Bøger i AMS/MAA Textbooks serien

Provides a gentle introduction to advanced mathematics for students who previously have not had extensive exposure to proofs. The book is intended to ease the student's transition from algorithmic mathematics to the world of mathematics that is built around proofs and concepts.

Takes an Inquiry-Based Learning approach to the subject, leading students to discover for themselves the main themes and techniques. Concepts are introduced conversationally through extensive examples and student investigation before being formally defined.

Provides an introduction to how investments grow over time. This is done in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true. Among the modern financial topics introduced are: arbitrage, options, futures, and swaps.

Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind ... negative numbers?... the metric system?... quadratic equations?... sine and cosine?... logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style.

Uses linear algebra as a vehicle to introduce students to the inner workings of mathematics. The structures and techniques of mathematics in turn provide an accessible framework to illustrate the powerful and beautiful results about vector spaces and linear transformations.

A thoroughly modern textbook for a differential equations course. The examples and exercises emphasize modelling not only in engineering and physics but also in applied mathematics and biology. There is an early introduction to numerical methods and, throughout, a strong emphasis on the qualitative viewpoint of dynamical systems.

Using this text, students work regularly with real data in moderately complex everyday contexts, using mathematics as a tool and common sense as a guide. The focus is on problems suggested by the news of the day and topics that matter to students, like inflation, credit card debt, and loans.

Presents the insights of abstract algebra in a welcoming and accessible way. The book succeeds in combining the advantages of rings-first and groups-first approaches while avoiding the disadvantages. The exposition is clear and conversational throughout. The book has numerous exercises in each section.

Provides a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat.

Takes a fresh and innovative look at the teaching and learning of calculus. This text places its emphasis on the approximating processes and thus illuminates the motivating ideas and makes clearer the scientific usefulness, indeed centrality, of the subject while paying careful attention to the theoretical foundations.

A manual to accompany the third edition of Mathematical Interest Theory. It contains solutions to all the odd-numbered problems in that text. Individuals preparing for the Society of Actuaries examination in Financial Mathematics should find that the detailed solutions contained are an invaluable aid in their study.

A textbook for a second course or capstone course in analysis for advanced undergraduate or beginning graduate students. By assuming the existence and properties of the Lebesgue integral, this book makes it possible for students who have previously taken only one course in real analysis to learn Fourier analysis in terms of Hilbert spaces.

Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification.

Presents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The material is presented through a series of approximately 360 strategically placed problems with connecting text. This is supplemented by 280 additional problems intended to be used as homework assignments.

An IBL textbook designed for a one-semester course on proofs (the "bridge course") that also introduces TeX as a tool students can use to communicate their work. Written in an easy-going style, the exposition is just enough to support the activities, and it is clear, concise, and effective.

Provides a clear and concise presentation of differential equations for undergraduates and beginning graduate students. The author makes a concerted effort to use plain language and to always start from a simple example or application.

A textbook on modeling that happens to focus on financial instruments for the management of economic risk. The book combines a study of mathematical modeling with exposure to the tools of probability theory, difference and differential equations, numerical simulation, data analysis, and mathematical analysis.