How to read this map¶
The course meets for 150 minutes a week across two sessions, and every week runs the same four beats: run, observe, explain, cost it. This table tells you which chapter to read before the week starts, what you will actually run once you are there, what the running is supposed to teach you, and what you owe by the end of it.
Read a little ahead, in order:
Before the week’s first session, read that week’s chapter, intuition first.
Read with Python open, or at least with the chapter’s simulation open. Every worked example is meant to be run, not only read.
Do the worked examples before the practice problems. Each new skill is demonstrated once, start to finish, before you are asked to use it.
Use the appendices whenever you get stuck: the formula summary, the Python quick reference, the dataset index, the cost model, the glossary, and answers to the odd-numbered problems.
If you want the full account of who the book is for and how each idea is built, read How to use this book first.
The map gives week numbers, not dates. Your section’s calendar dates come from the university academic calendar and from your instructor’s syllabus, and those are what govern due dates if the two ever disagree with this page.
The five keystone weeks¶
Five weeks carry ideas the rest of the course leans on. They are marked ★ in the table. If you fall behind, catch these up first, because a later week will not work without them.
| Week | Why it is a keystone |
|---|---|
| 4 | Softmax. Every claim the course makes about what a model “thinks” is a claim about this one function. |
| 7 | Quantization. The Theme S core: the same arithmetic is an environmental argument and an access argument. |
| 9 | Cosine similarity. Also the course’s controlled experiment, where size is the only variable allowed to move. |
| 12 | Uncertainty. The week a benchmark score stops being a number and becomes a random variable. |
| 13 | Measuring the measurement. The week the course was built around, and the one that is hardest to unlearn. |
Week 13 is the double keystone. It is the piece of this course that exists nowhere else, and it is the answer to the question of why a mathematics department, rather than a computer science department, teaches it.
The fifteen weeks¶
| Week | Chapter | What you run | What you learn | What is due |
|---|---|---|---|---|
| 1 | Ch 1, Where is this running, and what did it cost? | Your first generation, on the machine in front of you. Time the load, time the answer, and write down what the run consumed. | The course’s two measuring sticks: does it work, and what did it cost to run. Both get a number, from the first day. | Lab 0, first run and cost baseline (60 pts). Concept check 1. |
| 2 | Ch 2, Numbers all the way down: tokens | The tokenizer, on your own name, on Bakersfield, and on 1234567. | Tokens are discrete ids into a fixed vocabulary, and they are not words. Bakersfield is three pieces, ['B', 'akers', 'field']. Every digit of 1234567 is its own token, which is the mechanical reason these models are bad at arithmetic. | Concept check 2. |
| 3 | Ch 3, What is a parameter? | A real 896 by 896 weight matrix, loaded and described. A full inventory of where 494,032,768 parameters live. | A parameter is a learned number, and model size in bytes is a physical fact. The vocabulary table is 27.56 per cent of this model; all of attention is 8.92 per cent. The famous part is under a tenth of the machine. | Concept check 3. |
| 4 ★ | Ch 4, The probability of the next word | Softmax over the full 151,936-token vocabulary, for the prompt The capital of France is. | Logits become a probability distribution: every value positive, all of them summing to 1, and the order of the scores preserved. The model’s top choice is ' Paris' at 30.219 per cent, and its second choice is a fill-in-the-blank rule it learned from worksheets. | Concept check 4. |
| 5 | Ch 5, Temperature, and what it does not do | The same distribution at five temperatures, with its entropy and the count of tokens holding 90 per cent of the probability. | Temperature divides the logits before exponentiating; it flattens or sharpens, and it cannot reorder tokens. At T = 0.25 one token holds 90 per cent of the mass. At T = 2.0 it takes 41,274 of them. The sentence “temperature makes the model creative” does not survive this week. | Concept check 5. |
| 6 | Ch 6, Bits, precision, and rounding | A floating point number taken apart bit by bit, then the storage arithmetic for a whole model. | Why a “1 GB model” is 1 GB: 494,032,768 parameters at two bytes each is 0.988 GB in half precision, 1.976 GB at full precision. Precision is a choice with a price tag. | Concept check 6. |
| 7 ★ | Ch 7, Quantization: what you lose, what it buys | A real weight tensor quantized two ways, one scale for the whole tensor and one scale per 32-weight block, at 8, 6, 4, 3 and 2 bits. Then Lab 1 on a whole model: size, speed, quality, and energy. | Quantization is rounding to fewer levels. Per-tensor rounding fails because one outlier sets the scale: at 4 bits the mean error is 46.6 per cent of a weight’s standard deviation. Per-block rounding fixes it, to 7.2 per cent. Then the turn: the same arithmetic that makes a model cheap to run is what makes it possible to own. | Lab 1, quantization: size, speed, quality, energy (140 pts). Concept check 7. |
| 8 | Ch 8, A sentence is an arrow | Dot products by hand, in two dimensions, on vectors you can draw. | A vector has a direction and a length, and the dot product measures how much two of them point the same way. No model needed yet; the geometry comes first. | Concept check 8. |
| 9 ★ | Ch 9, Similarity is geometry | Cosine similarity, first on hand-drawn 2-D vectors, then on real 384-dimensional sentence embeddings. Also the controlled comparison: one model family, one question bank, one procedure, size as the only variable that moves. | Cosine is the dot product divided by both lengths, which is why doubling a vector changes nothing: for a = (3,4) and d = (6,8), cosine is exactly 1.0000. Length is not meaning. Two sentences sharing no content words score 0.612. | Concept check 9. |
| 10 | Ch 10, Retrieval: the open-book exam | Nearest-neighbour retrieval over a Kern County and CSUB corpus. Lab 2. | Retrieval is cosine similarity with a sort on the end. The query “Which California county is Bakersfield in?” scores 0.910, then 0.719, then 0.089. The gap between rank 2 and rank 3 is the whole idea. | Lab 2, retrieval on a Kern County corpus (100 pts). Concept check 10. |
| 11 | Ch 11, Can a model take a test? | A twenty-question bank, scored end to end. Lab 3. | Accuracy is a sample proportion, which makes it a random variable rather than a fact. And answer extraction is a decision you make, not a reading you take. | Lab 3, benchmark a model, report accuracy with an interval (120 pts). Concept check 11. |
| 12 ★ | Ch 12, Is that score real? | A Wald interval and a 10,000-resample bootstrap, seeded 20260912, on the letter-scored result of 5 correct out of 20. | The honest statement is not 25.0 per cent. It is a 95 per cent interval from 6.0 per cent to 44.0 per cent, and the bootstrap agrees at 5.0 to 45.0 per cent. With twenty questions the interval is so wide it is nearly useless, which is itself the lesson about benchmark sizes. Some textbook intervals also run past 100 per cent, so the formula has assumptions. | Concept check 12. |
| 13 ★★ | Ch 13, Measure your measurement | One model, twenty questions, three defensible scoring procedures, plus four cyclic rotations of every set of options. | The same model on the same questions scores 25.0, 35.0 or 15.0 per cent depending only on how you score it. The naive scorer was measuring the model’s preference for the letter A, which it chose on 16 of 20 questions. Under rotation only 1 of 20 answers held. The standardization is the lesson, and the conclusion is that no single number should have been reported. | Concept check 13. |
| 14 | Ch 14, Bias in the benchmark, and who pays | A subgroup breakdown of a benchmark score, then an accounting of who bears the cost of compute. Lab 4. | One average hides who the model fails, and the subgroups have to be looked at on purpose. Then the Theme S close: the cost of computation is not distributed the way its benefits are, and both halves of that sentence can be measured. | Lab 4, subgroup bias and distributional cost of compute (140 pts). Concept check 14. |
| 15 | Ch 15, Capstone | Your own model, your own question, your own evaluation, run honestly and reported in full. | How to state a quantitative result with the uncertainty it deserves and a resource-cost accounting attached, in front of an audience, in a few minutes. | Capstone project and lightning presentation (200 pts). |
Graded work at a glance¶
Total 1000 points. Percentages are the design of the course, not an afterthought.
| Item | Points | Share |
|---|---|---|
| Weekly concept checks (14 at 10 points) | 140 | 14% |
| Lab 0, first run and cost baseline | 60 | 6% |
| Lab 1, quantization: size, speed, quality, energy | 140 | 14% |
| Lab 2, retrieval on a Kern County corpus | 100 | 10% |
| Lab 3, benchmark a model, report accuracy with an interval | 120 | 12% |
| Lab 4, subgroup bias and distributional cost of compute | 140 | 14% |
| Essay: two factors and their connectedness | 100 | 10% |
| Capstone project and presentation | 200 | 20% |
There is no high-stakes exam. Interpretation is graded as heavily as computation.
The essay does not sit in a fixed week of the course design, so it does not appear in the table above; your syllabus sets its date. Everything else is due in the week shown.
One thing to notice about the order¶
The course does not name model failure until late, on purpose. You will meet a model failing in Weeks 1 through 10 without anyone handing you a vocabulary for it: a tokenizer that cannot count digits, a distribution that flattens into noise, a quantizer that throws a weight away. The taxonomy arrives in Module E, once you have enough experience of the thing to argue with the labels. Week 1 asks you what surprised you; Week 13 is where that paragraph gets its answer.