Covering Systems: Intellectual Property and Innovation

This lecture discusses covering systems in mathematics, particularly focusing on Erdős's questions regarding arithmetic progressions and moduli. It begins with a definition of covering systems and presents key questions posed by Erdős and others about the properties of these systems. The instructor explains the concept of a covering system as a finite collection of sets of integers that cover all residues modulo a certain number. The lecture then transitions to a summary of week five of a course on innovation, emphasizing the importance of protecting intellectual property. The instructor outlines the distinctions between different types of intellectual property, including trade secrets, trademarks, patents, and copyrights, and discusses their advantages and disadvantages. The lecture also covers complementary assets necessary for commercializing innovations and legal considerations such as liability and incorporation. Finally, the instructor addresses the concept of pivoting in business and the importance of scaling up operations effectively as a company grows.