SCHOOL 01 · TECHNOLOGY & ENGINEERING
School of Science, Mathematics & Simulation Understand the World. Model It. Test It. Build the mathematical, scientific and computational foundations required to understand complex systems and transform ideas into measurable models and simulations. ACADEMIC METHOD 01 Understand
02 Model
03 Calculate
04 Simulate
05 Predict
06 Validate
07 Apply
Why mathematics and science matter
A disciplined way to turn questions into evidence. The School provides the scientific and mathematical foundations required to understand complex systems, construct models, analyze data, perform computational experiments and develop technologies grounded in measurable evidence.
What problem are we solving? Which assumptions shape the model? What does the result physically mean? How can we test it? Where can simulation fail?
ACADEMIC STRUCTURE
15 shared learning areas 01 Mathematical Foundations02 Algebra & Functions03 Geometry & Trigonometry04 Calculus05 Linear Algebra06 Differential Equations & Dynamical Systems07 Probability & Statistics08 Discrete Mathematics09 Numerical & Computational Mathematics10 Optimization11 Physics & Physical Modeling12 Scientific Computing13 Modeling & Simulation14 Applied Mathematics for Engineering & Autonomous Systems15 Quantitative Methods for Financial MarketsLEARNING PATHWAYS
Recommended learning pathways 9 COURSES Robotics Mathematics 0.2 Foundations of Algebra1.2 Geometry & Trigonometry2.1 Calculus I: Differential Calculus2.4 Linear Algebra4.1 Ordinary Differential Equations3.1 Probability6.1 Numerical Methods9.1 Mathematical Modeling10.1 Mathematics for RoboticsExplore this pathway ↓ 8 COURSES AI Mathematics 1.1 Functions & Mathematical Modeling2.1 Calculus I: Differential Calculus2.3 Multivariable Calculus2.4 Linear Algebra3.1 Probability3.2 Statistics8.1 Mathematical Optimization10.3 Mathematics for Artificial IntelligenceExplore this pathway ↓ 7 COURSES Control Mathematics 1.1 Functions & Mathematical Modeling2.1 Calculus I: Differential Calculus2.4 Linear Algebra4.1 Ordinary Differential Equations4.2 Dynamical Systems6.1 Numerical Methods10.2 Mathematics for Control SystemsExplore this pathway ↓ 11 COURSES Simulation Specialist 2.1 Calculus I: Differential Calculus2.2 Calculus II: Integral Calculus2.4 Linear Algebra3.1 Probability3.2 Statistics4.1 Ordinary Differential Equations6.1 Numerical Methods7.1 Python for Scientific Computing9.1 Mathematical Modeling9.2 Simulation Fundamentals9.3 Advanced SimulationExplore this pathway ↓ 10 COURSES Quantitative Markets 1.1 Functions & Mathematical Modeling2.1 Calculus I: Differential Calculus2.4 Linear Algebra3.1 Probability3.2 Statistics3.3 Applied Statistics & Data Modeling8.1 Mathematical Optimization11.1 Mathematics of Financial Markets11.2 Statistics for Financial Markets11.3 Financial SimulationExplore this pathway ↓ Complete Curriculum
Thirteen progressive levels. One connected foundation. Search courses, lessons or labs Level All levels Level 0 Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Level 10 Level 11
36 courses shown
MF LEVEL 0 · Mathematical Readiness Mathematical Foundations Mathematical Foundations
+ 1 classes Modules 0–14: bilingual draft for administrator review 1 labs 16 mathematical laboratory tools Prerequisites None; diagnostic is advisory
Where this knowledge goes next Algebra & Functions
Open course → 0.1 LEVEL 0 · Mathematical Readiness Arithmetic & Numerical Reasoning Mathematical Foundations
+ 7 classes Numbers and number systems Arithmetic operations Fractions, decimals and percentages Ratios and proportions Scientific notation and orders of magnitude Units and conversions Estimation, significant figures and numerical reasoning 4 labs Measurement & Units Estimation Scientific Calculator Error in Measurement Prerequisites None
Open course → 0.2 LEVEL 0 · Mathematical Readiness Foundations of Algebra Algebra & Functions
+ 6 classes Variables and expressions Equations and inequalities Exponents and roots Polynomials and factoring Rational expressions Systems of equations 3 labs Equation Solver Graphing Algebra with Python Prerequisites Course 0.1 or readiness check
Open course → 1.1 LEVEL 1 · Core Mathematics Functions & Mathematical Modeling Algebra & Functions
+ 8 classes Functions, domain and range Linear and polynomial functions Rational functions Exponential and logarithmic functions Piecewise and inverse functions Function composition Graph interpretation Building mathematical models 3 labs Function Visualization Population Growth Modeling Sensor Calibration Prerequisites Course 0.2
Where this knowledge goes next Computing · Robotics · AI
Open course → 1.2 LEVEL 1 · Core Mathematics Geometry & Trigonometry Geometry & Trigonometry
+ 8 classes Euclidean and coordinate geometry Distance, angles and triangles Circles Vectors Sine, cosine and tangent Trigonometric identities Radians and polar coordinates Forces and motion applications 4 labs Triangle Measurement Robot Geometry Vector Navigation 2D Positioning Simulation Prerequisites Course 0.2
Where this knowledge goes next Mechanical Design · Robotics
Open course → 1.3 LEVEL 1 · Core Mathematics Mathematical Proof & Scientific Reasoning Mathematical Foundations
+ 7 classes Logic and statements Implication and quantifiers Sets and relations Direct and indirect proof Counterexamples Mathematical induction Scientific reasoning 0 labs Reasoning seminar; no laboratory required.
Prerequisites Course 0.2
Where this knowledge goes next Computing · Research
Open course → 2.1 LEVEL 2 · Calculus & Linear Algebra Calculus I: Differential Calculus Calculus
+ 9 classes Limits Continuity Derivatives Differentiation rules Chain rule Implicit differentiation Rates of change Optimization Curve analysis 4 labs Numerical Derivative Velocity from Position Data Optimization Experiment Derivative Visualization Prerequisites Courses 1.1 and 1.2
Where this knowledge goes next Physics · AI · Control
Open course → 2.2 LEVEL 2 · Calculus & Linear Algebra Calculus II: Integral Calculus Calculus
+ 9 classes Antiderivatives Definite integrals Fundamental theorem of calculus Integration techniques Areas and volumes Work Numerical integration Improper integrals Sequences and series 3 labs Numerical Integration Energy Calculation Area Under Sensor Data Prerequisites Course 2.1
Where this knowledge goes next Physics · Engineering
Open course → 2.3 LEVEL 2 · Calculus & Linear Algebra Multivariable Calculus Calculus
+ 7 classes Functions of several variables Partial and directional derivatives Gradient Multiple integrals Vector fields Line and surface integrals Divergence and curl 3 labs 3D Function Visualization Gradient Descent Visualization Vector Field Simulation Prerequisites Course 2.2 and Course 2.4 recommended
Where this knowledge goes next Robotics · Optimization · Machine Learning
Open course → 2.4 LEVEL 2 · Calculus & Linear Algebra Linear Algebra Linear Algebra
+ 9 classes Vectors and matrices Matrix operations Systems and Gaussian elimination Determinants Vector spaces, basis and dimension Linear transformations Eigenvalues and eigenvectors Orthogonality and least squares Matrix decompositions 4 labs Matrix Calculator Linear Transformation Visualizer Robot Coordinate Transformation Least-Squares Data Fitting Prerequisites Course 1.1
Where this knowledge goes next Robotics · AI · Control · Simulation
Open course → 3.1 LEVEL 3 · Probability, Statistics & Data Probability Probability & Statistics
+ 9 classes Random experiments and sample spaces Events and conditional probability Bayes’ theorem Random variables Probability distributions Expectation and variance Covariance Law of large numbers Central limit theorem 4 labs Coin & Dice Simulation Monte Carlo Probability Bayesian Reasoning Sensor Noise Simulation Prerequisites Course 1.1
Where this knowledge goes next AI · Robotics · Financial Markets
Open course → 3.2 LEVEL 3 · Probability, Statistics & Data Statistics Probability & Statistics
+ 9 classes Descriptive statistics Sampling Estimation Confidence intervals Hypothesis testing Correlation Regression Experimental design Statistical uncertainty 4 labs Data Exploration Regression Experimental Data Analysis Uncertainty Analysis Prerequisites Course 3.1
Where this knowledge goes next Research · AI · Financial Markets
Open course → 3.3 LEVEL 3 · Probability, Statistics & Data Applied Statistics & Data Modeling Probability & Statistics
+ 8 classes Multiple regression Model selection Residual analysis Time-series foundations Statistical modeling Bootstrap methods Monte Carlo methods Model validation 3 labs Model Selection Study Bootstrap Uncertainty Time-Series Exploration Prerequisites Course 3.2
Where this knowledge goes next AI · Financial Markets
Open course → 4.1 LEVEL 4 · Differential Equations & Dynamical Systems Ordinary Differential Equations Differential Equations & Dynamical Systems
+ 6 classes First-order ODEs Linear and separable equations Second-order equations Systems of ODEs Initial-value problems Numerical solutions 4 labs ODE Solver Mass-Spring-Damper Simulation Population Dynamics Battery Discharge Model Prerequisites Courses 2.1 and 2.4
Where this knowledge goes next Control · Mechanical Systems · Robotics
Open course → 4.2 LEVEL 4 · Differential Equations & Dynamical Systems Dynamical Systems Differential Equations & Dynamical Systems
+ 7 classes State variables and phase space Equilibrium and stability Linearization Nonlinear systems Oscillations Bifurcations Introduction to chaos 4 labs Pendulum Simulation Phase Portrait Predator-Prey Simulation Chaotic System Experiment Prerequisites Course 4.1
Where this knowledge goes next Control · Robotics
Open course → 4.3 LEVEL 4 · Differential Equations & Dynamical Systems Introduction to Partial Differential Equations Differential Equations & Dynamical Systems
+ 6 classes Heat equation Wave equation Laplace equation Boundary conditions Initial conditions Numerical approximation 2 labs Heat Diffusion Simulation Wave Propagation Simulation Prerequisites Courses 2.2 and 4.1
Where this knowledge goes next Physics · Energy Engineering
Open course → 5.1 LEVEL 5 · Physics & Physical Modeling Classical Mechanics Physics & Physical Modeling
+ 7 classes Position, velocity and acceleration Newton’s laws Forces Momentum Energy and work Rotational motion Torque and angular momentum 5 labs Projectile Motion Friction Experiment Pendulum Rotational Dynamics Robot Motion Model Prerequisites Courses 1.2 and 2.1
Where this knowledge goes next Mechanical Design · Robotics
Open course → 5.2 LEVEL 5 · Physics & Physical Modeling Electricity & Magnetism Foundations Physics & Physical Modeling
+ 7 classes Charge and electric fields Voltage and current Resistance Capacitance Magnetic fields Electromagnetic induction Electrical energy 3 labs Ohm’s Law RC Circuit Simulation Electromagnetic Induction Demonstration Prerequisites Course 2.1
Where this knowledge goes next Electrical, Electronics & Energy Engineering
Open course → 5.3 LEVEL 5 · Physics & Physical Modeling Waves, Signals & Oscillations Physics & Physical Modeling
+ 7 classes Harmonic motion Waves Frequency and phase Resonance Fourier concepts Sampling introduction Noise 4 labs Wave Generator Frequency Analysis Resonance Simulation Signal Sampling Experiment Prerequisites Courses 1.2 and 2.1
Where this knowledge goes next Electronics · Control · AI
Open course → 5.4 LEVEL 5 · Physics & Physical Modeling Thermodynamics Foundations Physics & Physical Modeling
+ 6 classes Temperature and heat Energy and work First law Second law Entropy Heat-transfer foundations 2 labs Thermal Cooling Experiment Heat Transfer Simulation Prerequisites Course 2.2
Where this knowledge goes next Mechanical Design · Energy Engineering
Open course → 6.1 LEVEL 6 · Numerical Methods Numerical Methods Numerical & Computational Mathematics
+ 9 classes Floating-point computation Numerical error Root finding Interpolation Numerical differentiation Numerical integration Linear-system solutions Numerical ODE solutions Stability, conditioning and convergence 5 labs Floating Point Error Newton–Raphson Solver Interpolation Numerical Integration Comparison ODE Numerical Solver Prerequisites Courses 2.2 and 2.4
Where this knowledge goes next Simulation · Control · AI
Open course → 6.2 LEVEL 6 · Numerical Methods Numerical Linear Algebra Numerical & Computational Mathematics
+ 5 classes Matrix conditioning Iterative solvers Sparse matrices Eigenvalue algorithms Numerical stability 2 labs Condition Number Explorer Sparse Solver Comparison Prerequisites Courses 2.4 and 6.1
Where this knowledge goes next Simulation · Control · AI · Robotics
Open course → 7.1 LEVEL 7 · Scientific Computing Python for Scientific Computing Scientific Computing
+ 7 classes Scientific Python fundamentals NumPy arrays Vectorized computation Matplotlib visualization SciPy Numerical experiments Reproducible computation 4 labs Scientific Notebook Data Visualization Numerical Experiment Simulation with Python Prerequisites Course 0.2; basic programming helpful
Where this knowledge goes next Computing & Software Engineering
Open course → 7.2 LEVEL 7 · Scientific Computing Computational Experimentation Scientific Computing
+ 7 classes Reproducibility Parameter sweeps Numerical experiments Data collection Validation Visualization Performance considerations 2 labs Reproducible Parameter Sweep Model Validation Notebook Prerequisites Courses 6.1 and 7.1
Where this knowledge goes next Research · Simulation
Open course → 8.1 LEVEL 8 · Optimization Mathematical Optimization Optimization
+ 8 classes Objective functions and constraints Convexity Unconstrained optimization Constrained optimization Lagrange multipliers Gradient methods Linear programming Nonlinear optimization 3 labs Optimization Visualizer Resource Allocation Trajectory Optimization Introduction Prerequisites Courses 2.1, 2.3 and 2.4
Where this knowledge goes next AI · Robotics · Control · Financial Markets
Open course → 8.2 LEVEL 8 · Optimization Computational Optimization Optimization
+ 5 classes Gradient descent Numerical optimization Search methods Optimization algorithms Multi-objective optimization 2 labs Gradient Descent Race Multi-Objective Trade-off Prerequisites Courses 6.1 and 8.1
Where this knowledge goes next AI · Robotics · Engineering Design
Open course → 9.1 LEVEL 9 · Modeling & Simulation Mathematical Modeling Modeling & Simulation
+ 8 classes Real system and research question Abstraction and assumptions Variables and parameters Equations and model construction Parameter estimation and calibration Sensitivity Validation Model limitations and revision 2 labs From Measurement to Model Sensitivity Study Prerequisites Levels 2–4 core
Where this knowledge goes next All Engineering Schools
Open course → 9.2 LEVEL 9 · Modeling & Simulation Simulation Fundamentals Modeling & Simulation
+ 6 classes Continuous and discrete simulation Time-step simulation Event-based simulation Monte Carlo simulation Deterministic and stochastic models Verification and validation 4 labs Monte Carlo Simulator Dynamic System Simulator Queue Simulation Random Process Simulation Prerequisites Courses 3.1, 4.1, 6.1 and 9.1
Where this knowledge goes next Robotics · Control · Financial Markets
Open course → 9.3 LEVEL 9 · Modeling & Simulation Advanced Simulation Modeling & Simulation
+ 6 classes Multi-domain simulation Parameter estimation Sensitivity analysis Uncertainty propagation Model comparison Simulation optimization 3 labs Uncertainty Propagation Model Comparison Simulation Optimization Prerequisites Course 9.2
Where this knowledge goes next Autonomous Technology Workshop
Open course → 10.1 LEVEL 10 · Applied Mathematics for Autonomous Technology Mathematics for Robotics Applied Mathematics for Engineering & Autonomous Systems
+ 7 classes Coordinate systems Vectors and matrices Rotation matrices Homogeneous transformations Robot geometry Jacobian foundations Optimization and probability foundations 3 labs 2D Robot Transformations 3D Coordinate Frames Manipulator Geometry Prerequisites Courses 1.2, 2.4, 3.1 and 8.1
Where this knowledge goes next Robotics & Autonomous Systems
Open course → 10.2 LEVEL 10 · Applied Mathematics for Autonomous Technology Mathematics for Control Systems Applied Mathematics for Engineering & Autonomous Systems
+ 7 classes Differential equations Linear algebra State variables Laplace transform Transfer functions Stability mathematics Frequency-domain foundations 2 labs State-Space Explorer Transfer Function Response Prerequisites Courses 2.4 and 4.1
Where this knowledge goes next Automation & Control
Open course → 10.3 LEVEL 10 · Applied Mathematics for Autonomous Technology Mathematics for Artificial Intelligence Applied Mathematics for Engineering & Autonomous Systems
+ 5 classes Linear algebra Probability and statistics Optimization Calculus Information-theory foundations 2 labs Loss Surface Explorer Probability Calibration Prerequisites Courses 2.3, 2.4, 3.2 and 8.1
Where this knowledge goes next Artificial Intelligence & Perception
Open course → 10.4 LEVEL 10 · Applied Mathematics for Autonomous Technology Mathematics for Signals & Sensors Applied Mathematics for Engineering & Autonomous Systems
+ 7 classes Signals Sampling Noise Filtering foundations Fourier analysis Probability Sensor uncertainty 2 labs Sampling & Aliasing Sensor Noise Filter Prerequisites Courses 3.1 and 5.3
Where this knowledge goes next Electronics · Robotics · AI
Open course → 11.1 LEVEL 11 · Quantitative Financial Mathematics Mathematics of Financial Markets Quantitative Methods for Financial Markets
+ 7 classes Percentages and returns Compounding Logarithmic returns Expected value Variance and covariance Correlation Risk-measurement foundations 2 labs Return & Compounding Explorer Portfolio Covariance Prerequisites Courses 1.1 and 3.1
Where this knowledge goes next Stock Trading & Financial Markets
Open course → 11.2 LEVEL 11 · Quantitative Financial Mathematics Statistics for Financial Markets Quantitative Methods for Financial Markets
+ 7 classes Financial data Distributions and sampling Regression Volatility Correlation Time-series foundations Statistical uncertainty 2 labs Volatility Estimation Rolling Correlation Prerequisites Courses 3.2 and 3.3
Where this knowledge goes next Stock Trading & Financial Markets
Open course → 11.3 LEVEL 11 · Quantitative Financial Mathematics Financial Simulation Quantitative Methods for Financial Markets
+ 6 classes Random-process foundations Monte Carlo methods Scenario simulation Risk simulation Backtesting concepts Limits, bias and uncertainty 3 labs Educational Monte Carlo Scenario Risk Backtest Limitations Prerequisites Courses 3.3, 8.1 and 11.1
Where this knowledge goes next Stock Trading & Financial Markets
Open course → LEVEL 12 · ADVANCED ELECTIVES Choose a specialization—students do not need every elective. Advanced Linear Algebra Real Analysis Complex Variables Fourier Analysis Advanced Differential Equations Stochastic Processes Bayesian Statistics Advanced Optimization Numerical PDEs Computational Physics Nonlinear Dynamics & Chaos Graph Theory Information Theory Operations Research Mathematical Finance Uncertainty Quantification
INTERACTIVE LABORATORY
Science, Mathematics & Simulation Laboratory These browser tools are mathematical or computer simulations—not physical experiments. Change the parameters, compare results and question the model. Explore all reusable simulator components + Function Plotter Vector Visualizer Matrix Transformation Visualizer Derivative Visualizer Integral Visualizer Probability Simulator Distribution Explorer Regression Explorer Monte Carlo Simulator ODE Solver Pendulum Simulator Mass-Spring-Damper Simulator Heat Equation Simulator Optimization Visualizer Robot Coordinate Transform Simulator
Mathematical Simulation Visualizes a defined mathematical relationship.Computer Simulation Executes an algorithmic representation.Virtual Laboratory Guides a controlled digital experiment.Physical Laboratory Requires real measurement, equipment and safety controls.
APPLY & VALIDATE
Interdisciplinary Capstones CAPSTONE 01 Model a Physical System Measurements → Model → Equations → Simulation → Prediction → Experiment → Validation
Physics · Modeling · Research CAPSTONE 02 Autonomous Vehicle Motion Simulation Geometry → Calculus → Linear Algebra → Dynamics → Numerical Simulation
Robotics · Automation & Control CAPSTONE 03 Sensor Uncertainty & Estimation Measurement → Probability → Statistics → Simulation → Validation
Electronics · Robotics · AI CAPSTONE 04 Financial Risk Simulation Data → Probability → Monte Carlo → Scenarios → Limitations
Stock Trading & Financial Markets · Educational simulation only CLASS TEMPLATE Why it matters → objectives → prerequisites → theory → worked examples → practice → laboratory → knowledge check → references EXERCISE PROGRESSION Foundation → Practice → Applied → Challenge → Research / Exploration ASSESSMENT SYSTEM Knowledge checks · quizzes · problem sets · lab reports · computational assignments · projects · final assessment CONTENT GOVERNANCE Sources → AI draft → academic review → approved → published TRACEABLE KNOWLEDGE
Library & source map Scientific integrity Every class distinguishes definitions, mathematical results, assumptions, measurements, approximations, hypotheses and simulation results. SI units are the default; uncertainty, numerical error and limitations are stated.
A simulation is not reality. A model is a simplified representation whose results depend on assumptions, parameters, algorithms and numerical accuracy. Start your journey
Observe → Question → Measure → Model → Calculate → Simulate → Predict → Test → Validate → Improve → Share Knowledge Learn Together. Research Together. Build Together.