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
 Alekseev, V.B., Abel's Theorem
in Problems and Solutions, Moscow State University, Moscow (1976).
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
. He kindly provides information on abstract algebra as well as hints on selected exercises and a very well-organized bibliography.