Mathematics

Logic Category Theory Algebraic Topology Algebraic Geometry Differential Geometry

Geometry Topology Analysis Algebra Differential Equations Number Theory Combinatorics

Discrete Mathematics

Philosophy of Mathematics

Didactical Papers In Mathematics


Mathematics, in its contemporary form, is a formalized science that studies abstract structure. Prior to the 20th century algebraic revolution, mathematics was the study of space and quantity, akin to Kant's categories.


Elementary Mathematics

https://cs.uwaterloo.ca/~alopez-o/math-faq/


http://www.urbanomic.com/document/mathematical-thought/

http://math.ucr.edu/home/baez/twf.html

http://www.mathpages.com/

http://web.archive.org/web/20150208035000/http://www.math-atlas.org/

princeton companion to mathematics

princeton companion to applied mathematics

mathematics unlimited

math unlimited

Applied Mathematics

princeton companion to applied mathematics

http://bactra.org/notebooks/

https://subwiki.org/wiki/Main_Page

Introduction to Algebra: http://www.math.harvard.edu/~ctm/home/text/class/harvard/55a/08/html/home/course/course.pdf

Introduction to Analysis: http://www.math.harvard.edu/~ctm/home/text/class/harvard/55b/09/html/home/course/course.pdf

Foundations of Mathematics

see also Logic, Philosophy of Mathematics, Analytic Philosophy

Applications

see also Applied Mathematics

http://mathoverflow.net/questions/2556/real-world-applications-of-mathematics-by-arxiv-subject-area

Reference Websites

http://mathworld.wolfram.com/

http://www.encyclopediaofmath.org/

Online Math Notes

https://www.ams.org/open-math-notes AMS Open Math Notes

http://e-booksdirectory.com/listing.php?category=3 Mathematics eBooks

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