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 k-times-differentiable functions
- Central difference formulae
- Newton-Raphson with convergence criteria
- Systematic computation of limits
Smoothing:
- To prove AM-GM & Jensen's inequality
- Maximum area of polygon given perimeter
- Maximum expression value using brackets
Multi-dimensional analysis:
- Multi-dimensional IVT, which proves:
- Poincaré–Miranda theorem
- Ham sandwich theorem [consider all hyperplanes that bisect one piece]
Inversion:
Common oversights
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Member for 4 years, 1 month
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Last seen May 31 '20 at 15:32
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Top network posts
- 72 Are proofs by contradiction really logical?
- 68 How many atoms does it take for us to perceive colour?
- 67 How to represent "not an empty set"?
- 65 Is it impossible to perfectly fit a polynomial to a trigonometric function on a closed interval?
- 64 Do you say "good game" after a game in which your opponent played poorly?
- 56 Physical meaning of the Lebesgue measure
- 55 Calculus, water poured into a cone: Why is the derivative non-linear?
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May 17 '19
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Aug 13 '17
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Aug 13 '17