Combinatorial Problems and Exercises, Second Edition - Problem-Solving

Our review of Combinatorial Problems and Exercises, Second Edition finds it to be a focused, exercise-driven resource for readers who want to learn combinatorial methods by doing. The book is best for advanced undergraduates, graduate students, and practitioners who appreciate learning through problems rather than through long theoretical exposition; the single biggest reason to buy is the book's extensive collection of exercises paired with a separate section of hints and a full solutions section that make it practical for self-study and classroom use.

Key Features

• Exercise-centered approach: The book teaches methods through carefully chosen problems so readers develop practical problem-solving skills rather than only passive knowledge.
• Separate hints section: Hints are provided in their own section to help readers nudge themselves forward without seeing full solutions immediately.
• Complete solutions: A dedicated solutions section supplies detailed solutions so learners can check their reasoning and learn from worked examples.
• Updated material: This revised edition adds exercises on random walks on graphs and links to eigenvalues, expansion, and electrical resistance to reflect developments since the original publication.
• Compact reference dictionary: A dictionary section gives clear definitions of combinatorial notions used throughout, making the book convenient as a quick reference while solving problems.

Who It's For

This book is ideal for students in mathematics, computer science, or related fields who want a hands-on introduction to combinatorial techniques and for instructors looking for a source of class problems and homework sets. The emphasis on exercises and worked solutions makes it particularly suitable for self-learners who need a structured practice path.

Readers seeking a textbook with extended theoretical exposition, comprehensive proofs of broad theory, or an introductory text aimed at absolute beginners with no prior discrete math background should look elsewhere; this book assumes some mathematical maturity and benefits those ready to engage with problems directly.

Pros & Cons

Pros

• Extensive exercise collection supports active learning and skill building.
• Hints and full solutions sections let readers gauge progress and learn from mistakes.
• Updated problems on random walks connect classical combinatorics with spectral and probabilistic ideas.

Cons

• Not a gentle introductory text; readers without some background may find it challenging.
• Coverage emphasizes problems over long theoretical discussions, so it may not replace a standard textbook for theory-heavy courses.

Specifications

Title	Combinatorial Problems and Exercises, Second Edition
Author / Brand	L. Lovasz
Content focus	Exercises with hints, detailed solutions, and a dictionary of notions
Edition notes	Revised edition with added exercises on random walks, eigenvalues, expansion
Intended audience	Advanced undergraduates, graduate students, instructors, self-learners
Use cases	Self-study, classroom problem sets, reference for combinatorial techniques

Our Verdict

Combinatorial Problems and Exercises, Second Edition is a high-value resource for readers who learn by working problems and who already have some mathematical background. Its strong collection of exercises, separate hints, and full solutions make it an excellent companion for coursework or independent study, while the updated material ties classical combinatorics to modern spectral and probabilistic topics.

Frequently Asked Questions

Does this edition include new material compared with the original?
Yes; the revised edition adds exercises on random walks on graphs and their relations to eigenvalues, expansion properties, and electrical resistance.

Are full solutions provided?
Yes; the book contains a third section with detailed solutions and a separate hints section to support learning.

Is this suitable for beginners in combinatorics?
It is best for readers with some mathematical maturity; absolute beginners may prefer a text with more introductory exposition before attempting these problems.