This course focuses on developing these skills through problem solving, puzzles, and exposure to a wide range of topics in mathematics. Students learn to distinguish between inductive and deductive reasoning and examine the roles played by each in mathematics. Students' introduction to inductive reasoning begins with a search for patterns in data, progressing from specific cases to general rules. Students master material by considering puzzles, logic problems, algebraic concepts, patterns and permutations, and real-world questions that can be answered using these techniques. As they move on to topics in deductive reasoning, students learn to use a system of logic to draw conclusions from statements that are accepted as true.
Emphasis is placed on the importance of proving conclusions using sound arguments.
Students learn how to write direct and indirect proofs, becoming familiar with terminology used in formal logic. Exposure to the techniques and structures of formal proofs is an excellent preparation for many of the topics covered in geometry. The Johns Hopkins University. All rights reserved.