44 Great Books

Using MathSciNet, I found the most cited book in each of 44 “pure” areas of Mathematical Subject Classification, from General (00) to Probability (60). The results are below. Bold font indicates I own the book. Italic: used to own, but not anymore.

Area Title Authors(s)
General Real and complex analysis Rudin
History and biography A course of modern analysis. Whittaker, Watson
Mathematical logic and foundations Classical descriptive set theory Kechris
Combinatorics Symmetric functions and Hall polynomials Macdonald
Order, lattices, ordered algebraic structures Lattice theory Birkhoff
General algebraic systems A course in universal algebra Burris, Sankappanavar
Number theory The arithmetic of elliptic curves Silverman
Field theory and polynomials Local fields Serre
Commutative algebra Commutative algebra Eisenbud
Algebraic geometry Algebraic geometry Hartshorne
Linear and multilinear algebra Matrix analysis Horn, Johnson
Associative rings and algebras Hopf algebras and their actions on rings Montgomery
Nonassociative rings and algebras Infinite-dimensional Lie algebras Kac
Category theory; homological algebra Categories for the working mathematician MacLane
K-theory Cyclic homology Loday
Group theory and generalizations Endliche Gruppen Huppert
Topological groups, Lie groups Groupes et algèbres de Lie Bourbaki
Real functions Convex analysis Rockafellar
Measure and integration Geometric measure theory Federer
Functions of a complex variable Bounded analytic functions Garnett
Potential theory Nonlinear potential theory of degenerate elliptic equations Heinonen, Kilpeläinen, Martio
Several complex variables and analytic spaces Function theory in the unit ball of Cn Rudin
Special functions Special functions Andrews, Askey, Roy
Ordinary differential equations Introduction to functional-differential equations Hale, Verduyn Lunel
Partial differential equations Elliptic partial differential equations of second order Gilbarg, Trudinger
Dynamical systems and ergodic theory Random dynamical systems Arnold
Difference and functional equations Stability of functional equations in several variables Hyers, Isac, Rassias
Sequences, series, summability Divergent Series Hardy
Approximations and expansions Constructive approximation DeVore, Lorentz
Harmonic analysis on Euclidean spaces Harmonic analysis Stein
Abstract harmonic analysis Abstract harmonic analysis Hewitt, Ross
Integral transforms, operational calculus The classical moment problem and some related questions in analysis Akhiezer
Integral equations Evolutionary integral equations and applications Prüss
Functional analysis Sobolev spaces Adams
Operator theory Semigroups of linear operators and applications to partial differential equations Pazy
Calculus of variations and optimal control Optimization and nonsmooth analysis Clarke
Geometry Projective geometries over finite fields Hirschfeld
Convex and discrete geometry Convex bodies: the Brunn-Minkowski theory Schneider
Differential geometry Differential geometry, Lie groups, and symmetric spaces Helgason
General topology General topology Engelking
Algebraic topology Algebraic topology Spanier
Manifolds and cell complexes Introduction to compact transformation groups Bredon
Global analysis, analysis on manifolds Introduction to the modern theory of dynamical systems Katok, Hasselblatt
Probability theory and stochastic processes Convergence of probability measures Billingsley

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