All Courses

Comprehensive foundation in linear algebra, calculus, differential geometry, tensor calculus, and complex analysis.

Vector spaces, linear maps, eigenvalues, inner products, the spectral theorem, and applications across the sciences.

Probability spaces, random variables, limit theorems, statistical inference, Bayesian methods, and stochastic processes.

ODEs/PDEs, special functions, complex analysis, integral transforms, calculus of variations, and Green’s functions.

Numerical linear algebra, root finding, ODE/PDE integration, spectral methods, optimisation, and scientific computing.

Manifolds, tangent spaces, differential forms, Lie groups, Riemannian geometry, fibre bundles, and connections.

Mathematical ideas from antiquity through the 20th century — algebra, geometry, analysis, set theory, and computation.

Lagrangian and Hamiltonian formulations, action principles, symmetries, and conservation laws.

Laws of thermodynamics, heat engines, entropy, thermodynamic potentials, and kinetic theory.

Microcanonical, canonical, and grand canonical ensembles. Partition functions, phase transitions, and critical phenomena.

Navier–Stokes equations, fluid dynamics, boundary layers, turbulence, and magnetohydrodynamics (MHD).

Wave phenomena, electromagnetic waves, interference, diffraction, polarization, and optical phenomena.

Graduate-level electrodynamics: Maxwell’s equations, EM waves, Fresnel equations, waveguides, retarded potentials, and Larmor radiation.

Wave functions, operators, measurement, uncertainty, angular momentum, spin, perturbation theory — with full Griffiths solutions.

Canonical quantization, Dirac fields, gauge theories, renormalization, and the Standard Model. With Peskin & Schroeder solutions.

Quantum optics, laser physics, Bose–Einstein condensation, cold atoms, and quantum information.

Standard Model, QCD, electroweak theory, Higgs mechanism, experimental methods, and beyond-SM physics.

Nuclear forces, binding energy, decay, fission, fusion, shell model, reactor physics, and nucleosynthesis.

Crystal structure, electronic bands, superconductivity, magnetism, topological phases, and quantum many-body physics.

Single-particle motion, kinetic theory, MHD, waves in plasmas, fusion, and astrophysical plasmas.

Grand unification, dualities, supersymmetry, string theory, and the modern programme of unifying the fundamental forces.

Approaches to quantum gravity: canonical quantisation, loop quantum gravity, string theory, asymptotic safety, holography.

Lorentz transformations, four-vectors, relativistic dynamics, and electrodynamics in covariant form.

Differential geometry, Einstein field equations, Schwarzschild solution, gravitational waves, and cosmology.

FLRW cosmology, CMB, structure formation, inflation, dark matter, dark energy, and observational cosmology.

Cosmic inflation: motivations, single-field models, perturbations, reheating, primordial spectra, and observational tests.

Evidence for dark matter, candidates from WIMPs to axions to primordial black holes, direct and indirect detection.

Acceleration of cosmic expansion, the cosmological constant, quintessence, modified gravity, and observational programmes.

Sakharov conditions, electroweak baryogenesis, GUT-scale mechanisms, leptogenesis, and the matter–antimatter asymmetry.

Cosmology meets particle physics: inflation, dark matter, dark energy, baryogenesis, and the early-Universe particle physics.

Linearised gravity, source modelling, detectors (LIGO/Virgo/LISA), data analysis, and multi-messenger astronomy.

Distance ladders, CMB measurements, large-scale structure, weak lensing, and the cosmological surveys reshaping the field.

Schwarzschild and Kerr metrics, event horizons, ergospheres, Hawking radiation, thermodynamics, and astrophysical observations.

Stellar structure and evolution, compact objects, galactic dynamics, high-energy astrophysics, and observational techniques.

A gentler entry to astrophysics: the night sky, stars and lifecycles, galaxies, cosmology, and observation.

Numerical relativity, GW data analysis, spectral methods, lattice quantum gravity, and high-performance scientific computing.

Solar interior, atmosphere, magnetism, dynamo theory, solar wind, flares and CMEs, and space-weather impacts.

Solar-terrestrial physics: corona, solar wind, magnetopause, magnetosphere, ionosphere, radiation belts, storms, and aurora.

Crafoord Prize–winning discoveries in astronomy and astrophysics, with full background and modern context.

Geometric analysis on 3-manifolds, Ricci flow, and Perelman’s proof of the Geometrization (and Poincaré) conjecture.

A unified introduction to Earth’s systems: lithosphere, hydrosphere, atmosphere, biosphere, and deep-time history.

Plate tectonics, mantle convection, earthquake mechanics, mountain building, and the deep-time history of the lithosphere.

Atmospheric radiation, the carbon cycle, climate feedbacks, ocean–atmosphere coupling, paleoclimate, and modelling.

Atmospheric dynamics, weather systems, monsoons, hurricanes, climate variability, and the modern observing system.

Radiation, chemistry, aerosols, clouds and microphysics, atmospheric circulation, and remote-sensing of the atmosphere.

Ocean circulation, mesoscale dynamics, biogeochemistry, sea ice, marine ecosystems, and the role of oceans in climate.

Remote sensing, satellite missions, atmospheric retrievals, land-cover classification, and applications to climate.

Distribution of life across Earth, island biogeography, dispersal and vicariance, latitudinal gradients, and conservation.

World biomes from boreal forest and tundra to tropical rainforest, savanna, desert, and marine ecosystems.

How climate change reshapes biodiversity: range shifts, phenology, ocean warming, coral bleaching, and conservation.

Marine biodiversity from coastal to abyssal: kelp forests, coral reefs, deep-sea ecosystems, and ocean conservation.

Crafoord Prize–winning discoveries in the geosciences — climate, ocean dynamics, glaciology, and Earth systems.

Structure and reactivity of carbon compounds: bonding, mechanisms, stereochemistry, synthesis, and spectroscopy.

Quantum chemistry, statistical thermodynamics, kinetics, spectroscopy, and the physical foundations of chemistry.

Atomic structure, chemical bonding, crystallography, semiconductors, polymers, and diffusion. MIT 3.091 lectures.

Amino acids, proteins, enzymes, nucleic acids, carbohydrates and lipids, metabolism — the chemistry of life.

A tour of Nobel Prize–winning discoveries in chemistry: ideas, experiments, and the chemists who reshaped the field.

DNA structure and replication, transcription, translation, gene regulation, and modern molecular methods.

Bacterial architecture, the cell wall (Gram +/−), genetics and operons, flagellar motility and chemotaxis, biofilms, antibiotics and resistance, the microbiome, and pathogenesis.

Viral structure and capsids, the Baltimore classification, life cycle, RNA and DNA viruses, bacteriophages and CRISPR, vaccines and antivirals, and viral evolution.

Glycolysis, TCA cycle, oxidative phosphorylation, lipid and amino acid metabolism, and integrated regulation.

Membrane transport, bioenergetics, signalling, muscle, neurophysiology, epithelial transport, and calcium dynamics.

Compartmentalisation, membrane biophysics, the nucleus, ER, mitochondria, lysosomes, peroxisomes, and condensates.

Bioenergetics, the electron transport chain, ATP synthase, mitochondrial dynamics, biogenesis, and disease.

V-ATPase, hydrolases, autophagy, lysosomal storage disorders, mTORC1 signalling, and cellular homeostasis.

Cisternal architecture, COPI/COPII trafficking, glycosylation, sorting at the TGN, and Golgi-related disease.

ER architecture, protein folding and translocation, the unfolded protein response, ER–membrane contacts, and disease.

Ribosome architecture, translation initiation–elongation–termination, the peptidyl-transferase reaction, and antibiotics.

Actin, microtubules, intermediate filaments, motor proteins, polymer dynamics, and cell mechanics.

Embryonic and induced pluripotent cells through tissue-specific stem cells, niche signalling, and regenerative medicine.

Cellular and systems neuroscience, computational models, sensory and motor systems, and clinical neuroanatomy.

Predictive coding, free-energy principle, hierarchical generative models, and active inference in neuroscience.

Molecular clockwork, peripheral oscillators, light entrainment, the cell cycle, metabolism, sleep, and chronotherapy.

Genomics, proteomics, transcriptomics, and metabolomics. DNA sequencing, RNA-Seq, mass spec, and multi-omics integration.

Sequence alignment, genome assembly, phylogenetics, transcriptomics, structural prediction, and statistical methods.

Drug-receptor theory, pharmacokinetics, autonomic and CNS pharmacology, cardiovascular agents, chemotherapy, and toxicology.

Molecular and cellular biophysics, electrophysiology, transport, computational and medical biophysics, and human physiology.

Geometric structures in biology: protein topology, membrane curvature, tissue mechanics, and biological pattern formation.

Translating biological designs into engineering: gecko adhesion, lotus surfaces, butterfly photonics, shark skin.

Photosynthesis, lipid and nitrogen metabolism, hormone signalling, secondary metabolites, and plant stress biology.

Plant–animal chemical interactions: secondary metabolites, allelopathy, induced defences, and ecosystem chemistry.

Floral development, pollination biophysics, plant–pollinator coevolution, and the genetics of flowering.

How animals sense the world: vision, electroreception, magnetoreception, infrared sensing, sonar, and chemoreception.

Prebiotic chemistry, RNA world, metabolism-first hypotheses, hydrothermal vents, and the emergence of cellular life.

Emerging strategies in disease research: omics-driven medicine, organoids, CRISPR therapeutics, and AI diagnostics.

Crafoord Prize–winning discoveries in the biosciences — evolution, ecology, and molecular biology.

Bird flight mechanics, feather aerodynamics, navigation and magnetoreception, vocal-tract acoustics, high-altitude physiology.

Eagle aerodynamics, soaring and thermal exploitation, raptor vision, talon mechanics, and predator energetics.

Antarctic adaptations of emperor penguins: huddling thermodynamics, deep-dive physiology, and incubation in extreme cold.

Penguin locomotion in water and ice, thermoregulation, diving physiology, and Southern Ocean ecology.

Long-distance navigation in birds and monarch butterflies: magnetoreception, sun and star compasses, and energetics.

Pigeon homing biophysics: magnetoreception, olfactory maps, sun compass, infrasound cues, and long-range navigation.

Honeybee flight aerodynamics, waggle-dance communication, vision and polarisation, and colony decision making.

Ant locomotion, gripping, collective behaviour, pheromone communication, and the biophysics of social-insect colonies.

Spider silk mechanics, web architecture, hydraulic locomotion, vibrational sensing, and venom chemistry.

Flight aerodynamics, exoskeletal mechanics, sensory systems, metabolic scaling, and insect diversity principles.

Whales and dolphins: echolocation, deep-dive physiology, hydrodynamics of fluking, and brain morphology.

Pinniped diving physiology, hydrodynamics, sensory whiskers, thermoregulation, and the air–sea interface.

Polar seal physiology: deep-dive bradycardia, blubber thermoregulation, sensory systems under ice, and pinniped ecology.

Polar bear physiology: thermal insulation, fasting metabolism, locomotion on sea ice, and Arctic adaptation.

Cat biomechanics: righting reflex, predatory locomotion, vision and tapetum lucidum, and feline physiology.

Predation across vertebrates and invertebrates: hunting biomechanics, sensory ecology, energetics, and ecosystems.

African savanna ecosystems: large-mammal physiology, predator–prey dynamics, fire ecology, and grassland evolution.

Elephant biomechanics: trunk muscular hydrostat, infrasound communication, locomotion energetics, and cognition.

Giraffe cardiovascular physiology, neck biomechanics, blood-pressure regulation, and the anatomy of the tallest mammal.

Rhino biomechanics, horn keratin, thermoregulation, social behaviour, and conservation biology.

Hippo physiology: aquatic locomotion, skin secretions, thermoregulation, jaw mechanics, and the ecology of a megaherbivore.

Desert physiology of camels: water economy, thermoregulation, fat-lobe metabolism, and dehydration adaptations.

Reptile physiology: ectothermy, locomotion, scaling and integument, sensory systems, and venom biochemistry.

Tree biomechanics: xylem hydraulics, wind loading, growth and mechanical scaling, and the physiology of long-lived trees.

Wheat physiology and crop science: grain biochemistry, gluten, photosynthesis, drought response, and food security.

Vitis vinifera physiology: berry development, sugar accumulation, anthocyanin chemistry, terroir, and viticulture.

Algorithms, data structures, complexity, programming languages, systems, networks, databases, and theoretical foundations.

Shannon entropy, channel capacity, source and channel coding, error-correcting codes, rate-distortion, quantum information.

Supervised, unsupervised, and reinforcement learning: optimisation, kernel methods, deep architectures, probabilistic models.

Population-based, gradient-free optimisation: GAs, evolution strategies, CMA-ES, genetic programming, neuroevolution, novelty/Quality-Diversity, evolutionary RL, and open-endedness.

AI for science: protein structure prediction, molecular generation, foundation models, geometric deep learning, and self-driving labs.

MAML + equivariant NNPs (NequIP) + Nakajima–Zwanzig memory kernels + cusp catastrophe + RPMD. Twelve advanced graduate modules connecting machine learning methodology to non-Markovian protein dynamics.

Quantum gates and circuits, quantum algorithms (Shor, Grover), error correction, and current hardware platforms.

Time–frequency analysis, Fourier and wavelet transforms, sampling, spectral estimation, filter design, stochastic signals.

From RC and RLC circuits through diodes, BJTs, MOSFETs, op-amps, digital logic, and analog–digital interfacing.

Pulsed and CW radar, Doppler, range–rate processing, antennas, signal processing, and modern radar applications.

Physics from Galileo through Einstein and the Standard Model — ideas, instruments, and the people who shaped them.

A history of modern mathematics through its highest honours — laureates, theorems, and the ideas that reshaped the field. Includes laureate video interviews.

A history of theoretical physics through the ICTP Dirac Medal — laureate lectures on string theory, supergravity, QFT, statistical physics, and quantum mechanics.

A history of theoretical physics through the German Physical Society’s highest honour (since 1929) — laureate lectures plus the Lise Meitner Lecture series.

A unified history of mathematics and physics from antiquity through quantum mechanics — ideas, instruments, and people.

Music from antiquity to the modern era: tuning systems, notation, composers, performance, and the dialogue with science.

The mathematical structure of music: tuning systems, harmonic analysis, group theory of pitch, and instrument physics.

What is a scientific theory? Realism, falsifiability, paradigms, scientific revolutions, and the demarcation problem.

A tour of Nobel Prize–winning discoveries in physics: ideas, experiments, and the physicists who reshaped the field.