Many talented young problem solvers can find their first math circle visits challenging because they simply haven’t been exposed to some of the concepts and tools of discrete mathematics. In the US many of these concepts are reserved for “university level” mathematics but it has been proven that these ideas can be well understood and applied by very young students. The students who add these concepts to their toolbox will have much more success in math circles and math contests as well as a great advantage going on to university.

To help fill this void, the good people at IMACS, creators of the popular eIMACS courses, have launched a series of short and focused online courses under the title of **Elements of Mathematics: Foundations**. The first course in this series, **Operational Systems**, focuses on the very important concept of modular arithmetic and is free for students who register before January 1, 2013.

This course covers modular arithmetic using secret codes and online games. Learn about operational systems and their properties (commutativity, associativity, neutral elements, invertibility) by building interactive machines and evaluating non-numeric operations. Get a solid introduction to the concepts of least common multiple and greatest common divisor, as well as to the geometric notions of midpoint and reflection.

IMACS has provided the following description of the origins of this series and curriculum.

The Elements of Mathematics: Foundations online courses are based on *Book 0: Intuitive Background* of the *Elements of Mathematics (EM)* series of textbooks. *EM* is the result of a collaborative effort of an international team of eminent mathematicians and mathematics educators.

Through more than a decade of research and development, these scholars created an original curriculum that is fun and engaging for talented middle and high school students while maintaining a level of mathematical rigor found only at the university level. Aimed solely at talented students and unconstrained by the need to follow a standards-based curriculum, *EM* focused on providing precocious students with a deep understanding of mathematical structure.

Along the way, *Book 0: Intuitive Background* covered all of middle and high school mathematics except calculus before the end of middle school. After completing the *Intuitive Background* series, students would begin the *EM formal logic* series which covered a significant portion of a college undergraduate mathematics degree by the end of high school. The formal logic segment of the *EM* curriculum is already available online at www.eimacs.com as part of the *Advanced Mathematical Logic* track.

Don’t allow yourself to forget over the holidays, sign up for the first course in the series today.