Mathematical Logic Category Theory Algebraic Topology Algebraic Geometry Differential Geometry

Geometry Topology Analysis Differential Equations Number Theory Combinatorics

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.

see also Philosophy of Mathematics

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

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

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

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