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Geometry of Differential Forms
Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global …
Algebra: Chapter 0
An Introduction to Morse Theory
In a very broad sense, 'spaces' are objects of study in geometry, and 'functions' are objects of study in analysis. There are, however, deep relations between functions defined on …
Math from Three to Seven
Snowbird Lectures in Algebraic Geometry
A significant part of the 2004 Summer Research Conference on Algebraic Geometry (Snowbird, UT) was devoted to lectures introducing the participants, in particular, graduate …
Problems and Theorems in Linear Algebra
There are a number of very good books available on linear algebra. From this one might deduce that the existing books contain all that one needs to know in the best possible form …
Representations of Algebras
Generalized Cohomology
In the 1950s, Eilenberg and Steenrod presented their famous characterization of homology theory by seven axioms. Somewhat later, it was found that keeping just the first six of …
Fermat's Last Theorem
Differential Geometry
Enumerative Geometry And String Theory
Perhaps the most famous example of how ideas from modern physics have revolutionized mathematics is the way string theory has led to an overhaul of enumerative geometry, an area of …
A Terse Introduction to Linear Algebra
Linear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications.