What do the integers have in common with the symmetries of a triangle? In the 19th century, mathematicians invented groups as ...
One of the first major steps down this road was taken in the late 18th and early 19th centuries. It involved a field called group theory, and it changed math — theoretical and applied — as we know it.
First Steps for Math Olympians considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone ...