Self-Studying Math: A Framework

Introduction

• Math major at an elite college involves:
  • Hundreds of proofs, thousands of theorems
  • Fields: Calculus, Differential Equations, Topology, Mod Analysis, Abstract Algebra
• Studying math requires self-discipline and focus
• My background:
  • Columbia University, Math and Operations Research
  • Mostly self-taught math for several reasons:
    1. Nature of math requires constant attention
    2. Sometimes skipped lectures
    3. Professors too genius to teach well
• Self-studying: most crucial skill with 7,500 hours of practice
• Purpose: Share a step-by-step self-study process for math

Framework for Self-Studying Math

1. Definitions

• Understand the topic by reading definition/rules/theorems
• Example: Linear equation definition
• Don’t be intimidated by complex definitions; understanding usage can be more important

2. Examples

• After definitions, study examples to see application
• Analogy: Tool (definition) and ways to use it (examples)
• Work through examples to understand each step
• Example: Solving linear equations through given examples
• Practice similar questions to ensure comprehension

3. Filling Knowledge Gaps

• If confused, look up specific terms or steps
• Example: Understanding “integrating factor” by Googling it
• Be specific in searches to avoid overwhelming information
• Avoid deep dives that could distract from the main topic
• Mark aspects you don’t fully understand for later study
• Stay focused on current study session

4. Exercises

• Practice with 10-20 questions per topic
• Initially, refer to examples for similar exercise questions
• Later, aim to solve independently
• Check answer keys to learn correct methods and address mistakes
• Practice is crucial for reinforcing understanding

Time Management during Study Sessions

• 1-hour session breakdown:
  • 30 mins: Practice questions
  • 20 mins: Working through examples
  • 10 mins: Definitions and filling knowledge gaps
• Adjust time if necessary based on understanding and needs

Memorization Tips

• Repetition through practice helps in memorizing definitions/theorems
• Create a formula/theorem sheet for reference during practice
• Eventually, practice without the sheet to ensure memorization

Conclusion

• Practicing self-study methods improves understanding and retention
• Invite viewers to share their experiences with the method
• Emphasize staying active in learning and practice frequently

Motivation: Self-studying math can be fulfilling, challenging, and fun

Resources: Skillshare sponsorship for additional learning resources

Notes by: H 👨‍🎓