Developing logic and mathematical/ physical thinking

[Anonymous No.10798513]

Hi sci, currently at my first year of mathematics at University. The biggest problem I found so far is the logic behind mathematics and physics theories. While studying I often find myself asking "yeah, this step makes totally sense, but how do I 'reach' this idea by myself?". That's why I'm having many troubles studying, because I actively understand what I'm studying but can't seem to understand the ideas behind it, so that I can be able to recall the steps, for example in a demonstration, by myself. Any suggestions on how to overcome this difficulty? I think just memorizing this stuff is useless in order to be able to develop ideas in the future, but I find myself stuck at the moment

[Anonymous No.10799266]

>>10798513
It's just a set of tricks and principles you can find in a GRE math prep book.

e.g., General principles like proof by contradiction, mathematical induction, etc. There are also specific tools you can use when faced with novel situations.

At a deeper level, stuff like theorems are odd in the sense that the steps leading to them all make logical sense but there isn't a general procedure to efficiently identify all possible math theorems. At best you can make algorithms that will prove certain classes of math theorems.

Reading history of math, math puzzles, and doing math proofs can help give you better intuitions.

[Anonymous No.10799300]

>>10798513
You have to try to understand the concepts at a fundamental level to the point that you can complete them through deductive reasoning. If you can understand it the same way you understand how gravity or a refrigerator works then you're ahead of 99% of all people. 100% of all people on this board, even.

[Anonymous No.10800520]

>>10799266
Any suggestions on books that I should buy?

[Anonymous No.10800538]

>>10798513
Gz

[Anonymous No.10800549]

>>10798513
Any examples?
I can't tell if you are lost in the mathematical theorem-proving or the math-applied-to-physics.

[Anonymous No.10800555]

>>10798513
is it intuitive?

[Anonymous No.10801199]

>>10800549
Mostly on Mathematical theorem proving, math applied on physics is more intuitive, because it provides a geometrical representation that allows me to visualize what I'm doing/proving and also demonstrations are generally more "mechanical" and mostly algebraical, rather than math's ones. Meanwhile, the ideas behind theorems are unknown for me, that's why I'm trying to understand the logic behind it. A stupid example is defining the value of ε in some demonstration about limits, how can I arbitrarily decide that in a theorem is L/2, in another is 0, without just memorizing it? Intermediate steps are generally clear, but fundamental steps can't come to my mind automatically

[Anonymous No.10802327]

>>10798513
As someone who has made it over the hill you are trying to get over. The answer is to just keep pushing and practicing. You will get the hang it. Struggling with these things will give you the sea legs you need to arrive at the solutions yourself.