Home / Learn / Math for Computing

📐 Math for Computing

Linear algebra, probability, numerics. 51 topics, from beginner to advanced.

Mathematics is the language of computing. This area covers linear algebra, probability and statistics, numerical methods and the precision limits of floating-point arithmetic. These tools power graphics, machine learning, simulation and data analysis, and they explain why some computed results are only approximately right.

Who this area is for

Students who need the mathematics behind algorithms, machine learning and graphics, and programmers who want a refresher before a technical course.

Real-world use cases

Rotating and scaling 3D objects with matrix multiplication.
Estimating the uncertainty of an A/B test result with probability.
Recognizing why summing many floating-point numbers can drift from the exact answer.
Using a confidence interval to decide whether an A/B test result is real or noise.
Solving a small linear system to balance flows in a network.

Topics in Math for Computing

Beginner (17)

Number Systems — Naturals, integers, rationals and reals.
Algebra Review — Manipulating expressions and solving equations.
Exponents and Logarithms — Powers and their inverses, central to complexity.
Summations and Series — Adding sequences of terms.
Functions and Graphs — Visualizing relationships between quantities.
Vectors — Quantities with magnitude and direction.
Dot Product — Scalar measuring alignment between two vectors.
Matrices — Rectangular arrays representing linear maps.
Matrix Multiplication — Combining matrices by row-column products.
Determinants — Scalar indicating invertibility and volume scaling.
Probability Basics — Measuring the likelihood of events.
Random Variables — Numeric outcomes of random processes.
Expected Value — Probability-weighted average outcome.
Mean, Median and Mode — Common measures of central tendency.
Variance and Standard Deviation — Measures of spread around the mean.
Combinatorial Probability — Computing odds using counting.
Conditional Probability — Probability of an event given another occurred.

Intermediate (17)

Bayes' Theorem — Updating beliefs using evidence.
Probability Distributions — Functions describing how values are spread.
Normal Distribution — Bell-shaped distribution common in nature.
Binomial and Poisson Distributions — Models for counts of successes and rare events.
Law of Large Numbers — Sample averages converge to expectation.
Central Limit Theorem — Sums of many variables tend toward the bell curve.
Hypothesis Testing — Deciding whether data contradict a claim.
Confidence Intervals — Ranges likely containing a true parameter.
Linear Systems — Sets of linear equations solved together.
Gaussian Elimination — Row operations solving linear systems.
Eigenvalues and Eigenvectors — Directions a matrix only stretches.
Singular Value Decomposition — Factorization revealing matrix structure.
Orthogonality and Projections — Perpendicular vectors and closest-point maps.
Derivatives — Rate of change of a function.
Partial Derivatives and Gradients — Multivariable slopes pointing uphill.
Integrals — Accumulated area under a curve.
Taylor Series — Approximating functions by polynomials.

Advanced (17)

Optimization — Finding inputs minimizing or maximizing a function.
Convex Optimization — Optimizing convex functions with guaranteed global optima.
Lagrange Multipliers — Optimizing subject to equality constraints.
Linear Programming — Optimizing a linear objective under linear constraints.
Simplex Method — Classic algorithm for linear programs.
Numerical Methods — Approximate computation of mathematical problems.
Floating Point Error — Rounding and precision limits in machine arithmetic.
Root Finding — Methods like Newton's to solve f(x)=0.
Numerical Integration — Approximating integrals by sampling.
Interpolation — Estimating values between known points.
Markov Chains — Processes where the next state depends only on the current one.
Monte Carlo Methods — Estimating quantities by random sampling.
Stochastic Processes — Collections of random variables evolving over time.
Maximum Likelihood Estimation — Choosing parameters that make data most probable.
Bayesian Inference — Updating parameter distributions with data.
Information Entropy Math — Entropy and KL divergence formulas.
Fourier and Laplace Transforms — Transforms converting signals between domains.

How to study Math for Computing

Do the calculations by hand first, then check them with a short program. Connect each concept to a computing use, such as using matrices for transforms or probability for randomized algorithms.

Frequently asked questions

How much math do I need for computer science?

Algebra and logic are essential from the start. Linear algebra, probability and calculus become important for graphics, machine learning and scientific computing.

Why is 0.1 + 0.2 not exactly 0.3 in code?

Binary floating-point cannot represent 0.1 exactly, so small rounding errors appear. Use integers for money or a decimal type when exact values matter.

What is a matrix used for in programming?

Matrices represent transformations, grids of data, and systems of equations. They are central to graphics, physics simulations and neural networks.

Which math topic matters most for programming?

Discrete math, probability and linear algebra cover most computing work. Discrete math matters for algorithms, probability for randomness and data, and linear algebra for graphics and machine learning.

Can I skip the proofs and still apply the math?

You can apply most results without reproducing the proofs. Understanding what an assumption means, though, is important, because misusing a result is a common error.

Open the interactive Math for Computing area Take the Math for Computing quiz