Learn the links.
Keep the ideas.

Bézier curves: a curve from repeated interpolation

Affine interpolation · Recursive curve construction · Subdivision and local parameters · Derivatives and parameter speed

• Straight steps. Curved paths. ↗

Binary search: precise boundaries

Sorted search contract · Interval decisions · Boundary results · Progress and cost

• Binary search, one decision at a time ↗

Boolean logic: from truth values to valid inference

Truth values and connectives · Material implication · Logical equivalence · Valid inference

• Boolean logic explorer ↗

Cache decisions: FIFO, LRU and capacity

Requests and cache state · FIFO and recency · Capacity and misses · Reading a trace

• Cache decisions ↗

Complex multiplication: turn, scale, repeat

Points and the imaginary unit · Distance and direction · Multiplication as a transformation · Repeated products

• Turn, scale, repeat ↗

Counting principles: order and reuse

Counting a complete choice · Order and distinct roles · Unordered selections · Boundary and model checks

• Counting principles ↗

DC circuits: current, connections and power

Current and resistance · Series connections · Parallel connections · Energy and power

• DC circuits lab ↗

Directed graphs: from arrows to dependency plans

directed-links · reachability · dependency-orders · cycles-and-updates

• Dependency plan ↗
• Critical-path timing ↗

Discrete Fourier: coefficients, pairs and reconstruction

Finite sample grids · Fourier coefficients · Real-sample frequency pairs · Reconstruction and residuals

• Discrete Fourier lab ↗

Enzymes: energy, speed and control

Reaction energy · Catalytic pathways · Binding and saturation · Enzyme regulation

• Enzyme kinetics ↗

Euclid's algorithm — remainders, gcds, and integer combinations

Division with remainder · Gcd and common divisors · Invariant and termination · Integer combinations

• Euclid, one division at a time ↗

Feedback control: correction, fixed points and stability

Read one update · Close the loop · Find the fixed point · Test decay and growth · Separate tracking and disturbance · Read the model's limits

• When correction overshoots ↗

Finite convolution: indices, contributions, and filters

Indices and support · Shift and sum · Finite filter responses · Properties and operation choice

• Finite convolution lab ↗

Floating point: when stored coordinates change the answer

Binary representation · Spacing and ties · Range limits · Rounded arithmetic · Stored geometry · Coordinate choices · Sensitivity and scale

• Floating point ↗

When groups and totals disagree

Denominators · Group composition · Reference mix · Causal questions

• When groups and totals disagree ↗

Hash tables: follow the probe

Home slots and collisions · Probe order and stopping · Deletion and duplicates · Capacity and cost

• Hash tables: follow the probe ↗

Least squares: fit a line and read its residuals

Residuals and squared error · The fitted line and the mean · Changing data and units · Interpretation limits

• Least squares ↗

Causal order with Lamport and vector clocks

causal-order · lamport-clocks · vector-clocks · reading-concurrency

Study the course and work through its companion guide.

Markov chains: where probability goes next

State and transition rules · Probability flow · Repeated steps and observations · Stationary distributions · Cycles and closed states

• Markov chains ↗

Mathematical induction: a base, a bridge, every integer

Statement and domain · Successor algebra · Finding proof gaps · Coverage and exact certificates

• Induction lab ↗

Measurement uncertainty: what more readings can tell you

Readings and correction · Scatter and mean · Shared calibration · Combining and deciding

• Measurement lab ↗

Membrane transport: direction, selectivity, and energy

Membrane selectivity · Passive transport · Osmosis · Active transport

Study the course and work through its companion guide.

Inheritance: from gametes to probabilities

Alleles and segregation · Genotype and phenotype · One-locus crosses · Independent two-locus crosses

• Inheritance lab ↗

Minimum spanning forests: connect without cycles

The spanning objective · Safe edge choices · Components and cycles · Reading the result

• Minimum spanning forests ↗

Momentum and collisions: what stays, what changes

Signed momentum · System momentum · Collision models · Energy accounting · Model boundaries

• Momentum and collisions ↗

Maximum flow: capacity, rerouting and a cut certificate

capacity-and-conservation · path-bottlenecks · residual-rerouting · augmenting-paths · cut-certificates

• Maximum flow ↗

Newton's method: tangent steps, exact residuals and visible limits

Tangent steps · Exact residuals · Failure and repetition · Interpreting a run

• Newton's method ↗

Coupled motion: two patterns inside one system

restoring-and-coupling · normal-coordinates · initial-motion · energy-and-limits

• Normal Modes ↗

Numerical precision: decimal intent, binary Number and exact comparisons

Exact representations · Conversion and arithmetic · Comparison and order · Integer guarantees

• Numerical precision lab ↗

Coherent waves: from phasors to interference

complex-amplitude · vector-addition · relative-phase · model-boundaries

• Coherent waves ↗

Probability foundations: count, condition, and update

Sample spaces · Conditional probability · Independence · Bayes' rule

Study the course and work through its companion guide.

Rates and accumulation: motion, signed area and traveled distance

Rate and units · Signed accumulation · Local and interval rates · Reading a continuous curve

• Rates and accumulation ↗

RC transients: charge, time and energy

Capacitor voltage and current · Time constants · General voltage steps · Energy flow

• RC transients ↗

Reading data and evaluating evidence

Rates and denominators · Summaries and spread · Comparisons and context · Study design

Study the course and work through its companion guide.

Recursion and the call stack: waiting, returning, reusing

Base cases and progress · Suspended calls and returns · Calls and active depth · Memoized reuse

• Calls, returns, and remembered work ↗

Retries: one request, uncertain replies

Repeated state changes · Operation identity · Durable result records · Limits of retry guarantees

Study the course and work through its companion guide.

Sampling: different signals, identical observations

sample-clock · frequency-aliases · recovery-assumptions · acquisition-choices

• Sampling & aliasing ↗

Shortest paths: from a promising route to a proven distance

weighted-paths · tentative-distances · settling-vertices · algorithm-limits

• Shortest paths ↗

SQL query foundations — rows, NULLs, groups, and joins

rows · nulls · groups · joins

• Follow the rows ↗

Reaction amounts: ratios, limits and leftovers

reaction-ratios · limiting-reactants · excess-and-scaling · theoretical-amounts

• The limiting reactant ↗

Units and dimensions: conversions that preserve meaning

Factors and prefixes · Area and volume · Rates and density · Dimensions and models

• Unit conversion explorer ↗

Vector geometry: moves, projections and transformations

Displacement · Length and direction · Dot products · Projection · Matrix actions · Order and information

• Vector geometry explorer ↗

Weighted intervals: choose, compare, reconstruct

compatible-intervals · prefix-subproblems · take-or-skip · reconstruct-and-check

• Weighted intervals ↗