This course is for experienced students who can solve at least a few problems in the AIME contest and qualify or almost qualify for USA(J)MO. In this course, the students learn more in-depth math concepts and problem-solving strategies that involve more rigorous mathematical writing and a broad range of topics. Students are trained to comfortably solve the AIME problems to qualify for USA(J)MO, also to comfortably write mathematical proofs for problems at the USA(J)MO level, aiming to win USA(J)MO and get into the prestigious MOSP. The topics include everything covered in MC-III with more depth, and additional topics such as quadratic residue, Diophantine equations, recurrence, proving inequalities, mathematical induction, functional equations, generating functions, inversion, projective geometry, and rigorous proof-writing practices. Through the effective guidance and direction by our experienced teachers, students develop strong problem solving skills that make them perform well in AIME and USA(J)MO.