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Higher Algebra Books

This section contains free e-books and guides on Higher Algebra, some of the resources in this section can be viewed online and some of them can be downloaded.

Workbook In Higher Algebra

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):

s 194Pages

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):

s 593Pages

Some Higher Algebra

This note explains the following topics: Stable infinity categories, (infinity , 1)-categories, Monoidal structures, Duality, Compactly generated stable categories, Compactness, Algebra in stable categories, Rigid monoidal categories, DG categories.

Author(s):

s 84Pages

Higher Algebra I Course Notes

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):

s 94Pages

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):

s NAPages

Higher Algebra II (PDF 950P)

This note covers the following topics: Disintegration and Assembly, Associative Algebras and Their Modules, Algebras and Modules over alpha operads, Little Cubes and Factorizable Sheaves, Algebraic Structures on alpha Categories, Algebra in the Stable Homotopy Category.

Author(s):

s 950Pages

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):

s 42Pages

A Guide to Arithmetic

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Author(s):

s NAPages

Elementary Algebra Course Notes

These notes are designed for students who have done very little mathematics in high school and, in particular, have never done any calculus. Topics covered includes: Real Numbers, Inequalities and Absolute Values, Arithmetic and Geometric Series, Probability and the Binomial Theorem, Logs and Exponentials, Trigonometric Functions, Complex Numbers, Polynomials and Systems of Linear Equations.

Author(s):

s NAPages

Higher Algebra Lecture Notes

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Author(s):

s NAPages