S. Fiorini and R. J. Wilson, Edge Colourings of Graphs (Research Notes in Mathematics 16, Pitman, 1977), 154 pp., £6–50.
Ian Muir Anderson · Proceedings of the Edinburgh Mathematical Society · 1979
This book is intended as a text for a course on complex analysis at the advanced undergraduate level.It is in two parts.The first part contains all the material which is covered in a first course on complex analysis: namely, power series, Cauchy's theorem and consequences, calculus of residues, conformal mapping and harmonic functions.Cauchy's theorem is proved by Artin's method.However the text contains a section giving the more recent proof due to Dixon.A novel feature of the book is a proof of the Jordan canonical decomposition of a matrix by contour integration.The second part contains more advanced topics: applications of the maximum modulus theorem, Weierstrass's factorisation theorem, Mittag-Leffler's theorem, elliptic functions, the gamma function, analytic continuation, the Riemann mapping theorem and the little Picard theorem.The book is concisely and well written.The exercises are numerous and varied.I would strongly recommend this text to Honours students pursuing a course on complex analysis.