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Resources Lessons People



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 | Number Theory | Combinatorics | Graph Theory
Abstract Algebra | Linear Algebra | Geometry | Algebraic Geometry | Topology
Real Analysis | Complex Analysis | Calculus | ODEs
Probability Theory | Statistics | Category Theory


News

General News:
ScienceDaily/Mathematics

arXiv Preprints:
(General Mathematics) | Logic | Number Theory | Combinatorics
Group Theory | Representation Theory | Rings and Algebras |
Differential Geometry | Algebraic Geometry | General Topology | Classical Analysis & ODEs
Complex Variables | Analysis of PDEs | Probability | Statistics Theory | 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 | Geogebra || AoPS Community

Advanced:
MIT OCW | Oxford Notes || OverLeaf || MathOverflow

Wish for ways to share these with those learning rightly.
Be hopeful for the Mathematics Resources yet to come.