A free, self-paced textbook in 7 chapters. Read a chapter, then drill it with the 1040 companion flashcards using spaced repetition.
The most basic operations in mathematics, after addition and multiplication, are powers and roots. An exponent tells you how many times to multiply a base by itself: \(a^n\) means...
Algebra is the language of unknowns. A variable, usually a letter like \(x\) or \(\theta\), stands in for a number we may or may not know, and an expression combines variables with...
A function is a rule that assigns exactly one output to each input, written \(y = f(x)\) and read \(f\) of \(x\). The domain is the set of valid inputs and the range is the set of...
A sequence is an ordered list of numbers indexed by the positive integers, \(a_1, a_2, a_3, \ldots\), with a general term \(a_n\) given by some formula. The simplest families are a...
Calculus is built on the idea of a limit. The notation \(\lim_{x \to a} f(x) = L\) means that as \(x\) gets arbitrarily close to \(a\), the values \(f(x)\) get arbitrarily close to...
Multivariable calculus extends differentiation to functions of many variables. The partial derivative \(\partial f/\partial x_i\) measures how \(f\) changes when only \(x_i\) moves...
Probability theory formalizes uncertainty. A sample space \(\Omega\) contains all possible outcomes, and events are subsets of \(\Omega\). For a uniform sample space, the probabili...