Recommendations for problem-solving books include "How to Solve It" by Polya, which provides valuable strategies for tackling problems but may be more beneficial for those already familiar with the concepts. Titu Andreescu is mentioned as a notable figure in the field, with resources available through the Art of Problem Solving website, which offers a range of books aimed at high school and undergraduate students, including materials suitable for preparing for competitions like the Putnam. The consensus emphasizes that the best way to improve problem-solving skills is through practice and engagement with various problems.