In 1801 in *Disquisitiones Arithmeticae* the German mathematician Carl Friedrich Gauss introduces the modern concepts of congruence and arithmetic of residue classes, which are of fundamental importance and revolutionize many of the problems we find in number theory. In this class we establish the main properties and applications of congruences. Fermat's Little Theorem, Euler's Theorem, the Chinese Remainder Theorem, and Gauss's method for finding the date of Easter are some of the highlights of your experience in this class.

The American Mathematical Competition 8 (AMC 8) and Mathcounts are some of the most prestigious middle school math competitions in the world. Designed to promote the development of problem-solving skills, increase student's interest in mathematics, and create a positive attitude towards analytical thinking, these competitions attract hundreds of thousands of students from around the world. Many of the participants go on to become famous mathematicians, scientists, engineers, and pioneers in the world of science and technology. If you're looking to be among this elite group of the future, this is the place to start! This class will expose you to a variety of topics in the middle school curriculum, from a fun and engaging problem-solving perspective.

Calculus is the branch of mathematics that studies limits, continuity, derivatives, integrals, and infinite series. Isaac Newton and Gottfried Leibniz independently developed calculus in the late 17th century. Since its invention, calculus has been critical in the development of the world as we know it today. Calculus is used in almost every branch of the physical sciences, actuarial sciences, computer science, engineering, medicine, economics, etc. This class offers an in-detail study of calculus, and is ideal for students preparing for the Advanced Placement (AP) exams, which are used in the admission process by most colleges and universities throughout the world.

Developed originally by Greek astronomers, trigonometry is one of the oldest branches of mathematics. It studies the relationships between sides and angles in a triangle, and has evolved from its use in surveying, navigation, and architecture to present applications in the rise and fall of food supplies, brain wave patterns, oceanography, digital music and imaging, CAT and MRI scanning, and many other phenomena, to name a few. In-detail study of trigonometry improves critical thinking and promotes the student's problem-solving abilities. I invite you to sign-up for the best trigonometry class in the world, complete with lots of applications to geometry and algebra.

The world of mathematics extends well-beyond the regular high-school curriculum. If you're searching to see what else is out there, this class offers a glimpse into several fascinating topics in mathematics, from algebra and combinatorics to geometry and trigonometry.

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