∎ QED
20 topics · 262 subtopics

Every topic, from truth tables to eigenvalues

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Logic

∧

Propositional Logic

Connectives, truth tables, equivalences and normal forms. 13 subtopics.
∀

Predicate Logic

Quantifiers, predicates, binding, and validity. 13 subtopics.
⊕

Boolean Algebra

Axioms, laws, simplification and Boolean functions. 13 subtopics.

Sets, Relations & Functions

∈

Sets

Set-builder notation, operations, and set identities. 13 subtopics.
R

Relations

Properties of relations, composition, and representations. 13 subtopics.
≡

Equivalence Relations

Equivalence classes, partitions and quotient sets. 13 subtopics.
⊑

Orderings & Lattices

Partial orders, Hasse diagrams, bounds, lattices. 13 subtopics.
ƒ

Functions

Injective, surjective, bijective, composition, inverse. 13 subtopics.

Discrete Structures

◦

Graphs

Terminology, connectivity, trees, paths and cycles. 14 subtopics.
Σ

Induction & Recursion

Mathematical, strong & structural induction; recursion. 13 subtopics.

Foundations

×

Algebra

Foundational algebra to close prerequisite gaps. 13 subtopics.
𝑖

Complex Numbers

Arithmetic, the Argand plane, polar form and De Moivre. 13 subtopics.

Calculus & Linear Algebra

∫

Calculus

Limits, derivatives, integrals and their applications. 13 subtopics.
λ

Linear Algebra

Matrices, systems, determinants, eigenvalues. 13 subtopics.
𝑦′

Differential Equations

Solving and modelling with ODEs, from separable to systems. 14 subtopics.

Probability & Counting

𝔼

Probability

Events, conditional probability, random variables. 13 subtopics.
#

Combinatorics

Counting principles, permutations, combinations. 13 subtopics.
∣

Number Theory

Divisibility, primes, gcd, modular arithmetic. 13 subtopics.

Statistics & Data

σ

Statistics

Describing data, distributions, estimation and hypothesis tests. 13 subtopics.

Geometry & Trigonometry

θ

Trigonometry

Triangles, the unit circle, identities and periodic functions. 13 subtopics.

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