Reading room
Books, essays and courses to read alongside Lemma
33works that their authors publish openly online, from a first look at calculus to research blogs. Each link opens the author's or publisher's own page.
Books
Whole textbooks, the way their authors wrote them.
Calculus Made EasyThe classic that set out to make calculus friendly, and still does: “What one fool can do, another can.”Public domain (Project Gutenberg)Read ↗Calculus for Beginners and ArtistsShort chapters from MIT that build calculus from the ideas up, with little machinery.Published openly by the authorRead ↗CalculusStrang's whole calculus textbook, third edition. Some of Lemma's calculus problems come from it.CC BY-NC-SA 4.0 (MIT OpenCourseWare)Read ↗Active CalculusCalculus taught through activities: you work each idea out before the book explains it.CC BY-NC-SA 4.0Read ↗Calculus, Volume 1A complete first course in limits, derivatives and integrals, with worked examples throughout.Creative Commons (OpenStax)Read ↗Calculus: Early TranscendentalsA full single- and multivariable course from Whitman College, plainly written.Creative CommonsRead ↗Book of ProofThe gentlest bridge from computing answers to writing proofs: sets, logic, induction, functions.Published openly by the authorRead ↗Discrete Mathematics: An Open IntroductionCounting, sequences, logic, graphs and proof, with an investigation to open every chapter.CC BY-SA 4.0Read ↗Linear AlgebraA first course that teaches proofs alongside the matrices, with answers to every exercise.Creative CommonsRead ↗Linear AlgebraThe UC Davis course book, with review problems and short videos for each section.Published openly by the authorRead ↗Linear Algebra Done RightThe second course: vector spaces and linear maps first, determinants last. Fourth edition, open access.CC BY-NC 4.0Read ↗Basic Analysis: Introduction to Real AnalysisWhy calculus works: the real numbers, sequences, continuity and the integral, proved carefully.Creative CommonsRead ↗Introduction to ProbabilityProbability with history, simulation and plenty of exercises, from Dartmouth.GNU Free Documentation LicenseRead ↗An Infinitely Large NapkinA tour of undergraduate and graduate mathematics, written for olympiad students who want to see what comes next.Published openly by the authorRead ↗Euclid's ElementsAll thirteen books, with interactive diagrams and a guide to each proposition.Published openly by the authorRead ↗Amusements in MathematicsFour hundred puzzles from the great English puzzler. Some of Lemma's puzzles come from here.Public domain (Project Gutenberg)Read ↗
Essays and articles
Short pieces on what mathematics is and how to do it.
Introduction to Mathematical ArgumentsA short Berkeley handout on what a proof is, with the standard ways to write one.Published openly by the authorRead ↗There's More to Mathematics than Rigour and ProofsThe three stages of a mathematical education, and why intuition comes back after rigour.Published openly by the authorRead ↗On Proof and Progress in MathematicsA Fields medallist on how mathematicians actually come to understand things.Published openly by the authorRead ↗The Two Cultures of MathematicsProblem-solvers and theory-builders, and why combinatorics deserves the respect theory gets.Published openly by the authorRead ↗Olympiad articles and handoutsHandouts on geometry, inequalities and functional equations, and how to write up a solution.Published openly by the authorRead ↗Expository articlesTao's short explanatory pieces across analysis, combinatorics and number theory.Published openly by the authorRead ↗
Blogs and magazines
Working mathematicians and writers, posting as they go.
Quanta Magazine: MathematicsWell-told stories about new results and the people who prove them.Published openly by the authorRead ↗What's newLecture notes, new results and career advice from one of the most prolific mathematicians alive.Published openly by the authorRead ↗Gowers's WeblogMathematics, how it's done and how it's published, from a Fields medallist.Published openly by the authorRead ↗Math ∩ ProgrammingMathematics explained by building it in code, from graph theory to cryptography.Published openly by the authorRead ↗
Courses and videos
Lectures and notes from full university courses.
Essence of Linear AlgebraShort animated videos that show what matrices and determinants mean geometrically.Published openly by the authorRead ↗Essence of CalculusCalculus rediscovered visually, one idea per video.Published openly by the authorRead ↗18.06SC Linear AlgebraStrang's famous lectures, with recitation videos, problem sets and exams with solutions.CC BY-NC-SA 4.0 (MIT OpenCourseWare)Read ↗6.042J Mathematics for Computer ScienceProofs, counting, graphs and probability, with the full course text by Lehman, Leighton and Meyer.CC BY-NC-SA 4.0 (MIT OpenCourseWare)Read ↗Paul's Online Math NotesClear notes and worked examples from algebra through differential equations.Published openly by the authorRead ↗
Problem archives
Somewhere to go when Lemma's library isn't enough.