Henry Carter Hull

A first-class mathematician's lucid, unhurried account of the science of numbers from arithmetic through the calculus. -- James R. Newman, The World of Mathematics. This highly accessible introduction to mathematics is geared toward readers seeking a firm grasp of the essentials of mathematical theory and practice. The treatment also offers a concise outline of mathematical history and a clearer notion of why mathematicians do what they do. Author...

Do not worry about your difficulties in mathematics, I can assure you that mine are still greater.-Albert Einstein Everyone has heard students' most common complaint in math class: "Why do I need to learn this? I'll never use it when I'm older!" Some of us have even been that complainer. Many people's difficulties with learning math in school follow them into adulthood, by which time they often assume that it's too late to do anything about it. But...

Mathematical induction -- along with its equivalents, complete induction and well-ordering, and its immediate consequence, the pigeonhole principle -- constitute essential proof techniques. Every mathematician is familiar with mathematical induction, and every student of mathematics requires a grasp of its concepts. This volume provides an introduction and a thorough exposure to these proof techniques. Geared toward students of mathematics at all...

Topology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students familiar with multivariable calculus. Rigorous but not abstract, the treatment emphasizes the geometric nature of the...

Highly recommended. - The Times (London) Educational Supplement "It will delight both young and old." - The American Mathematical Monthly "A truly lively and unusual, not to mention precise, textbook." - New York Public Library "The calculus book looks great. There has never been anything like it." - Martin Gardner, longtime author of the "Mathematical Games" column for Scientific American Filled with humorous illustrations as well as lively and absorbing...

Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous...

This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition of mathematic fundamentals. Rather than a system of theorems with completely developed proofs or examples of applications, readers will encounter a coherent presentation of mathematical ideas that begins with the natural numbers and basic laws of arithmetic...

Almost all adults suffer a little math anxiety, especially when it comes to everyday problems they think they should be able to figure out in their heads. Want to figure the six percent sales tax on a $34.50 item? A 15 percent tip for a $13.75 check? The carpeting needed for a 121/2-by-17-foot room? No one learns how to do these mental calculations in school, where the emphasis is on paper-and-pencil techniques. With no math background required and...

Suitable for advanced undergraduates and graduate students in mathematics, this introduction to topological groups presumes familiarity with the elementary concepts of set theory, elements of functional analysis, functions of real and complex variables, and the theory of functions of several variables. Chapters I to V deal with the algebraico-topological aspect of the subject, and Chapters VI to IX emphasize its analytical aspect. After an introductory...

Geared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective. The text focuses on classical umbral calculus, which dates back to the 1850s and continues to receive the attention of modern mathematicians. Subjects...