# Concept derivation guides 299 concept teaching guides, separate from the 36,000 individual question derivations. [Search all questions & derivations →](/en/explore/) [← Previous](/en/derivations/?page=12#results)[1](/en/derivations/?page=1#results) … [12](/en/derivations/?page=12#results) 13 299 results · Page 13 of 13 Concept guide ## [CLT qualification and a finite lattice audit](/en/derivations/derivation-mko-central-limit-theorem-finite-variance-iid-01/?from=%2Fen%2Fderivations%2F%3Fpage%3D13) Separate finite-n moments from the named CLT application. Central limit theorem for finite-variance IID sequences derivation-mko-central-limit-theorem-finite-variance-iid-01 Concept guide ## [Finite-valued IID strong-law qualification and fixed-n boundaries](/en/derivations/derivation-mko-strong-law-large-numbers-finite-valued-iid-01/?from=%2Fen%2Fderivations%2F%3Fpage%3D13) Match the named SLLN hypotheses while separating prefix audits from a.s. proof. Strong law of large numbers for finite-valued IID sequences derivation-mko-strong-law-large-numbers-finite-valued-iid-01 Concept guide ## [Pointwise coverage, averaging and selection](/en/derivations/derivation-mko-finite-confidence-interval-coverage-01/?from=%2Fen%2Fderivations%2F%3Fpage%3D13) Compute pointwise and worst-case coverage of a fixed interval procedure. Confidence-interval coverage in a finite model derivation-mko-finite-confidence-interval-coverage-01 Concept guide ## [Complete inverse pairing and both Wilson directions](/en/derivations/derivation-mko-wilson-theorem-01/?from=%2Fen%2Fderivations%2F%3Fpage%3D13) For n>1, (n-1)!=-1 mod n exactly when n is prime; the full modulo-7 inverse table checks 6!=6 mod 7. Wilson theorem derivation-mko-wilson-theorem-01 Concept guide ## [Extracting 3-adic factors of signed integers](/en/derivations/derivation-mko-p-adic-valuation-integers-01/?from=%2Fen%2Fderivations%2F%3Fpage%3D13) v3(-108)=3,v3(18)=2,v3(-1944)=5,v3(-90)=2; zero uses infinity. p-adic valuation of integers derivation-mko-p-adic-valuation-integers-01 Concept guide ## [Star closure with epsilon and a complete length slice](/en/derivations/derivation-mko-regular-expression-01/?from=%2Fen%2Fderivations%2F%3Fpage%3D13) Give typed AST semantics, complete bounded enumeration and membership obligations. Regular expression derivation-mko-regular-expression-01 Concept guide ## [DFA-loop quantifiers and the a^n b^n contradiction](/en/derivations/derivation-mko-pumping-lemma-regular-languages-01/?from=%2Fen%2Fderivations%2F%3Fpage%3D13) Expose quantifier order, the all-pump-count loop argument and every legal split. Pumping lemma for regular languages derivation-mko-pumping-lemma-regular-languages-01 Concept guide ## [Qualified Newton updates and a finite trace](/en/derivations/derivation-mko-newton-method-01/?from=%2Fen%2Fderivations%2F%3Fpage%3D13) Take two exact Newton steps for x^2-2 from one, and audit root-first stopping and a cycle boundary. Newton method for root finding derivation-mko-newton-method-01 Concept guide ## [Nonuniform trapezoids and signed error](/en/derivations/derivation-mko-trapezoidal-quadrature-01/?from=%2Fen%2Fderivations%2F%3Fpage%3D13) For f(x)=x^2 and nodes (0,1/2,2), compute T, I-T and absolute error. Composite trapezoidal quadrature derivation-mko-trapezoidal-quadrature-01 Concept guide ## [Safe descent steps for a positive diagonal quadratic](/en/derivations/derivation-mko-gradient-descent-01/?from=%2Fen%2Fderivations%2F%3Fpage%3D13) Take two steps with alpha=1/4 for a specified quadratic and prove the per-step descent condition. Gradient descent derivation-mko-gradient-descent-01 Concept guide ## [Regular multipliers and a complete squared-distance solution](/en/derivations/derivation-mko-lagrange-multiplier-condition-01/?from=%2Fen%2Fderivations%2F%3Fpage%3D13) Minimize the squared distance to (1,2) subject to x_1+x_2=0; find the point and multiplier and independently prove the minimum. Necessary Lagrange multiplier condition for equality constraints derivation-mko-lagrange-multiplier-condition-01 [← Previous](/en/derivations/?page=12#results)[1](/en/derivations/?page=1#results) … [12](/en/derivations/?page=12#results) 13 299 results · Page 13 of 13