How To Figure Out Math Proofs On Your Own

Tips for Improving Problem Solving Skills

• Before attempting a problem, revisit the key results and techniques covered in that section to aid in problem-solving.

• Spending extended time on a problem is normal, but if stuck, it's okay to refer to the solution after thorough attempts on your own.

• After reviewing the solution, it's crucial to analyze and fully understand each step before trying to recreate it independently.

• Reproducing the solution without looking at it directly promotes a deeper understanding of the problem-solving process.

Understanding every single step in the solution is crucial. Reproducing it on your own is essential for true comprehension.

Using Key Results and Techniques

• Making use of key results and techniques from the section being studied can provide insights into tackling specific problems effectively.

• Incorporating learned techniques and results from the section can often be the key to unlocking challenging problems.

"What was covered in that section that's different? What key technique is used in the proofs in that section that is different?"

Deep Reflection and Analysis of Solutions

• Analyzing the solution thoroughly and attempting to recreate it independently promotes a more profound understanding of concepts.

• Deep reflection is necessary to grasp why specific techniques are employed in solutions and how they can be applied in future problem-solving.

"How would you as an individual person come up with that solution on your own?"

Importance of Analyzing Induction Hypothesis

• After completing an induction proof, it is crucial to reflect on the induction hypothesis and understand why the proof may fail without it.

• Rather than just using the hypothesis during the proof, consider what happens when it is removed and why the proof becomes incomplete.

• This practice of critically evaluating the failure points can be applied to various proofs, enhancing problem-solving skills.

• Take time to deeply comprehend the solutions, ensuring the ability to independently redo them and grasp each step thoroughly.

Reflecting on the induction hypothesis post-proof is essential for understanding why a proof may fail without it and improving problem-solving skills.