Understand the World. Model It. Test It. ACADEMIC METHOD
Understand → Model → Calculate → Simulate → Predict → Validate → 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?
LEARNING 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 Level All levels LEVEL 0 · Mathematical Readiness LEVEL 1 · Core Mathematics LEVEL 2 · Calculus & Linear Algebra LEVEL 3 · Probability, Statistics & Data LEVEL 4 · Differential Equations & Dynamical Systems LEVEL 5 · Physics & Physical Modeling LEVEL 6 · Numerical Methods LEVEL 7 · Scientific Computing LEVEL 8 · Optimization LEVEL 9 · Modeling & Simulation LEVEL 10 · Applied Mathematics for Autonomous Technology LEVEL 11 · Quantitative Financial Mathematics
36 of 36 courses
MF LEVEL 0 · Mathematical Readiness Mathematical Foundations Mathematical Foundations
Open course 0.1 LEVEL 0 · Mathematical Readiness Arithmetic & Numerical Reasoning Mathematical Foundations
Open course 0.2 LEVEL 0 · Mathematical Readiness Foundations of Algebra Algebra & Functions
Open course 1.1 LEVEL 1 · Core Mathematics Functions & Mathematical Modeling Algebra & Functions
Open course 1.2 LEVEL 1 · Core Mathematics Geometry & Trigonometry Geometry & Trigonometry
Open course 1.3 LEVEL 1 · Core Mathematics Mathematical Proof & Scientific Reasoning Mathematical Foundations
Open course 2.1 LEVEL 2 · Calculus & Linear Algebra Calculus I: Differential Calculus Calculus
Open course 2.2 LEVEL 2 · Calculus & Linear Algebra Calculus II: Integral Calculus Calculus
Open course 2.3 LEVEL 2 · Calculus & Linear Algebra Multivariable Calculus Calculus
Open course 2.4 LEVEL 2 · Calculus & Linear Algebra Linear Algebra Linear Algebra
Open course 3.1 LEVEL 3 · Probability, Statistics & Data Probability Probability & Statistics
Open course 3.2 LEVEL 3 · Probability, Statistics & Data Statistics Probability & Statistics
Open course 3.3 LEVEL 3 · Probability, Statistics & Data Applied Statistics & Data Modeling Probability & Statistics
Open course 4.1 LEVEL 4 · Differential Equations & Dynamical Systems Ordinary Differential Equations Differential Equations & Dynamical Systems
Open course 4.2 LEVEL 4 · Differential Equations & Dynamical Systems Dynamical Systems Differential Equations & Dynamical Systems
Open course 4.3 LEVEL 4 · Differential Equations & Dynamical Systems Introduction to Partial Differential Equations Differential Equations & Dynamical Systems
Open course 5.1 LEVEL 5 · Physics & Physical Modeling Classical Mechanics Physics & Physical Modeling
Open course 5.2 LEVEL 5 · Physics & Physical Modeling Electricity & Magnetism Foundations Physics & Physical Modeling
Open course 5.3 LEVEL 5 · Physics & Physical Modeling Waves, Signals & Oscillations Physics & Physical Modeling
Open course 5.4 LEVEL 5 · Physics & Physical Modeling Thermodynamics Foundations Physics & Physical Modeling
Open course 6.1 LEVEL 6 · Numerical Methods Numerical Methods Numerical & Computational Mathematics
Open course 6.2 LEVEL 6 · Numerical Methods Numerical Linear Algebra Numerical & Computational Mathematics
Open course 7.1 LEVEL 7 · Scientific Computing Python for Scientific Computing Scientific Computing
Open course 7.2 LEVEL 7 · Scientific Computing Computational Experimentation Scientific Computing
Open course 8.1 LEVEL 8 · Optimization Mathematical Optimization Optimization
Open course 8.2 LEVEL 8 · Optimization Computational Optimization Optimization
Open course 9.1 LEVEL 9 · Modeling & Simulation Mathematical Modeling Modeling & Simulation
Open course 9.2 LEVEL 9 · Modeling & Simulation Simulation Fundamentals Modeling & Simulation
Open course 9.3 LEVEL 9 · Modeling & Simulation Advanced Simulation Modeling & Simulation
Open course 10.1 LEVEL 10 · Applied Mathematics for Autonomous Technology Mathematics for Robotics Applied Mathematics for Engineering & Autonomous Systems
Open course 10.2 LEVEL 10 · Applied Mathematics for Autonomous Technology Mathematics for Control Systems Applied Mathematics for Engineering & Autonomous Systems
Open course 10.3 LEVEL 10 · Applied Mathematics for Autonomous Technology Mathematics for Artificial Intelligence Applied Mathematics for Engineering & Autonomous Systems
Open course 10.4 LEVEL 10 · Applied Mathematics for Autonomous Technology Mathematics for Signals & Sensors Applied Mathematics for Engineering & Autonomous Systems
Open course 11.1 LEVEL 11 · Quantitative Financial Mathematics Mathematics of Financial Markets Quantitative Methods for Financial Markets
Open course 11.2 LEVEL 11 · Quantitative Financial Mathematics Statistics for Financial Markets Quantitative Methods for Financial Markets
Open course 11.3 LEVEL 11 · Quantitative Financial Mathematics Financial Simulation Quantitative Methods for 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
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. 