How/When do you get to the point of solving textbooks easily

  • Thread starter Thread starter random_soldier
  • Start date Start date
  • Tags Tags
    Point Textbooks
Click For Summary
SUMMARY

The discussion centers on developing the ability to formulate and understand complex questions in academic settings, particularly during a PhD program. Key skills include categorizing concepts, such as "polarity," across various disciplines like electronics and psychology, and utilizing set theory to grasp mathematical concepts, including infinity and cardinality. The participant emphasizes the importance of context in determining the appropriate category and tools for understanding a subject. Mastery of these skills leads to a more profound comprehension of interdisciplinary topics.

PREREQUISITES
  • Understanding of set theory and its applications in mathematics.
  • Familiarity with concepts of polarity across different scientific disciplines.
  • Knowledge of limits and infinitesimals in calculus.
  • Ability to categorize and contextualize complex questions in academic research.
NEXT STEPS
  • Explore advanced set theory concepts, including Cantor sets and cardinality.
  • Research the application of polarity in various scientific fields, such as physics and psychology.
  • Study the principles of limits and infinitesimals in calculus for deeper mathematical understanding.
  • Develop skills in categorizing and contextualizing academic questions for interdisciplinary research.
USEFUL FOR

PhD students, educators, and researchers seeking to enhance their analytical skills and interdisciplinary understanding in mathematics, physics, and related fields.

random_soldier
Messages
80
Reaction score
10
So I was having a discussion with one of my teachers and they mentioned along the way in my PhD, I would learn how to formulate and/or understand where a question is coming from, be able to solve it and know exactly when I arrive at a satisfactory conclusion.

This would be quite a handy skill to develop from the get go itself, if I did not misconstrue the meaning. Any/all here know what I am speaking of and how I would inculcate such an ability?
 
Physics news on Phys.org
Categories help me determine the subject. Example: a lecture mentions "polarity". Term common in electronics, physics, chemistry, even psychology. Context helps determine the category; the category includes 'tools' to understand the subject.

Set theory helps me understand almost everything in mathematics. For instance, people have difficulty grasping "infinity"? My working definition involves 'some measure of a Cantor set'. Example: counting numbers, limited set of integers, cardinality of the set. Choose the set that matches the data and the metric applicable to the context under discussion.

Many concepts from math and physics such as limits and infinitesimals help me understand arguments and reasoning in other subjects.
 

Similar threads

Classical Looking for a physics textbook which shows how to develop theory
  • · Replies 4 ·
Replies
4
Views
3K
Algebra What's a good first textbook on Quaternions?
  • · Replies 3 ·
Replies
3
Views
2K
MHB How to read research paper, textbook, long text content?
  • · Replies 1 ·
Replies
1
Views
1K
Are difficult textbook problems enough to "think like a physicist"?
  • · Replies 4 ·
Replies
4
Views
2K
How to Use AOPS Books for Self-Learning: Tips and Recommendations
  • · Replies 6 ·
Replies
6
Views
10K
Calculus Reference Textbook Request
  • · Replies 20 ·
Replies
20
Views
6K
Book on how to define ideas rigorously
  • · Replies 6 ·
Replies
6
Views
2K
How much physics is needed for Bialek's Biophysics book?
  • · Replies 4 ·
Replies
4
Views
3K
Textbooks for various topics in math for scientists
  • · Replies 2 ·
Replies
2
Views
1K
How do you guys read a textbook?
  • · Replies 7 ·
Replies
7
Views
4K