Learning Path — Probability Theory
Suggested preparation for Probability Theory. Choose an entry point that fits your preparation.
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Entry / bridge route · Additional preparation for research reading · All paths
Entry / bridge route
Calculus
Use limits, derivatives, integrals and series; distinguish computation from justification.
Calculus, Volume 1 — Gilbert Strang and Edwin 'Jed' Herman. Direct open PDF
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You can solve representative differentiation, integration and convergence exercises and explain the hypotheses used.
Probability Theory
Study random variables and elementary limit phenomena before measure-theoretic probability.
Introduction to Probability, 2nd edition — Charles M. Grinstead and J. Laurie Snell. Open online text / archive
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You can use expectation, conditioning and elementary distributions; elementary probability does not replace measure-theoretic preparation.
Research reading: additional tools
Choose according to the particular text, not as an obligation to complete every foundation again.
Proofs & Mathematical Writing
Read quantified statements; write direct, contrapositive, contradiction and induction arguments.
Book of Proof — Richard Hammack. Direct open PDF
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You can explain the quantifiers in a statement and write these forms of proof without relying on a worked solution.
Real Analysis
Prove convergence, continuity, compactness and differentiation/integration results.
Basic Analysis I — Jiří Lebl. Direct open PDF
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You can work with epsilon arguments and prove standard compactness and convergence results, not just calculate limits.
Measure & Integration
Build measures, measurable functions, integrals and convergence theorems.
Measure, Integration & Real Analysis — Sheldon Axler. Direct open PDF
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You can apply monotone/dominated convergence and Tonelli/Fubini with their hypotheses checked.