Bøker i Carus Mathematical Monographs-serien

Combinatorics is a vibrant and active area of pure mathematical research with many applications. This volume shows that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas.

The finite field distance problem poses the analogous question in a vector space over a finite field. The problem is relatively new but remains tantalizingly out of reach. This book provides an accessible, exciting summary of known results.

Allows Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the construction of regular $n$-gons and the properties of roots of unity, and then on to the solvability of polynomial equations by radicals and beyond.

Treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space.

One of the principles of mathematical growth is that the relabelling process often suggests a new generation of problems. Means become ends; the medium rapidly becomes the message. This book is not wholly self-contained. Readers will find that they should be familiar with the elementary portions of linear algebra and of the theory of functions of a complex variable.

Illustrates how simple observations can be made the starting point of rich and fruitful theories and how the same theme recurs in seemingly unrelated disciplines. Mark Kac conveyed his infectious enthusiasm for mathematics and its applications in his lectures, papers, and books. Two of his papers won Chauvenet awards for expository excellence.

Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry.