2m ) | Size: 727 MB