1. The “Socratic Teacher” Prompt
“I am working on [Insert Math Problem]. Do not give me the answer. Instead, ask me a series of leading questions to help me solve it step-by-step on my own.”
2. The “Visual Learner” Translation
“Explain the concept of [e.g., Eigenvectors] using a real-world physical analogy. How would I visualize this movement in 3D space?”
3. The “Common Pitfalls” Warning
“I’m about to solve a set of problems on [e.g., Integration by Parts]. What are the 3 most common mistakes students make with this specific method that I should watch out for?”
4. The “Simplifier” (Feynman Technique)
“Explain [e.g., Taylor Series] to me as if I am a 10-year-old who only knows basic algebra. Avoid jargon until the very end.”
5. The “Exam Simulator”
“I have a test on [Chapter Name] tomorrow. Generate 3 ‘Easy,’ 3 ‘Medium,’ and 2 ‘Hard’ practice problems for me. Provide the solutions only after I submit my attempts.”
6. The “Code-to-Math” Bridge
“Show me how to write a simple Python script to calculate the area under the curve for [Insert Function]. Explain how the code relates to the Calculus formula.”
7. The “Proof Breakdown”
“Here is a mathematical proof: [Paste Proof]. Break this down line-by-line and explain the logical ‘jump’ between each step in plain English.”
8. The “Reverse Engineering” Prompt
“Here is the final answer to a problem: [Insert Answer]. Show me three different possible paths or methods that could have been used to reach this result.”
9. The “Connection” Prompt
“How does the concept of [e.g., Derivatives] in Calculus directly relate to what I learned in [e.g., Linear Algebra]? Give me one specific example where they overlap.”
10. The “Memory Palace” Prompt
“Create a mnemonic device or a short story to help me remember the formulas for [e.g., Volume of Solids of Revolution].”