Overview: What Is the Art of Problem Solving Series?
The Art of Problem Solving (AoPS) series is a collection of mathematics textbooks originally designed for students preparing for math olympiads and competitions. Written by Richard Rusczyk and collaborators, the series spans topics from introductory algebra all the way through calculus and number theory. Over the years, it has become a popular choice not just for competition students, but for any learner who wants to develop genuine mathematical depth.
The Books in the Series
- Introduction to Algebra — Covers algebra fundamentals with a focus on reasoning over rote procedure.
- Introduction to Geometry — A thorough geometry course, including proofs.
- Introduction to Number Theory — Explores divisibility, primes, and modular arithmetic.
- Introduction to Counting & Probability — Combinatorics and probability from the ground up.
- Intermediate Algebra, Geometry, and beyond — For students who have mastered the intro books.
- Precalculus and Calculus — Upper-level books for advanced students.
What Makes AoPS Different?
Most school textbooks teach you a procedure, show you examples, then ask you to repeat the procedure. AoPS does the opposite: it presents a challenging problem before explaining the concept, asking you to think it through yourself first. This approach builds the problem-solving instinct that procedural learning often skips entirely.
The writing is clear and engaging — conversational in places — which is uncommon for math textbooks. The authors genuinely seem to enjoy mathematics, and that enthusiasm comes through.
Strengths
- Develops real mathematical thinking, not just formula application.
- Excellent problem sets — graded from accessible to genuinely challenging.
- Thorough coverage — topics are treated in real depth, not skimmed.
- Great for self-study — explanations are clear enough to follow without a teacher.
- Solutions manuals available — full worked solutions for every problem.
Weaknesses
- Not for everyone: students who need step-by-step scaffolding may find the problem-first approach frustrating initially.
- Pacing is demanding: these books cover material more deeply but may move faster through curriculum topics than students expect.
- Price: the books are more expensive than standard school textbooks, though used copies are readily available.
- Competition-flavoured: some problems are more relevant to math competitions than everyday school exams.
Who Should Use AoPS?
| Student Type | Recommendation |
|---|---|
| Student preparing for math olympiads/competitions | Strongly recommended — this is what it was built for. |
| Advanced learner who wants depth beyond school curriculum | Excellent choice. |
| Average student wanting to improve grades | May be too challenging — try an intro level first. |
| Parent supplementing home education | Very good, especially with the solutions manual. |
| Adult refreshing math skills | Good for motivated self-learners who enjoy challenge. |
Final Verdict
The Art of Problem Solving series earns its strong reputation. If you want to truly understand mathematics — not just pass tests — these books are among the best resources available at any price point. Start with the Introduction to Algebra volume to get a feel for the style, and if it clicks, the rest of the series is a genuinely rewarding journey through mathematics.
Best for: Motivated learners aged 11+ who want mathematical depth.
Difficulty level: Moderate to challenging.
Self-study friendly: Yes, with the solutions manual.