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Top rated mathematics reference books

Here are some top-rated mathematics reference books, organized by category:

Algebra and Number Theory

1. "A Course in Algebra" by E. Artin: A classic graduate-level textbook covering group theory, ring theory, and field theory.
2. "Algebra" by Michael Artin: A comprehensive undergraduate textbook on algebra, including linear algebra and abstract algebra.
3. "Introduction to Number Theory" by Gareth A. Jones and Josephine M. Jones: A gentle introduction to number theory, covering topics like divisibility, prime numbers, and congruences.
4. "Number Theory" by Henryk Iwaniec and Emmanuel Kowalski: A graduate-level textbook on number theory, including topics like modular forms and the distribution of prime numbers.

Calculus and Analysis

1. "Calculus" by Michael Spivak: A classic undergraduate textbook on calculus, including differential equations and multivariable calculus.
2. "Real Analysis" by Walter Rudin: A graduate-level textbook on real analysis, covering topics like measure theory and functional analysis.
3. "Functional Analysis" by Walter Rudin: A comprehensive graduate-level textbook on functional analysis, including topics like operator theory and Banach spaces.
4. "Differential Equations and Dynamical Systems" by Lawrence Perko: A graduate-level textbook on differential equations and dynamical systems, including topics like bifurcation theory and chaos theory.

Geometry and Topology

1. "Geometry: Euclid and Beyond" by Robin Hartshorne: A comprehensive undergraduate textbook on geometry, including Euclidean geometry, projective geometry, and differential geometry.
2. "Differential Geometry" by Manfredo P. do Carmo: A graduate-level textbook on differential geometry, covering topics like curves and surfaces, and Riemannian geometry.
3. "Topology" by James R. Munkres: A classic undergraduate textbook on topology, including point-set topology and algebraic topology.
4. "Algebraic Topology" by Allen Hatcher: A comprehensive graduate-level textbook on algebraic topology, including topics like homotopy theory and homology theory.

Probability and Statistics

1. "Probability and Statistics" by Morris H. DeGroot: A classic undergraduate textbook on probability and statistics, including topics like random variables, probability distributions, and statistical inference.
2. "Probability: Theory and Examples" by Rick Durrett: A graduate-level textbook on probability theory, covering topics like measure theory, stochastic processes, and martingales.
3. "Statistics" by David J. Freedman, Robert Pisani, and Roger Purves: A comprehensive undergraduate textbook on statistics, including topics like data analysis, statistical inference, and regression analysis.
4. "Time Series Analysis" by James D. Hamilton: A graduate-level textbook on time series analysis, including topics like ARIMA models, spectral analysis, and forecasting.

Other Math Topics

1. "Mathematics: Its Content, Methods and Meaning" by A. Aleksandrov, A. N. Kolmogorov, and M. A. Lavrent'ev: A comprehensive reference book on mathematics, covering topics like algebra, geometry, and analysis.
2. "The Feynman Lectures on Physics" by Richard P. Feynman, Robert B. Leighton, and Matthew Sands: A classic textbook on physics, including mathematical topics like calculus, differential equations, and group theory.
3. "Mathematical Methods for Physicists" by George B. Arfken and Hans J. Weber: A comprehensive graduate-level textbook on mathematical methods for physicists, including topics like differential equations, group theory, and differential geometry.
4. "The Handbook of Mathematical Functions" by Milton Abramowitz and Irene A. Stegun: A classic reference book on mathematical functions, including topics like special functions, orthogonal polynomials, and statistical distributions.

Note that this is not an exhaustive list, and there are many other excellent mathematics reference books available. The best book for you will depend on your specific needs and level of mathematical background.