Counting and Addition
Numbers and quantities · Addition as combining · Place value
22 lectures · 6 practices · 7 assessmentsView course outline →THE ARK CURRICULUM · VERSION 1
Start with counting, everyday science, your first line of code or your first business decision. Follow clear prerequisites through university foundations, advanced specialisations and research pathways.
English throughout. These are detailed course outlines, not a library of finished videos. This broad roadmap remains open to specialist expansion; no finite catalogue covers every result in a growing field.
Build the picture, explain the rule, work an example, then justify it. Visual constructions, worked problems and proofs.
Numbers and quantities · Addition as combining · Place value
22 lectures · 6 practices · 7 assessmentsView course outline →Subtraction · Multiplication · Division
24 lectures · 6 practices · 7 assessmentsView course outline →Fractions · Fraction arithmetic · Decimals and percentages
26 lectures · 6 practices · 7 assessmentsView course outline →Proportion · Measurement · Data sense
26 lectures · 6 practices · 7 assessmentsView course outline →Signed numbers · Expressions · Equations
24 lectures · 6 practices · 7 assessmentsView course outline →Coordinates and lines · Systems · Functions
24 lectures · 6 practices · 7 assessmentsView course outline →Polynomials · Quadratics · Rational and exponential functions
26 lectures · 6 practices · 7 assessmentsView course outline →Geometric reasoning · Triangles and circles · Space and transformations
26 lectures · 6 practices · 7 assessmentsView course outline →Trigonometric functions · Trigonometric reasoning · Precalculus synthesis
25 lectures · 6 practices · 7 assessmentsView course outline →Limits and continuity · Differentiation · Applications
26 lectures · 6 practices · 7 assessmentsView course outline →Integration · Integral applications · Series
26 lectures · 6 practices · 7 assessmentsView course outline →Matrix arithmetic · Solving systems · Vectors and structure
30 lectures · 6 practices · 7 assessmentsView course outline →Geometry of linear maps · Spectral methods · Decompositions and forms
24 lectures · 6 practices · 7 assessmentsView course outline →Several variables · Multiple integrals · Vector fields
25 lectures · 6 practices · 7 assessmentsView course outline →Ordinary equations · Systems and transforms · Nonlinear dynamics
24 lectures · 6 practices · 7 assessmentsView course outline →Proof language · Counting and relations · Graphs and algorithms
28 lectures · 6 practices · 7 assessmentsView course outline →Probability models · Sampling and estimation · Inference and regression
29 lectures · 6 practices · 7 assessmentsView course outline →Real numbers and sequences · Continuity and compactness · Functions and integration
24 lectures · 6 practices · 7 assessmentsView course outline →Groups · Rings and fields · Number theory
28 lectures · 6 practices · 7 assessmentsView course outline →Complex differentiability · Residues · Fourier analysis
25 lectures · 6 practices · 7 assessmentsView course outline →Point-set topology · Manifolds and curvature · Algebraic topology
25 lectures · 6 practices · 7 assessmentsView course outline →Measure and probability · Functional analysis · Partial differential equations
25 lectures · 6 practices · 7 assessmentsView course outline →Optimisation · Reliable computation · Stochastic models
27 lectures · 6 practices · 7 assessmentsView course outline →Algebra and geometry pathways · Logic and deeper analysis · Research craft
27 lectures · 6 practices · 7 assessmentsView course outline →Predict, observe a demonstration, draw a model, then test its limits. Diagrams, virtual experiments, data analysis and simulations.
Observe and measure · Motion and forces intuitively · Energy and evidence
25 lectures · 6 practices · 7 assessmentsView course outline →Scientific measurement · Kinematics · Two-dimensional motion
24 lectures · 6 practices · 7 assessmentsView course outline →Newtonian forces · Conservation laws · Rotation and gravity
29 lectures · 6 practices · 7 assessmentsView course outline →Fluids · Thermal phenomena · Thermodynamics
26 lectures · 6 practices · 7 assessmentsView course outline →Oscillations and waves · Sound · Light and images
26 lectures · 6 practices · 7 assessmentsView course outline →Electric fields · Circuits · Magnetism
27 lectures · 6 practices · 7 assessmentsView course outline →Experimental design · Computation · Evidence and reporting
24 lectures · 6 practices · 7 assessmentsView course outline →Lagrangian mechanics · Hamiltonian mechanics · Nonlinear mechanics
24 lectures · 6 practices · 7 assessmentsView course outline →Electrostatics · Magnetostatics and induction · Maxwell theory
25 lectures · 6 practices · 7 assessmentsView course outline →Experimental foundations · One-dimensional quantum systems · Measurement and operators
24 lectures · 6 practices · 7 assessmentsView course outline →Angular momentum and atoms · Approximation methods · Many particles and information
25 lectures · 6 practices · 7 assessmentsView course outline →Statistical foundations · Quantum statistics · Collective behaviour
24 lectures · 6 practices · 7 assessmentsView course outline →Special relativity · General relativity · Cosmology
25 lectures · 6 practices · 7 assessmentsView course outline →Crystals and electrons · Devices and collective states · Modern materials
24 lectures · 6 practices · 7 assessmentsView course outline →Nuclear and particle foundations · Plasma physics · Astrophysics
24 lectures · 6 practices · 7 assessmentsView course outline →Field theory entry · Modern research methods · Research frontiers
24 lectures · 6 practices · 7 assessmentsView course outline →Connect visible observations, particle models and chemical notation. Molecular models, reaction accounting and supplied laboratory data.
Matter around us · Particles and substances · Changes and evidence
24 lectures · 6 practices · 7 assessmentsView course outline →Atomic structure · Periodic patterns · Bonding and structure
25 lectures · 6 practices · 7 assessmentsView course outline →Chemical language · Reaction accounting · Solutions and gases
25 lectures · 6 practices · 7 assessmentsView course outline →Chemical energy · Reaction rates · Equilibrium
24 lectures · 6 practices · 7 assessmentsView course outline →Acids and bases · Aqueous analysis · Redox and cells
25 lectures · 6 practices · 7 assessmentsView course outline →Carbon structures · Three-dimensional molecules · Mechanistic language
25 lectures · 6 practices · 7 assessmentsView course outline →Substitution and elimination · Functional-group chemistry · Synthesis reasoning
26 lectures · 6 practices · 7 assessmentsView course outline →Quantitative measurement · Separations and spectra · Structure determination
24 lectures · 6 practices · 7 assessmentsView course outline →Thermodynamics · Phase and chemical equilibria · Kinetics
24 lectures · 6 practices · 7 assessmentsView course outline →Quantum molecular models · Bonding approximations · Spectroscopy and statistical chemistry
24 lectures · 6 practices · 7 assessmentsView course outline →Main-group chemistry · Transition metals · Organometallic and bioinorganic concepts
24 lectures · 6 practices · 7 assessmentsView course outline →Biomolecular structures · Enzymes and energetics · Metabolic chemistry
24 lectures · 6 practices · 7 assessmentsView course outline →Materials · Environmental chemistry · Industrial systems
24 lectures · 6 practices · 7 assessmentsView course outline →Computational methods · Laboratory reasoning · Research pathways
25 lectures · 6 practices · 7 assessmentsView course outline →Zoom from organism to mechanism, then evaluate the biological evidence. Annotated systems, sequence analysis and observational investigations.
Recognising life · Life at different scales · Organisms and surroundings
24 lectures · 6 practices · 7 assessmentsView course outline →Molecules of life · Cell organisation · Membranes and transport
26 lectures · 6 practices · 7 assessmentsView course outline →Energy transformations · Cell division · Communication and organisation
25 lectures · 6 practices · 7 assessmentsView course outline →Inheritance models · Complex inheritance · Genetic information
24 lectures · 6 practices · 7 assessmentsView course outline →Evolutionary mechanisms · Evidence and relationships · Biodiversity
25 lectures · 6 practices · 7 assessmentsView course outline →Plant structure · Plant reproduction and regulation · Plant ecology and production
24 lectures · 6 practices · 7 assessmentsView course outline →Movement and nutrition · Exchange and regulation · Coordination and development
24 lectures · 6 practices · 7 assessmentsView course outline →Populations and communities · Ecosystems · Conservation
25 lectures · 6 practices · 7 assessmentsView course outline →Genome maintenance · Gene expression · Genomic evidence
24 lectures · 6 practices · 7 assessmentsView course outline →Microbial systems · Immune foundations · Evidence and society
24 lectures · 6 practices · 7 assessmentsView course outline →Development · Cellular neuroscience · Systems neuroscience
24 lectures · 6 practices · 7 assessmentsView course outline →Biological statistics · Computational biology · Systems biology
24 lectures · 6 practices · 7 assessmentsView course outline →Biotechnology concepts · Biophysics · Applied biology
24 lectures · 6 practices · 7 assessmentsView course outline →Research design · Integrative frontiers · Research communication
24 lectures · 6 practices · 7 assessmentsView course outline →Follow a real task through a system, then design and troubleshoot it. System diagrams, design reviews and bounded prototypes.
Everyday systems · Using computers · Digital judgement
24 lectures · 6 practices · 7 assessmentsView course outline →Representing information · Computer architecture · Operating systems
24 lectures · 6 practices · 7 assessmentsView course outline →Connected devices · Internet services · Web foundations
24 lectures · 6 practices · 7 assessmentsView course outline →Computational thinking · Data structures · Algorithmic reasoning
24 lectures · 6 practices · 7 assessmentsView course outline →Requirements and design · Team development · Reliable delivery
25 lectures · 6 practices · 7 assessmentsView course outline →Relational modelling · Querying data · Reliable storage
25 lectures · 6 practices · 7 assessmentsView course outline →Frontend systems · Backend services · Application delivery
24 lectures · 6 practices · 7 assessmentsView course outline →Infrastructure · Distributed systems · Operations
24 lectures · 6 practices · 7 assessmentsView course outline →Security reasoning · Secure design · Defensive operations
25 lectures · 6 practices · 7 assessmentsView course outline →Electronics foundations · Embedded computing · Connected devices
24 lectures · 6 practices · 7 assessmentsView course outline →Robot geometry · Feedback control · Autonomous systems
24 lectures · 6 practices · 7 assessmentsView course outline →Human-centred design · Media systems · Graphics and interaction
24 lectures · 6 practices · 7 assessmentsView course outline →Engineering design · Technology infrastructure · Emerging systems
24 lectures · 6 practices · 7 assessmentsView course outline →Theory of computation · Advanced systems · Research and capstone
24 lectures · 6 practices · 7 assessmentsView course outline →Begin with a baseline, trace a model, measure errors and improve it. Data experiments, evaluations, model tracing and reproducible projects.
What AI does · Data and mistakes · Using AI thoughtfully
24 lectures · 6 practices · 7 assessmentsView course outline →Linear and differential tools · Probability for learning · Data preparation
25 lectures · 6 practices · 7 assessmentsView course outline →Search problems · Reasoning systems · Decisions and planning
24 lectures · 6 practices · 7 assessmentsView course outline →Regression · Classification · Model evaluation
26 lectures · 6 practices · 7 assessmentsView course outline →Unsupervised learning · Probabilistic models · Specialised learning
24 lectures · 6 practices · 7 assessmentsView course outline →Neural networks · Optimisation · Generalisation and experiments
25 lectures · 6 practices · 7 assessmentsView course outline →Image representations · Vision tasks · Modern vision
24 lectures · 6 practices · 7 assessmentsView course outline →Language representations · Attention and transformers · Language tasks
24 lectures · 6 practices · 7 assessmentsView course outline →Generative modelling · Language-model adaptation · Multimodal systems
24 lectures · 6 practices · 7 assessmentsView course outline →Retrieval systems · Application design · Evaluation and operation
25 lectures · 6 practices · 7 assessmentsView course outline →Decision models · Learning algorithms · Reliable sequential learning
24 lectures · 6 practices · 7 assessmentsView course outline →ML systems · Efficiency · Production reliability
25 lectures · 6 practices · 7 assessmentsView course outline →Causal reasoning · Responsible systems · Scientific assessment
24 lectures · 6 practices · 7 assessmentsView course outline →Research foundations · Research directions · Research capstone
25 lectures · 6 practices · 7 assessmentsView course outline →Predict the output, trace state, write a small program and debug it. Coding, trace tables, tests and original portfolio projects.
First programs · Values and names · Input and choices
24 lectures · 6 practices · 7 assessmentsView course outline →Decisions · Loops · Functions
28 lectures · 6 practices · 7 assessmentsView course outline →Sequences · Mappings and sets · Text processing
30 lectures · 6 practices · 7 assessmentsView course outline →Persistent data · Error handling · Standard tools
27 lectures · 6 practices · 7 assessmentsView course outline →Debugging · Testing · Project structure
26 lectures · 6 practices · 7 assessmentsView course outline →Object models · Python object protocols · Types and design
26 lectures · 6 practices · 7 assessmentsView course outline →Algorithm analysis · Core structures · Algorithmic patterns
25 lectures · 6 practices · 7 assessmentsView course outline →Safe automation · HTTP clients · Persistent applications
24 lectures · 6 practices · 7 assessmentsView course outline →Numerical arrays · Tabular data · Visual analysis
26 lectures · 6 practices · 7 assessmentsView course outline →Web service design · Persistence and security · Shipping services
24 lectures · 6 practices · 7 assessmentsView course outline →Language mechanisms · Concurrency · Performance and internals
28 lectures · 6 practices · 7 assessmentsView course outline →Packaging and maintenance · Applied projects · Research and contribution
24 lectures · 6 practices · 7 assessmentsView course outline →Open with a question, reveal the mechanism, distinguish evidence from speculation. Visual explanations, evidence checks and mission tradeoffs.
Eclipse geometry · Our solar system · Observing evidence
21 lectures · 6 practices · 7 assessmentsView course outline →Time and clocks · Gravity and timing · Speculation and evidence
21 lectures · 6 practices · 7 assessmentsView course outline →Getting there · Surviving and exploring · Planning responsibly
23 lectures · 6 practices · 7 assessmentsView course outline →Start with a delivery problem, build the project artifact, simulate a change and defend the decision. Project charters, schedules, risk registers, delivery simulations and benefits reviews.
Projects and value · Starting responsibly · Planning a small project
24 lectures · 6 practices · 7 assessmentsView course outline →Investment justification · Project governance · Selecting projects
24 lectures · 6 practices · 7 assessmentsView course outline →Discovering needs · Defining scope · Managing change
24 lectures · 6 practices · 7 assessmentsView course outline →Estimating work · Network schedules · Resource-constrained delivery
24 lectures · 6 practices · 7 assessmentsView course outline →Cost planning · Buying responsibly · Contract administration
24 lectures · 6 practices · 7 assessmentsView course outline →Risk discovery · Risk response · Quality management
24 lectures · 6 practices · 7 assessmentsView course outline →Building teams · Stakeholder engagement · Leading delivery
24 lectures · 6 practices · 7 assessmentsView course outline →Adaptive delivery · Scrum in practice · Flow and hybrid methods
24 lectures · 6 practices · 7 assessmentsView course outline →Measuring performance · Recovering delivery · Closing and learning
24 lectures · 6 practices · 7 assessmentsView course outline →Programme management · Portfolio management · Project management offices
24 lectures · 6 practices · 7 assessmentsView course outline →Digital delivery · Physical delivery · Public and social projects
24 lectures · 6 practices · 7 assessmentsView course outline →Complexity and evidence · AI and project analytics · Integrated delivery studio
24 lectures · 6 practices · 7 assessmentsView course outline →State the question and assumptions, draw the model, analyse evidence and test competing explanations. Economic diagrams, synthetic datasets, calculations and evidence-based policy memos.
Choice and scarcity · Markets around us · Economic reasoning
24 lectures · 6 practices · 7 assessmentsView course outline →Markets and responsiveness · Consumers and firms · Market limits
24 lectures · 6 practices · 7 assessmentsView course outline →Measuring an economy · Output and stabilisation · Growth and international links
24 lectures · 6 practices · 7 assessmentsView course outline →Mathematical models · Statistical reasoning · Economic data practice
24 lectures · 6 practices · 7 assessmentsView course outline →Consumer theory · Producer theory · Welfare and equilibrium
24 lectures · 6 practices · 7 assessmentsView course outline →Long-run growth · Short-run dynamics · Open-economy macroeconomics
24 lectures · 6 practices · 7 assessmentsView course outline →Regression foundations · Credible estimation · Causal designs
24 lectures · 6 practices · 7 assessmentsView course outline →Strategic interaction · Behavioural economics · Markets and competition
24 lectures · 6 practices · 7 assessmentsView course outline →Public economics · Environmental economics · Health and education economics
24 lectures · 6 practices · 7 assessmentsView course outline →International trade · Development economics · Labour economics
24 lectures · 6 practices · 7 assessmentsView course outline →Money and banking · Time-series analysis · Applied economic decisions
24 lectures · 6 practices · 7 assessmentsView course outline →Advanced theory pathways · Advanced empirical pathways · Research capstone
24 lectures · 6 practices · 7 assessmentsView course outline →Trace cash flows, calculate a transparent model, stress-test assumptions and explain risk. Fictional USD budgets, statement analysis, valuation models and risk scenarios.
Understanding money · Time and borrowing · Responsible choices
24 lectures · 6 practices · 7 assessmentsView course outline →Time value of money · Investment calculations · Reliable models
24 lectures · 6 practices · 7 assessmentsView course outline →Reading statements · Performance analysis · Financial diagnosis
24 lectures · 6 practices · 7 assessmentsView course outline →Investment decisions · Financing decisions · Risk and managerial judgement
24 lectures · 6 practices · 7 assessmentsView course outline →Market structure · Institutions · Market behaviour
24 lectures · 6 practices · 7 assessmentsView course outline →Measuring investments · Portfolio theory · Portfolio process
24 lectures · 6 practices · 7 assessmentsView course outline →Fixed-income analysis · Derivative contracts · Valuation and hedging
24 lectures · 6 practices · 7 assessmentsView course outline →Business valuation · Corporate transactions · Funding new ventures
24 lectures · 6 practices · 7 assessmentsView course outline →Credit decisions · Bank and insurer management · Enterprise financial risk
24 lectures · 6 practices · 7 assessmentsView course outline →Corporate treasury · International finance · Planning and control
24 lectures · 6 practices · 7 assessmentsView course outline →Financial technology · Sustainability and impact · Governance and regulation
24 lectures · 6 practices · 7 assessmentsView course outline →Quantitative foundations · Advanced finance pathways · Research and investment committee studio
24 lectures · 6 practices · 7 assessmentsView course outline →Study an original business case, compare options, make a decision and defend implementation. Case discussions, business plans, management simulations and original consulting projects.
How businesses work · Organisations and their environment · Learning through business cases
24 lectures · 6 practices · 7 assessmentsView course outline →Clear business writing · Presentations and teamwork · Professional judgement
24 lectures · 6 practices · 7 assessmentsView course outline →Managing organisations · People at work · Leadership practice
24 lectures · 6 practices · 7 assessmentsView course outline →Accounting foundations · Accounting cycles · Reporting and judgement
24 lectures · 6 practices · 7 assessmentsView course outline →Understanding costs · Decision support · Planning and control
24 lectures · 6 practices · 7 assessmentsView course outline →Business quantitative tools · Evidence and uncertainty · Analytical decisions
24 lectures · 6 practices · 7 assessmentsView course outline →Understanding customers · Marketing decisions · Responsible marketing
24 lectures · 6 practices · 7 assessmentsView course outline →Digital channels · Sales management · Customer experience
24 lectures · 6 practices · 7 assessmentsView course outline →Operating systems · Quality and improvement · Supply chains
24 lectures · 6 practices · 7 assessmentsView course outline →Building the workforce · Developing and rewarding people · Employment relationships
24 lectures · 6 practices · 7 assessmentsView course outline →Legal foundations · Ethics and governance · Responsible enterprise
24 lectures · 6 practices · 7 assessmentsView course outline →Finding opportunities · Launching ventures · Growing responsibly
24 lectures · 6 practices · 7 assessmentsView course outline →Enterprise information systems · Digital transformation · Managing AI responsibly
24 lectures · 6 practices · 7 assessmentsView course outline →Global business environments · International expansion · Managing across borders
24 lectures · 6 practices · 7 assessmentsView course outline →Strategic diagnosis · Strategic choices · Strategy execution
24 lectures · 6 practices · 7 assessmentsView course outline →Executive judgement · Negotiation and influence · Organisational transformation
24 lectures · 6 practices · 7 assessmentsView course outline →Research design · Gathering and interpreting evidence · Consulting practice
24 lectures · 6 practices · 7 assessmentsView course outline →Integrative general management · Advanced elective pathways · Business research and venture studio
24 lectures · 6 practices · 7 assessmentsView course outline →Watch one concept, predict what happens, work a real example, practise with support, then solve a fresh problem independently. Each section has a checkpoint and a test. Each course ends with a project and a cumulative test.
Review after one day, one week and one month. Quiz and test progression uses the platform’s existing 70% threshold. Projects use an explicit self-review rubric; passing does not certify professional competence.
Advanced mathematics needs extended proof work; coding needs local practice; sciences need supervised laboratory experience beyond videos. Interactive tools currently cover selected sample concepts. The catalogue specifies further practices for on-demand preparation.