Mathematical Logic Category Theory Algebraic Geometry Differential Geometry

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

Reflections on Mathematics

mathematics as dialectic between the sensible and the intelligible, gluing together planes of immanence

# Foundations of Mathematics

see also Logic, Philosophy of Mathematics, Analytic Philosophy

# Category Theory

# Set Theory

# Logic

# Algebra

# Analysis

# Topology

# Geometry

# Differential Equations

# Mathematical Physics

# Applied Mathematics

# Probability and Statistics

# Real World Applications of Mathematics

see also Applied Mathematics

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