What is the proper way to study Mathematics? | IIT prof's tips

Key wellness / self-care & productivity strategies for studying Mathematics

• Reduce over-reliance on the teacher

  • Use the teacher mainly for initial guidance (intro/pointers).
  • Build mathematical maturity through your own thinking; otherwise you may “move up grades” without truly learning the subject.

• Adopt a structured self-study flow (ideal 3-step loop)

  • Teacher introduction → self-study → problem solving
  • Aim for comprehensive understanding, not just finishing topics.

• Choose the right learning resources

  • Pick one very good textbook (quality > quantity).
  • Avoid books that are mostly pattern-based solved problems marketed for high marks.
  • Recommended types/sources mentioned:
    • NCRT textbooks (NCERT)
    • Expert-written school textbooks
    • University-level texts (for Class 11–12 level)

• Self-study method: learn + internalize theorems

  • Study the theorems yourself
  • Go line-by-line to grasp core concepts from explanations
  • After studying, close the book and reproduce the theorem from memory
    • Framed as reinforcement (not rote learning), because it creates mental connections.

• Develop “mathematical maturity” by thinking beyond the text

  • After proving/learning a theorem, think hard about implications
  • Try to predict:
    • possible corollaries
    • adjacent explanations
    • related results that aren’t explicitly given

• Use solved examples as practice for applying concepts (not as patterns to memorize)

  • Before reading the solution:
    • Close the solution
    • Read the problem, then apply theorems you learned
  • Only then compare with the official approach.
  • If you can’t solve it, you should still learn the theorem application by attempting first.

• Problem-solving progression: don’t skip “easy” problems

  • Level up step-by-step
  • Don’t treat easy problems as beneath you.
  • Master fundamentals before moving to harder/competitive-level problems.
  • Practice until your mind has “acclimatized” to the concepts.

• Try problems on your own before looking at solutions

  • Exhaust possibilities first
  • If stuck, then check the solution—but:
    • don’t just read it passively.

• Do “postmortem analysis” after checking solutions

  • After failing, ask:
    • Why didn’t you think in the right direction?
    • What does this reveal about your theorem understanding or cross-topic connections?
  • After succeeding:
    • analyze why you reached the correct path (what reasoning/connection worked)

Presenters / sources

• Presenter (implied from the narration): An IIT professor (name not provided in the subtitles)
• Sources/books mentioned: NCRT textbooks (NCERT); also referenced as written by school teachers and university teachers