Skip links
mathematical space (5)

Best Preparation Books for AIME | Mathematical Space

When preparing for the AIME (American Invitational Mathematics Examination), it’s important to choose the right books that help strengthen your problem-solving skills and build a solid foundation in the topics tested. Below are some highly recommended books and resources to help you prepare for the AIME:

1. “The Art and Craft of Problem Solving” by Paul Zeitz

  • Why it’s useful: This book is a fantastic resource for developing your problem-solving skills. It goes beyond just solving specific problems; it teaches you how to think critically and approach math problems from different angles, which is key for AIME-style questions.
  • Topics covered: Includes a broad range of topics in algebra, geometry, number theory, combinatorics, and more.
  • Skill level: Beginner to advanced, as it builds progressively.

2. “Problem-Solving Strategies” by Arthur Engel

  • Why it’s useful: This book is a deep dive into a variety of mathematical techniques and strategies commonly used in math competitions like the AIME. It provides methods for solving problems in an organized and strategic way.
  • Topics covered: A broad spectrum of mathematical concepts and techniques, including combinatorics, number theory, geometry, and inequalities.
  • Skill level: Intermediate to advanced.

3. “AIME Preparation” by Richard Rusczyk (Art of Problem Solving Series)

  • Why it’s useful: This is a comprehensive resource focused specifically on preparing for the AIME. It is written by Richard Rusczyk, co-founder of Art of Problem Solving (AoPS), and includes a vast collection of problems modeled after actual AIME questions.
  • Topics covered: Covers all of the key areas on the AIME (algebra, geometry, combinatorics, number theory, and more).
  • Skill level: Intermediate to advanced.

4. “Mathematical Olympiad Challenges” by Titu Andreescu and Razvan Gelca

  • Why it’s useful: This book is excellent for developing high-level problem-solving techniques. While it’s not specifically tailored for the AIME, it contains many problems from math Olympiads, which are often similar in style and difficulty.
  • Topics covered: Covers a broad range of topics, including algebra, geometry, number theory, combinatorics, and functional equations.
  • Skill level: Advanced.

5. “Introduction to Number Theory” by David M. Burton

  • Why it’s useful: Number theory is an essential component of the AIME, and this book offers a solid foundation in the subject. It’s a bit more theoretical but very useful for understanding the number-theoretic principles behind many AIME questions.
  • Topics covered: Divisibility, prime numbers, modular arithmetic, Diophantine equations, and more.
  • Skill level: Intermediate to advanced.

6. “Art of Problem Solving Volume 1: The Basics” by Richard Rusczyk

  • Why it’s useful: This is a great starting point for students who are newer to math competitions. It teaches the basics of problem-solving in a systematic way, preparing you for the more challenging problems found on the AIME.
  • Topics covered: Focuses on algebra, number theory, combinatorics, and geometry. It’s an excellent resource for foundational knowledge.
  • Skill level: Beginner to intermediate.

7. “Art of Problem Solving Volume 2: And Beyond” by Richard Rusczyk

  • Why it’s useful: This book is a continuation of Volume 1 and goes into more advanced topics and problems. It’s a great resource if you’re comfortable with the basics and want to tackle more complex concepts.
  • Topics covered: Advanced combinatorics, algebraic manipulation, functional equations, and geometry.
  • Skill level: Intermediate to advanced.

8. “Competition Math for Middle School” by Jason Boyd

  • Why it’s useful: Although this book is geared toward middle school students, it’s excellent for building a solid foundation in basic problem-solving strategies, especially for beginners. It will help you learn the basics of math competition problems and prepare for more advanced challenges.
  • Topics covered: Arithmetic, geometry, basic number theory, algebra, and probability.
  • Skill level: Beginner to intermediate.

9. “MOEMS Practice Tests” by The Mathematical Olympiads for Elementary and Middle Schools (MOEMS)

  • Why it’s useful: Though this resource is more geared toward younger students, practicing with it can help you get used to the style and structure of competition-style questions, especially in combinatorics and elementary number theory. MOEMS problems can serve as good preparation for AIME problems.
  • Topics covered: Basic number theory, elementary geometry, and combinatorics.
  • Skill level: Beginner to intermediate.

**10. AIME Past Exam Problems (Official Source)

  • Why it’s useful: There’s no substitute for practicing the real thing. Make sure you download and work through past AIME exams to familiarize yourself with the test format, question types, and time management.
  • Where to find: You can find past AIME exams and answer keys on the official website of the Art of Problem Solving (AoPS), or through the MAA (Mathematical Association of America).
  • Skill level: All levels (depending on the exam year).

Bonus Resources for AIME Preparation:

  • Art of Problem Solving (AoPS) Online Community: AoPS has an online forum where students share problems, solutions, and study strategies. You can find solutions to practice problems and interact with other students preparing for the AIME.
  • AoPS Online Classes: If you’re looking for structured courses, AoPS offers online classes tailored to math competitions. These courses are great if you prefer a more guided approach.

Conclusion

To best prepare for the AIME, a combination of books and practice problems is essential. Start with books that focus on building your problem-solving skills, like “The Art and Craft of Problem Solving” and “Problem-Solving Strategies”, and then move on to more focused materials like AoPS’ AIME prep books and past exams. Make sure to practice regularly with a variety of problems, focusing on topics like combinatorics, number theory, algebra, and geometry.

Good luck with your preparation! You’ve got this!

 

Preparing for the AIME? Join Mathematical Space for expert-led online classes and personalized preparation tips. Visit our website today to get started!

Leave a comment

Home
Account
Cart
Search
This website uses cookies to improve your web experience.