A collection of modern math learning resources. Uses books and videos.
- OpenAlgebra free, links to short videos
- Ximera free interactive mathematics textbooks (Ohio StateU)
- Math.net brief lexis of math topics (up to calc)
- Khan Academy free, recommended by many schools for practice, limited
- Coolmath free, existed early online, good visual examples (up to pre-calc)
- Calculus.org various links to calculus resources
- RealNotComplex several links of math topics
Advanced Algebra v 1.0 Tome, mid reference- Algebra Collection diverse, brief with links
- Before Calculus pick it
- Precalculus Collection Various books on precalculus, an AIO bundle
- Trig Worksheet diagram worksheet
- Understanding Linear Algebra good book, clear
- Interactive Linear Algebra great book, 450 pages
- Tea Time Linear Algebra best book possibly
- Linear Algebra 4th Edtion - Hefferon small font, clear
- GNU Octave Intro Bonus
- Abstract Algebra
- A Gentle Introduction to the Art of Mathematics 'intro to proofs'
- Probability for the Enthusiastic Beginner intense 'beginner' book
- Introduction to Probability full resources, perhaps best stats book
- Introductory Statistics Explained Balka, stats sage, very organized
- Multivariable Calculus ok intro to calculus, use 'early transcendental' versions
- Vector Calculus 'calc3'
- Measure, Integration & Real Analysis difficult text
- YoutubePlaylistCalc &Length, use 'YouTube Speed Controller'
- StatQuest statistics, and some AI stuff
- 3Blue1Brown some good videos
- To The Point Math his breakdown from algebra to calc
- The Organic Chemistry Tutor imo, him and Leonard are the only 2 channels. TOCT teaches every subject efficiently.
- Mathematical Monk byte-sized scientific maths (2010), check probability playlist
- HamblinMath variety of math vids, check linear algebra playlist
M4ML Machine Learning math course
- Desmos useful graphs
- Symbolab
- Sagemath
- Singular might be useful
- GNU Octave maybe also useful, works with matlab
- VisualFractions useful examples
- Cymath, Mathway, & Tiger-algebra check answers
- Magma
- Typst Modern TeX alternative
- CopyPasteMathjax
- SpeedCrunch&Insect calculators
- Pre-Algebra
- Beginning and Intermediate Algebra
- Trigonometry
- Precalculus - Wallace, many learning materials
- Calculus: Basic Concepts for High Schools - L.V. Tarasov
- Multivariable Calculus - G. Cain, J. Herod (Georgia Tech)
- Basics of Algebra, Topology, and Differential Calculus - Gallier (UPenn) TOME, good
- Online Mathematics Textbooks
- Free Mathematics Books
- American Mathematical Society - Expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. Useful, many articles dating back to early 1900s
- Institute of Mathematics and its Applications - News, opinions, and articles related to mathematics, so the reader stays updated. Interesting posts
- Canadian Mathematical Society - Unique, challenging math problems designed for undergraduate levels. Includes an Olympiad Corner. Hyper-organized open resources
- BetterExplained - Maintained by Kalid Azad
- How to Become a Pure Math Statistician list of undergrad resources, 2012
- Recreations in Math - H. E. Licks (1917) this is a pretty interesting book, it goes over the history of math
- Magic Squares and Cubes - W. S. Andrews (1917) goes over magic squares and their history, interesting but extra material
- Basic Concepts of Mathematics - Elias Zakon
- Sets, Relations, Functions same thing, but specific
- An Introduction to Set Theory - Weiss, kinda boring, but maybe important
- An Introduction to Formal Logic - P.D. Magnus (University at Albany)
- A Problem Course in Mathematical Logic - Stefan Bilaniuk (Trent University)
- Infinite Descent into Pure Math decent alternative
- Language, Proof, and Logic advanced text on 'logic'
- Formal Logic brief
- Predictive Arithmetic old book, maybe useful?
- Proofs and Concepts: fundamentals of abstract math easy intro to proofs, 2016
- Book of Proof ok proofs book
- Logic and Proof another good intro
- Open Logic Textbook L collaborative effort, main contributors listed here
- Category Theory for Computing Science ok, maybe useful at some point
- Applied Category Theory maybe useful, organized Fong & Spivak
- Homotopy Type Theory definitely interesting
- Elementary Number Theory ok intro text
- Elementary Number Theory:Primes, Congruences, and Secrets great brief text
- A Course on Number Theory light text on number theory
- Number Theory for Beginners old classic
- Introduction to the Theory of Numbers mid
- Number Theory: A Contemporary Introduction interesting text, although font sucks
- Yet Another Introductory Number Theory Textbook decent
- Introduction to Algebraic Number Theory - F. Oggier interesting stuff, worth reading
- Algebraic Number Theory edited many times, worth reading at some point
- A Course In Algebraic Number Theory
- Introduction to Analytic Number Theory ok text w notation
- Elements of Analytic Number Theory organized
- Intermediate Algebra Gregg Waterman, OIT
- College Algebra Waterman, OIT
- Algebra Collection diverse, brief author links
- College Algebra Leithold, 1980
- Introduction to Abstract Algebra Introductory text with notation
- Abstract Algebra: AMS Classic, timeless book
- Introduction to Modern Algebra Clear text, must read
- Algebraic Methods - F. Oggier (Check their extra works at their .io domain)
- An Undergraduate Course in Abstract Algebra - Howlett, author tried to make the subject easy
- Synopsis of Pure Mathematics Ramanujan used it, careful its from 1886
- Noncommutative Rings
- Group Theory - J.S. Milne good
- Notes on Finite Group Theory - Peter J. Cameron ok, interesting at some point
- Fundamentals of Linear Algebra - Carrell good
- Understanding Linear Algebra - David Austin good, organized in a friendly way
- Linear Algebra and Matrices - Martin Fluch good
- Linear Algebra vid
- Vector Space Theory - Howlett interesting text, watermarked
- Linear Algebra - Hefferon font sucks, but ok
- Intro Linear Algebra solid, may need formatting or update Waterman, 2016
- Elementary Linear Algebra dated, possibly useful Munkres, 1964
- A First Courses in Linear Algebra - Breezer
- Linear Algebra - Cherney, etc
- Introduction to Applied Linear Algebra - Boyd (Stanford), Vandenberghe (UCLA) This book is pretty good
- Elements of Abstract & Linear Algebra good, by Connell
- Immersive Linear Algebra - J. Ström etc Interesting way to teach the subject, and isn't swarmed with words
- Interactive Linear Algebra - Margalit and Rabinoff Read the PDF, the site can be confusing, text heavy, in depth
- Linear Algebra 5th ed I heard this was good
- Linear Algebra Linear Algebra Done Wrong - Sergei Treil
- Serge Lang Intro to / linear algebra (Optional, has 2 versions) terse, dated w errors
- Fields and Galois Theory - J.S. Milne ok
- Basic Combinatorics Good
- Applied Combinatorics ok but formatting
- Foundations of Combinatorics with Applications direct, dated
- Analytic Combinatorics good book, 800+ pages
- Graph Theory 5th Edition - Diestel recent but text heavy
- Graph Theory - explanatory, but lengthy, old but few good resources on subject
- Euclid's Elements Redux Rare
- Non Euclidean Geometry MAA
- Introduction to Euclidean Space
- Geometry and Its Applications new
- Classical Euclidean Geometry
- Geometry
- Analytic Geometry - George Wentworth, etc (1922) also old, maybe useful
- Lectures on Differential Geometry - Wulf Rossmann good to read at some point
- Semi-Riemann Geometry and General Relativity - Shlomo Sternberg advanced
- Introduction to Algebraic Geometry - Igor V. Dolgachev mid read
- Algebraic Geometry - Gallier, Shatz (UPenn) avg
- Algebraic Geometry - J.S. Milne straightforward
- Principles of Topology Croom (easiest introduction)
- Topology Munkres (highly recommended)
- General Topology good
- Topology for Computing
- Topology, Geometry and Gauge fields: Foundations good examples
- Topology Topics wiki
- Algebraic Topology ok
- A Concise Course in Algebraic Topology good
- Algebraic Topology ok
- Topology: A Categorical Approach topology using category theory
Precalculus ok book, 1k pages- Elementary Calculus: An Approach Using Infinitesimals Good
- The Calculus 7 Legendary calculus book single variable
- A ProblemText in Advanced Calculus ok eventually
- Calculus and Linear Algebra. Vol. 1 old but ok book, combines topics well and even has a refresher of prior maths
- Calculus and Linear Algebra. Vol. 2 ^2
- Elementary Calculus GREAT book, has followups
- Active Calculus Challenging workbooks, has elegant formatting
- Calculus Made Easy - Silvanus P. Thompson (1910) Important
- An Introduction to Real Analysis ok
- Elementary Real Analysis GREAT book
- Basic Analysis: Introduction to Real Analysis current 2023, open source, webwork GREAT book
- Sequential Introduction Real Analysis best intro?
- Analysis I Blog recommended, 'superior to Rudin' , Tao
- Understanding Analysis Abbot real analysis of the single variable, good
- Differential and Integral Calculus, Vol.1 Courant Calculus, praised as legendary
- Introduction to Calculus and Analysis, Vol. 1 Courant Calculus with Analysis, classic 1965 Excellent
- Lecture Notes in Real Analysis ok eventually
- Modern Real Analysis ok
- Mathematical Analysis Vol I
- Mathematical Analysis Vol II ok^2 w solutions
- The Calculus of Functions of Several Variables ok at some point
- Tea Time Numerical Analysis ok
- Complex Analysis
- Lecture Notes: Fourier Transform and its Applications Well explained, in depth
- Fourier Analysis - Lucas I - good as a starting point, 20pgs
- Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications html, but organized, might replace
- Introduction to Complex Analysis ok
- An Introduction to Complex Analysis and Geometry brief
- Complex Variables ok, more indepth
- Complex Analysis fair
- Interactive Complex Analysis interactive deep dive
- An Introduction to Functional Analysis ok at some point
- Functional Analysis: Lecture Notes very explanatory, text heavy
- Topics in Real and Functional Analysis might be important at some point
- Functional Analysis ok, somewhat crammed
- Theory of Functions of a Real Variable ok, organized
- An Introduction to Measure Theory - Terence Tao (UCLA) ok
- Lecture Notes in Measure Theory - Steve Cheng
- Measure Theory good, short
- Measure and Integration more in-depth
- Lecture notes: Measure Theory sparse
- Elementary Differential Equations With Boundary Value Problems - Trench pretty good text
- Notes on Partial Differential Equations ok, organized (section needs a revamp)
- A Short Introduction to Probability - Kroese (University of Queensland) good intro
- Probability and Statistics Cookbook - Vallentin (UC Berkeley) cookbook cheatsheet
- The Only Probability Cheatsheet You'll Ever Need - Chen, also check Introduction to Probability
- Introduction to Probability Good, Larson 1995
- Foundations of Constructive Probability Theory - Yuen-Kwok Chan, ok text
- Theory of Statistics - J Gentle (lengthy, good)
- Odds and Ends: Introducing Probability & Decision with Visual Emphasis fun w examples
- Knowing the Odds: An Introduction to Probability elegant, bridges intermediate/advanced concepts
- Seeing Theory visual
- Beginning Statistics or (v2 'Introductory Statistics: A First Course')
- Statistics: An Introduction Many exercises, Larson 1975
- Introductory Statistics Prem, decent
- Probability and Statistics for Economists Bruce, good
- Econometrics Bruce, good
- Introduction to Statistics and Econometrics ok
- Intro to Probability Theory & Statistical Inference Good, indepth, Larson 1991
- An Introduction to Statistical Learning with Applications in Python in Python or R
- Statistical Learning Theory - Percy Liang ok notes
- Machine Learning for Engineers and Scientists great introduction to machine learning, 2022
- Reinforcement Learning: An Introduction wordy, hard to read font, but DOES introduce the topic
- Probabilistic Machine Learning: An Introduction
- Essential Statistical Physics
- Probability and Stochastic Processes with Applications Some explanation
- Lecture Notes on Stochastic Processes not bad, but brief notes
- Introduction to Stochastic Processes - Lecture Notes another good review
- Applied Stochastic Processes in science and engineering historical notes of processes
- An Introduction to Stochastic Processes in Continuous Time brief explanatory process
- Markov Chains and Mixing Times Indepth on Markov Chains
- Introduction to Numerical Analysis Clear notes
- Numerical Analysis concise, good intro with examples
- Advanced Numerical Methods and Applications to Industrial Problems Advanced, details application of mathematical modeling
- Introduction to Signal Processing thick, but good book
- Think DSP Incredibly short python book on DSP concepts
- Linear algebra, signal processing, and wavelets: Unified Might be important eventually
- Mathematics for Computer Science - Good reference, brief 2015
- Isomorphism fun math programming book
- TheoryOfComputation good
- Discrete Structures for Computer Science:Counting, Recursion, and Probability optional
- PML Machine Learning
- Lecture Notes on Optimization grad level
- Computer Networks detailed, good book
- Computer Networking Principles & Practice eh
- Information Theory, Inference, and Learning Algorithms good intro book, pair with prerquisite
- Chaos: Classical and Quantum wacky writing, maybe something of interest
- Deep Learning Introduction relevant by Durham University
- OpenMLGuide updated guide to learn AI/ML
- Algorithm and Systems Analysis old book on algorithms
- Mathematical Biology pretty good, straightforward
- Introduction to Continuum Mechanics Advanced text
- Mathematical Tools for Physics - James Nearing
- An Introduction to Mechanics more modern, eh text
- Physics, Parts 1 & 2, Combined Edition 1966 raved as the best book to learn physics, updated version Principles of Physics is easier to read.
- Mechanics Introduction 2016, seems good
- Fundamental University Physics Vol 3 classic series, interesting, referenced as the best
- The Mechanical Universe: Introduction to Mechanics and Heat classic, contains calculus, 1985
- K-12 Aptitude Decline
- Test Score Success Correlation
- The Quest for Artificial Intelligence
- The Beginnings & Evolution of Algebra
- Number Theory: An Approach Through History
- The Exact Sciences in Antiquity seems good
- Greek Mathematical Thought possibly biased
Since there are many resources out there, the priority is to add notable but also niche ones that happen to be modern. If a source is incorrect or too outdated to use, and has too many critical errors, the goal is to replace or remove it. To contribute;
- Fork the repo, make a new branch.
- Make necessary changes within that branch.
- Commit changes with clear notes and pull request.
Any contributions are appreciated!