Wearing Gauss’s Jersey focuses on "Gauss problems," problems that can be very tedious and time consuming when tackled in a traditional, straightforward way but if approached in a more insightful fashion, can yield the solution much more easily and elegantly. The book shows how mathematical problem solving can be fun and how students can improve their mathematical insight, regardless of their initial level of knowledge. Illustrating the underlying unity in mathematics, it also explores how problems seemingly unrelated on the surface are actually extremely connected to each other.
Each chapter starts with easy problems that demonstrate the simple insight/mathematical tools necessary to solve problems more efficiently. The text then uses these simple tools to solve more difficult problems, such as Olympiad-level problems, and develop more complex mathematical tools. The longest chapters investigate combinatorics as well as sequences and series, which are some of the most well-known Gauss problems. These topics would be very tedious to handle in a straightforward way but the book shows that there are easier ways of tackling them.
Table of Contents
Arithmetic Sequences and Series. Geometric Sequences and Series. Counting and Combinatorics. Polynomials and Their Roots. Rates and Ratios. Changing Perspectives (Algebra and Geometry, and Other Perspective Changes). Complex Numbers. Number Theory and Modular Arithmetic. Miscellaneous and Contest Problems. Calculus. Epilogue. Conclusions.