Master Olympiad Mathematics: USAMO &
USAJMO Preparation

Master Olympiad Mathematics: USAMO & USAJMO Preparation

The pinnacle of high school mathematics competitions

The pinnacle of high school mathematics competitions

Qualifying to the USA Mathematical Olympiad (USAMO) and USA Junior Mathematical Olympiad (USAJMO) represent the highest level of mathematical achievement for high school students. These prestigious competitions identify the nation’s most promising mathematical minds and serve as the gateway to the International Mathematical Olympiad (IMO) Team USA selection. AwesomeMath prepares exceptional students to excel at this elite level through rigorous, proof-based training.

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The USA(J)MO Challenge

Proof-Based Mathematical Excellence

Unlike competitions involving many computations, the USA(J)MO demands rigorous proof-based excellence. Each exam spans two days with 4.5 hours per session, featuring three problems daily that require complete mathematical justification and sophisticated reasoning.

Selective Qualification Process

The USAMO targets 11th-12th graders and exceptional performers from lower grades, while the USAJMO serves primarily 10th graders and younger students demonstrating advanced mathematical maturity. Selection depends on your USAMO Index (AMC 12 score + 10×AIME score) or USAJMO Index (AMC 10 score + 10×AIME score), with only 250-300 students qualifying for USAMO and 230-270 for USAJMO annually.

Deep Mathematical Thinking

Problems span algebra, combinatorics, geometry, and number theory – each requiring deep insight, creative problem-solving, and mathematical maturity that extends far beyond numerical or algorithmic skills. Success in the USA(J)MO preparation demands a fundamentally different approach to mathematics.

What Makes Olympiad Math Different

Mathematical Olympiad preparation requires a major shift from computation to proof. Success demands rigorous, elegant mathematical arguments that stand up to expert scrutiny.

The multi-day format also tests intellectual endurance and resilience. Each problem may require hours of focused thinking, multiple approaches, and strategic pivoting when initial strategies prove insufficient. Graders evaluate not just answers but the clarity, completeness, and often elegance of your mathematical reasoning – each problem is scored 0-7 points based on proof quality and depth.

This is proof-based mathematics at its finest, where creativity meets rigor and intuition pairs with formal justification.

Fall 2025 Semester

Algebra

Complex Numbers, Trigonometry, and Roots of Unity

Combinatorics

Extreme Principle and Advanced Graph Theory

Geometry

Mass points, Barycentric Coordinates I and II

Number Theory

Quadratic Diophantine Equations: I and II

Spring 2026 Semester

Algebra

Graphs of Functions, Transformations of Functions, Quadratic/Discriminants

Combinatorics

PIE (Probability), Basic Probability-Geometric, Conditional Probability

Geometry

Angle Chasing, Similar Triangles, Areas-ratios

Number Theory

Digit Problems, Floor/Fractional Part, Arithmetic Functions

Course Structure and Commitment

Our 90-minute weekly sessions immerse you in Olympiad-level problem-solving with expert instructors who understand the demands of elite mathematical competition. Expect 4+ hours of challenging homework weekly – this time investment could separate qualifiers from medalists.

Instructors provide personalized feedback on proof-writing and problem-solving approaches, helping you develop the mathematical skills essential for USAMO preparation. However, olympiad success requires substantial self-directed study, persistence through difficult problems, and independent mathematical exploration. We provide the roadmap; your dedication drives the journey.

Level 3 Summer Program Course

Perfect for students who can consistently score well on the AIME and are seriously pursuing USA(J)MO prep. Our intensive summer program courses provide focused, proof-oriented training that accelerates your olympiad development.

Core Courses:

Algebra 3.5

This is an Olympiad-level algebra course and a proof based course. The first part of the course focuses on the abstract algebraic structure of polynomials, such as root locations, polynomial divisibility, and irreducibility. This part also introduces the basic concept of ring theory. The second part of the course focuses on studying inequalities such as AM-GM-HM, Cauchy-Schwarz, Power-mean, Muirhead’s, Schur’s, and Jensen’s inequalities and inequalities related to symmetric polynomials. It is also focused on techniques in inequalities such as smoothing, fudging, and ordering. The last part of the course focuses on the fundamental technique of solving functional equations. It covers all levels of USA(J)MO and any national-Olympiad-level contest, including TST and IMO. A student with a strong algebra background and an AIME score of 10 or above should consider this course. It is strongly advised that students have good experience in proofreading.

Combinatorial Arguments

This is an Olympiad Level and proof based course. The course introduces advanced methods of mathematical proofs, including the Pigeonhole Principle, the wellordering principle, colorings, assigning weights, bijections/mappings, recursion, counting in two ways, and combinatorial constructions. Topics may include graph theory and combinatorial geometry. A focal point of the course is combinatorial number theory. It covers all levels of USA(J)MO and any national-Olympiad-level contest, including TST and IMO. A student who is familiar with mathematics proofs and has an AIME score of 10 or above should consider this course.

Geometric Proofs

This is the Olympiad-level geometry course. The course focuses on classical topics such as concurrency, collinearity, cyclic quadrilaterals, special centers/points of triangles, and geometric constructions. The student will be introduced to the important transformations, translations, reflections, and spiral similarities, with a touch on projective and inversive geometry. It covers the hard end of AIME, all levels of USA(J)MO, and any national-Olympiad-level contest, including TST and IMO. A student with a strong background in geometry and an AIME score of 10 or above should consider this course.

Number Theory 3

This is an Advanced Olympiad-level number theory course. The course focuses on in-depth discussions of Diophantine equations, residue classes, quadratic reciprocity, central binomial technique, primitive roots and algebraic integers. The course also introduces the student to the notion and theory of finite fields and p-adic numbers. A student with a strong background in number theory and easily qualifies for USA(J)MO should consider this course.

Each course emphasizes proof-based mathematics essential for USA(J)MO success, with problems selected to mirror competition difficulty and style. Detailed topics, prerequisites, and schedules are available in our course catalog.

Level 3 Summer Program Courses

Perfect for students who can consistently score well on the AIME and are seriously pursuing USA(J)MO prep. Our intensive summer program courses provide focused, proof-oriented training that accelerates your olympiad development.

Core Courses:

Algebra 3.5

This is an Olympiad-level algebra course and a proof based course. The first part of the course focuses on the abstract algebraic structure of polynomials, such as root locations, polynomial divisibility, and irreducibility. This part also introduces the basic concept of ring theory. The second part of the course focuses on studying inequalities such as AM-GM-HM, Cauchy-Schwarz, Power-mean, Muirhead’s, Schur’s, and Jensen’s inequalities and inequalities related to symmetric polynomials. It is also focused on techniques in inequalities such as smoothing, fudging, and ordering. The last part of the course focuses on the fundamental technique of solving functional equations. It covers all levels of USA(J)MO and any national-Olympiad-level contest, including TST and IMO. A student with a strong algebra background and an AIME score of 10 or above should consider this course. It is strongly advised that students have good experience in proofreading.

Combinatorial Arguments

This is an Olympiad Level and proof based course. The course introduces advanced methods of mathematical proofs, including the Pigeonhole Principle, the wellordering principle, colorings, assigning weights, bijections/mappings, recursion, counting in two ways, and combinatorial constructions. Topics may include graph theory and combinatorial geometry. A focal point of the course is combinatorial number theory. It covers all levels of USA(J)MO and any national-Olympiad-level contest, including TST and IMO. A student who is familiar with mathematics proofs and has an AIME score of 10 or above should consider this course.

Geometric Proofs

This is the Olympiad-level geometry course. The course focuses on classical topics such as concurrency, collinearity, cyclic quadrilaterals, special centers/points of triangles, and geometric constructions. The student will be introduced to the important transformations, translations, reflections, and spiral similarities, with a touch on projective and inversive geometry. It covers the hard end of AIME, all levels of USA(J)MO, and any national-Olympiad-level contest, including TST and IMO. A student with a strong background in geometry and an AIME score of 10 or above should consider this course.

Number Theory 3

This is an Advanced Olympiad-level number theory course. The course focuses on in-depth discussions of Diophantine equations, residue classes, quadratic reciprocity, central binomial technique, primitive roots and algebraic integers. The course also introduces the student to the notion and theory of finite fields and p-adic numbers. A student with a strong background in number theory and easily qualifies for USA(J)MO should consider this course.

Each course emphasizes proof-based mathematics essential for USA(J)MO success, with problems selected to mirror competition difficulty and style. Detailed topics, prerequisites, and schedules are available in our course catalog.

What Makes Our Program Unique

The AwesomeMath Olympiad Approach

Our methodology centers on proofs, not memorization or formula application. We teach you to make creative connections between seemingly disparate mathematical topics – the hallmark of olympiad problem-solving that distinguishes medalists from participants.

Dr. Titu Andreescu, former USA IMO Team Leader and USAMO Chairman, legendary problem creato , and internationally recognized mathematical educator, personally curates the AwesomeMath curriculum. Our expert faculty bring decades of olympiad coaching experience, having guided numerous students to IMO medals.

You’ll learn from instructors who have stood where you stand and achieved what you aspire to accomplish.

Olympiad-Level Resources

Supplement your training with AwesomeMath’s specialized publications designed for serious mathematical Olympiad competitors:

– Problems from the Book, Number Theory: Concepts and Problems, Graphs: An Introduction

– Advanced competition problem collections

– IMO-level problem collections spanning decades of competition

– Specialized topic books covering advanced techniques in each Olympiad domain

These resources complement your coursework and provide additional practice essential for USA(J)MO and IMO preparation.

Beyond USAMO – The IMO Pathway

USAMO success opens doors to the Mathematical Olympiad Program (MOP), the intensive summer training camp for America’s top mathematical talent. From MOP, the six-member IMO team emerges through rigorous testing and selection.

AwesomeMath students have achieved remarkable success: multiple gold, silver, and bronze IMO medalists, consistent MOP qualifiers, and students who’ve represented the U.S.A. on the international stage with distinction. Our USAMO prep methodology creates a direct, proven pathway to international competition and mathematical excellence.

Success Stories

“AwesomeMath’s Advanced Problem Solving courses transformed my proof-writing ability. I went from USAJMO qualifier to USAMO bronze medalist in one year. The feedback on my proofs was invaluable.” – Michael Chen, IMO team member

“The Level 3 courses taught me to think like an Olympiad mathematician. I earned 28/42 on the USAMO and qualified for MOP. AwesomeMath gave me the tools and confidence to compete at the highest level.” – Sarah Williams, MIT Mathematics

Are You Ready?

Academy Advanced Problem Solving 4

Prerequisites: Scoring 7+ on the AIME demonstrates the foundational problem-solving skills necessary for effective Olympiad training. Students with lower scores may benefit from our intermediate-level courses first to build the required mathematical sophistication.

Commitment: USA(J)MO preparation demands significant time investment – 5-6 hours weekly minimum for meaningful progress. Success requires resilience, genuine passion for challenging mathematics, and willingness to struggle productively with difficult problems.

Level 3 Summer Program Courses

Prerequisites: These courses are proof oriented. They are well suited for students who can easily pass AIME and are seriously preparing for Math Olympiad contests. New students to the summer program need to successfully complete Part II of the admission test.

Assess your readiness honestly. Olympiad mathematics rewards persistence, deep thinking, and creative exploration over computational speed. If you’re ready to embrace the challenge, we’re ready to guide you.

Are You Ready?

Academy Advanced Problem Solving 4

Prerequisites: Scoring 7+ on the AIME demonstrates the foundational problem-solving skills necessary for effective Olympiad training. Students with lower scores may benefit from our intermediate-level courses first to build the required mathematical sophistication.

Commitment: USA(J)MO preparation demands significant time investment – 5-6 hours weekly minimum for meaningful progress. Success requires resilience, genuine passion for challenging mathematics, and willingness to struggle productively with difficult problems.

Level 3 Summer Program Courses

Prerequisites: These courses are proof oriented. They are well suited for students who can easily pass AIME and are seriously preparing for Math Olympiad contests. New students to the summer program need to successfully complete Part II of the admission test.

Assess your readiness honestly. Olympiad mathematics rewards persistence, deep thinking, and creative exploration over computational speed. If you’re ready to embrace the challenge, we’re ready to guide you.

Take the Next Step

Ready to pursue excellence in mathematical Olympiad competition?
Join students who are transforming their mathematical abilities and are competing at the highest levels.

Ready to pursue excellence in mathematical Olympiad competition? Join students who are transforming their mathematical abilities and are competing at the highest levels.

Enroll in Advanced Problem Solving 4

Explore Level 3 Summer Program Courses

Join the elite community of mathematical Olympiad competitors. Transform your problem-solving ability, master proof-based mathematics, and compete at the highest level. Your journey to USAMO, MOP, and potentially IMO starts here.

Master Olympiad Mathematics: USAMO & USAJMO Preparation

The pinnacle of high school mathematics competitions

The USA(J)MO Challenge