06. Patterns Across Mathematics
Chapter 6. Patterns Across Mathematics Mathematics is organized by recurring patterns. The same forms of reasoning appear in algebra, geometry, topology, analysis, combinatorics, computation, and logic. Once these patterns are recognized, new subjects become easier to learn because their methods are no longer isolated. This chapter studies several of the most common patterns. Duality appears when a concept has a counterpart obtained by reversing direction, exchanging roles, or changing perspective....