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Resources
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People
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Mathematics
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Resources
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Be thankful for the Mathematics Resources we have.
Think of ways to share these with those learning rightly.
Priced Books
Foundational Level:
Israel M. Gelfand, Alexander Shen (1993), Algebra; Birkhäuser.
Serge Lang (1971), Basic Mathematics; Springer.
Intermediary Level:
Serge Lang (2012), A First Course in Calculus (5th ed.); Springer.
H. S. M. Coxeter, Samuel L. Greitzer (1967), Geometry Revisited; American Mathematical Society.
Undergraduate Level:
Logic:
Dirk van Dalen (2013), Logic and Structure; Universitext.
Number Theory:
Alan Baker (2012), A Comprehensive Course on Number Theory; Cambridge University Press.
Combinatorics:
John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff (2008), Combinatorics and Graph Theory (2nd ed.); Springer.
Abstract Algebra:
Rudolf Lidl, Günter Pilz (2009), Applied Abstract Algebra (2nd ed.); Springer.
Linear Algebra:
Serge Lang (2004), Linear Algebra (3rd ed.); Springer.
Geometry:
Alexander Ostermann, Gerhard Wanner (2012), Geometry by Its History; Springer.
Topology:
Klaus Jänich (1995), Topology; Springer.
Analysis:
Walter Rudin (1986), Real and Complex Analysis (3rd ed.); McGraw-Hill Education.
Calculus:
Michael Spivak (2006), Calculus; Cambridge University Press.
Probability:
Achim Klenke (2020), Probability Theory: A Comprehensive Course (3rd ed.); Springer.
Statistics:
Larry A. Wasserman (2004), All of Statistics: A Concise Course in Statistical Inference; Springer.
Graduate Level:
Set Theory:
Thomas Jech (2011), Set Theory; Springer.
Number Theory:
Jean-Pierre Serre (1978), A Course in Arithmetic; Springer.
Graph Theory:
Reinhard Diestel (2018), Graph Theory; Springer.
Abstract Algebra:
Serge Lang (2013), Algebra (3rd ed.); Springer.
Linear Algebra:
Steven Roman (2007), Advanced Linear Algebra (3rd ed.); Springer.
Algebraic Geometry:
Robin Hartshorne (1977), Algebraic Geometry; Springer.
Geometric Topology:
Glen E. Bredon (2010), Topology and Geometry; Springer.
Complex Analysis:
Serge Lang (2003), Complex Analysis (4th ed.); Springer.
PDEs:
Lawrence C. Evans (2010), Partial Differential Equations (2nd ed.); American Mathematical Society.
Category Theory:
Saunders MacLane (1998), Categories for the Working Mathematician (2nd ed.), Springer.
History Books (by their Goodreads ratings):
Mathematics History I:
Carl Benjamin Boyer (2011), A History of Mathematics (3rd ed.); Jossey-Bass.
Mathematics History II:
John Stillwell (2010), Mathematics and Its History (3rd ed.); Springer.
Mathematics History III:
Jan Gullberg, Peter Hilton (1997), Mathematics: From the Birth of Numbers; W W Norton & Co Ltd.
Historical:
Euclid's Elements: (c. 300 BCE)
Euclid; Sir Thomas L. Heath (tr) (1908), The Thirteen Books of Euclid’s Elements; Dover.
Reference Works:
Mathematics Handbook:
I. N. Bronshtein, K. A. Semendyayev, Gerhard Musiol, Heiner Mühlig (2007), Handbook of Mathematics (5th ed.); Springer.
Core Theorems:
Oliver Knill (Ongoing), Some Fundamental Theorems in Mathematics.
Free Books
Foundational Level:
Openstax (2020), Prealgebra.
Openstax (2021), Algebra and Trigonometry (2nd ed.).
Intermediary Level:
G. H. Hardy (1908), A Course in Pure Mathematics; Dover Publications.
Undergraduate to Graduate Level:
Logic:
The Open Logic Text, The Open Logic Project.
Set Theory:
Set Theory: An Open Introduction, The Open Logic Project.
Number Theory:
Victor Shoup, Computational Introduction to Number Theory and Algebra.
Combinatorics, Graph Theory:
Mitchel T. Keller, William T. Trotter (2017), Applied Combinatorics.
Abstract Algebra:
Thomas W. Judson (2018), Abstract Algebra: Theory and Applications.
Linear Algebra:
Jim Hefferon (2020), Linear Algebra (4th ed.).
Geometry:
Michael P. Hitchman (2018 edition), Geometry with an Introduction to Cosmic Topology.
Algebraic Geometry:
The Stacks Project, Columbia University.
Topology:
Ronald C. Freiwald (2014), An Introduction to Set Theory and Topology.
Geometric topology:
Bruno Martelli (2016), An Introduction to Geometric Topology.
Real Analysis:
John M. Erdman (2012), Companion to Real Analysis.
Complex Analysis:
Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka (2002), A First Course in Complex Analysis.
Calculus:
Gilbert Strang, Calculus, MIT.
Differential Equations:
William F. Trench (2013), Elementary Differential Equations.
Probability:
Mark Huber (2021 ed.), Probability: Lectures and Labs.
Statistics:
Michael J. Evans, Jeffrey S. Rosenthal, Probability and Statistics: The Science of Uncertainty (2nd ed.); University of Toronto.
WikiBooks:
Formal Logic
|
Set Theory
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Number Theory
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Combinatorics
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Graph Theory
Abstract Algebra
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Linear Algebra
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Geometry
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Algebraic Geometry
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Topology
Real Analysis
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Complex Analysis
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Calculus
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ODEs
Probability Theory
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Statistics
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Category Theory
News
General News:
ScienceDaily/Mathematics
arXiv Preprints:
(General Mathematics)
|
Logic
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Number Theory
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Combinatorics
Group Theory
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Representation Theory
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Rings and Algebras
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Differential Geometry
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Algebraic Geometry
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General Topology
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Classical Analysis & ODEs
Complex Variables
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Analysis of PDEs
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Probability
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Statistics Theory
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Category Theory
Major Closed Journals (by their
SJR Rank
):
Publications Mathématiques
Journal of the American Mathematical Society
Annals of Mathematics
Selected Open Journals:
DeGruyter Open Mathematics
Springer: Journal of Mathematics in Industry
Selected Video Channels:
Institute for Advanced Study (IAS)
Clay Mathematics Institute
Graduate Mathematics
Web Resources
Foundational:
Khan Academy
|
Mathigon
||
Soroban Exam
Intermediary:
Paul's Online Notes
||
SageMath
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Geogebra
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AoPS Community
Advanced:
MIT OCW
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Oxford Notes
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OverLeaf
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MathOverflow
Wish for ways to share these with those learning rightly.
Be hopeful for the Mathematics Resources yet to come.
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