Reference sheets, tools and guides

Reference sheet

SAT Math reference sheet

The definitions, formulas and conditions of the SAT Math course on one page, unit by unit, with links to the lessons that explain each topic in full.

• SAT Math

Reference sheet

Precalculus reference sheet

The main definitions, formulas, identities and conditions of the precalculus course on one page, unit by unit, with links to the lessons that explain each topic in full.

• Precalculus

Reference sheet

Foundations for Calculus reference sheet

The main definitions, formulas and conditions of the foundations course on one page, unit by unit, with links to the lessons that explain each topic in full.

• Foundations for Calculus

Reference sheet

Calculus reference sheet

The main definitions, formulas and conditions of the calculus course on one page, unit by unit, with links to the lessons that explain each topic in full.

• Calculus

Reference sheet

Integrals reference sheet

The main integrals, methods, theorems and conditions of the integrals course on one page, unit by unit, with links to the chapter pages that explain each topic in full.

• Integrals From Easy to Advanced

Reference sheet

Multivariable and Vector Calculus reference sheet

The main definitions, formulas and conditions of the multivariable and vector calculus course on one page, unit by unit, with links to the lessons that explain each topic in full.

• Multivariable and Vector Calculus

Reference sheet

Differential Equations reference sheet

The main definitions, formulas, theorems and conditions of the differential equations course on one page, unit by unit, with links to the lessons that explain each topic in full.

• Differential Equations

Reference sheet

Linear Algebra I reference sheet

The main definitions, formulas, theorems and algorithms of Linear Algebra I on one page, unit by unit, with links to the lessons that explain each topic in full.

• Linear Algebra I

Reference sheet

Linear Algebra II reference sheet

The main definitions, theorems and factorizations of Linear Algebra II with their hypotheses, unit by unit, with links to the lessons that explain each topic in full.

• Linear Algebra II

Reference sheet

Introduction to Probability reference sheet

The main definitions, formulas, distributions and conditions of Introduction to Probability on one page, unit by unit, with links to the lessons that explain each topic in full.

• Introduction to Probability

Reference sheet

Statistics reference sheet

The main definitions, formulas, tests and conditions of the statistics course on one page, unit by unit, with links to the lessons that explain each topic in full.

• Statistics

Reference sheet

Multivariate statistics reference

The main definitions, formulas and conditions of multivariate statistical analysis on one page, from mean vectors and the multivariate normal to classification and clustering.

• Multivariate Statistical Analysis

Reference sheet

Linear algebra refresher

The vector and matrix facts multivariate statistics leans on, from eigenvalues and the spectral decomposition to quadratic forms and expected values.

• Multivariate Statistical Analysis

Reference sheet

Machine Learning reference sheet

The main definitions, formulas, metrics and algorithms of the machine learning course on one page, unit by unit, with links to the lessons that explain each topic in full.

• Machine Learning

Reference sheet

Financial Engineering for Quants reference sheet

The main definitions, pricing formulas, models and conventions of the financial engineering course on one page, unit by unit, with links to the lessons that explain each topic in full.

• Financial Engineering for Quants

Interactive tool

Unit circle explorer

Move a point around the unit circle and watch its coordinates become cosine and sine, with exact values at the special angles.

• Precalculus
• Foundations for Calculus
• SAT Math

Interactive tool

Function transformation explorer

Shift, stretch and reflect a parent graph with four sliders, and follow its key points, its formula, its domain and its range as they move.

• Precalculus
• Foundations for Calculus
• SAT Math

Interactive tool

Tangent line explorer

Slide a point along a curve and watch the tangent line and the derivative change with it.

• Calculus
• Precalculus
• Foundations for Calculus

Interactive tool

Riemann sum explorer

Cover the region under a curve with rectangles or trapezoids and compare their total with the exact integral.

• Calculus
• Precalculus
• Foundations for Calculus

Interactive tool

Taylor polynomial explorer

Raise the degree of a Taylor polynomial, move its center and see where the polynomial follows the function and where it breaks away.

• Calculus

Interactive tool

Vector field explorer

Place a circle in a vector field and compare its circulation and flux with the double integrals of curl and divergence from Green's theorem.

• Multivariable and Vector Calculus

Interactive tool

Covariance explorer

Change the spread and correlation of two variables and watch the covariance matrix, its ellipses and the principal axes follow.

• Multivariate Statistical Analysis

Guide

How to study with video lectures

Habits that turn watching a lecture into being able to do the math yourself, from pausing before answers to reviewing a day and a week later.