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Caltech study resources

Resources for Caltech students writing proofs, prepping take-home exams, and getting the most from a small cohort.

Optimized for Caltech · Small-cohort STEM students focused on labs, proofs, and research.

Showing 8 resources

How to Prove It (Velleman), structured study

intermediate

A chapter-by-chapter path through logic, sets, and standard proof techniques for shoring up a proof-heavy core.

Proof craftTextbook45 min per section

Proof-technique decision card

beginner

A one-card prompt for choosing induction, contradiction, or construction before writing the first line.

Proof craftFreeReference card10 min to make

Open courseware real analysis lectures

advanced

Free rigorous lectures to reinforce epsilon-delta arguments when the core sequence moves faster than you can absorb.

Core supportFreeVideo lectures60 min
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Per-course definitions sheet

beginner

A living document of exact statements and theorems so every argument rests on precise terms.

Core supportFreeTemplate25 min weekly

Timed take-home simulation kit

intermediate

A plan for running a self-proctored practice set under the real allowed time and notes before the exam window.

Take-home prepFreePractice protocol90 min per run

Counterexample journal

intermediate

A running log of edge cases that broke your proofs, reviewed weekly to build reliable instincts.

Take-home prepFreeJournal20 min weekly

Pair-explain proof protocol

beginner

A turn-taking format where two classmates present arguments aloud to expose hidden gaps.

PeersFreePair session60 min

Faculty office-hours question sheet

beginner

A short prep that turns a vague stuck feeling into the exact lemma to ask about in a small-cohort office hour.

PeersFreeWorksheet15 min before each visit

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Should I use free resources first?

Yes. Start with free resources until your error log shows a specific gap that needs a paid course, book, or tutor.

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Caltech study resources
Focus target: Caltech
Block 1 (25 min): closed-book recall or one timed practice set.
Break (5 min): mark confusing items without opening a new task.
Block 2 (25 min): correct misses and write the next first step.
Done: one score/error note plus one queued task for tomorrow.
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