Study Guide & Practice Routes

Find a starting point, rebuild missing skills, and practise before moving on

1. Start from the beginning

The primers are a learning route, not an entrance exam. Start with Primer 0 if mathematical notation or proofs feel unfamiliar. Continue with Primer A for vectors and matrices, then Primer B for calculus and optimization. Their opening refreshers help rebuild the algebra, matrix arithmetic and derivatives used later.

Primer C introduces probability; Primer D introduces systems and control; Primer E introduces reinforcement learning and neural networks. These subjects are taught here. You do not need a previous course in them.

After the primers, read the numbered modules in order for the most direct route through the whole site. For a shorter route, use the tracks below and follow each module’s “Before you start” links whenever a listed skill is unfamiliar.

2. Find and repair a knowledge gap

Use these questions to locate a gap. Try answering first, then open the worked check. If the explanation is unfamiliar, follow its review link and practise the Easy problems there before returning.

3. Work through a section

1. Check the prerequisites. Follow a linked definition you cannot explain and try its Easy practice. Return to your original page afterward.
2. Read the idea and the small example. Identify what goes in, what comes out, and what the guarantee says in words. Copy one calculation and fill in its intermediate algebra.
3. Read a theorem in two passes. First list its assumptions and conclusion. Then follow the proof and mark where each assumption is used. Optional literature comparisons can wait until the core example is clear.
4. Practise in order. Easy rebuilds notation and calculation; Medium applies a method; Hard combines methods or audits a guarantee. Use a hint before the solution. After checking, close the solution and redo the problem without looking.
5. Use the explorer to test understanding. Predict what changing one parameter will do, change it, and explain the result. A simulation helps understanding; the theorem’s assumptions determine what is guaranteed.
6. Check readiness to continue. Explain the main idea without the page, solve an Easy problem and a Medium problem, and say why the important assumptions matter. If one part fails, use the review link for that part and retry.

4. Find practice by topic

Primer routes link to section-by-section practice. Each numbered module’s graded set starts with four Easy exercises, continues with four Medium exercises, and ends with four Hard exercises. The original longer assignments remain available after that set.

5. Choose a research track

Use the numbered order when studying everything. For a focused track, read its core modules and fill in their linked prerequisites before tackling the proofs. A module’s reading route distinguishes its first-pass material from later comparisons.

• Safe exploration: 1, 3, 4, 5, 6, 7, then 11. Module 11 also uses CMDPs from 8 and control mathematics from 2.
• Certified neural networks: 1, 2, 12, 13, 14, 15. Review the linked control and barrier prerequisites before the closed-loop material in 14.
• Safe reinforcement learning: 1, 2, 3, 7, 8, 9. Modules 4–6 provide additional safe-exploration background where the prerequisite boxes call for it.
• Safety filters and control: 1, 2, 3, 7, 8, 10, 11. Review 4 for Module 11’s safe-expansion construction.