Rigorous Elementary Mathematics: The Complete Series (Rigorous Elementary Mathematics, Second Edition)

The four pillars of mathematical contests and olympiads are: algebra, counting, number theory, and geometry. Rigorous Elementary Mathematics: The Complete Series, Second Edition builds the four subjects from the ground up. It features the full second edition of the series in a single collected volume with a new epilogue. Valuable passages include proofs of difficult multivariable inequalities, counting using Burnside’s lemma from group theory, a full proof of Zsigmondy's theorem via cyclotomic polynomials, and a complete proof that classifies all directrix-eccentricity-focal parameter triples for ellipses, parabolas, and hyperbolas. Throughout the book, three ideas are reinforced: writing the same object in multiple ways, breaking up equality using antisymmetry, and using equivalence relations. There are hundreds of substantive problems included for the reader’s practice, with complete solutions provided. This compiled second edition includes additional theorems and problems, refreshed diagrams, corrections, and a more integrated experience across the four subject areas. It is suggested that the book be read by those who have prior experience with mathematical proofs and problem-solving. Read more