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.
Higher algebra, a sequel to elementary algebra for schoolsHenry
Sinclair Hall, Samuel Ratcliff KnightOnline
| 593 Pages
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.
Some Higher AlgebraDennis GaitsgoryPDF
| 84 Pages
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.
Higher Algebra I Course NotesEyal Z. Goren, Mcgill UniversityPDF
| 94 Pages
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.
Homotopical and Higher AlgebraETH Zurich University
Online | NA Pages | English
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 Algebra II (PDF 950P)Jacob LuriePDF
| 950 Pages
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.
Tools From Higher Algebra (PDF 42P)Noga
| 42 Pages
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.
|A Guide to Arithmetic|
Elementary Algebra Course NotesChristopher
| NA Pages
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.
|Higher Algebra Lecture Notes|