Advanced calculus with applications in statistics

Advanced calculus has had a fundamental and seminal role in the development of the basic theory underlying statistical methodology. The last thirty years have seen a remarkable growth in the field of statistics, further underscoring the interconnection between the disciplines and the need for students and professionals to acquire a facility in the fundamentals of advanced calculus. Filling the information gulf often faced by graduate students in statistics with an experience of only introductory calculus, this applications-oriented text is a clear, well-paced, and highly rigorous introduction to the themes and topics central to advanced calculus. The book's careful theoretical explanation makes it also suitable for students in mathematics, especially those who may be interested in a minor in statistics. In addition, the book can serve as a reference for a wide spectrum of advanced calculus topics for practicing statisticians. If used as a text, the entire book would be suitable for a two-semester or three-quarter course. Each chapter in the book features a complete section describing specific applications in statistics of the material given. Numerous exercises, all classified by discipline (mathematics and statistics), are provided, in addition to an annotated bibliography for the benefit of the reader. The book's sequence of topics builds gradually from the fundamentals of advanced calculus, progressing finally to more specialized subject areas. The material in Chapters 1-6 cover the core of advanced calculus including continuity, differentiation, integration, and the theory of infinite sequences and series. Multidimensional calculus is discussed in Chapter 7. Chapters 8 and 9, more specialized than 1-7, cover certain aspects of optimization in statistics and approximation of continuous functions. This is the only advanced calculus book that emphasizes applications in statistics. Students and professionals will find Advanced Calculus with Applications in Statistics an authoritative, yet practical look at the important role of mathematics in the development of the theory of statistics.