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Research · the notebook

The notebook

The circled answer is the least interesting thing I make. The mind-map, the false start, the scratch that reorganized the whole problem, the proof written out clean — that's the work, and that's what doing mathematics is. I'm a math thinker, not an answer-circler: once a task is solved the desire for it quietly ends, and I'm already on to the next. So this is a record of the thinking, not a wall of trophies.

Scratch: q-series and the q-Pochhammer symbol
Scratchq-series and the q-Pochhammer symbolTaylor's Theorem (anthology)
Scratch: Hensel's analogy — ℤ and ℂ[X]
ScratchHensel's analogy — ℤ and ℂ[X]Taylor's Theorem (anthology)
Scratch: The binomial theorem
ScratchThe binomial theoremTaylor's Theorem (anthology)
Scratch: Limits, continuity, and the metric axioms
ScratchLimits, continuity, and the metric axiomsTaylor's Theorem (anthology)
Scratch: Topology on ℝ, integration, and the MVT
ScratchTopology on ℝ, integration, and the MVTTaylor's Theorem (anthology)
Formal proof: Taylor series of sin, cos, and exp
Formal proofTaylor series of sin, cos, and expTaylor's Theorem (anthology)
Problem solution: Expanding a polynomial about a = 4
Problem solutionExpanding a polynomial about a = 4Taylor's Theorem (anthology)
Mind-map: Mapping the change-of-basis web
Mind-mapMapping the change-of-basis webPillars — change of basis
Problem solution: A (nearly) impossible integral
Problem solutionA (nearly) impossible integralVălean — (Almost) Impossible Integrals
Formal proof: Every subgroup of a cyclic group is cyclic
Formal proofEvery subgroup of a cyclic group is cyclicAbstract Algebra (Judson)
Scratch: An object that almost satisfies the theorem
ScratchAn object that almost satisfies the theoremCounterexamples in Analysis

Seeded with placeholders for now — the real scans are going up page by page, many tied to the reading series (a problem's handwritten solution beside the typed context).