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Suitable for a graduate course in commutative algebra, this title focuses on the algebraic underpinnings of algebraic geometry and of number theory. It also features chapters that include some algebraic theory of elliptic curves (featuring the Mordell-Weil theorem) and valuation theory, including local fields.

Presents a comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. This title provides basic examples of this kind of theory by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices.

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As the open-source and free competitor to expensive software like Maple™ and MATLAB®, Sage offers anyone with access to a web browser the ability to use cutting-edge mathematical software and display his or her results for others. This book is an introduction to Sage for undergraduate students toward the end of Calculus II or higher-level course work. The audience of the book is not only math majors, but also physics, engineering, finance, sta...

Understanding and working with the models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Covering the topic of financial modelling and optimization, this book helps readers obtain a self-contained introduction to the underlying mathematics. It is suitable as a graduate textbook.