You now have five tools: plugging numbers into a formula, a machine that turns inputs into one output, a graph, a straight line, and the average of a list. That is the whole floor this course stands on. Why stop to read a roadmap? Because a long book is easier when you know where each piece goes, and because two parts of this course, the labs and the appendices, work differently from an ordinary textbook. This section explains all three, and ends with an honest list of what we assume you already know.
Think of this course as one long recipe book. This chapter taught you to read a recipe card, run a kitchen machine, read a floor map, lay a string across the tiles, and share out cookies fairly. Those are the habits every page ahead uses.
The first recipe you will cook is one you already know: half of 2, a fifth of 3, plus 1, which is 2.6. Chapter 1 calls that a prediction. Chapter 2 pushes the 2.6 through one more gadget that squeezes any number into the range from 0 to 1, and out comes 0.931. That little two-step gadget is a neuron. Chapters 3 to 5 wire many of them together. Chapters 6 to 10 teach how the book's recipes fix their own mistakes: measure how wrong the dish came out, work out which amounts to nudge, and nudge them. Chapters 11 to 13 are about cooking for real, with all the things that go wrong in a real kitchen.
Some sections end with a card marked 🧪, a "Computational Laboratory." It is an optional extra: the same numbers from that section, ready to run on a computer so you can change one and watch what happens. You never need it to understand the lesson or to answer the questions. If you do want to try it, the "Open in Google Colab" button runs it in your web browser with nothing to install, and Appendix E walks through that button step by step.
The appendices at the very back teach the software itself: the Python language, and the tools the labs use. They are there when you want them. And here is what we assume you can already do: add, subtract, multiply, and divide, with decimals and negatives. That, plus this chapter, is the whole entry ticket.
Start with a number you know: the recipe 0.5(2) + 0.2(3) + 1 = 2.6. Chapter 1 calls this same calculation a prediction and gives the 0.5, the 0.2, and the +1 their proper names. Chapter 2 sends the 2.6 through one more machine, a gentle squashing step, and out comes 0.931. That two-step object is a neuron, and the rest of the book grows out of it.
The roadmap is the list of the course's fourteen chapters, in the order they depend on each other. The labs are short prepared notebooks of runnable code, one for roughly every third section. The appendices are six extra chapters that teach the software the labs use.
The roadmap, chapter by chapter:
| Chapter | Title | The question it answers |
|---|---|---|
| 0 | Before we start: numbers, letters, and graphs | What algebra do I need? (This chapter.) |
| 1 | Predictions, features, and the simplest model | How does a formula make a guess? |
| 2 | From a linear model to a neuron | What is one neuron, start to finish? |
| 3 | Vectors and matrices: many numbers at once | How do I write a long list of numbers in one symbol? |
| 4 | Layers, networks, and the forward pass | How do many neurons work together? |
| 5 | Activation functions, one by one | What are the different "squashing steps"? |
| 6 | Probability and surprise | How do we score a guess about a category? |
| 7 | Loss functions: one number for how wrong | How wrong is the network, as one number? |
| 8 | Slopes, derivatives, and gradients | Which way should each number move? |
| 9 | Gradient descent: learning by walking downhill | How does the network improve, step by step? |
| 10 | Backpropagation: how every weight learns | How is the "which way" found for every number at once? |
| 11 | The training loop in practice | What does a real training run look like? |
| 12 | Overfitting, regularization, and evaluation | Did it really learn, or just memorize? |
| 13 | Training deep networks: initialization and normalization | Why do big networks need extra care? |
Chapters 1 to 5 build the network and run it forward. Chapters 6 to 10 build the machinery that improves it. Chapters 11 to 13 are about doing that well in practice. Every chapter uses all five tools from this one.
A Computational Laboratory, marked with a 🧪 sign near the end of a section, is a prepared notebook that reproduces that section's exact numbers in Python. The lesson never depends on it: every fact and every check question stands on its own without any code. The card offers two links. "Download .ipynb" saves the notebook file. "Open in Google Colab" opens the same file in a free tool that runs in a web browser, on Google's computers, so nothing needs installing. Appendix E, "Google Colab," explains that tool from the first click. Each lab has a level. "Run it" means run the cells and watch the lesson's numbers appear. "Modify it" means change one value and re-run. "Build it" means write a short piece yourself, with a check cell that tells you if it matches.
The appendices, lettered A to F, teach Python, NumPy, Matplotlib, Jupyter notebooks, Google Colab, and PyTorch. They sit after Chapter 13, are not on the course exam, and can be read at any point, or never. Read Appendix A and E before your first lab if you have never written a line of code.
What this course assumes: arithmetic with decimals and negative numbers, and the five tools of this chapter. Nothing else. No calculus, no statistics, no programming. Where a chapter needs a fact beyond these, it teaches it there, from small numbers first.
Which chapter answers this question?
Each card is a question a reader might bring to this book. Using the roadmap table above, sort each one into the stretch of chapters where it gets answered.
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What this task checks
Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.
The compiler says
A model answer
Correct answer
Also accepted:
Why
Why
A friendly preview: the recipe, then the squash
The first box is the recipe with the second ingredient fixed at 3, so 2 becomes 2.6. The second box is the squashing step Chapter 2 teaches; it turns any number into one between 0 and 1. Send the chip 2 through and read both numbers. Then send 6 and −2 and notice the outputs never leave the 0-to-1 range.
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Where you are on the road
Each mark is a chapter. Find the three stretches, and notice that everything to the right of this chapter uses the five tools you just learned.
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Worked example
Basic: where does one question live?
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1
A reader asks, "When the network guesses 2.6 and the true answer was 3, how do we turn that miss into a single score?" Which chapter answers it?
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2
The question is about scoring a miss, not about building the guess. That rules out Chapters 1 to 5, which build the network and run it forward.
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3
Chapter 7 is titled "Loss functions: one number for how wrong." A loss function is exactly a score for a miss. Chapter 1 also has a section, "How wrong was the guess," that meets the idea first with small numbers.
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4\boxed{\text{First met in Chapter 1; fully answered in Chapter 7.}}
This is how the roadmap is meant to be used: find the stretch, then the chapter whose title names the question.
Worked example
Common trap: treating a lab as a prerequisite
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1
A reader reaches the 🧪 card at the end of "Straight lines, slope, and intercept," cannot get Colab to open, and decides they cannot continue until it works. Is that right?
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2the card sits after the applied block for a reason
The wrong belief: the lab is a step in the lesson, so the lesson is blocked without it.
the card sits after the applied block for a reason
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3
Every lab reproduces numbers the section already computed by hand. The check questions are written to be answerable with pencil and paper alone. The lab is a second way to see the same numbers move, never the only way.
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4\boxed{\text{No. Answer the check, move on, and return to the lab later.}}
If the trouble is Colab itself, Appendix E covers it from the first click.
Where this goes next
This course, Chapter 1 through Chapter 13
Each tool from this chapter has a home address in the roadmap. Plugging into a formula is Chapter 1's "A linear model is a weighted sum." The machine picture is Chapter 4's "A network is a function built from functions." Reading a graph is Chapter 1's "Fitting a line by eye" and Chapter 11's "Watching training: the loss curve." Slope and intercept are Chapter 1's two knob sections and, later, the whole of Chapter 8. Sums and averages are Chapter 7's mean squared error and Chapter 9's "A few examples at a time." When a later chapter feels hard, the fix is usually one of these five tools, and this chapter is the place to come back to.
Check your understanding (counts toward your progress)
Which of this chapter's five tools does Chapter 8, "Slopes, derivatives, and gradients," grow directly out of?
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Averages feed the loss chapters, 7 and 9, not the slope chapter.
The roadmap is a map of the book, not a mathematical tool.
Plugging in is used everywhere, but Chapter 8's new idea is steepness.
Why
A derivative is "rise over run" measured on a curve at a single point. It is this chapter's slope, taken further.
In the friendly preview, the recipe's output 2.6 is pushed through a second machine and comes out as 0.931. Which chapter teaches that second machine?
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Loss functions score how wrong a guess is; they do not squash the guess.
Backpropagation finds which way every number should move.
Chapter 13 is about training very deep networks well.
Why
The squashing step that turns any number into one between 0 and 1 is the second half of a neuron, and Chapter 2 builds it.
The calculation 0.5(2) + 0.2(3) + 1 = 2.6 from this chapter reappears first in which chapter, and under what name?
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Chapter 8 is about steepness. The recipe is a plain weighted sum, and it is a guess.
Chapter 12 asks whether a network memorized. The recipe is the very first guess, long before that.
2.6 is not between 0 and 1, so it is not a probability.
Why
Chapter 1 calls this exact sum a prediction and names its parts. Chapter 2 then squashes the 2.6 into 0.931 to make a neuron.
Check your understanding (counts toward your progress)
What does the "Open in Google Colab" button do?
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Colab runs on Google's computers; the only thing you need is a browser. A separate "Download" link saves the file if you want it.
It opens the notebook for you to run; nothing is sent anywhere.
Grading happens on the lesson page, never in the notebook.
Why
Colab is a browser-based place to run notebooks. Appendix E explains it from the first click.
Which of these is true of the appendices?
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They can be read at any point, or never, depending on whether you want to run the labs.
They teach tools: Python, NumPy, Matplotlib, Jupyter, Colab, PyTorch.
Chapters 11 to 13 are core chapters about training in practice.
Why
Appendices A to F are tooling chapters. They sit after Chapter 13 and are excluded from the exam.
Practice: The whole chapter in five problems (5 problems · doesn’t affect your progress)
Work out y = 0.5\,x_1 + 0.2\,x_2 + 1 when x_1 = 4 and x_2 = 15, as a final check on plugging into a formula.
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Why
2 + 3 + 1 = 6. Multiply first, then add.
Correct answer
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Why
If f(x) = 2x + 3, work out f(7) as a final check on function notation.
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Why
2(7) + 3 = 17: input 7, output 17.
Correct answer
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Why
The row "input 7, output 17" of that table becomes which point on the graph?
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Why
Input across, output up: 7 across, 17 up.
(7, 17)
The graph of f(x) = 2x + 3 is a straight line. Using the points (7, 17) and (0, 3), compute its slope by rise over run.
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Why
(17 - 3)/(7 - 0) = 14/7 = 2, the number multiplying x.
Correct answer
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Why
The outputs f(0), f(1), f(2), f(3) of f(x) = 2x + 3 are 3, 5, 7, 9. Find their mean.
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Why
Sum 3 + 5 + 7 + 9 = 24, count 4, mean 6. Notice the mean of evenly spaced numbers sits exactly in the middle of them.
Correct answer
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Why