User:IssaRice/List of mathematical difficulties: Difference between revisions
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
This pages lists some of the concepts in math that I had the most difficulty with. | This pages lists some of the concepts in math that I had the most difficulty with. | ||
==months of confusion== | |||
* material implication (introductory sources don't even mention the deduction theorem...) | * material implication (introductory sources don't even mention the deduction theorem...) | ||
| Line 8: | Line 10: | ||
* determinant of a matrix (watching https://www.youtube.com/watch?v=xX7qBVa9cQU cured me once and for all!) | * determinant of a matrix (watching https://www.youtube.com/watch?v=xX7qBVa9cQU cured me once and for all!) | ||
* chain rule of differentiation (the problem here was that i needed to study linear algebra beforehand) | * chain rule of differentiation (the problem here was that i needed to study linear algebra beforehand) | ||
* lots of the basic concepts in computability theory: recursive set, recursively enumerable set, partial recursive function, etc. etc. I think the boolos/jeffrey/burgess book is great in a way, but also really sucks in a way (it just doesn't emphasize the stuff i want emphasized) | * lots of the basic concepts in computability theory: recursive set, recursively enumerable set, partial recursive function, etc. etc. I think the boolos/jeffrey/burgess book is great in a way, but also really sucks in a way (it just doesn't emphasize the stuff i want emphasized) | ||
==days of confusion== | |||
* why the godel completeness theorem and incompleteness theorem don't contradict each other | * why the godel completeness theorem and incompleteness theorem don't contradict each other | ||
==ongoing confusion== | |||
* recursion theorem/diagonalization lemma (i still don't understand this, but i think i'm getting there... i probably need to know more category theory first, maybe lambda calculus) | |||
Revision as of 08:08, 8 February 2020
This pages lists some of the concepts in math that I had the most difficulty with.
months of confusion
- material implication (introductory sources don't even mention the deduction theorem...)
- the idea of a random variable, and how it relates to the sample space
- expansion of sample space
- the fact that we often only care about properties of random variables that are shared among all random variables with the same distribution
- singular value decomposition, and classification of linear operators (once i did everything in a 2d real vector space, and could picture the geometry of each type of operator, everything made sense)
- determinant of a matrix (watching https://www.youtube.com/watch?v=xX7qBVa9cQU cured me once and for all!)
- chain rule of differentiation (the problem here was that i needed to study linear algebra beforehand)
- lots of the basic concepts in computability theory: recursive set, recursively enumerable set, partial recursive function, etc. etc. I think the boolos/jeffrey/burgess book is great in a way, but also really sucks in a way (it just doesn't emphasize the stuff i want emphasized)
days of confusion
- why the godel completeness theorem and incompleteness theorem don't contradict each other
ongoing confusion
- recursion theorem/diagonalization lemma (i still don't understand this, but i think i'm getting there... i probably need to know more category theory first, maybe lambda calculus)