If I use a resource, I usually cite it in the post where the resource is used. However, sometimes I use it for multiple posts, and don’t mention it anywhere.

So I list the references here.


Calculus Resources

  1. Math.StackExchange for wonderful problems.
  2. On Euler’s footsteps E.V. Shchepin’s Uppsala Lectures on Calculus.
  3. Michael Corral’s ebook Vector Calculus, available legally free.
  4. Oregon State’s Vector Calculus Study Guide
  5. University of Utah’s Supplements to Vector Calculus

Classical Mathematics

  1. Dmitry Fuchs and Serge Tabachnikov’s Mathematical Omnibus: Thirty Lectures on Classic Mathematics, American Mathematical Society (2007) 463 pages. E-draft available.

Linear Algebra

  1. Tom Denton and Andrew Waldron’s Linear Algebra in Twenty Five Lectures, 395 pages.
  2. Isaiah Lankham, Bruno Nachtergaele and Anne Schilling’s Linear Algebra – As an Introduction to Abstract Mathematics, vi+241 pages.

Including differential equations, Fourier analysis, and higher analysis.

  1. John Hunter and Bruno Nachtergaele’s Applied Analysis.
  2. Nordgren’s Notes for Partial Differential Equations, upper division undergraduate course Math118A at UC Davis. See also his notes for 118B.


  1. Virtual Laboratories in Probability and Statistics.
  2. Gravner’s Lecture Notes for Math 135 [].


  1. John C. Baez’s “The Octonions” (arXiv:math/0105155).
  2. H. Albuquerque and S. Majid’s “Quasialgebra structure of the octonions” (arXiv:math/9802116).

Finite Groups
Most finite groups emerge when studying coding theory, or some similar discrete situation. They are particularly interesting in connection with Vertex Algebras, and more generally “moonshine”.

  1. Robert Wilson’s The Finite Simple Groups (Springer GTM). [He has interesting eprints too]
  2. Terry Gannon’s Moonshine Beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics (Cambridge University Press, 2006).
  3. Richard Lyons’ “Automorphism groups of sporadic groups” (arXiv:1106.3760 [math.GR]).
  4. Gerald Hoehn, Ching Hung Lam, Hiroshi Yamauchi’s “McKay’s E7 observation on the Baby Monster” and “McKay’s E6 observation on the largest Fischer group” (arXiv:1002.1777 [math.QA]).
  5. Ching Hung Lam, Hiromichi Yamada, Hiroshi Yamauchi’s “Vertex operator algebras, extended E8 diagram, and McKay’s observation on the Monster simple group” (arXiv:math/0403010).


Classical Physics Resources
Although I haven’t gotten here yet, I should note a few references I’m using.

  1. Roger D. Blandford and Kip S. Thorne’s Applications of Classical Physics
  2. Hugh D. Young and Roger A. Freedman’s University Physics (Prepared Exclusively for the Physics Department of UC Davis), taken from the 11th ed. (2004).
  3. John Armstrong’s Series on Electromagnetism (begins with discussing Coulomb’s law).

Quantum Field Theory Resources

  1. Massimo Di Pierro’s “An Algorithmic Approach to Quantum Field Theory” (arXiv:hep-lat/0509013)
  2. Robin Ticciati’s Quantum Field Theory for Mathematicians [Cambridge University Press, Encyclopedia of Mathematics and its Applications, 2008]


  1. J.D. Murray’s Mathematical Biology: I. An Introduction. 3d ed. Springer.
  2. J.D. Murray’s Mathematical Biology: II. Spatial Models and Biomedical Applications. 3d ed. Springer.
  3. Jane B. Reece, Lisa A. Urry, Michael L. Cain and Steven A. Wasserman’s Campbell Biology. Now in its 9th ed.


Shahn Majid’s Good Writing Guide.

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