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The Real Numbers and Real Analysis
This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.
Proofs and Fundamentals
The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.
A First Course in Geometric Topology and Differential Geometry
The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.
Experiments in Topology
Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.
Thinking Recursively
The process of solving large problems by breaking them down intosmaller, more simple problems that have identical forms. ThinkingRecursively: A small text to solve large problems. Concentrating onthe practical value of recursion. this text, the first of its kind,is essential to computer science students' education. In thistext, students will learn the concept and programming applicationsof recursive thinking. This will ultimately prepare students foradvanced topics in computer science such as compiler construction,formal language theory, and the mathematical foundations ofcomputer science. Key Features: * Concentration on the practical value of recursion. * Eleven chapters emphasizing recursion as a unifiedconcept. * Extensive discussion of the mathematical concepts which helpthe students to develop an appropriate conceptual model. * Large number of imaginative examples with solutions. * Large sets of exercises.
The Bear's Song
Papa Bear wakes up to find his son missing, and his search leads him to an opera house and a command performance.
Coins, Trade, and the State
Framed by the decline of the Heian aristocracy in the late 1100s and the rise of the Tokugawa shogunate in the early 1600s, Japan’s medieval era was a chaotic period of diffuse political power and frequent military strife. This instability prevented central authorities from regulating trade, issuing currency, enforcing contracts, or guaranteeing property rights. But the lack of a strong central government did not inhibit economic growth. Rather, it created opportunities for a wider spectrum of society to participate in trade, markets, and monetization. Peripheral elites—including merchants, warriors, rural estate managers, and religious leaders—devised new ways to circumvent older form...
Combinatorics and Graph Theory
These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.
The Wonderful Fluffy Little Squishy
One morning, Eddie wakes up and hears her little sister say these words: birthday--mama--present--fluffy--little--squishy. Worried that her sister will find one before she does, Eddie runs off on a hunt. But where should she begin? At the neighborhood shops, maybe? Eddie's search, magical and entirely her own, leads her just where she needs to go.
