Algebra Notes

Exactly what it sounds like.

This is nominally me consolidating my notes in undergraduate algebra, but quickly spiraled into a much larger work. The style of writing is halfway between a (terse) textbook and a set of personal notes.

Note that this is currently a work in progress. There are missing sections in the attached PDF (the current version), some citation issues, along with what I can only assume are copious typos and errors. If you find any, please let me know!

I’ve also included a list of the references used in the text on this page for your convenience. I can’t guarantee the usefulness of any of these sources to you, but they are all available (and more professionally done than this project).

2024

  1. continuous functor
    nLab authors
    Aug 2024
    \hrefhttps://ncatlab.org/nlab/revision/continuous+functor/15Revision 15
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  2. complete category
    nLab authors
    Aug 2024
    \hrefhttps://ncatlab.org/nlab/revision/complete+category/7Revision 7
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  3. representable functor
    nLab authors
    Aug 2024
    \hrefhttps://ncatlab.org/nlab/revision/representable+functor/57Revision 57
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  4. limits of presheaves are computed objectwise
    nLab authors
    Aug 2024
    \hrefhttps://ncatlab.org/nlab/revision/limits+of+presheaves+are+computed+objectwise/4Revision 4
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  5. hom-functor preserves limits
    nLab authors
    Aug 2024
    \hrefhttps://ncatlab.org/nlab/revision/hom-functor+preserves+limits/11Revision 11
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2023

  1. Math 412: Advanced Linear Algebra Lecture Notes
    Lior Silberman
    Aug 2023
    HTML

2022

  1. milne.png
    Fields and Galois Theory (v5.10)
    James S. Milne
    Aug 2022
    Available at www.jmilne.org/math/
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2021

  1. modern_alg.png
    Introduction to Modern Algebra and Its Applications
    Nadiya Gubareni
    Aug 2021

2020

  1. Introductory Category Theory Notes
    Daniel Epelbaum, and Ashwin Trisal
    Aug 2020
    Accessed: 2024-10-08
    HTML

2017

  1. The Yoneda Lemma
    Aug 2017
    Accessed: 2024-26-07
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2013

  1. homotopy.png
    Homotopy Type Theory: Univalent Foundations of Mathematics
    The Univalent Foundations Program
    Aug 2013
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2012

  1. universal.png
    A Course in Universal Algebra
    Stanley Burris, and H.P. Sankappanavar
    Aug 2012
    HTML

2011

  1. Math 320 : Abstract Algebra I, Presentation on the structure theorem for finite Abelian groups
    David Lantz
    Aug 2011
    HTML

2010

  1. categories.png
    Categories for the Working Mathematician
    Saunders Mac Lane
    Aug 2010
    HTML
  2. Math 619 : Abstract Algebra I Lecture Notes, Week 13
    Bernard Badzioch
    Aug 2010
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2009

  1. basic_algebra.png
    Basic Algebra I
    Nathan Jacobson
    Aug 2009

2007

  1. lin_alg.png
    Advanced Linear Algebra
    Steven Rotman
    Aug 2007
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2005

  1. algebra.png
    Algebra
    Serge Lang
    Aug 2005
    HTML

1999

  1. real_analysis.png
    Real Analysis: Modern Techniques and Their Applications
    Gerald B. Folland
    Aug 1999
  2. FOM: Russel paradox for naive category theory
    Aug 1999
    Accessed: 2024-31-07
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  3. Studying mobile context-aware social services in the wild
    Eknath Ghate
    In Cyclotomic Fields and Related Topics: Proceedings of the Summer School , Aug 1999
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