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01 / field guide

Mathematics

See patterns and relationships. A set of interactive reference concepts, arranged by idea rather than sequence. The launch set includes 20 free concepts and 8 all-access concepts.

28launch concepts
in this field
01

Algebra & Functions

free / beginner

Functions

A function is a rule for turning one quantity into another.

all access / beginner

Quadratics

Watch a parabola change shape as its coefficients move.

free / intermediate

Exponentials & Logarithms

See repeated multiplication grow, then reverse the question with a logarithm.

02

Calculus

free / intermediate

Derivatives

See a secant line become a tangent, one small step at a time.

all access / intermediate

Integrals

Build area from thin slices and watch accumulation take shape.

free / intermediate

Limits & Continuity

Approach a point from either side and see when the values agree.

free / intermediate

Sequences & Series

Reveal an ordered pattern term by term, then watch its sum grow.

all access / advanced

Differential Equations

Start with a local rule for change and build the curve it produces.

all access / advanced

Multivariable Calculus

Move beyond curves into surfaces, gradients, and higher-dimensional change.

03

Linear Algebra

free / intermediate

Vectors & Matrices

Move a vector through a transformation and track what survives.

all access / advanced

Eigenvectors

Find the directions a transformation leaves pointing the same way.

free / advanced

Linear Algebra II

See rank, span, and kernel account for what a linear map keeps and loses.

04

Probability & Discrete

all access / beginner

Probability

Count possible outcomes and see chance become a long-run pattern.

05

Geometry & Periodicity

all access / beginner

Trigonometry

Turn an angle around the unit circle and unwrap it into a wave.

06

Algebra & Geometry

free / intermediate

Complex Numbers

See imaginary numbers become a real geometric plane.

07

Analysis & Signals

all access / advanced

Fourier Series

Build complex waves from the simplest repeating shapes.

08

Applied Mathematics

free / intermediate

Optimization

Find the best answer when every choice changes the trade-off.

09

Structures

free / intermediate

Number Theory

Explore the patterns hidden inside whole numbers and primes.

free / advanced

Abstract Algebra

Compare different systems by the operations and symmetries they share.

free / advanced

Group Theory

Use reversible operations to map the hidden symmetries of a system.

free / advanced

Ring Theory

Compare addition and multiplication in finite systems where zero can change the rules.

010

Patterns Over Time

free / advanced

Chaos & Dynamical Systems

Watch tiny changes grow into behavior that looks impossible to predict.

011

Foundations

free / beginner

Set Theory

Build a language for collections, membership, and structure.

free / intermediate

Mathematical Logic

Turn statements into rules that can be checked step by step.

free / beginner

Proofs & Reasoning

See how definitions and small steps support a general claim.

012

Discrete Mathematics

free / intermediate

Combinatorics

Count structured possibilities without listing every case.

free / intermediate

Graph Theory

Turn connections into a structure you can trace, color, and optimize.

013

Geometry

free / beginner

Euclidean Geometry

Turn points, lines, and angles into invariants you can see and prove.

The roadmap

More ways to get curious.

These are the next ideas planned for Mathematics. The 28-concept launch set is live; these 34 ideas are the next layer of depth.

34+planned concepts
on the horizon
01Coming soon
Linear Algebra

Eigenvalues & Eigenvectors

Build a visual intuition for eigenvalues & eigenvectors, with patterns and examples you can reuse.

02Coming soon
Linear Algebra

Tensor Algebra

Build a visual intuition for tensor algebra, with patterns and examples you can reuse.

03Coming soon
Geometry

Projective Geometry

Build a visual intuition for projective geometry, with patterns and examples you can reuse.

04Coming soon
Geometry

Differential Geometry

Build a visual intuition for differential geometry, with patterns and examples you can reuse.

05Coming soon
Geometry

Topology

Build a visual intuition for topology, with patterns and examples you can reuse.

06Coming soon
Analysis

Real Analysis

Build a visual intuition for real analysis, with patterns and examples you can reuse.

07Coming soon
Analysis

Complex Analysis

Build a visual intuition for complex analysis, with patterns and examples you can reuse.

08Coming soon
Analysis

Measure Theory

Build a visual intuition for measure theory, with patterns and examples you can reuse.

09Coming soon
Analysis

Functional Analysis

Build a visual intuition for functional analysis, with patterns and examples you can reuse.

10Coming soon
Computation

Numerical Methods

Build a visual intuition for numerical methods, with patterns and examples you can reuse.

11Coming soon
Computation

Numerical Linear Algebra

Build a visual intuition for numerical linear algebra, with patterns and examples you can reuse.

12Coming soon
Calculus

Partial Differential Equations

Build a visual intuition for partial differential equations, with patterns and examples you can reuse.

13Coming soon
Calculus

Vector Calculus

Build a visual intuition for vector calculus, with patterns and examples you can reuse.

14Coming soon
Probability

Stochastic Processes

Build a visual intuition for stochastic processes, with patterns and examples you can reuse.

15Coming soon
Probability

Markov Chains

Build a visual intuition for markov chains, with patterns and examples you can reuse.

16Coming soon
Applied Mathematics

Game Theory

Build a visual intuition for game theory, with patterns and examples you can reuse.

17Coming soon
Applied Mathematics

Decision Theory

Build a visual intuition for decision theory, with patterns and examples you can reuse.

18Coming soon
Applied Mathematics

Information Theory

Build a visual intuition for information theory, with patterns and examples you can reuse.

19Coming soon
Applied Mathematics

Coding Theory

Build a visual intuition for coding theory, with patterns and examples you can reuse.

20Coming soon
Applied Mathematics

Mathematical Modeling

Build a visual intuition for mathematical modeling, with patterns and examples you can reuse.

21Coming soon
Applied Mathematics

Operations Research

Build a visual intuition for operations research, with patterns and examples you can reuse.

22Coming soon
Geometry

Convex Geometry

Build a visual intuition for convex geometry, with patterns and examples you can reuse.

23Coming soon
Discrete Mathematics

Discrete Mathematics

Build a visual intuition for discrete mathematics, with patterns and examples you can reuse.

24Coming soon
Discrete Mathematics

Recurrence Relations

Build a visual intuition for recurrence relations, with patterns and examples you can reuse.

25Coming soon
Discrete Mathematics

Generating Functions

Build a visual intuition for generating functions, with patterns and examples you can reuse.

26Coming soon
Analysis

Asymptotic Analysis

Build a visual intuition for asymptotic analysis, with patterns and examples you can reuse.

27Coming soon
Number Theory

The Riemann Hypothesis

Build a visual intuition for the riemann hypothesis, with patterns and examples you can reuse.

28Coming soon
Geometry

Algebraic Geometry

Build a visual intuition for algebraic geometry, with patterns and examples you can reuse.

29Coming soon
Structures

Category Theory

Build a visual intuition for category theory, with patterns and examples you can reuse.

30Coming soon
Structures

Lie Groups

Build a visual intuition for lie groups, with patterns and examples you can reuse.

31Coming soon
Patterns Over Time

Dynamical Systems

Build a visual intuition for dynamical systems, with patterns and examples you can reuse.

32Coming soon
Applied Mathematics

Control Theory

Build a visual intuition for control theory, with patterns and examples you can reuse.

33Coming soon
Probability

Mathematical Statistics

Build a visual intuition for mathematical statistics, with patterns and examples you can reuse.

34Coming soon
Applied Mathematics

Cryptography

Build a visual intuition for cryptography, with patterns and examples you can reuse.

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