Study Guide

• First and foremost, solve the problem sets using only pen, paper, and a calculator. After completing a problem by hand, slightly modify the conditions or variables and solve it again. Then, input the new values into the Python script and compare the results with your hand-calculated solution.

• Buddy system: Study with a classmate. Teaching and helping one another significantly deepens understanding of the material. Students are strongly encouraged to work through problem sets collaboratively. For example, one student solves the odd-numbered problems while the other solves the even-numbered ones; then each explains their solutions to the other.

• Practice, practice, practice: As the saying goes, “practice makes perfect.” More accurately in this context, “good practice makes perfect.” That means pen-and-paper-first practice. Use Python as a verification tool, not a crutch. Always derive the solution analytically on paper first. Only after obtaining a complete hand-calculated result should you run the corresponding Python script. This approach echoes a proverb commonly attributed to Confucius:

  I hear and I forget

  I see and I remember

  I do and I understand

• Maintain a solution notebook: For each major problem, keep a single document (physical or digital) containing:

  • The full hand derivation
    
  • Key numerical results with units
    
  • A brief paragraph summarizing insights or reconciling any intermediate discrepancies

  This record becomes an invaluable review resource before exams.