Mathematics: ABEGG'S RULE, ABEL'S THEOREM
, ARCHIMEDES' PROBLEM, BERNOULLI'S THEOREM, DE MOIVRE'S THEOREM, DE MORGAN'S THEOREM, DESARGUES' THEOREM, DESCARTES' RULE OF SIGNS, EUCLID'S ALGORITHM, EULER'S EQUATION/FORMULA, FERMAT'S PRINCIPLE, FOURIER'S THEOREM, GAUSS'S THEOREM, GOLDBACH'S CONJECTURE, HUDDE'S RULES, LAPLACE'S EQUATIONS, NEWTON'S METHOD/PARALLELOGRAM, PASCAL'S LAW/TRIANGLE, RIEMANN'S HYPOTHESIS
388] has claimed to be the first of having the converse of Abel's theorem
appeared in print.
It covers classical proofs, such as Abel's theorem
, and topics not included in standard textbooks like semi-direct products, polycyclic groups, Rubik's Cube-like puzzles, and Wedderburn's theorem, as well as problem sequences on depth.
We proceed to prove an analogue of Abel's theorem
for boundedly convergent double series.
He continues with Abel's theorem
, the gamma function, universal covering spaces, Cauchy's theorem for non-holomorphic functions and harmonic conjugates.
He then considers the work of Lagrange, Galois and Kronecker in concert, the process of computing Galois groups, solvable permutation groups, and the lemniscate, including the lemniscatic function, complex multiplication and Abel's theorem