Bøger i Mathematical Association of America Textbooks serien

A classic advanced textbook, containing a cross-section of ideas, techniques and results that give the reader an unparalleled introductory overview of the subject. The author gives an integrated presentation of overall theory and its applications in, for example, the study of groups of matrices, and group representations.

Written for advanced undergraduate and graduate students in mathematics, this introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author tells the story of the mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work of Jordan, Borel, and Lebesgue.

This book is written as both a stepping stone to higher calculus and analysis courses, and as a foundation for deeper reasoning in applied mathematics. As well as a rigorous account of sequences, series, functions and sets, the reader will also find fascinating historical material and over 600 exercises.

The essential tools for studying ordinary differential equations are given a modern treatment in this book, beginning with analytical methods, before progressing to graphical and numerical methods, bifurcation theory, higher-dimensional theory, and dynamical systems. Ideal for undergraduates in engineering and the applied sciences, particularly biology.

Combinatorics is the mathematics of counting. This text presents the topics covered in undergraduate courses in combinatorics and advanced discrete mathematics, as well as in some introductory graduate courses. Uniquely, it features over 350 reading questions that provide checkpoints for learning and prepare the reader for the end-of-section exercises.

This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers.

This is a concise introduction to Fourier series covering history, major themes, theorems, examples, and applications. It can be used for self study, and to supplement, enhance, and embellish undergraduate courses on mathematical analysis. Exercises of varying levels of difficulty are scattered throughout the book to test understanding.

Essentials of Mathematics is designed as both a textbook and outside reading for college students who want to prepare themselves for mathematics courses beyond the first-year level and take courses in which proofs play a major role. There are also narratives on the nature of mathematics and the mathematics profession.

The language of mathematics has proven over centuries of application to be an indispensable tool for the expression and analysis of real problems. Here Kalman explains for an audience of non-mathematicians the relevance of mathematical models to phenomena ranging from population growth and economics to medicine and the physical sciences.

This book demonstrates how complex numbers and geometry can be blended together to give easy proofs of many theorems in plane geometry.

A fascinating collection of geometric proofs and properties.