Tweet | ## Summing It Up: |

We use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem. Appropriate for numbers novices as well as college math majors,
"Offers a clear and beautiful progression from addition to modern number theory." "The authors did a remarkable job in making some aspects of modern number theory very accessible to readers with only a minimal knowledge of mathematics, say a student who had a first calculus course. However, also mathematicians who do not have number theory as their main focus will enjoy this book." "Ash and Gross do a masterful job of leading students from finite sums to modular forms and to the forefront of modern number theory. . . . This is an excellent piece of mathematical writing." "[A]n accessible and fun introduction to modular forms. . . . [ " "Readers of the books [
- Elliptic Tales: Curves, Counting, and Number Theory. [Hardcover and Paperback]
- Fearless Symmetry: Exposing the Hidden Patterns of Numbers. [Paperback]
- Elliptic Tales: Curves, Counting, and Number Theory. [Hardcover and Paperback]
- Fearless Symmetry: Exposing the Hidden Patterns of Numbers. [Paperback]
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