Abstract Algebra Algebra Algebraic Geometry Algebraic Topology Applied Mathematics Arithmetic Geometry Basic Algebra Basic Mathematics Calculus Category Theory Classical Analysis Combinatorics Commutative Algebra Complex Algebra Complex Analysis Differential Algebra Differential Analysis Differential Calculus Differential Equations Differential Geometry Differential Topology Discrete Mathematics Elliptic Curves Fourier Analysis Functional Analysis Fractals Fractional Calculus Geometric Algebra Geometry Geometric Topology Groups Theory Graph Theory Harmonic Analysis Higher Algebra History of Mathematics Homological Algebra Integral Calculus K-theory Lie Algebra Linear Algebra Mathematical Analysis Mathematical Series Modern Geometry Multivairable Calculus Number Theory Numerical Analysis Probability Theory Real Analysis Rings and Fileds Riemannian Geometry Theorems in Calculus Topology Trigonometry Set Theory Constants & Numerical Sequences
Lecture notes on Nichols algebras
This note contains below topics, Preliminaries on Lie algebras, Preliminaries on braided tensor categories, Preliminaries on quantum groups, Nichols algebras, Nichols algebras via quantum symmetrizer, Categorical algebras, Quantum symmetrizer, First examples, Nichols algebras as universal Hopf algebras, Categorical Hopf algebras, Root systems, Root system from Nichols algebras, Axiomatization of generalized root systems, Hyperplane arrangements, Cartan graph and Weyl groupoid, Classification in Rank 2.
Author(s): Simon D. Lentner
93 Pages 
Lecture Notes on Non Commutative Distributions
This note contains below topics, Basic Definitions and Examples, OperatorValued Distributions and OperatorValued Cauchy Transform, NonCommutative Functions, The OperatorValued Cauchy Transform, OperatorValued Freeness, OperatorValued Free Central Limit Theorem and OperatorValued Semicircular Elements, Matrices of Semicirculars and MatrixValued Semicirculars and Block Random Matrices, Polynomials in Free Semicirculars and Linearization, Combinatorial and Analytic Description of OperatorValued Freeness Free Cumulants and RTransforms, OperatorValued Free Convolution via Subordination Function and the Distribution of Polynomials in Free Variables, Distribution of Rational Expressions in Free Random Variables, Unbounded Rational Expressions, Some OfftheRecord Remarks.
Author(s): Roland Speicher
123 Pages
A Treatise on Elementary and Higher Algebra
This note explains the following topics, Subtraction, Division, Elimination by comparison, General rule for extracting any root of a polynomial, Multiplication and division of surds, First and second rule for quadratic equations, Properties of the roots of quadratic equations, Binomial and multinomial Theorem demonstrated, Summation ofin and
Author(s): Theodore Strong
NA Pages
This note explains the following topics, Group Theory, Sylows Theorem, Field and Galois Theory, Elementary Factorization Theory, Dedekind Domains, Module Theory, Ring Structure Theory, Tensor Products.
Author(s): David Surowski
194 Pages
This book explains the following topics, Groups, The Sylow theorems, The JordanHolder theorem and solvable groups, Free groups and free products, Modules, Localization of rings and modules, Free modules and rank, Infinite Galois theory, Cyclotomic fields, Kummer Theory, Cyclic Galois extensions, Calculation of Galois groups.
Author(s): Eyal Z. Goren, Mcgill University
94 Pages