Connected Mathematics
Follow the ideas instead of memorizing isolated rules. See how equations transform into functions, derivatives feed integrals, probability becomes statistics, and matrices turn systems into solvable structures.
Algebra & Functions
Move from a line to systems, quadratics, roots, transformations and inverse relationships.
Linear Equation
Solve a first-degree equation for one unknown.
Equation of a Line
Connect slope and intercept to a linear function.
Systems of Equations
Find values that satisfy several equations together.
Quadratic Formula
Find the roots of any quadratic equation.
Function Transformation
Shift, reflect and scale a parent function.
Inverse Function
Reverse a one-to-one function’s input-output mapping.
Calculus
Start with limits, measure change with derivatives, then accumulate change with integrals.
Limit
Describe the value a function approaches.
Power Rule
Differentiate polynomial powers efficiently.
Chain Rule
Differentiate a composition of functions.
Definite Integral
Accumulate signed area over an interval.
Integration by Parts
Integrate products by reversing the product rule.
Taylor Series
Approximate a function using its derivatives.
Probability & Statistics
Build from event probability to conditional reasoning, distributions, standardized scores and inference.
Probability
Measure the likelihood of an event.
Conditional Probability
Update an event’s probability when another event is known.
Bayes’ Theorem
Reverse conditional probabilities using prior evidence.
Normal Distribution
Model continuous values clustered around a mean.
Z-Score
Express a value in standard deviations from the mean.
Confidence Interval
Estimate a population parameter with quantified uncertainty.
Linear Algebra & Matrices
Represent vectors and systems with matrices, then solve, transform and reveal their structure.
Dot Product
Measure vector alignment and produce a scalar.
Vector Projection
Resolve one vector along the direction of another.
Determinant
Measure matrix scaling and test invertibility.
Matrix Inverse
Construct the transformation that reverses a matrix.
Gaussian Elimination
Use row operations to solve linear systems.
Eigenvalues & Eigenvectors
Find directions preserved by a linear transformation.