KnowledgeInSight

Program map

Every course, module, and lesson in What Mathematicians Do, in order. Jump anywhere: nothing is locked, and the sequence is a suggestion rather than a gate.

Program overview

Course 1 Number and Structure

3 modules · 6 lessons · 8h 58m

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  1. Module 1 Number Theory 2 lessons

    1. 1.1Number Theory: Primes, divisibility, and Euclid's proof that the primes never run out1h 3m
    2. 1.2Number Theory: Codes, cryptography, and the Riemann Hypothesis1h 33m

  2. Module 2 Algebra 2 lessons

    1. 2.1Algebra: From solving for an unknown to studying symmetry and structure1h 3m
    2. 2.2Algebra: Symmetry in crystals, codes, and puzzles, and what algebra still can't classify1h 33m

  3. Module 3 Linear Algebra 2 lessons

    1. 3.1Linear Algebra: Systems of equations, vectors, and matrices from the Nine Chapters to Gauss1h 3m
    2. 3.2Linear Algebra: Search, graphics, and machine learning: linear algebra at scale1h 33m

  4. ProjectExplain the Mathematics Inside One Technology3 items

    1.  Explain the Mathematics Inside One Technology1h 10m

Course 2 Space and Shape

2 modules · 4 lessons · 6h 22m

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  1. Module 1 Geometry 2 lessons

    1. 1.1Geometry: Euclid's axioms, proof, and the parallel postulate1h 3m
    2. 1.2Geometry: Curved space, GPS, and the packing of spheres1h 33m

  2. Module 2 Topology 2 lessons

    1. 2.1Topology: What survives stretching: polyhedra, Möbius strips, and invariants1h 3m
    2. 2.2Topology: Knots, DNA, data, and the Poincaré conjecture1h 33m

  3. ProjectSame Shape or Not?3 items

    1.  Same Shape or Not?1h 10m

Course 3 Change and Motion

2 modules · 4 lessons · 6h 22m

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  1. Module 1 Calculus 2 lessons

    1. 1.1Calculus: Instantaneous speed and areas under curves: limits, derivatives, and integrals1h 3m
    2. 1.2Calculus: Optimization, physics, and economics, and the questions calculus leaves open1h 33m

  2. Module 2 Differential Equations and Dynamical Systems 2 lessons

    1. 2.1Differential Equations: Laws of change: differential equations from planetary orbits to population growth1h 3m
    2. 2.2Differential Equations: Weather, epidemics, chaos, and the Navier–Stokes problem1h 33m

  3. ProjectModel One Change3 items

    1.  Model One Change1h 10m

Course 4 Chance and Data

2 modules · 4 lessons · 6h 22m

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  1. Module 1 Probability 2 lessons

    1. 1.1Probability: The problem of points: how Pascal and Fermat put a number on chance1h 3m
    2. 1.2Probability: Insurance, genetics, and random algorithms, and the open questions of chance1h 33m

  2. Module 2 Statistics 2 lessons

    1. 2.1Statistics: From mortality tables to inference: learning about a population from a sample1h 3m
    2. 2.2Statistics: Clinical trials, psychometrics, and the replication crisis1h 33m

  3. ProjectRead a Statistical Claim3 items

    1.  Read a Statistical Claim1h 10m

Course 5 Logic, Proof, and Computation

3 modules · 6 lessons · 8h 58m

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  1. Module 1 Logic and Set Theory 2 lessons

    1. 1.1Logic and Set Theory: From Aristotle's syllogisms to Cantor's infinities: the logic of proof1h 3m
    2. 1.2Logic and Set Theory: Gödel's incompleteness, the continuum hypothesis, and logic in circuits and databases1h 33m

  2. Module 2 Combinatorics and Graph Theory 2 lessons

    1. 2.1Graph Theory: Counting arrangements and the bridges of Königsberg1h 3m
    2. 2.2Graph Theory: Networks, scheduling, map coloring, and Ramsey numbers1h 33m

  3. Module 3 Computation 2 lessons

    1. 3.1Computation: Algorithms and the limits of computation, from Euclid's algorithm to Turing1h 3m
    2. 3.2Computation: Efficient algorithms, P versus NP, and computers that help prove theorems1h 33m

  4. ProjectExplain a Limit3 items

    1.  Explain a Limit1h 10m