I usually have lots of questions. Here are some types of questions that I tended to ask:
Here is my rough summary of the basic proof structure that underlies the field, am I getting anything horribly wrong?
Examples: There is a series of proof at the heart of Linear Algebra that roughly goes from the introduction of linear maps in the real numbers to the introduction of linear maps in the complex numbers, then to finite fields, then to duality, inner product spaces, and then finally all the powerful theorems that tend to make basic linear algebra useful.
Other example: Basics of abstract algebra, going from groups and rings to modules, fields, general algebra’s, etcs.
“I got stuck on this exercise and am confused how to solve it”. Or, “I have a solution to this exercise but it feels really unnatural and forced, so what intuition am I missing?”
I have this mental visualization that I use to solve a bunch of problems, are there any problems with this mental visualization and what visualization/intuition pumps do you use?
As an example, I had a tutor in Abstract Algebra who was basically just: “Whenever I need to solve a problem of “this type of group has property Y”, I just go through this list of 10 groups and see whether any of them has this property, and ask myself why it has this property, instead of trying to prove it in abstract”
How is this field connected to other ideas that I am learning?
Examples: How is the stuff that I am learning in real analysis related to the stuff in machine learning? Are there any techniques that machine learning uses from real analysis that it uses to achieve actually better performance?
I usually have lots of questions. Here are some types of questions that I tended to ask:
Here is my rough summary of the basic proof structure that underlies the field, am I getting anything horribly wrong?
Examples: There is a series of proof at the heart of Linear Algebra that roughly goes from the introduction of linear maps in the real numbers to the introduction of linear maps in the complex numbers, then to finite fields, then to duality, inner product spaces, and then finally all the powerful theorems that tend to make basic linear algebra useful.
Other example: Basics of abstract algebra, going from groups and rings to modules, fields, general algebra’s, etcs.
“I got stuck on this exercise and am confused how to solve it”. Or, “I have a solution to this exercise but it feels really unnatural and forced, so what intuition am I missing?”
I have this mental visualization that I use to solve a bunch of problems, are there any problems with this mental visualization and what visualization/intuition pumps do you use?
As an example, I had a tutor in Abstract Algebra who was basically just: “Whenever I need to solve a problem of “this type of group has property Y”, I just go through this list of 10 groups and see whether any of them has this property, and ask myself why it has this property, instead of trying to prove it in abstract”
How is this field connected to other ideas that I am learning?
Examples: How is the stuff that I am learning in real analysis related to the stuff in machine learning? Are there any techniques that machine learning uses from real analysis that it uses to achieve actually better performance?