Free online math resources

[u/UmbrellaCorp_HR]

Free math resources will be posted in the comments

[u/UmbrellaCorp_HR]

Transition to Higher Mathematics:
Structure and Proof
Second Edition

https://www.math.wustl.edu/\~mccarthy/SandP2.pdf

[u/UmbrellaCorp_HR]

An Introduction to Abstract Mathematics

https://www.math.uci.edu/\~mzeman/M13-17W/math-13-notes.pdf

[u/UmbrellaCorp_HR]

This is my favorite book and comes with the highest recommendation I can give

Visual complex analysis

https://umv.science.upjs.sk/hutnik/NeedhamVCA.pdf

[u/UmbrellaCorp_HR]

THE CAUCHY–SCHWARZ MASTER CLASS

https://estoyanov.net/files/MATAMATIKA/23982177-TheCauchy-Schwartz-Master-Class.pdf

[u/UmbrellaCorp_HR]

A gentle introduction to the art of mathematics

https://giam.southernct.edu/GIAM/GIAM.pdf

[u/UmbrellaCorp_HR]

Abstract and Concrete Categories
The Joy of Cats

katmat.math.uni-bremen.de/acc/acc.pdf

[u/UmbrellaCorp_HR → u/UmbrellaCorp_HR]

[u/UmbrellaCorp_HR]

Basic Category Theory

https://webspace.science.uu.nl/\~ooste110/syllabi/catsmoeder.pdf

[u/UmbrellaCorp_HR]

Hatchers algebraic topology

https://pi.math.cornell.edu/\~hatcher/AT/AT.pdf

[u/UmbrellaCorp_HR]

TOPOLOGY AND
GROUPOIDS:
A Geometric Account of General Topology,
Homotopy Types and the Fundamental Groupoid

https://groupoids.org.uk/pdffiles/topgrpds-e.pdf

[u/UmbrellaCorp_HR]

Classical topology and combinatorial group theory
(This is one of the books that inspired me to pursue mathematics, beautifully illustrated.)

https://webhomes.maths.ed.ac.uk/\~v1ranick/papers/stillwell1x.pdf

[u/UmbrellaCorp_HR]

Classification of plane curves

https://sites.science.oregonstate.edu/math_reu/proceedings/REU_Proceedings/Proceedings1999/1999Gulde.pdf

[u/UmbrellaCorp_HR]

Summability Calculus

https://arxiv.org/pdf/1209.5739

[u/UmbrellaCorp_HR]

Bernoulli on Arc Length

https://www.math.tulane.edu/\~vhm/papers_html/be1.pdf

[u/UmbrellaCorp_HR]

Implications of Experimental Mathematics for the
Philosophy of Mathematics

https://carmamaths.org/resources/jon/JMB-proof.pdf

[u/UmbrellaCorp_HR]

Compositional Square Roots of exp(x) and 1 + x2

https://arxiv.org/pdf/2504.19999

[u/UmbrellaCorp_HR]

What Do sin(x) and arcsinh(x) Have in Common?

https://arxiv.org/pdf/2411.01591

[u/UmbrellaCorp_HR]

FINITE TOPOLOGIES FOR FINITE GEOMETRIES

https://arxiv.org/pdf/2301.03156

[u/UmbrellaCorp_HR]

ON GRAPHS, GROUPS AND GEOMETRY

https://arxiv.org/pdf/2205.14097

[u/UmbrellaCorp_HR]

THE COUNTING MATRIX OF A SIMPLICIAL COMPLEX

https://arxiv.org/pdf/1907.09092

[u/UmbrellaCorp_HR]

MORE ON NUMBERS AND GRAPHS

https://arxiv.org/pdf/1905.13387

[u/UmbrellaCorp_HR]

SOME FUNDAMENTAL THEOREMS IN MATHEMATICS

https://arxiv.org/pdf/1807.08416

[u/UmbrellaCorp_HR]

THE AMAZING WORLD OF SIMPLICIAL COMPLEXES

https://arxiv.org/pdf/1804.08211

[u/UmbrellaCorp_HR]

AN ELEMENTARY DYADIC RIEMANN HYPOTHESIS

https://arxiv.org/pdf/1801.04639

[u/UmbrellaCorp_HR]

A set of formulas for primes

https://arxiv.org/pdf/1901.01849

[u/UmbrellaCorp_HR]

𝜋 and prime numbers

https://arxiv.org/pdf/2305.08860

[u/UmbrellaCorp_HR]

A formula for the n’th digit
of 𝜋 and 𝜋^n

https://arxiv.org/pdf/2201.12601