2.1. Mathematical Reasoning

Try these first

1. 1.

   What is a proof in mathematics?

   Hint

   Consider how you validate a statement mathematically.

2. 2.

   Define Mathematical Reasoning.

   Hint

   Think about why reasoning is essential in logic.

3. 3.

   What is mathematical reasoning primarily concerned with?

   • Constructing random algorithms
   • Deriving logical conclusions
   • Speeding up code

   Hint

   Think about how mathematicians ensure their statements hold true.

4. 4.

   A proof by contradiction assumes what?

   • True
   • False

   Hint

   This type of proof is named for what it aims to expose.

5. 5.

   Prove by induction that for all integers n ≥ 1, the sum of the first n even numbers equals n(n + 1).

   Hint

   Set up your base case carefully, and then demonstrate the inductive step.

6. 6.

   Demonstrate how mathematical reasoning is crucial in validating an algorithm's performance.

   Hint

   Consider time complexity notation and proofs of correctness.