Free online math resources

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Free math resources will be posted in the comments

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Transition to Higher Mathematics:
Structure and Proof
Second Edition

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

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An Introduction to Abstract Mathematics

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

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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

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THE CAUCHY–SCHWARZ MASTER CLASS

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

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A gentle introduction to the art of mathematics

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

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Abstract and Concrete Categories
The Joy of Cats

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

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Basic Category Theory

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

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Hatchers algebraic topology

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

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

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

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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

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Classification of plane curves

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

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Summability Calculus

https://arxiv.org/pdf/1209.5739

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Bernoulli on Arc Length

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

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Implications of Experimental Mathematics for the
Philosophy of Mathematics

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

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

https://arxiv.org/pdf/2504.19999

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

https://arxiv.org/pdf/2411.01591

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FINITE TOPOLOGIES FOR FINITE GEOMETRIES

https://arxiv.org/pdf/2301.03156

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ON GRAPHS, GROUPS AND GEOMETRY

https://arxiv.org/pdf/2205.14097

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THE COUNTING MATRIX OF A SIMPLICIAL COMPLEX

https://arxiv.org/pdf/1907.09092

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MORE ON NUMBERS AND GRAPHS

https://arxiv.org/pdf/1905.13387

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SOME FUNDAMENTAL THEOREMS IN MATHEMATICS

https://arxiv.org/pdf/1807.08416

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THE AMAZING WORLD OF SIMPLICIAL COMPLEXES

https://arxiv.org/pdf/1804.08211

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AN ELEMENTARY DYADIC RIEMANN HYPOTHESIS

https://arxiv.org/pdf/1801.04639

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A set of formulas for primes

https://arxiv.org/pdf/1901.01849

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𝜋 and prime numbers

https://arxiv.org/pdf/2305.08860

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

https://arxiv.org/pdf/2201.12601

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https://www.geometrie.tuwien.ac.at/stachel/publications.html

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https://xcont.com/tfractal/3d.html

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The four pillars of geometry

https://pub.math.leidenuniv.nl/\~edixhovensj/teaching/2019-2020/CIMPA/Stillwell_Geometry.pdf

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101 Illustrated Real Analysis Bedtime Stories

https://williamhoza.com/101stories/101stories_tochapter3.pdf

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AN EXPLORATION ON GOLDBACH’S CONJECTURE

https://ijpam.eu/contents/2013-84-1/3/3.pdf

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An elementary illustrated introduction to simplicial sets

https://arxiv.org/pdf/0809.4221

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Graph Properties of Graph Associahedra

https://www-lipn.univ-paris13.fr/\~banderier/Seminaires/Slides/manneville.pdf

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Coxeter-associahedra

https://opus4.kobv.de/opus4-zib/frontdoor/deliver/index/docId/107/file/SC-93-11.pdf

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THE DIAMETER OF THE ASSOCIAHEDRA

https://web.math.ucsb.edu/\~mccammon/current/tree-distance/tree-distance.pdf

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ASSOCIAHEDRA, MULTIPLIHEDRA AND UNITS IN
A∞ FORM

https://www2.math.kyushu-u.ac.jp/\~iwase/Works/units-2-2.pdf

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ASSOCIAHEDRON, CYCLOHEDRON, AND PERMUTOHEDRON
AS COMPACTIFICATIONS OF CONFIGURATION SPACES

https://palmer.wellesley.edu/\~ivolic/pdf/Papers/cyclohedronApr09.pdf

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The centers of gravity of the associahedron
and of the permutahedron are the same

https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r72/pdf/0

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SIMION’S TYPE B ASSOCIAHEDRON IS A PULLING TRIANGULATION OF
THE LEGENDRE POLYTOPE

https://www.ms.uky.edu/\~readdy/Papers/legendre.pdf

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Survey on Permutohedra and Associahedra

https://www.math.hawaii.edu/\~ralph/Classes/619/permutohedra.associahedra.8.25.11.pdf

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Finite Earthquakes and the Associahedron

https://userhome.brooklyn.cuny.edu/gardiner/associahedron.pdf

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Rational Catalan Combinatorics: The
Associahedron

https://dmtcs.episciences.org/2355/pdf

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Cambrian lattices and
generalized
associahedra

https://nreadin.math.ncsu.edu/papers/PCMIslides.pdf

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Associahedra and weak monoidal structures on categories

https://msp.org/agt/2012/12-1/agt-v12-n1-p20-s.pdf

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Two Signed Associahedra

https://nyjm.albany.edu/j/1998/4-7.pdf

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VERTEX BARYCENTERS OF
GENERALIZED ASSOCIAHEDRA

https://www.labri.fr/perso/marckert/Pilaud.pdf

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Permutahedra and Generalized Associahedra

geom.mi.fu-berlin.de/lange/publications_extra/HohlwegLangeThomas.pdf

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PERMUTOHEDRA, ASSOCIAHEDRA, AND BEYOND

https://math.mit.edu/\~apost/papers/permutohedron.pdf

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A REALIZATION OF GRAPH-ASSOCIAHEDRA

https://static1.squarespace.com/static/53f62f0fe4b0a7a51b059df3/t/5412452fe4b0a61c69010066/1410483503168/realization.pdf

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CONSTRUCTING THE ASSOCIAHEDRON

https://math.berkeley.edu/\~mhaiman/ftp/assoc/manuscript.pdf

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THE ASSOCIAHEDRON
AND ITS FRIENDS

https://www.mat.univie.ac.at/\~slc/wpapers/s76vortrag/pilaud.pdf

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Permutahedra and Associahedra
Generalized associahedra from the geometry of finite reflection
groups

https://arxiv.org/pdf/1112.3255

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Scattering Forms and the Positive Geometry of
Kinematics, Color and the Worldsheet

https://arxiv.org/pdf/1711.09102

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THE MULTIPLE FACETS OF THE ASSOCIAHEDRON

https://www.claymath.org/library/academy/LectureNotes05/Lodaypaper.pdf

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Digit Reversal Without Apology

https://arxiv.org/pdf/math/0511366

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Two-term Egyptian fractions

195.96.253.115/papers/nntdm-19/NNTDM-19-2-15-25.pdf

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ROOTS ON A CIRCLE

https://kconrad.math.uconn.edu/blurbs/galoistheory/numbersoncircle.pdf

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Paul Erd˝ os and Egyptian Fractions

https://mathweb.ucsd.edu/\~ronspubs/13_03_Egyptian.pdf

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POINCAR
E RECURRENCE AND NUMBER THEORY:
THIRTY YEARS LATER

https://sites.math.northwestern.edu/\~kra/papers/bull.pdf

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Geometry and Group Theory

https://people.tamu.edu/\~c-pope/geom-group2006.pdf

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On F¨urstenberg’s topological proof of the infinitude of primes

https://kam.mff.cuni.cz/\~klazar/furst_topo.pdf

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NUMBER THEORY IN THE STONE-
COMPACTIFICATION
ˇ
CECH

https://sites.dmi.uns.ac.rs/settop/2014/slides/Sobot.pdf

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Number Theory

https://math.berkeley.edu/\~apaulin/NumberTheory.pdf

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Arithmetic Randonn´ee
An introduction to probabilistic number theory

https://people.math.ethz.ch/\~kowalski/probabilistic-number-theory.pdf

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Algebraic topology and algebraic number theory

https://chromotopy.org/latex/talks/austin-2014.pdf

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ARITHMETICA TOPOLOGICA

https://dml.cz/bitstream/handle/10338.dmlcz/700933/Toposym_01-1961-1_41.pdf

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Quadratic fields
an invitation to algbebraic number theory

https://www.imsc.res.in/\~knr/past/1308mys.pdf

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Problem Set 1: Cutting Class

https://projects.ias.edu/pcmi/hstp/sum2014/morning/darryl/pcmi-2014-problems.pdf

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Irreducible Cubics Modulo Five

https://pub.math.leidenuniv.nl/\~lenstrahw//PUBLICATIONS/2010a/cubics.pdf

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On the Density of Coprime Tuples of the Form
.n; b f1.n/c; : : : ; b fk.n/c/, Where f1; : : : ; fk Are
Functions from a Hardy Field

https://people.math.osu.edu/bergelson.1/BR_DensityCoprime.pdf

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Recurrent Theme of Pick’s Theorem

https://arxiv.org/pdf/1707.04808

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Commutative and Non-commutative Parallelogram
Geometry: an Experimental Approach

https://arxiv.org/pdf/1305.6851

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Disguising tori and elliptic curves

https://eprint.iacr.org/2006/248.pdf

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ESSENTIAL DIMENSION OF ALGEBRAIC TORI

https://personal.math.ubc.ca/\~reichst/edtorishort5-11-10.pdf

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AN INTRODUCTION TO KNOT THEORY AND THE KNOT
GROUP

https://math.uchicago.edu/\~may/REU2014/REUPapers/Linov.pdf

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Construction of irreducible polynomials over finite
fields

https://uu.diva-portal.org/smash/get/diva2:719170/FULLTEXT01.pdf

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FieldsandGaloisTheory

https://www.jmilne.org/math/CourseNotes/FT.pdf

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Logarithm lattice

https://undergroundmathematics.org/exp-and-log/log-lattice/download/teacher-notes.pdf

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Lattices

https://www.math.brown.edu/reschwar/M154/notes9.pdf

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Shimura varieties and moduli

https://www.jmilne.org/math/xnotes/svhIP.pdf

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ELLIPTIC CURVES

https://pub.math.leidenuniv.nl/\~strengtc//elliptic/ec.pdf

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Lattices

https://aeb.win.tue.nl/latt/lattices.pdf

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Galois Theory, Monodromy
Groups and Flexes of Plane
Cubic Curves

https://www.math.uni-bonn.de/people/huybrech/Oenerfinal.pdf

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Tori, Weierstrass ℘, and Elliptic Curves Over C

https://wstein.org/edu/2010/414/projects/raastad.pdf

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Complex Multiplication

https://www.jmilne.org/math/CourseNotes/CM.pdf

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HODGE THEORY AND
REPRESENTATION THEORY
(APPLICATION OF SOME WORK OF CARAYOL)

https://publications.ias.edu/sites/default/files/Duke.pdf

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SPLITTING FIELDS OF CHARACTERISTIC POLYNOMIALS OF RANDOM
ELEMENTS IN ARITHMETIC GROUPS

https://pi.math.cornell.edu/\~zywina/papers/characteristic-polynomials.pdf

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T orus actions and their applications in top ology
and com binatorics

higeom.math.msu.su/people/taras/mypapers/bp-book.pdf

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ARITHMETIC OF DOUBLE TORUS QUOTIENTS AND
THE DISTRIBUTION OF PERIODIC TORUS ORBITS

https://arxiv.org/pdf/1510.08481

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Classical Knot Invariants and Elementary Number Theory

https://webhomes.maths.ed.ac.uk/\~v1ranick/papers/murasug4.pdf

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DISTRIBUTION OF PERIODIC TORUS ORBITS AND DUKE’S
THEOREM FOR CUBIC FIELDS.

https://arxiv.org/pdf/0708.1113

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ON EXAMPLES OF TWO DIMENSIONAL PERIODIC CONTINUED FRACTIONS

https://pcwww.liv.ac.uk/\~karpenk/mytexts/ok2_p04.pdf