Mathematical Foundations and Note-Taking

Perfecting Mathematical Notation

After returning to academia following a decade in industry, I discovered the importance of clear mathematical notation. Here’s why it matters:

1. Context switching between work and academic projects requires crystal-clear notation to avoid misinterpretation and time waste.
2. Writing mathematics clearly helps crystallize problem-solving approaches, as pattern recognition often relies heavily on visual processing.
3. Practice writing challenging symbols (like Greek letters) until they become second nature. Even small practice sessions during downtime can make a significant difference.
4. This process often reveals knowledge gaps, creating opportunities for targeted learning and review.

Documentation and Organization

The PhD Notebook System

Maintain a dedicated notebook for your doctoral journey. Use it to:

• Document topics that need refreshing
• Record detailed notes from your research
• Capture valuable insights about study skills
• Note effective presentation techniques
• Track potential sponsor requirements

Task Management Strategy

The Two-Category System

Divide tasks into two distinct categories to maximize productivity:

Brain-Intensive Work:

• Homework assignments
• Literature reviews
• Debugging complex programs
• Algorithm generalization
• Technical paper reading and writing

Administrative/Mechanical Work:

• Note organization
• Plot refinement
• LaTeX formatting
• Basic code maintenance
• Email management
• Workspace organization
• Creating study materials

Essential Tips for Success

Organization and Time Management

• List Everything: Use TODO markers (searchable with ctrl+f) to track pending tasks
• Learn to Decline: Focus on two primary goals: sponsored project completion and PhD progress
• Maintain Your Timecard: Benefits include:
  • Keeping management satisfied
  • Tracking accomplishments
  • Ensuring legal compliance

Academic Success Strategies

• Embrace Memorization: While understanding principles is crucial, having key theorems readily available in memory is invaluable
• Create Reference Materials: Develop comprehensive cheat sheets combining text, equations, and diagrams
• Prioritize Learning: Focus on understanding rather than grades, while meeting program requirements
• Verbalize Your Work: Explain concepts to others, particularly non-experts, to solidify understanding and improve communication skills

Remember: Being able to communicate complex ideas clearly is fundamental to becoming an effective scientist. While work problems should stay at work, discussing academic challenges with others can provide valuable perspective and deepen understanding.