CM601/602 – Math Contest Level 6 Classes (AIME Advanced)
- All class materials including recordings (viewing only) are available immediately after each class until 3 months after the last day of class in Canvas
- No TA Session. Written solutions and video solutions will be provided
2024 Spring (CM601B)
CM601B
Instructor: Osman Nal, Ph.D.
Wednesday 7 – 9PM CST
Dates: Feb 7 – May 1
No Class Date: March 13
Prereq: JMO Index 200+ (AIME 8+)
Fee: $979
2023 Fall (CM601A)
CM601A
Instructor: Osman Nal, Ph.D.
Wednesday 7 – 9PM CST
Dates: Sept 13 – Dec 6
No Class Date: Nov 22
Prereq: JMO Index 200+ (AIME 8+)
Fee: $979
Class Description: The CM601/602 course is a two-year course with classes spanning across four semesters. The main goal of CM 601 and CM 602 classes is to help students improve scoring on AIME. This class mainly covers advanced techniques to solve hard AIME questions.
What will be covered: All 4 subjects (Algebra, Geometry, Number Theory, and Combinatorics) will be covered in this two-year class. The difficulty level is from hard AIME (AIME problem 10-15).
Time Required: Students are expected to attend the weekly 2-hr lecture. Students are expected to spend around 3-4 hours on homework problems each week.
Prerequisite: Students who will enroll in CM601 classes are expected to have 200+ on USAJMO Index (AIME 8+) and/or have completed our CM600 course for both the fall and spring semesters. Students with an AIME score 9-10 may find the class material challenging.
Who should skip this course? Students who scored 13+ on AIME.
Note: After you add 601/602 to your cart, you will be on the waiting list until it is approved by our staff (usually within one business day). After it is approved, you will receive an invoice. If it is not approved or if we need any additional information, we will contact you via email or phone.
FAQ’s:
I have an AIME score of 10. Should I take CM601/602 or CM701/702?
The goals and the content covered in these two classes (CM601 vs CM701) are completely different. CM601/602 focus on computational math and will help students improve their AIME scores. CM701/702 are proof-based classes that will help students improve their performance on contests such as USA(J)MO (and it will indirectly help improve their AIME scores). For students who are not certain if they will qualify for USA(J)MO next year, we encourage them to improve their AIME score first and take CM601/602. For those who really want to improve both, they can take CM601/602 and CM701/702 simultaneously.
Can I take CM602 this year even though I did not take CM601 last year?
Yes, if your AIME score and USAJMO Index meet the requirements, you can take CM602 without taking CM601. CM601/602 is a 2-year course and we have structured it in a way that attending the first year is not the prerequisite for attending the second year, and vice versa.
The course material covered: The topics for this AIME advanced preparation course will be repeated every 2 years. They will be available in the following waves:
- Year 1: 601 A/ 601 B
- Year 2: 602 A/ 602 B
Additional course details and expected topics and material are listed below:
Year 1 Fall (12 weeks): 601A
Week 1-7 GEOMETRY
Week 1: Angles; Similarity of triangles;
Week 2: Pythagorean theorem, Length and area; Angle bisector theorem; Stewart theorem
Week 3: Cyclic quadrilaterals; Ptolemy theorem
Week 4: Law of Cosines; Law of Sines; applications of trigonometric identities
Week 5: Circles; Power of a point; Radical axes;
Week 6: Geometric transformations (reflection and rotation)
Week 7: Adv. topics I: Incenter-Excenter Lemma
Week 8-12 NUMBER THEORY
Week 8: Euclidean algorithm; Prime factorization; powers of primes (perfect squares and cubes)
Week 9: Order modulo a prime; Fermat’s Little theorem
Week 10: Euler’s theorem; Arithmetic functions
Week 11: Congruences; Chinese remainder theorem
Week 12: Chicken McNugget theorem; Bezout theorem
Year 1 Spring (12 weeks): 601B
Week 1-5 COMBINATORICS
Week 1:
Week 2: Combo II :: Probability; Bayes’ formula
Week 3: Combo III :: State Diagrams
Week 4: Combo IV :: Recursions
Week 5: Combo V :: Graphs; Cycles; Symmetry; Burnside Lemma
Week 6-12 ALGEBRA
Week 6: Algebra I :: Polynomials; Vieta formulas; Complex Numbers; Power Sums
Week 7: Algebra II :: Functions; piecewise; periodic; floor; absolute value; logarithms; trigonometric
Week 8: Algebra III :: Inequalities and optimization; Cauchy-Schwarz inequality; geometric optimization
Week 9: Algebra IV :: Sequences and Series
Week 10: Algebra V :: Algebraic Manipulations
Week 11: Potpourri (1 of 2)
Week 12: Potpourri (2 of 2)
Year 2 Fall (12 weeks): 602A
Week 1-7 GEOMETRY
Week 1: Ratio lemma; Ceva theorem; Menelaus theorem
Week 2: Homothety (dilation); Nine-Point Circle; Special triangles
Week 3: Coordinates (distance formula; etc.)
Week 4: Solid (3D) geometry (dihedral angle, volume, …)
Week 5: Geometric inequalities and optimization (Leibniz and Euler inequalities)
Week 6: Adv. topics II: Simson line; Spiral similarity
Week 7: Adv. topics III: Projective Geometry
Week 8-12 NUMBER THEORY
Week 8: Solving Diophantine equations
Week 9: Modular Arithmetic; Wilson’s theorem
Week 10: Quadratic Diphantine equations; Pell-type equations
Week 11: Legendre’s Function; lifting the exponent
Week 12: Quadratic residues; Legendre Symbol
Year 2 Spring (12 weeks): 602B
Week 1-5 COMBINATORICS
Week 1: CCC; PIE; Bijections; Distribution
Week 2: Probability; Bayes’ formula; Conditional probability
Week 3: State Diagrams and Expected Value
Week 4: Fibonacci Numbers; Recursion
Week 5: Graphs; Cycles; Symmetry; Burnside Lemma
Week 6-9 ALGEBRA
Week 6: Algebraic Manipulations; Polynomials; Vieta formulas; Power Sums
Week 7: Functions; piecewise, periodic functions; floor and absolute value; logarithms
Week 8: Inequalities and optimization; Cauchy-Schwarz inequality; geometric optimization
Week 9: Sequences and Series
Week 10-12 REVIEW
Week 10: Review 1
Week 11: Review 2
Week 12: Review 3