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How to use this book

Pick a starting level, then work through each lesson in six steps

Find your entry point

The quickest way is the one-minute placement check: press Find my level on the home page. It asks up to seven short questions and stops at the first skill you have not met yet. You can also choose from this table.

If youStart with
are a young learner with a grown-up reading alongLevel 0
know fractions and basic chanceLevel 1
know algebra and want to learn causal thinkingLevel 2
need the math toolkit: complex numbers, matrices, entropyLevel 3
know statistics and want causal inference or causal MLLevel 4
want quantum information from the ground upLevel 5
are ready for quantum causal models and indefinite causal orderLevel 6
want research-level quantum ML and open problemsLevel 7

Work through a lesson in six steps

  1. Read the three short paragraphs under “Learn”. Each technical word is defined before the lesson uses it.

  2. Study the key relation box and the worked example.

  3. Try the exercise before you open its solution.

  4. Answer the multiple-choice question, then open the answer to see why it is right.

  5. Open the linked lab. Change one input at a time, and predict the result before you look.

  6. Read the caution box. It says what the lesson’s model assumes and where it stops working.

Features you can use

Hover over a cross-reference, citation, or glossary term to preview it without leaving the page. Press Ctrl + K (or ⌘ + K on a Mac) to search every lesson. Drag the sliders in the lab figures, rotate the 3-D plots, and hover for exact values. These figures run in your browser. The plotting library loads from a CDN, but nothing you do in a figure is sent anywhere. The sun and moon button in the top bar switches between light and dark mode, and the download button at the top of each lab saves it as a notebook (.ipynb).

Run the code yourself

Run the labs explains three ways to run the notebooks: on your own computer, on Google Colab, or on Binder.