Designed for one-semester courses at the senior undergraduate level, this book is written for mathematics students and teachers, as well as others needing to learn mathematical analysis for engineering, physics, biology or finance. Nominal divisions between pure and applied mathematics have been merged to provide easier access. Applications are included from differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.

Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another...

Makes the intrinsically advanced theory of wavelets accessible to senior undergraduate students with a mathematical background.

A leading authority on orthogonal polynomials details their relationships with Painleve equations with clear proofs, examples, and exercises.