Vectors from boxes to similarity
Edit coordinates and inspect alignment, contribution traces, norms, dot products, and cosine similarity.
Open full-screen Python lab ↗A complete course · six parts
Learn the mathematics
before it has a job.
The book begins with two self-contained tutoring chapters for readers whose last formal mathematics course was calculus. Only after those foundations are secure does it introduce the search problem, the proof, approximate encryption, HDL, and the production implementation.
Begin with four boxes → Open the live Doolittle core atlas ↗ Enter the pure-GPU chip deep dive ↗- Sections
- 52
- Guided time
- 58h 56m
- Assumed math
- None recalled
Hands-on laboratory atlas
Python you can change. Proofs you can attack. Pipelines you can stall.
These are reactive Marimo applications, not screenshots. They execute entirely in your browser with Pyodide WebAssembly, keep their construction code visible, and are embedded again at the moment each chapter needs them.
Build convolution one loop at a time
Construct every pair, route it to a bucket, and change only the boundary rule to obtain negacyclic multiplication.
Open full-screen Python lab ↗Derive and attack the score-tap layout
Solve the index equation, inspect contributor bounds, and probe the proof with small exact examples.
Open full-screen Python lab ↗Spend a fixed-point precision budget
Change values and scale bits while tracking rounding error, product scale, integer growth, and remaining headroom.
Open full-screen Python lab ↗Trace a valid-ready pipeline
Change downstream stalls and latency while watching offers, transfers, accepted order, and completion order.
Open full-screen Python lab ↗Detailed contents
Fifty-two sections, one continuous argument
Each section contains explanations, worked examples, visual models, retrieval questions, and a compact section summary. Studios close each chapter with cumulative practice.
01
Part I · Chapter 1
Thinking in ordered lists
The language of positions, sums, and matching coordinates
- 1.1An ordered list is more than a bag of numbersVIDEO48 min
- 1.2Indices: names for positions52 min
- 1.3From repeated addition to sigma notationINTERACTIVE55 min
- 1.4Multiply matching positions52 min
- 1.5The dot product, built one operation at a timeVIDEOPYTHON LAB60 min
- 1.6Chapter studio: make the notation yours65 min
02
Part I · Chapter 2
Multiplication that remembers position
Polynomials and convolution without assumed algebra or number theory
- 2.1Powers as position labels52 min
- 2.2A polynomial is a labeled list55 min
- 2.3Multiply every term by every term60 min
- 2.4Why products gather into output bucketsVIDEOINTERACTIVE58 min
- 2.5Convolution: finally, a name for the bucket rulePYTHON LAB65 min
- 2.6When the output list has a fixed lengthVIDEO60 min
- 2.7Chapter studio: follow every product70 min
03
Part II · Chapter 3
A problem worthy of the machinery
Embeddings, similarity search, and the privacy boundary
- 3.1From rich objects to ordered listsVIDEO58 min
- 3.2Similarity as a dot productPYTHON LAB60 min
- 3.3From one score to nearest neighborsINTERACTIVE60 min
- 3.4What must remain private—and from whom65 min
- 3.5When an allowed operation is still too expensive68 min
- 3.6Chapter studio: specify the computation70 min
04
Part III · Chapter 4
Make multiplication find matching coordinates
Deriving the reversal instead of presenting a trick
- 4.1The mismatch: diagonals are not matching positions62 min
- 4.2Choose the destination before choosing the layout64 min
- 4.3Solve the index equationVIDEOPYTHON LAB70 min
- 4.4Give every vector its own landing stripINTERACTIVE70 min
- 4.5Laboratory: make the score appearINTERACTIVE75 min
- 4.6Chapter studio: derive layouts from constraints75 min
05
Part III · Chapter 5
Prove the coefficient means what we claim
Support, wraparound, invariants, and complexity
- 5.1Why neighboring blocks cannot leak into a scoreVIDEO72 min
- 5.2Why negacyclic wrap cannot corrupt a score tap72 min
- 5.3Turn the proof into invariants66 min
- 5.4Build the cost model before stating the payoffINTERACTIVE75 min
- 5.5What the layout buys—and what it gives up68 min
- 5.6Chapter studio: attack the proofPYTHON LAB75 min
06
Part IV · Chapter 6
Approximate arithmetic under encryption
CKKS introduced as layers, not alphabet soup
- 6.1Why approximate arithmetic is acceptable here62 min
- 6.2Scale, round, compute, unscaleVIDEOINTERACTIVEPYTHON LAB72 min
- 6.3One message seen through several moduli75 min
- 6.4Ciphertexts are structured objects70 min
- 6.5A faster representation for the same product78 min
- 6.6Follow error and precision end to end75 min
- 6.7Chapter studio: keep the layers separate75 min
07
Part V · Chapter 7
Hardware, beginning with time
A patient introduction to HDL and streaming datapaths
- 7.1Why build hardware for this computation62 min
- 7.2Signals, bits, and widths70 min
- 7.3Combinational logic: outputs now72 min
- 7.4Registers: values that survive a clock edge75 min
- 7.5Valid and ready: a conversation between stagesVIDEOINTERACTIVEPYTHON LAB78 min
- 7.6Parallel lanes and pipelined throughput75 min
- 7.7Read a small SystemVerilog module slowly80 min
- 7.8Chapter studio: think in cycles80 min
08
Part VI · Chapter 8
Walk the real implementation
From source contracts to the score engine and back
- 8.1The complete data journeyVIDEOINTERACTIVE70 min
- 8.2The encoders enforce the mathematical layout75 min
- 8.3The score engine is simpler than the story around itPYTHON LAB80 min
- 8.4Extract, unscale, and rank on the client70 min
- 8.5Verification across representations75 min
- 8.6Final studio: defend the design90 min
The teaching contract
No unexplained machinery.
Every compact formula is first expanded into ordinary steps. Every new term is named only after its underlying action is visible. Every boundary rule gets a picture and a worked example.
The book expects persistence, not prior number theory. Optional formal notation is placed behind disclosures so it can enrich the lesson without blocking the main path.