Down Free Books - Livres Gratuits: Mathématique

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Elementary Mathematical Analysis

Elementary Mathematical Analysis

This book aims to present a course suitable for students in the first year of our colleges, universities, and technical schools. It presupposes on the part of the student only the usual minimum entrance requirements in elementary algebra and plane geometry

https://archive.org/download/elementarymathem00younrich/elementarymathem00younrich.pdf

Multivector Differential Calculus

Multivector Differential Calculus

This paper treats the fundamentals of the multivector differential calculus part of geometric calculus. The multivector differential is introduced, followed by the multivector derivative and the adjoint of multivector functions. The basic rules of multivector differentiation are derived explicitly, as well as a variety of basic multivector derivatives

Calculus of Variations

Calculus of Variations

These lecture notes are intended as a straightforward introduction to the calculus of variations which can serve as a textbook for undergraduate and beginning graduate students. The text covers functions of n variables and ordinary differential equations

http://www.math.uni-leipzig.de/~miersemann/variabook.pdf

Set Theory and Topology: An Introduction to the Foundations of Analysis

Set Theory and Topology: An Introduction to the Foundations of Analysis

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of number systems

http://www.felixnagel.org/publications/nagel_set_theory_and_topology_part_i.pdf

part1

http://www.felixnagel.org/publications/nagel_set_theory_and_topology_part_ii.pdf

part2

A Course in Mathematical Analysis

A Course in Mathematical Analysis

Edouard Goursat's three-volume 'A Course in Mathematical Analysis' remains a classic study and a thorough treatment of the fundamentals of calculus. As an advanced text for students with one year of calculus, it offers an exceptionally lucid exposition

https://archive.org/download/courseinmathemat01gouruoft/courseinmathemat01gouruoft.pdf

part1

https://archive.org/download/courseinmathemat02gouruoft/courseinmathemat02gouruoft.pdf

part2

https://archive.org/download/courseinmathemat03gouruoft/courseinmathemat03gouruoft.pdf

part3

Lie Algebras

Lie Algebras

The Campbell Baker Hausdorff formula, sl(2) and its representations, classical simple algebras, Engel-Lie-Cartan-Weyl, conjugacy of Cartan subalgebras, simple finite dimensional algebras, cyclic highest weight modules, Serre’s theorem, Clifford algebras and spin representations, Kostant Dirac operator, the center of Ug

http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf

A Course in Universal Algebra

A Course in Universal Algebra

This text is not intended to be encyclopedic; rather, a few themes central to universal algebra have been developed suficiently to bring the reader to the brink of current research. The choice of topics most certainly reflects the authors' interests: a brief but substantial introduction to lattices, the most general and fundamental notions of universal algebra, a careful development of Boolean algebras, discriminator varieties, the introduction to some basic concepts, tools, and results of model theory

http://www.math.uwaterloo.ca/~snburris/htdocs/UALG/univ-algebra.pdf

An Invitation to General Algebra and Universal Constructions

An Invitation to General Algebra and Universal Constructions

From the contents: Free groups; A Cook's tour of other universal constructions; Ordered sets, induction, and the Axiom of Choice; Lattices, closure operators, and Galois connections; Categories and functors; Universal constructions in category-theoretic terms; Varieties of algebras; Algebra and coalgebra objects in categories, and functors having adjoints

http://math.berkeley.edu/~gbergman/245/3.0.pdf

The Octonions

The Octonions

The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon their applications in quantum logic, special relativity and supersymmetry

http://math.ucr.edu/home/baez/octonions/oct.pdf

Commutator Theory for Congruence Modular Varieties

Commutator Theory for Congruence Modular Varieties

This book presents the basic theory of commutators in congruence modular varieties and some of its strongest applications. The authors take an algebraic approach, using some of the shortcuts that Taylor and others have discovered

http://www.math.hawaii.edu/~ralph/Commutator/comm.pdf

Clifford Algebra, Geometric Algebra, and Applications

Clifford Algebra, Geometric Algebra, and Applications

These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra construction with geometric applications in mind, as well as in an algebraically more general form which is well suited for combinatorics, and for defining and understanding the numerous products and operations of the algebra

Smarandache Semirings, Semifields and Semivector Spaces

Smarandache Semirings, Semifields and Semivector Spaces

This is the first book on the Smarandache algebraic structures that have two binary operations. Semirings are algebraic structures with two binary operations enjoying several properties and it is the most generalized structure -- for all rings and fields are semirings

http://fs.gallup.unm.edu//Vasantha-Book3.pdf

Smarandache Loops

Smarandache Loops

The purpose of this book entirely lies in the study, introduction and examination of the Smarandache loops based on a paper about Special Algebraic Structures by Florentin Smarandache. We expect the reader to have a good background in algebra and more specifically a strong foundation in loops and number theory

http://fs.gallup.unm.edu//Vasantha-Book4.pdf

Smarandache Rings

Smarandache Rings

The author embarked on writing this book on Smarandache rings (S-rings) specially to motivate both ring theorists and Smarandache algebraists to develop and study several important and innovative properties about S-rings

http://fs.gallup.unm.edu//Vasantha-Book5.pdf

Smarandache Near-rings

Smarandache Near-rings

Near-rings are one of the generalized structures of rings. This is a book on Smarandache near-rings where the Smarandache analogues of the near-ring concepts are developed. The reader is expected to have a good background both in algebra and in near-rings; for, several results are to be proved by the reader as an exercise

Introduction to Non-Linear Algebra

Introduction to Non-Linear Algebra

Concise introduction to a relatively new subject of non-linear algebra: literal extension of text-book linear algebra to the case of non-linear equations and maps. This powerful science is based on the notions of discriminant (hyperdeterminant) and resultant, which today can be effectively studied both analytically and by modern computer facilities

Infinite-dimensional Lie Algebras

Infinite-dimensional Lie Algebras

Contents: Central extensions; The Virasoro algebra; The Heisenberg algebra; Enveloping algebras; A little infinite-dimensional surprise; Hands-on loop and affine algebras; Simple Lie algebras; Kac-Moody Lie algebras; Classification of generalised Cartanmatrices; Dynkin diagrams; Forms, Weyl groups and roots; Root spaces; Affine Lie algebras and Kac-Moody Lie algebras; etc

http://www.maths.ed.ac.uk/~igordon/LA1.pdf

Algebraic Logic

Algebraic Logic

Part I of the book studies algebras which are relevant to logic, e.g. algebras which were obtained from logics. Part II deals with the methodology of solving logic problems by (i) translating them to algebra (the process of algebraization), (ii) solving the algebraic problem, and (iii) translating the result back to logic

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.81.1784&rep=rep1&type=pdf

Lectures on Quadratic Forms

Lectures on Quadratic Forms

From the table of contents: Vector groups and linear inequalities (Vector groups, Lattices, Characters, Diophantine approximations); Reduction of positive quadratic forms; Indefinite quadratic forms; Analytic theory of Indefinite quadratic forms

http://www.math.tifr.res.in/~publ/ln/tifr07.pdf

Noncommutative Rings

Noncommutative Rings

From the table of contents: Morita equivalence (Hom, Bimodules, Projective modules ...); Localization and Goldie's theorem; Central simple algebras and the Brauer group; Maximal orders; Irreducible representations; Growth of algebras

http://www-math.mit.edu/~etingof/artinnotes.pdf