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Analysis is at the very core of mathematics, studying limit processes, inequalities, integration, differentiation, measure theory, and analytic functions. It is replete with a roster of giants — Newton, Leibnitz, Cauchy, Riemann, Fourier, Hardy, Weierstrass, Gauss, Stokes, Poincare — and is the original home for topics which have become major branches of mathematics in their own right — topology, differential equations, differential geometry, dynamical systems. Analysis also provides both the theoretical and the practical basis for the mathematics of the sciences and engineering, not to mention other areas in mathematics itself, from analytic number theory to computational mathematics.

Though no Mathematics department covers the full range of analysis, here at UT we have broad strengths, with faculty specializing in complex and real analysis, metric spaces, Fourier analysis and wavelets, operator theory and functional analysis, discrete conformal geometry (via circle packing), Schramm Loewner Evolution, and von Neumann algebras. These are not only fascinating topics to pursue, but the foundational graduate courses in real/complex analysis, a common prelim sequence, and linear and functional analysis are critical to many other topics of study, both pure and applied.