Essays about Modern Algebra: From Classical Topics to New Problems

This book about modern algebra contains gapless readable proofs, exercises with solutions and algorithms. The geometric construction of the regular 17, 257 and even the 65 537-gon are given in complete details, including programming codes. The theory of geometrical constructions and its connection to Galois theory is treated in detail. Later parts deal with totally positive real numbers as sums of squares, cyclotomic polynomials, Chebychev polynomials, Gaussian periods, Galois theory, and m...