Bøger i Dolciani Mathematical Expositions serien

Represents the fruits of 15 years of work in geometry by prize-winning authors Tom Apostol and Mamikon Mnatsakanian. Using new and intuitively rich methods, they give beautifully illustrated proofs of results, the majority of which are new, and frequently develop extensions of familiar theorems.

Describes techniques for solving problems in maxima and minima other than the methods of calculus.

A concise guide to support an undergraduate real analysis course.

A concise but accessible guide to functional analysis that begins with the basics before moving on to more advanced topics.

An accessible introduction to plane algebraic curves that also serves as a natural entry point to algebraic geometry.

A collection of 90 short elementary gems from algebra, geometry, combinatorics, and Number Theory.

An exploration of the mathematics of twenty geometric diagrams that play a crucial role in visualizing mathematical proofs.

The derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there is a variety of integrals, developed over the years for a variety of purposes, and this book describes them. No other single source treats all of the integrals of Cauchy, Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Steiltjes, Henstock-Kurzweil, Weiner, and Feynman.

A collection of over 250 multiple-choice problems to challenge and delight everyone from school students to professional mathematicians.

A beautifully illustrated collection of striking and original results in geometry. Recommended for students and teachers of geometry and calculus.

Offers an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. With its exceptionally clear prose, hundreds of exercises, and historical motivation, this is a textbook for a second undergraduate course in number theory.

Explores recurrent phenomena, including astronimcal transits and conjuctions, lifecycles of cicadas, and eclipses, by way of continued fraction expansions. The deeper purpose is to find patterns, solve puzzles, and discover some appealing number theory.

Introduces the richness and variety of inequalities in mathematics using illustration and visualisation.

A guide to the hidden byways of algebra, calculus and geometry, for the seasoned mathematical traveller.