Skip to content
FREE · CALCULUS · LINEAR ALGEBRA · PROBABILITY

Math concepts explained with videos

Understand math, one concept at a time.

Watch the explanation. Read the notes. Jump to the moment.

THE LIBRARY, AT A GLANCE

A growing library of mathematical understanding.

Explore videos, concepts and reviewed notes across every source language.

Mathematics videos
660
Hours of video
69.5
Knowledge concepts
540
Learning cards
8,819

Explore mathematics, one concept at a time.

Understand math concepts with videos that show how an idea works, and readable notes that help you revisit it. These math videos with notes connect definitions, worked examples, learning maps and knowledge graphs. Move from a question to a concept, then jump to the moment that explains it. Start with something familiar and follow a nearby idea when you need another perspective.

In calculus, limits describe what happens near a point. Derivatives make that local behavior useful for understanding rates of change, while integrals describe accumulation across an interval. Explore these concepts together to see how a graph, a formula and a worked problem express the same mathematical idea. The calculus learning map provides an order for connecting definitions with applications.

Linear algebra starts with vectors and develops a language for transformations. Matrices organize those transformations and the calculations behind linear systems. Eigenvalues reveal directions whose behavior is especially simple. Comparing geometric explanations with algebraic examples can help you understand what a calculation means, rather than treating its steps as a recipe.

Probability adds a different question: what changes when new information arrives? Conditional probability describes a probability under a stated condition, and Bayes’ theorem connects that condition with updated beliefs. Each concept page brings together its definition, reviewed questions and answers, related concepts and available video explanations. Use the concept index to find another starting point, or browse the video directory when you already know the topic, teaching style or length you want.

Browse every mathematics concept →
EXPLORE AN IDEA /

Real Analysis 24 | Pointwise Convergence

Open learning desk

01INSIDE

This segment introduces pointwise convergence for sequences of functions in real analysis.

[∀x~∈I∀ϵ>0∃N∈N∀n≥N:∣fn(x~)−f(x~)∣<ϵ]\left[ \forall \tilde{x} \in I \quad \forall \epsilon > 0 \quad \exists N \in \mathbb{N} \quad \forall n \geq N : \quad |f_n(\tilde{x}) - f(\tilde{x})| < \epsilon \right]

Pointwise Convergence Definition

A sequence of functions (fnf_n) with domain I converges pointwise to a function f if for every fixed point x̃ in I, the numerical sequence (fnf_n(x̃)) converges to f(x̃). This means the convergence property must hold individually at each point in the domain, reducing function convergence to ordinary sequence convergence.

From video-wide learning notes · English

02MOMENTS

Open moment0:00

Introduction and Recap

The Bright Side of Mathematics · YouTube · 8:13

Likes 0Dislikes 0Saves 0
Watch from 0:00

03CONNECTIONS

CONCEPT CONNECTIONS
  • Why this connection? · 0:28

    Reviewed English material v1: card "Pointwise Convergence Definition" at 0:28 — A sequence of functions (fnf_n) with domain I converges pointwise to a function f if for every fixed point x̃ in I, the numerical sequence (fnf_n(x̃)) converges to f(x̃). This means the convergence property must hold individually at each point in the domain, reducing function convergence to ordinary sequence convergence.

Inspect all connections

Connections across the video; no reviewed connection for this chapter yet.

CHOOSE A LEARNING ROUTE

A wider view.

All learning maps →
01

Calculus

Explore change, accumulation and approximation through single-variable calculus.

27 concepts · 23 with reviewed resources
02

Discrete Mathematics: Counting and Number Theory

Connect functions and counting with elementary number theory, graph structures and algorithmic reasoning. Shared concepts and reviewed map connections organize the path; video explanations are added as resources pass review.

18 concepts · 12 with reviewed resources
03

Mathematical Foundations and Proofs

Explore sets and relations; logic and statements; proof and infinity. Concepts and connections are available independently of video coverage.

20 concepts · 12 with reviewed resources
04

Linear algebra

Connect vectors, linear transformations and matrix computations, with geometric and algebraic viewpoints.

28 concepts · 24 with reviewed resources
05

Mathematical modeling

Turns engineering, economic, biological and social questions into variables, assumptions, solvable models, validated answers and an honest limits section.

58 concepts · 43 with reviewed resources
06

Probability and statistics

Move from uncertain events to random variables, probability models and evidence-based statistical inference.

36 concepts · 28 with reviewed resources
QUESTIONS THAT OPEN A DOORAll questions →
01

Besides physical education course teaching quality, what other applications are claimed for the fuzzy formula method?

02

How does the video estimate the probability that total time exceeds 9 hours?

03

What is conditional entropy H(X|Y) and how is it defined for discrete random variables?

04

What is the mathematical definition of a percent?

Other explanations to explore

Explore videos →