Learning Path — Combinatorics & Graph Theory
Suggested preparation for Combinatorics & Graph 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
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.
Combinatorics & Graph Theory
Count structures, use recurrences and reason about graphs.
Combinatorics and Graph Theory — David Guichard. Open online text / archive
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You can prove counting identities and elementary graph results; algebraic or probabilistic branches require additional tools.
Research reading: additional tools
Choose according to the particular text, not as an obligation to complete every foundation again.
Linear Algebra
Work with vector spaces, bases, linear maps, kernels, rank and eigenvalues.
Linear Algebra — Jim Hefferon. Open online text / archive
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You can prove rank–nullity, change bases and distinguish diagonalizable maps from general linear maps.
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.