The language of logic and patterns that forms the foundation of scientific understanding.
Jump to specific areas of mathematics that interest you most.
Each book has been carefully selected by experts and organized by learning progression.
Groups, rings, fields, modules.
David Steven Dummit, Richard M. Foote
Israel Nathan Herstein
Serge Lang
Ian Stewart
Marvin Marcus
Charles C. Pinter
Study of solutions of polynomial equations through geometric methods.
Igor Shafarevich
Robin Hartshorne
Algebraic numbers, quadratic fields, zeta functions, cyclotomic fields.
J. W. S. Cassels, A. Frohlich
Fundamental group, homology, cohomology.
Allen Hatcher
Edwin Spanier
Loring W. Tu, Raoul Bott
Fred H. Croom
Hajime Sato
Glen Bredon
Tammo tom Dieck
John Milnor, James Stasheff
Dale Husemöller
Vladimir G. Turaev
Prime number theorem, Dirichlet series, Sieve methods, Riemann zeta function, arithmetic functions.
Tom M. Apostol
Categories, morphisms, functors, natural transformations.
Steve Awodey
Tom Leinster
Unknown
Study of counting and arranging objects.
Unknown
Study of commutative rings and their ideals.
David Eisenbud
Atiyah, Macdonald
Study of functions of complex variables and their properties.
James Ward Brown, Ruel Vance Churchill
Jerrold E. Marsden, Michael J. Hoffman
Lars Ahlfors
Polya
Saff and Snider
Study of equations involving derivatives and their solutions.
Martin Braun
Richard C. DiPrima, William E. Boyce
J.D. Meiss
Peter Markowich
Richard K. Miller, Anthony N. Michel
Lawrence Perko
Richard E. Bellman
Gerald Teschl
John Guckenheimer, Philip Holmes
Morris Hirsch, Robert L. Devaney, Stephen Smale
Steven Strogatz
Study of geometric structures using calculus.
Michael Spivak
Manfredo Perdigao do Carmo
John M. Lee
John M. Lee
John M. Lee
Antoni A. Kosinski
Peter Petersen
Ib Madsen, Jxrgen Tornehave
Katsumi Nomizu, Shoshichi Kobayashi
Erwin Kreyszig
Dirk Jan Struik
Study of differentiable functions on manifolds.
John Lee
Alan Pollack, Victor Guillemin
Klaus Jänich, T. Bröcker
Morris Hirsch
John Milnor
David Bachman
Study of integers and their properties.
G.H. Hardy, E.M. Wright
Jean-Pierre Serre
Harvey Cohn
Kenneth F. Ireland, Michael I. Rosen
Ivan Niven, Herbert S. Zuckerman, Hugh L. Montgomery
David M. Burton
Long
Study of exotic geometries.
Unknown
Advanced theory of algebraic number fields and their extensions.
J. S. Milne
Study of mathematical reasoning and foundations.
Herbert B. Enderton
Herbert B. Enderton
Koblitz
Felix Hausdorff
Paul Halmos
Study of infinite-dimensional vector spaces with topology.
Walter Rudin
Peter D. Lax
Frigyes Riesz, Béla Szőkefalvi-Nagy
Yuli Eidelman, Vitali Milman, Antonis Ts Bellow
Michael Reed, Barry Simon
Kosaku Yosida
George Bachman, Lawrence Narici
Kreyszig
Study of topological spaces and continuous functions.
James Munkres
Klaus Jänich
Volker Runde
Mendelson
Study of graphs and their properties.
Adrian Bondy, U.S.R. Murty
Reinhard Diestel
Frank Harary
Gould
Study of algebraic structures arising from continuous symmetries.
Howard Georgi
William Futton, Joe Harris
Alexander Kirillov
Sigurður Helgason
Study of vector spaces and linear mappings between them.
Gilbert Strang
Serge Lang
Sheldon Axler
Kenneth Hoffman, Ray Kunze
Mirsky
Larry Smith
Cheney and Kincaid
Study of measures and measurable functions.
David M. Bressoud
Terence Tao
Study of numerical methods for solving mathematical problems.
Unknown
Study of methods to find minimum or maximum values.
Bernhardt Korte, Jens Vygen
Frederick S. Hillier, Gerald J. Lieberman
Michael Sipser
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein
Study of random phenomena and probability spaces.
Joseph K. Blitzstein, Jessica Hwang
P. A. P. Moran
Woodward
Study of real numbers and functions of a real variable.
Walter Rudin
Walter Rudin
H.L. Royden, P.M. Fitzpatrick
N. L. Carothers
John M. Howie
Miklós Laczkovich, Vera T. Sós
Schramm
Study of abstract algebraic structures by representing their elements as linear transformations.
Fulton and Harris
Pavel Etingof
Study of sets and their properties.
Unknown
Study of data collection, analysis, interpretation, and presentation.
Weatherburn
Weiss
Unknown
Study of random processes that evolve over time.
Gregory F. Lawler
Roy D. Yates
Richard Durrett
Study of symplectic manifolds and their properties.
Ana Cannas da Silva
Ana Cannas da Silva
Study of differentiation and integration of vector fields.
Coffin
Phillips
Phillips
Marsden and Tromba
Additional important mathematical topics and resources.
T. W. Körner
George Edward Martin
Louis Kattsoff
William Byers
Unknown
Unknown
Unknown
Unknown
