user21820
Foundations
 Axioms & Definitions
 Contradiction & Game semantics & True induction
 Circularity in mathematics & 'Paradoxes' resolved
 Building blocks & Incompleteness theorems
 Logic texts
Natural deduction
Rigour with intuition
 Naturals
 Reals & Real exponentiation & $\cos,\sin$ & $\exp(iπ)+1=0$
 General differentiation & applications
 Matrix multiplication
Beautiful stuff
Puzzles:
Finite differences:
Asymptotic expansions:
 For ktimesdifferentiable functions
 Central difference formulae
 NewtonRaphson with convergence criteria
 Systematic computation of limits
Smoothing:
 To prove AMGM & Jensen's inequality
 Maximum area of polygon given perimeter
 Maximum expression value using brackets
Multidimensional analysis:
 Multidimensional IVT, which proves:
 Poincaré–Miranda theorem
 Ham sandwich theorem [consider all hyperplanes that bisect one piece]
Inversion:
Common oversights
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