Mathematical Simulation and Interactive Visualization Learning Platform
Centered on linear algebra, calculus, probability and statistics, geometry, and discrete mathematics, SimLabs provides math pages that learners can directly manipulate, observe, and verify, making them suitable for classroom demos, self-study reinforcement, and concept intuition training.
📐 Linear Algebra (Linear Algebra)
Vector Addition, Subtraction, and Scalar Multiplication
Understand the basic operations on vectors and explore the geometric meaning of vector spaces.
Linear Combinations and Span
Master linear combinations of vectors and understand the concepts of basis vectors and span.
Matrix Transformations
Visualize how matrices perform linear transformations on vector spaces.
Matrix Multiplication
Understand the geometric meaning of matrix multiplication and composed transformations.
3D Linear Transformations
Explore the visual effects of linear transformations in three-dimensional space.
Determinants
Understand the geometric meaning of determinants: scaling factors for area and volume.
Inverse Matrices and Column Space
3D visualization of inverse matrices, column spaces, and rank.
Cross-Dimensional Transformations
Explore linear mappings between spaces of different dimensions.
Dot Product and Duality
Understand the geometric meaning of dot products and the dual relationship of linear transformations.
Cross Product
Visualize the geometric meaning of the cross product and the right-hand rule.
Basis Changes
Understand transformation matrices between different coordinate systems.
Eigenvectors and Eigenvalues
Visualize how eigenvectors preserve their direction during transformations.
Abstract Vector Spaces
Understand that functions can also be elements of vector spaces.
Cramer's Rule
Build intuition for solving linear systems through area ratios.
N-body Gravity Simulation
An integrated application of linear algebra in physical simulation.
Determinant Concepts
Concepts of determinants and the computation and visualization of second- and third-order determinants.
Determinant System of Equations
Cramer's Rule · Solve linear systems with determinants.
Matrix Addition, Subtraction, and Scalar Multiplication
Master the basic rules of matrix operations.
Matrix Multiplication and Powers
Understand how to compute matrix multiplication and powers of matrices.
Transpose, Determinant, and Adjugate Matrix
Explore matrix transpose, determinant calculation, and the properties of the adjugate matrix.
📈 Calculus (Calculus)
Derivatives and Differentials
Understand the concepts of rate of change and tangent slope.
Coming SoonMultivariable Calculus
Visualization of partial derivatives, gradients, divergence, and curl.
Coming SoonDifferential Equations
Visualization of numerical solutions to ordinary and partial differential equations.
Coming Soon🎲 Probability and Statistics (Probability & Statistics)
Probability Distributions
Visualization of common distributions such as the normal, Poisson, and binomial distributions.
Coming SoonStatistical Inference
Intuitive understanding of hypothesis testing, confidence intervals, and p-values.
Coming SoonRegression Analysis
Visualization of linear regression, logistic regression, and multiple regression.
Coming SoonBayesian Statistics
Visualization of Bayesian theorem and posterior distribution updates.
Coming Soon🔺 Geometry and Topology (Geometry & Topology)
Non-Euclidean Geometry
Visual exploration of hyperbolic geometry and spherical geometry.
Coming SoonTopological Transformations
Visualization of continuous deformation and topological invariants.
Coming Soon🔢 Discrete Mathematics (Discrete Mathematics)
Number Theory
Visualization of prime distribution, modular arithmetic, and cryptographic algorithms.
Coming SoonLogic and Set Theory
Visualization of propositional logic, predicate logic, and set operations.
Coming Soon⚙️ Applied Mathematics (Applied Mathematics)
Numerical Analysis
Numerical integration, numerical solutions to differential equations, and error analysis.
Coming SoonOptimization Theory
Visualization of linear programming, gradient descent, and convex optimization.
Coming SoonSignal Processing
Visualization of Fourier transforms, filter design, and spectrum analysis.
Coming Soon