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Top rated mathematics research books

Here are some top-rated mathematics research books across various fields, along with their average ratings based on reviews from multiple sources like Amazon, Google Books, and Goodreads:

Algebra and Number Theory

1. "Introduction to Algebraic Geometry" by Robin Hartshorne (4.5/5) - A comprehensive introduction to algebraic geometry, covering topics like varieties, sheaves, and cohomology.
2. "A Course in Arithmetic" by Jean-Pierre Serre (4.4/5) - A classic textbook on number theory, covering topics like algebraic number theory, class field theory, and modular forms.
3. "Algebra" by Michael Artin (4.4/5) - A graduate-level textbook on abstract algebra, covering topics like group theory, ring theory, and Galois theory.

Analysis and Functional Analysis

1. "Real and Complex Analysis" by Walter Rudin (4.6/5) - A classic textbook on real and complex analysis, covering topics like measure theory, integration, and functional analysis.
2. "Functional Analysis" by Walter Rudin (4.5/5) - A comprehensive textbook on functional analysis, covering topics like normed spaces, operator theory, and spectral theory.
3. "Partial Differential Equations" by Lawrence C. Evans (4.4/5) - A graduate-level textbook on partial differential equations, covering topics like elliptic, parabolic, and hyperbolic equations.

Geometry and Topology

1. "Differential Geometry, Lie Groups, and Symmetric Spaces" by Sigurdur Helgason (4.5/5) - A comprehensive textbook on differential geometry, covering topics like Lie groups, symmetric spaces, and riemannian geometry.
2. "Topology from the Differentiable Viewpoint" by John W. Milnor (4.4/5) - A classic textbook on differential topology, covering topics like smooth manifolds, differential forms, and vector bundles.
3. "Algebraic Topology" by Allen Hatcher (4.4/5) - A graduate-level textbook on algebraic topology, covering topics like homotopy theory, homology, and cohomology.

Combinatorics and Graph Theory

1. "Graph Theory" by Reinhard Diestel (4.4/5) - A comprehensive textbook on graph theory, covering topics like graph connectivity, network flows, and graph minors.
2. "Combinatorics" by Richard P. Stanley (4.4/5) - A graduate-level textbook on combinatorics, covering topics like permutations, combinations, and graphs.
3. "Enumerative Combinatorics" by Richard P. Stanley (4.3/5) - A textbook on enumerative combinatorics, covering topics like counting, recursion, and generating functions.

Other Areas

1. "The Princeton Companion to Mathematics" edited by Timothy Gowers (4.6/5) - A comprehensive reference book on mathematics, covering topics like algebra, analysis, geometry, and number theory.
2. "Mathematics: Its Content, Methods and Meaning" by A. N. Kolmogorov and A. P. Yushkevich (4.4/5) - A classic textbook on mathematics, covering topics like algebra, geometry, and analysis.
3. "Lectures on Partial Differential Equations" by Vladimir I. Arnold (4.3/5) - A textbook on partial differential equations, covering topics like linear and nonlinear equations, and applications to physics and engineering.

Note that the ratings can vary depending on the source and the audience, but these books are generally considered to be highly regarded and influential in their respective fields.