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Tools From Higher Algebra (PDF 42P)
This note covers the following topics: group theory and graphs with large girth, expanders and superconcentrators, character sums and pseudo-random graphs, real varieties and sign patterns of polynomials, The Chevalley-Warning theorem, Abelian groups and regular graphs, hyperbolic geometry and triangulations of polytopes and polygons, the Erdos-Mozer conjecture and the hard Lefschetz theorem.
Author(s): Noga Alon
42 Pages 
An Introduction to Higher Categorical Algebra
This note covers introduction, Category theory, Ring theory, Module theory and deformation theory.
Author(s): David Gepner
69 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&
Author(s): Theodore Strong
NA Pages
This note explains the following topics: Group Theory, Sylow’s 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 Jordan-Holder 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
Homotopical and Higher Algebra
This note covers the following topics: The symmetric monoidal category nCob and nTFTs, Duality in monoidal categories, Presentation of 1Cob by generators and relations, 2TFTs and Frobenius algebra, Extending down TFTs, Bicategories, Symmetric monoidal bicategories, Symmetric monoidal structures on higher categories.
Author(s): ETH Zurich University
NA Pages
Tools From Higher Algebra (PDF 42P)
This note covers the following topics: group theory and graphs with large girth, expanders and superconcentrators, character sums and pseudo-random graphs, real varieties and sign patterns of polynomials, The Chevalley-Warning theorem, Abelian groups and regular graphs, hyperbolic geometry and triangulations of polytopes and polygons, the Erdos-Mozer conjecture and the hard Lefschetz theorem.
Author(s): Noga Alon
42 Pages