Derivatives as rates of change

Week 1: derivatives. Week 2: integrals. Week 3: probability. Week 4: statistics. Week 5: stochastic calculus foundations. Each of the first four days has one 60-minute session: 6 minutes of recall, 10 of experiments, 14 of theory, 20 of practice and 10 of transfer. On day five, revisit due questions and explain the week's ideas aloud without the solutions.

For two shorter sittings, pause after the theory stage: the first three stages total 30 minutes, and practice plus transfer total another 30. Resume later in this same browser. Write down predictions and intermediate calculations before checking answers; the time budget includes that work, not just reading.

Start each week with two questions from the previous week. On the last review day, mix questions from all five modules. If a prerequisite feels unfamiliar, repeat its session before moving on. Before stochastic calculus, review Taylor expansions, Gaussian variance, conditioning and expectation. Timing is a starting estimate, not a deadline.

These sessions build foundations. They do not cover every interview topic or demonstrate mastery by themselves. The statistics examples use explicit idealized assumptions, not real-market forecasts.

After those foundations, use the mathematical bridges and execution sessions to connect the ideas. Alternate a lesson with its Python implementation. Use Practice for fresh mixed questions and keep a mistake notebook; finish with a guided project you can explain and extend independently.