math
19 curated learning paths about math. Each path delivers daily 5-minute drops to build real knowledge over time.
🔵Learn Set Theory Basics: The Language Every Math Class Assumes
Stop squinting at ∪, ∩, and ∁ — shade Venn diagrams first, then translate them into clean notation, until you can model anything from music genres to probability events as sets you can actually picture.
∫Understand the Fundamental Theorem of Calculus
Build the Fundamental Theorem of Calculus from accumulation first — feel why differentiation undoes integration before you ever see the formal statement. You'll finish by pulling a real dataset and verifying the theorem numerically with your own code.
🧮Understand Vector Spaces: The Rulebook Behind Linear Algebra
See why polynomials, pixel images, and 3D arrows all live in the same mathematical world — then design your own vector space of polynomials up to degree two and compute its dimension from scratch.
🔗Understand Correlation vs Causation With Real Examples
Go beyond 'correlation is not causation' — learn to spot confounders, recognize when randomization or natural experiments are doing the real work, and leave with a 30-second rule of thumb you'll actually use on tomorrow's headline.
🎲Learn Bayes' Theorem and Actually Use It to Update Beliefs
Update beliefs the way doctors, rationalists, and spam filters actually do — starting with frequency trees, finishing with a real prior-posterior update on a coin you've flipped yourself.
📊Understand P-Hacking and Why It Wrecks Studies
See p-hacking with your own eyes — slice random data twenty ways, watch a 'significant' finding fall out of pure noise, then draft the pre-registration outline that would have stopped it.
📐Understand the Determinant Geometrically as Signed Volume
See the determinant as the signed area or volume your matrix multiplies space by — then compute it fluently, connect it to invertibility, eigenvalues, and Jacobians, and design matrices that scale area or flip orientation on demand.
📐Understand Eigenvectors and Eigenvalues Without the Algebra Fog
Build geometric intuition for eigenvectors before touching a formula — then compute them, connect them to PCA and PageRank, and build your own mini ranking system from scratch.
📈Understand Limits Intuitively Before You Touch Epsilon-Delta
Build a gut-level feel for limits through graphs, tables, and zoom-in experiments — then use that intuition to evaluate tricky expressions and invent your own limit-breaking function.
🎯Understand Proof by Induction: The Domino Argument That Works
Build intuition for mathematical induction through the domino analogy and concrete number examples, then prove classic identities and write your own induction proof from scratch.
📈Understand Compound Interest
Turn compound interest from a vague formula into a reliable mental tool — calculate growth over time, apply the Rule of 72 in seconds, and reason clearly about savings, debt, and long-horizon decisions.
⛓️Learn the Chain Rule: Differentiate Composed Functions with Confidence
Stop memorizing the chain rule formula and start seeing nested functions the way mathematicians do — as zoom levels on a curve. Finish by deriving a real-world rate of change from scratch.
📊Understand P-Values Without the Common Myths
Lock in the one-sentence correct definition of a p-value and spot the three misreadings that trip up even published scientists. Leave with a shareable mental model you can defend in any stats conversation.
🔢Learn Modular Arithmetic Basics: Clock Math That Secures the Internet
Start with the clock on your wall and finish by encrypting a short message with a toy RSA example, using primes you pick yourself. You'll feel modular arithmetic as a living tool, not a programming operator.
🎲Learn Permutations vs Combinations Without Memorizing Formulas
Stop memorizing nPr and nCr — answer two questions (does order matter? can things repeat?) and the right formula falls out. Ends with you inventing and solving your own counting puzzle.
🎲Understand the Law of Large Numbers and Stop Misreading Randomness
Watch averages crawl toward the true mean in live simulations, catch gambler's fallacy traps at a glance, and finish by estimating pi with your own Monte Carlo dart-throw. Fourteen drops that rebuild your intuition for randomness from the ground up.
📉Understand Gradient Descent
Stop treating the optimizer as a black box — walk a 2D loss surface by hand, feel why a learning rate that's too big diverges and one that's too small stalls, and learn to read SGD, momentum, and Adam loss curves the way a doctor reads a chart.
📉Understand the Bias-Variance Tradeoff
Turn the bias-variance formula into a hands-on debug checklist — read any train/val gap or learning curve and prescribe the right fix in minutes.
📉PCA: Dimensionality Reduction from Eigenvectors
Connect PCA to the eigenvectors of the covariance matrix, then compress a 50-feature dataset to 5 components and defend exactly how much information you kept.