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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 
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
Higher algebra, a sequel to elementary algebra for schools
This book is intended as a sequel to our Elementary Algebra for Schools. The first few chapters are devoted to a fuller discussion of Ratio, Proportion, Variation, and the Progressions, and then introduced theorems with examples.
Author(s): Henry Sinclair Hall, Samuel Ratcliff Knight
593 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