# Academa

> Academa, Inc. is a Delaware C corporation founded by Sina Atalay, co-founder and CEO, and Abdullah Geduk, co-founder and CTO. Sina is a Princeton PhD student currently on leave; Abdullah is a Penn State PhD student. Close friends who have built together since undergrad, they created Academa to make technical knowledge easier to understand through visual lectures and let learners request new lecture videos.

Published by [Academa, Inc.](https://academa.ai). Primary language: en-US.

Each video link below is a complete Markdown alternate containing the lecture summary, metadata, chapters, timestamp links, full transcript, and a timestamped account of everything shown in the film.

## Video lectures

- [Z-Pinch Fusion and Magnetic Pinch Relatives](https://academa.ai/@adamierymenko/lectures/z-pinch-fusion-and-magnetic-pinch-relatives.md): Physics; 10 minutes 33 seconds. How a plasma's own current confines it, why the Z-pinch is unstable, and how RFPs, sheared flow, FRCs and MagLIF answer that.
- [The Kim, Moin, and Moser (KMM) Velocity-Vorticity Spectral Formulation](https://academa.ai/@apo/lectures/the-kim-moin-and-moser-kmm-velocity-vorticity-spectral-formulation.md): Engineering; 19 minutes 45 seconds. How the KMM velocity-vorticity formulation removes pressure from channel-flow DNS, and why Fourier mode decoupling makes it so fast.
- [The Mechanics and Intuition of Potential Energy](https://academa.ai/@atalay/lectures/the-mechanics-and-intuition-of-potential-energy.md): Engineering; 15 minutes 31 seconds. Work, kinetic energy and potential energy derived from F = ma: the gradient theorem, mgh, spring potential, and a spring-block example.
- [Visualizing A\* Search: Pathfinding Through Heuristic Guidance](https://academa.ai/@bobby/lectures/visualizing-a-search-pathfinding-through-heuristic-guidance.md): Computer Science; 10 minutes 39 seconds. A\* search on one grid: g, h and f unpacked, an uninformed frontier flooding the maze, and an informed one steering to the goal.
- [Basics of Hindu Temple Architecture](https://academa.ai/@cv007/lectures/basics-of-hindu-temple-architecture.md): Engineering; 5 minutes. How a Hindu temple is set out: the square plan, the garbhagriha sanctum, the mandapa hall, and the tower that rises over the centre.
- [Mengenal Jenis-Jenis Bilangan untuk Siswa Kelas 6 SD](https://academa.ai/@najmah-fahmida/lectures/mengenal-jenis-jenis-bilangan-untuk-siswa-kelas-6-sd.md): Mathematics; 2 minutes 22 seconds. Kenali bilangan asli, cacah, bulat, prima, serta pecahan dan desimal lewat garis bilangan dan contoh sederhana untuk kelas 6 SD.
- [Operasi Hitung Bilangan Cacah dan Pecahan untuk Persiapan Ujian SD](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd.md): Mathematics; 16 minutes 49 seconds. Latihan lengkap operasi bilangan cacah, urutan kabataku, bentuk pecahan, desimal, persen, serta operasi pecahan untuk ujian SD.
- [Geometri Dasar untuk Persiapan TKA SD: Bangun Datar dan Bangun Ruang](https://academa.ai/@pustaka-belajar/lectures/geometri-dasar-untuk-persiapan-tka-sd-bangun-datar-dan-bangun-ruang.md): Mathematics; 11 minutes 9 seconds. Geometri untuk TKA SD: sifat bangun datar dan bangun ruang, keliling, luas, volume, luas permukaan, simetri lipat dan simetri putar.
- [أنواع الأعداد وفق منهج الصف التاسع في سلطنة عمان](https://academa.ai/@qrr-34tyt/lectures/%D8%A3%D9%86%D9%88%D8%A7%D8%B9-%D8%A7%D9%84%D8%A3%D8%B9%D8%AF%D8%A7%D8%AF-%D9%88%D9%81%D9%82-%D9%85%D9%86%D9%87%D8%AC-%D8%A7%D9%84%D8%B5%D9%81-%D8%A7%D9%84%D8%AA%D8%A7%D8%B3%D8%B9-%D9%81%D9%8A-%D8%B3%D9%84%D8%B7%D9%86%D8%A9-%D8%B9%D9%85%D8%A7%D9%86.md): Mathematics; 5 minutes 6 seconds. شرح عربي مبسط لأنواع الأعداد للصف التاسع: الطبيعية والصحيحة والنسبية وغير النسبية والحقيقية، مع خط الأعداد وخريطة الاحتواء.
- [Memahami Konsep Rasio dan Penerapannya - Matematika Kelas 6](https://academa.ai/@riskadina/lectures/memahami-konsep-rasio-dan-penerapannya-matematika-kelas-6.md): Mathematics; 10 minutes 25 seconds. Belajar rasio Matematika kelas 6: cara menulis dan menyederhanakan rasio, rasio senilai, tabel rasio, rasio satuan, dan penerapannya.
- [آلية الإرسال التلفزيوني ومخطط مراحله الأساسية](https://academa.ai/@samerso/lectures/%D8%A2%D9%84%D9%8A%D8%A9-%D8%A7%D9%84%D8%A5%D8%B1%D8%B3%D8%A7%D9%84-%D8%A7%D9%84%D8%AA%D9%84%D9%81%D8%B2%D9%8A%D9%88%D9%86%D9%8A-%D9%88%D9%85%D8%AE%D8%B7%D8%B7-%D9%85%D8%B1%D8%A7%D8%AD%D9%84%D9%87-%D8%A7%D9%84%D8%A3%D8%B3%D8%A7%D8%B3%D9%8A%D8%A9.md): Engineering; 8 minutes 13 seconds. شرح مبسط لمخطط الإرسال التلفزيوني: الكاميرا ومكبر الصورة، الميكروفون ومكبر الصوت، المازج، مكبر الإرسال، والهوائي الذي يشع الموجة.
- [3D Quench Simulation in No-Insulation HTS Coils: FiQuS/Pancake3D](https://academa.ai/@sina/lectures/3d-quench-simulation-in-no-insulation-hts-coils-fiqus-pancake3d.md): Engineering; 17 minutes 21 seconds. How FiQuS/Pancake3D simulates quenches in no-insulation HTS pancake coils: thin-shell contact layers, homogenised tape, one full transient.
- [How the World Wide Web Was Born: Protocols, Hypertext, and the Browser](https://academa.ai/@sina/lectures/how-the-world-wide-web-was-born-protocols-hypertext-and-the-browser.md): Computer Science; 11 minutes 25 seconds. Follow one click round the Web: URLs name documents, HTTP fetches them, HTML carries structure, and your browser paints the result.
- [Structuring CV Data in RenderCV: Headers, Sections, and Entry Types](https://academa.ai/@sina/lectures/structuring-cv-data-in-rendercv-headers-sections-and-entry-types.md): Computer Science; 10 minutes 30 seconds. A field by field tour of RenderCV's cv key: header connections, the sections dictionary, all nine entry types, Markdown and Typst text.
- [The Geometric Intuition Behind General Relativity](https://academa.ai/@sina/lectures/the-geometric-intuition-behind-general-relativity.md): Physics; 15 minutes 25 seconds. Why Newtonian gravity breaks the speed limit, and how one coincidence about mass turns gravity into the shape of spacetime.
- [The Secretary Problem: Picking from the Top 10 Percent](https://academa.ai/@sina/lectures/the-secretary-problem-picking-from-the-top-10-percent.md): Mathematics; 7 minutes 30 seconds. A hundred houses, one at a time, no going back. Why looking at 37 and then taking the best you have seen lands you in the top ten.
- [Understanding Activity and Workflow Task Event Histories in Temporal](https://academa.ai/@sina/lectures/understanding-activity-and-workflow-task-event-histories-in-temporal.md): Computer Science; 5 minutes 38 seconds. Strip the prefix from a Temporal event name and it names the task state: the lifecycle, the closed states, and the Start-To-Close window.
- [Understanding Divergence and Curl in Vector Calculus](https://academa.ai/@sina/lectures/understanding-divergence-and-curl-in-vector-calculus.md): Mathematics; 14 minutes 52 seconds. Divergence and curl from fluid flow: flux out of a small box, circulation round a small loop, the formulas, and a worked example.
- [Understanding Graphical Projections: Perspective, Oblique, and Orthographic](https://academa.ai/@sina/lectures/understanding-graphical-projections-perspective-oblique-and-orthographic.md): Engineering; 11 minutes 44 seconds. How perspective, oblique, orthographic and isometric projections work, why perspective looks real, and which drawings you can measure.
- [Understanding the Internet from First Principles with cURL](https://academa.ai/@sina/lectures/understanding-the-internet-from-first-principles-with-curl.md): Computer Science; 11 minutes 56 seconds. Clients, servers, IP addresses, DNS, TCP and HTTP explained from scratch, then made visible on screen with a few curl commands.
- [Understanding the Quadratic Formula and How It Works](https://academa.ai/@sina/lectures/understanding-the-quadratic-formula-and-how-it-works.md): Mathematics; 11 minutes 29 seconds. Derive the quadratic formula by completing the square, then read the discriminant to see two real roots, one, or a complex pair.
- [Why −(−a) = a Is Secretly a Theorem](https://academa.ai/@sina/lectures/why-a-a-is-secretly-a-theorem.md): Mathematics; 13 minutes 27 seconds. Two minus signs make a plus is a theorem: existence is free from the inverse axiom, uniqueness costs one slide of a bracket.
- [How Loosely Coupled INS/GNSS Integration Works](https://academa.ai/@yong/lectures/how-loosely-coupled-ins-gnss-integration-works.md): Engineering; 13 minutes 54 seconds. How an error-state Kalman filter fuses an inertial solution with a GNSS fix: mechanization, drift, innovation, and the four-satellite floor.
- [Accumulation and the Two Halves of Calculus](https://academa.ai/lectures/accumulation-and-rate-of-change.md): Mathematics; 15 minutes 24 seconds. Build the accumulation function from a rate graph, discover its slope is the rate, and reach the Fundamental Theorem of Calculus.
- [Alternating Current: Phasors and Power Factor](https://academa.ai/lectures/alternating-current-phasors-power-factor.md): Engineering; 19 minutes 12 seconds. Phasors, impedance and power factor for AC circuits: why current lags, what reactive power costs, and how a capacitor fixes it.
- [Backpropagation by Hand: From Computational Graphs to Matrix Gradients](https://academa.ai/lectures/backpropagation-is-the-chain-rule-on-a-graph.md): Machine Learning; 19 minutes 45 seconds. Follow a tiny neural network through exact forward values, scalar chain-rule backpropagation, matrix gradients, and activation-memory costs.
- [Why a 99% Accurate Test Can Still Be Wrong](https://academa.ai/lectures/bayes-through-the-medical-test-paradox.md): Statistics; 11 minutes 46 seconds. See how a 99% sensitive and 99% specific test can be wrong for a rare disease, then watch prevalence, accuracy, and retesting change the odds.
- [Overfitting Made Visible: Bias, Variance, and the Role of Data](https://academa.ai/lectures/bias-variance-and-the-shape-of-overfitting.md): Machine Learning; 13 minutes 23 seconds. See underfitting, overfitting, training and test error, bias, variance, and the stabilizing role of additional data in one visual experiment.
- [The Bloom Filter](https://academa.ai/lectures/bloom-filters.md): Computer Science; 14 minutes 14 seconds. How a Bloom filter tests membership in a few bits per item, why false positives happen, how to pick k, and why deletion is forbidden.
- [Boundary Layers and Drag: From No-Slip to the Drag Crisis](https://academa.ai/lectures/boundary-layer-drag-crisis.md): Physics; 22 minutes 21 seconds. Why ideal flow predicts zero drag, how the boundary layer fixes it, and why separation and dimples decide a sphere's drag.
- [The Central Limit Theorem, Shown by Sampling](https://academa.ai/lectures/central-limit-theorem-by-sampling.md): Statistics; 10 minutes 28 seconds. Watch a skewed population turn into the normal curve: samples of four, a wall of averages, and the sigma over root n law behind every error bar.
- [K-Means, Its Failure Modes, and Gaussian Mixture Models](https://academa.ai/lectures/clustering-k-means-and-where-it-fails.md): Machine Learning; 13 minutes 42 seconds. A practical visual guide to k-means iteration, its key failure modes, soft membership, and Gaussian mixtures with learned covariance.
- [Comparative Advantage: Why Both Countries Gain from Trade](https://academa.ai/lectures/comparative-advantage-gains-from-trade.md): Economics; 16 minutes 1 second. Why two countries both gain from trade even when one is slower at everything: opportunity cost, specialization and the frontier.
- [Multiplication as Turning](https://academa.ai/lectures/complex-multiplication-as-rotation.md): Mathematics; 14 minutes 9 seconds. Complex numbers as rotation: i as a quarter turn, lengths multiplying while angles add, Euler's formula, and the cube roots of one.
- [Concentration of Measure on the Sphere](https://academa.ai/lectures/concentration-on-the-sphere.md): Mathematics; 12 minutes 27 seconds. Why nearly all of a high-dimensional sphere lies within a whisker of any equator: Levy's isoperimetric inequality, concentration, and Dvoretzky's theorem.
- [Cournot Competition: Best-Response Dynamics and the Race to Equilibrium](https://academa.ai/lectures/cournot-duopoly-and-best-responses.md): Economics; 17 minutes 13 seconds. Watch Cournot firms chase best responses to equilibrium, then compare its price with monopoly, competition, and Bertrand pricing.
- [From One Decision Tree to a Random Forest](https://academa.ai/lectures/decision-trees-and-why-forests-beat-them.md): Machine Learning; 19 minutes 59 seconds. Grow, overfit, and prune one decision tree, then build a random forest and see why averaging decorrelated trees reduces prediction variance.
- [Deriving Keplerian Orbits from Conservation Laws](https://academa.ai/lectures/deriving-keplerian-orbits-from-conservation-laws.md): Physics; 18 minutes 56 seconds. Derive equal areas, conic orbits, Kepler's period law, orbital energy classes, and escape speed from conservation laws.
- [Shear and Moment Diagrams from First Principles](https://academa.ai/lectures/deriving-shear-moment-diagrams.md): Engineering; 18 minutes 24 seconds. Cut a beam, take the free body, and derive shear and moment diagrams from equilibrium, then from the two derivatives that govern them.
- [Diffusion Models: From Noise to Images](https://academa.ai/lectures/diffusion-models-learning-to-denoise.md): Machine Learning; 23 minutes 6 seconds. Learn how diffusion models add noise, train a supervised noise predictor, reverse the process, and steer images with text guidance.
- [Dijkstra's Algorithm as a Spreading Frontier](https://academa.ai/lectures/dijkstras-algorithm-a-spreading-frontier.md): Computer Science; 10 minutes 3 seconds. Watch Dijkstra's algorithm as a frontier of settled nodes spreading outward, and see why the greedy choice is provably safe.
- [Why Wind Tunnel Models Work: Dimensional Analysis of Aerodynamic Drag](https://academa.ai/lectures/dimensional-analysis-drag.md): Engineering; 16 minutes 46 seconds. Why a scale model predicts the drag on a real aircraft: count the dimensions, derive Reynolds and the drag coefficient, and see where Mach breaks similarity.
- [Divergence, and the Two Great Theorems](https://academa.ai/lectures/divergence-and-stokes-theorems.md): Mathematics; 9 minutes 31 seconds. Divergence as outward flow, the divergence theorem, and Stokes' theorem, built from one picture and one cancelling argument.
- [Driven Oscillators: Resonance, Phase, Damping, and Quality Factor](https://academa.ai/lectures/driven-oscillators-resonance-phase-damping-and-quality-factor.md): Physics; 11 minutes 53 seconds. Watch a live frequency sweep reveal resonance and phase, then connect damping and quality factor to ring-down and tuned structural control.
- [Edit Distance: From Memorization to Derivation](https://academa.ai/lectures/edit-distance-dp-derivation.md): Computer Science; 16 minutes 8 seconds. Derive the edit distance recurrence, fill its table cell by cell, recover the edits, and count the work plain recursion repeats.
- [Eigenvectors and Eigenvalues: The Directions a Matrix Can't Turn](https://academa.ai/lectures/eigenvectors-and-eigenvalues.md): Mathematics; 12 minutes 15 seconds. Watch a grid stretch and shear, find the arrows that never turn, and compute eigenvalues and eigenvectors of a 2x2 matrix.
- [From Twenty Questions to Entropy and Huffman Compression](https://academa.ai/lectures/entropy-as-twenty-questions.md): Computer Science; 14 minutes 31 seconds. Derive entropy from twenty questions, build a Huffman code, compare its length with the limit, and explain when files can compress.
- [Euler Buckling: Why Slender Columns Fail by Instability](https://academa.ai/lectures/euler-buckling-columns.md): Engineering; 17 minutes 33 seconds. Why slender columns buckle: the critical load derived from the deflected shape, effective length from inflection points, and the slenderness limit.
- [Everything Is Stokes' Theorem](https://academa.ai/lectures/everything-is-stokes-theorem.md): Mathematics; 12 minutes 35 seconds. What Stokes' theorem says: the fundamental theorem of calculus, line integrals and Green's theorem are one line, read at three dimensions.
- [Why a Magnet Falls Slowly Through a Copper Pipe](https://academa.ai/lectures/faraday-lenz-and-the-magnet-that-will-not-fall.md): Physics; 9 minutes 54 seconds. See how changing magnetic flux, Lenz's law, and electromagnetic drag make a magnet fall slowly through copper and power train brakes.
- [Frequency Response: From Poles and Zeros to Stability and Compensation](https://academa.ai/lectures/frequency-response-bode-closed-loop.md): Engineering; 27 minutes 21 seconds. Build Bode magnitude and phase curves from poles and zeros, define gain and phase margin, then see what lag and lead compensators change.
- [Electric Flux and Gauss’s Law: How Symmetry Reveals Electric Fields](https://academa.ai/lectures/gauss-law-and-what-flux-is-counting.md): Physics; 17 minutes 1 second. Build electric flux and Gauss’s law visually, apply symmetry to spheres, lines and sheets, then explain conductors and lightning shielding.
- [Gradient Descent: How the Learning Rate Shapes the Journey](https://academa.ai/lectures/gradient-descent-as-hiking-downhill-in-fog.md): Machine Learning; 14 minutes 17 seconds. See how learning rate controls gradient descent, from steady progress to crawling, divergence, narrow-valley zigzags, and momentum.
- [Why a Spinning Top Stays Up: Angular Momentum and Precession](https://academa.ai/lectures/gyroscopic-precession.md): Physics; 15 minutes 26 seconds. See why gravity turns a spinning top sideways, derive its precession rate, and connect the result to a suspended bicycle wheel.
- [The Halting Problem Is Undecidable](https://academa.ai/lectures/halting-problem-undecidability.md): Computer Science; 16 minutes 6 seconds. Cantor's diagonal, the table of programs against inputs, and the contrary program that proves no halting decider can exist.
- [Inside Kimi K3: Architecture of an Open Frontier Model](https://academa.ai/lectures/inside-kimi-k3-architecture.md): Machine Learning; 11 minutes 47 seconds. How Kimi K3 works: expert routing, delta attention, attention residuals, and the 2.5x scaling gain behind an open frontier model.
- [Kinematics of a Body: The Instantaneous Axis](https://academa.ai/lectures/instantaneous-axis-of-rotation.md): Engineering; 7 minutes 58 seconds. The rigid-body velocity relation, the instantaneous centre of a rolling wheel, and the screw axis that replaces it in three dimensions.
- [Linear Regression as Geometry](https://academa.ai/lectures/least-squares-is-a-projection.md): Statistics; 18 minutes 4 seconds. Learn linear regression through residual geometry, orthogonal projection, normal equations, R squared, and nearly parallel predictors.
- [Maximum Flow Equals Minimum Cut: Proof by Example](https://academa.ai/lectures/maxflow-mincut-theorem.md): Computer Science; 18 minutes 43 seconds. Max flow equals min cut, worked by hand on one small network: augmenting paths, a residual backward edge, and the cut that certifies the answer.
- [Monopoly, Marginal Revenue, and Price Discrimination](https://academa.ai/lectures/monopoly-marginal-revenue-and-price-discrimination.md): Economics; 15 minutes 22 seconds. Derive monopoly marginal revenue, compare monopoly with competition, and trace welfare under group and perfect price discrimination.
- [The Monty Hall Problem: Why Switching Wins](https://academa.ai/lectures/monty-hall.md): Statistics; 9 minutes 4 seconds. Fix one door, list every place the car can be, and count. Then watch the advantage vanish when the host stops knowing where the car is.
- [How Hyperlinks Become Votes: The PageRank Algorithm](https://academa.ai/lectures/pagerank-the-random-surfer.md): Computer Science; 11 minutes 38 seconds. Build PageRank from a random surfer on six pages: link matrix, power iteration, damping factor, dangling pages and rank sinks.
- [The Logistic Map: From Fixed Points to Chaos via Period-Doubling](https://academa.ai/lectures/period-doubling-logistic-map.md): Mathematics; 20 minutes 6 seconds. Watch one population equation lose its fixed point, double through two, four and eight cycles, and slide into chaos.
- [The Pigeonhole Principle: Choosing the Boxes](https://academa.ai/lectures/pigeonhole-principle-boxes.md): Mathematics; 10 minutes 49 seconds. State the pigeonhole principle in one line, then watch it prove three things that look nothing like it. The trick is choosing the boxes.
- [Planar Truss Analysis: Method of Joints](https://academa.ai/lectures/planar-truss-method-of-joints.md): Engineering; 15 minutes 20 seconds. Analyse one planar truss by the method of joints: support reactions, joint equilibrium, tension and compression signs, zero force members.
- [Rare Events in Continuous Time: From Poisson Arrivals to Exponential Waiting Times](https://academa.ai/lectures/poisson-processes-and-waiting-times.md): Statistics; 13 minutes 19 seconds. Derive Poisson counts and exponential waiting times from tiny independent intervals, then test their predictions with arrival data.
- [PCA from Geometric Intuition to Eigenvectors](https://academa.ai/lectures/principal-component-analysis-seen-geometrically.md): Machine Learning; 17 minutes 43 seconds. Understand PCA geometrically, connect maximum projected variance to covariance eigenvectors, and use scree plots, reconstruction, and scaling.
- [Automata Behind Regular Expressions](https://academa.ai/lectures/regex-to-automata.md): Computer Science; 17 minutes 24 seconds. Build the state machine behind a regular expression, run a string through it, determinise it, and meet the two things regexes cannot do.
- [Why Factoring Keeps Secrets: RSA Encryption](https://academa.ai/lectures/rsa-factoring-encryption.md): Mathematics; 18 minutes 4 seconds. Build RSA from scratch: modular arithmetic, key generation from two primes, and one message encrypted and decrypted by hand.
- [Why Truthful Bidding Works—and Why First-Price Bidders Shade](https://academa.ai/lectures/second-price-auctions-and-honest-bidding.md): Economics; 12 minutes 44 seconds. See truthful bidding proved by cases, first-price bid shading derived from incentives, and revenue equivalence stated with its assumptions.
- [When Every Subgroup Agrees but the Total Reverses the Result](https://academa.ai/lectures/simpsons-paradox.md): Statistics; 12 minutes 8 seconds. A concrete treatment example reveals Simpson's paradox, shows its unequal-weight geometry, and explains when pooled rates mislead.
- [Solving 2×2 Games by Hand: Best Responses, Pure Equilibria, and Mixing](https://academa.ai/lectures/solving-2-2-games-best-responses-pure-and-mixed-nash-equilibria.md): Economics; 23 minutes 27 seconds. Solve 2×2 games by hand using payoff matrices, best-response marks, pure Nash equilibria, expected payoffs, and mixed strategies.
- [Stokes' Theorem in Practice](https://academa.ai/lectures/stokes-theorem-in-practice.md): Mathematics; 4 minutes 38 seconds. Stokes' theorem on one exam question: swap the walk around the circle for the flux through the disc, and read the normal off the wording.
- [Supply and Demand in Motion: Equilibrium, Shifts, and Movements Along Curves](https://academa.ai/lectures/supply-and-demand-actually-moving.md): Economics; 14 minutes 14 seconds. Learn supply, demand, and equilibrium, then see how harvests, tastes, and new competitors shift curves and change market outcomes.
- [Support Vector Machines: Maximum-Margin Separation and the Kernel Trick](https://academa.ai/lectures/support-vector-machines-and-the-widest-corridor.md): Machine Learning; 16 minutes 3 seconds. A visual introduction to maximum-margin classifiers, support vectors, soft margins, nonlinear feature maps, and the kernel trick.
- [Building the Taylor Series: Convergence and Failure](https://academa.ai/lectures/taylor-sine-convergence-failures.md): Mathematics; 16 minutes 5 seconds. Build the Taylor polynomial of sine term by term, then see why the remainder, not the series, makes the equals sign true.
- [Why 23 People Make a Shared Birthday Likely](https://academa.ai/lectures/the-birthday-paradox.md): Statistics; 9 minutes 49 seconds. A visual explanation of why 23 people cross 50%, why one fixed birthday needs 253 others, and how the same logic predicts hash collisions.
- [The Bootstrap: Measuring How Much Your Estimate Could Have Wobbled](https://academa.ai/lectures/the-bootstrap.md): Statistics; 16 minutes 58 seconds. Learn bootstrap resampling through the mean and median, then see its assumptions, interpretation, and classic failure for sample maxima.
- [The Fastest Slide: Why the Cycloid Beats the Straight Line](https://academa.ai/lectures/the-brachistochrone.md): Physics; 11 minutes 20 seconds. Race three slides, derive the brachistochrone by calculus of variations, and see why every release height on a cycloid shares one arrival time.
- [The Centres of a Triangle](https://academa.ai/lectures/the-centres-of-a-triangle.md): Mathematics; 5 minutes 37 seconds. Medians, perpendicular bisectors, angle bisectors and altitudes: four rules, four centres, and the straight line three of them share.
- [The Market for Lemons: How Hidden Quality Can Make Good Products Disappear](https://academa.ai/lectures/the-market-for-lemons-how-hidden-quality-can-cause-a-market-collapse.md): Economics; 12 minutes 39 seconds. A used-car example explains adverse selection, market unraveling, the value of visible quality, and what common repairs actually fix.
- [The Method of Characteristics](https://academa.ai/lectures/the-method-of-characteristics.md): Mathematics; 12 minutes 57 seconds. Walk along the right curves and a first-order PDE becomes an ODE: characteristics, the solution f(x - ct), and where shocks come from.
- [Why Energy Is Quantised: From Standing Waves to Coloured Molecules](https://academa.ai/lectures/the-particle-in-a-box.md): Physics; 13 minutes 21 seconds. Why confined waves admit discrete energies, how box size controls spacing, and how the same model explains trends in conjugated dye colours.
- [The Transformer: From Recurrence Failure to Attention](https://academa.ai/lectures/the-transformer-from-recurrence-failure-to-attention.md): Machine Learning; 21 minutes 41 seconds. Build the Transformer from the failure of recurrence: queries, keys, values, scaled dot-product attention, many heads, and position.
- [NP-Completeness and Reduction: From Definitions to the 3-SAT to Vertex Cover Proof](https://academa.ai/lectures/three-sat-vertex-cover-reduction.md): Computer Science; 21 minutes 5 seconds. P and NP defined by verifiers, then the 3-SAT to Vertex Cover reduction built and argued in both directions on one formula.
- [Special Relativity: Light Clocks, Spacetime, and the Twin Paradox](https://academa.ai/lectures/time-dilation-from-a-light-clock.md): Physics; 19 minutes. Derive time dilation and length contraction, understand simultaneity, resolve the twin paradox, and explain atmospheric muons.
- [Torsion: From Geometry to Shaft Design](https://academa.ai/lectures/torsion-shafts.md): Engineering; 12 minutes 44 seconds. How twisting a round shaft gives shear strain linear in radius, the torque integral, the polar moment of area, and why drive shafts are tubes.
- [Who Really Bears a Tax? Tax Incidence, Elasticity, and Deadweight Loss](https://academa.ai/lectures/who-really-pays-a-tax.md): Economics; 13 minutes 49 seconds. See how elasticities split a per-unit tax, why remittance rules do not decide incidence, and why deadweight loss rises with tax squared.
- [Why the Rainbow Sits at 42 Degrees](https://academa.ai/lectures/why-the-rainbow-sits-at-42-degrees.md): Physics; 9 minutes 8 seconds. Derive the rainbow's 42 degree angle from one raindrop: refraction, one internal reflection, and the minimum of the deviation curve.

## Pages

- [Technical Knowledge, Explained Visually \| Academa](https://academa.ai/): Explore hand-maintained technical lecture videos, chat alongside each video, or ask Academa to create a new lecture about any technical topic.
- [@adamierymenko \| Academa](https://academa.ai/@adamierymenko): Explore the public technical lecture videos published by @adamierymenko on Academa.
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