Anonymous at Fri, 21 Jun 2024 11:54:03 UTC No. 16245472

this question is flawed

Anonymous at Fri, 21 Jun 2024 15:08:59 UTC No. 16245736

>>16245472
No it isn't. Reading a Calculus textbook in between the books of the curriculum of Math, or reading a proof book.

Anonymous at Fri, 21 Jun 2024 15:13:57 UTC No. 16245747

>>16245434
>Calculus
You'll need both eventually
Even if you're a physicist or, may Allah forgive me, an engineer, it's important to know how mathematicians work.

Anonymous at Fri, 21 Jun 2024 15:59:31 UTC No. 16245801

>>16245434
Mathematics should be learned informally with a hands-on approach, and not even one proof should be required for a novice. You can just learn how stuff works by seeing many examples. General proof? Why, i believe the book.
Once you know how things work you can read all the proofs, just to check no one lied to you.

Anonymous at Fri, 21 Jun 2024 16:21:20 UTC No. 16245821

>>16245801
This. Also I have never seen a math book that makes an effort to build concepts from other known concepts. The human mind is not a machine that admits knowledge on the basis of being true, new knowledge must be concatenated to old knowledge in order to make sense.

Anonymous at Fri, 21 Jun 2024 16:51:23 UTC No. 16245878

>>16245434
Read Pre-Calculus by Stitz and Zeiger then read Calculus - Infinitesimal Approach by Keisler. Any time the latter is unclear (it is usually good but occasionally unclear), cross reference Calculus volumes 1-2 by Apostol.
Once you have read those, you should be far enough along that you will know how you want to proceed beyond that.

Anonymous at Sat, 22 Jun 2024 08:20:51 UTC No. 16247096

>>16245434
Proofs if you want to learn academic math. Calculus if you want more applied math style

Anonymous at Sat, 22 Jun 2024 08:41:51 UTC No. 16247121

>THIS IS THE PYTHAGORAS THEOREM
>Draws a few triangles with a ruler and measures each side
>SEE THE THEOREM IS TRUE, LETS MOVE ON

Anonymous at Sat, 22 Jun 2024 10:25:58 UTC No. 16247215

You use predicate calculus for proofs anyways, so I don't really understand what op is asking

Anonymous at Sat, 22 Jun 2024 12:39:46 UTC No. 16247323

>>16247096
There's no such thing as "academic math". There's just math.
If you want to be a calculator, learn to calculate. If you want to do math, you have to do proofs.

Anonymous at Sat, 22 Jun 2024 12:40:50 UTC No. 16247325

>>16245821
> Also I have never seen a math book that makes an effort to build concepts from other known concepts
Literally every math book does this. Every math books builds concepts and ideas on top of other, prerequisite ideas.

Anonymous at Sat, 22 Jun 2024 12:45:01 UTC No. 16247327

>>16247215
Nobody uses predicate calculus for proofs except for a very short time in an introduction to logic course. Everyone quickly moves on to using their native language for proofs because it's simpler.

Anonymous at Sat, 22 Jun 2024 12:46:03 UTC No. 16247328

>>16247323
>If you want to do math, you have to do proofs.
You are a boring dogmatic retard and the reason everything is shit in the world

Anonymous at Sat, 22 Jun 2024 13:34:11 UTC No. 16247396

>>16247328
Math is about understanding, and in mathematics we tend to call this understanding "proofs". If you don't care about understanding what you're doing, why it works, then it's called engineering or being a code monkey. Just because it looks like math, doesn't mean it is math.

Anonymous at Sat, 22 Jun 2024 14:46:33 UTC No. 16247472

>>16247396
>Math is about understanding,
You dont get to decree anything about math. Shut the fuck up

Anonymous at Sat, 22 Jun 2024 15:07:40 UTC No. 16247507

>>16247472
You sound mad. Is everything ok?

Anonymous at Sat, 22 Jun 2024 17:05:02 UTC No. 16247705

>>16245434
do both

Anonymous at Sat, 22 Jun 2024 18:00:58 UTC No. 16247824

>>16247507
no

Anonymous at Sat, 22 Jun 2024 20:24:39 UTC No. 16248057

>>16247327
You still use the law of contraposition and demorgans law for everything

Anonymous at Sat, 22 Jun 2024 21:21:45 UTC No. 16248178

>>16247824
:(

Anonymous at Sat, 22 Jun 2024 21:56:07 UTC No. 16248246

>>16248057
You typically don't use a rigorous formal system or formal language when doing mathematics. Open a Springer Graduate book - most proofs are expressed in natural language. Yes they use lots of mathematical symbols and definitions but that doesn't make it a formal or first order language in the sense of predicate calculus. Proof by contradiction and proof by negation do pop up a lot, yes. They're elementary. DeMorgan's law(s) are hardly ever used - yes there's lots of versions of DeMorgan's laws in different situations but you don't use them in proofs. Most math students pick up just enough predicate logic as they need to do undergrad real analysis, epsilon-delta definition of continuity etc etc.

>>16245434
What do you mean "calculus"? If you mean differential and integral calculus, you can't "learn mathematics" just by doing this. Differential and integral calculus is just a small part of mathematics.

If you just want to learn calculus for applied math, learning just how to compute integrals won't get you very far. You'll be more comfortable if you can understand some basic theory including the construction of the Riemann integral - this really takes you into Real Analysis, the study of the structure of the reals. This is not an advanced topic, it's 2nd year undergrad stuff. But applied math also needs a lot of vector calculus and complex analysis, and you can't really feel comfortable with these until you understand proofs of basic facts.

Anonymous at Sat, 22 Jun 2024 22:08:55 UTC No. 16248264

>>16245736
If this is what OP meant, then having a solid grasp of calculus and a basic grasp of the concept of proof are both absolutely necessary.

"How to Think Like a Mathematician" by Houston, or "Introduce to Pure Mathematics" by Liebeck are both good intros to the idea of proof. Basic calculus you will pick up in lots of place. A lot of Spivak is overkill, especially for 1st year uni. Thompson and Gardner's Calculus Made Easy is nice.

Anonymous at Sun, 23 Jun 2024 19:33:22 UTC No. 16249723

>>16245434
Depends on your end goal

Anonymous at Mon, 24 Jun 2024 20:25:25 UTC No. 16251486

>>16245434
University level math is all about proofs.