/sci/ - Science & Math

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Anonymous Mon Oct 31 15:52:19 2022 No.14952408 [Reply] [Original]

I am decent at Math, but recently started learning how math proofs work, am having a little bit of a difficulty improving.
It seems like the best method to learn is just memorizing all of them and their steps,
What do you guys recommend to improve learning, any good books on the subject ?
thanks

>>	Anonymous Mon Oct 31 16:02:30 2022 No.14952416 >>14952408 Worthless worthless worthless!! kill maggot worthless maggot burn this maggot

>>	Anonymous Mon Oct 31 16:57:57 2022 No.14952520 >>14952416 you need to take your meds please

Anonymous Mon Oct 31 17:06:12 2022 No.14952541

>>14952408
never transitioned to the proof based maths, neither did like 80% of graduates. people who excelled at it all came from the olympics background, spent years on that. as one of my profs said, "mathematics is not a spectator sport"

the proofs you have to know for the exams come in the end-product form, with crucial steps omitted, so you just have to memorize the key points and fill in the blanks, they're useless as a didactic device. books about proofs theory, "how to prove it" etc, are useless as well, knowing about the types of proofs, stuff like that, doesn't make you good at doing them

if i had the time and the will to do it again, i'd start with euclid's elements, and some proof based course, graph theory for example, and go thoroughly through the exercises. "putnam nad beyond" is a nice collection of worked out examples.

the last thing, i'm not sure if the whole thing is worth the time. at the core of a proof is an intuition about how something works, the rest is tedious, laborious formalism. being able to read mathematical texts, experimenting, being able to handwave it, i don't ask for more.

Anonymous Mon Oct 31 22:45:15 2022 No.14953032

>>14952541
If you really understand the mathematical objects you're working with, you won't need to memorize any proofs. That understanding comes after doing lots of exercises, staring at definitions for a long time, working through examples, and generally gaining mathematical maturity over time. There's also a big difference between memorizing a proof and learning a proof: if you memorize that we need to pick delta to be epsilon squared over 2 that gives you no knowledge of or insight into the behavior of the object you're studying; it might be useful before an exam, but won't increase your mathematical ability. There's not much for you to do other than read a lot of proofs and do a lot of exercises, ideally from several sources. It'll come with time.

To be fair there are some proofs and solutions that rely on "tricks" or clever substitutions, especially in differential equations and other fields that rely heavily on guessing. But in the more "proof based maths" >>14952541 is talking about these are the significant minority. (also pretty sure we went to the same uni; heard a lot of "maths is not a spectator sport" in year 1)

If you want better or more specific advice OP you should give us more information. what classes are you taking? what in particular is giving you trouble?

Anonymous Mon Oct 31 22:54:19 2022 No.14953045

>>14952541
so you confirmed with that my fear, but surely there is a way to improve in the various crafts that creat the proof, like reading and writing logical steps in mathematical symbols.
I am sure that you are aware of books that have indepth example and exercises that allow you to take part actively in the learning process, like it should be.

I agree on your last point, it just feel like reinventing the wheel, that someone else already done it before, but nonetheless it's fascinating to see how smarter people come to that proof and their method

>>	Anonymous Mon Oct 31 23:00:07 2022 No.14953055 >>14953032 I am taking computer science, I like maths and would like to be proficient in it, because I want to pursue research in AI later on.

>>	Anonymous Mon Oct 31 23:04:38 2022 No.14953062 >>14952408 just practice take any textbook you like and do the exercises

>>	Anonymous Mon Oct 31 23:31:42 2022 No.14953099 >>14953045 putnam and beyond the art and craft of problem solving

Anonymous Mon Oct 31 23:37:07 2022 No.14953104

>>14952408
>>14953099
>good books
>putnam
The problem with recommending books and competitions on this public forum is bugmen will copy you
then your effort will be valued less in the grand scheme of things.
Look deep within yourself, build your own foundation and never tell it to anyone.

Anonymous Mon Oct 31 23:45:01 2022 No.14953109
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>>14953104
>The problem with recommending books and competitions on this public forum is bugmen will copy you
>then your effort will be valued less in the grand scheme of things.
>Look deep within yourself, build your own foundation and never tell it to anyone.

>>	Anonymous Mon Oct 31 23:49:35 2022 No.14953115 File: 108 KB, 1022x1024, 6543154345.jpg [View same] [iqdb] [saucenao] [google] >>14953099 thanks anon

>>	Anonymous Tue Nov 1 08:49:10 2022 No.14953720 >>14952408 A Pathway Into Number Theory - RP Burn Numbers and Functions: Steps Into Analysis - RP Burn i probably wouldnt hurt to solve a fair amount of logic puzzles first

Anonymous Tue Nov 1 09:31:56 2022 No.14953743
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>>14952408

Read A Primer of Abstract Mathematics, by Robert Ash.

This book is a million times clearer than every other math book I've read on the topic of basic proofs. It saved my ass sophomore year at UC Davis. Concise, no-nonsense to the point book that contains only important non-calculus math stuff you see in your sophomore year. Starts out with logic and set theory, moves on to basic number theory and combinatorics, and later linear algebra.

>>	Anonymous Tue Nov 1 20:30:51 2022 No.14954839 >>14953720 thanks >logic puzzles first I guess you mean like in puzzle books like: Of Course! The Greatest Collection Of Riddles & Brainteasers For ExpandingYour Mind By Zack Guido. >>14953743 thanks I will keep that in mind

>>	Anonymous Wed Nov 2 14:23:46 2022 No.14956177 >>14952408 >What do you guys recommend to improve learning, any good books on the subject ? https://uwosh.edu/mathematics/outreach/big-ideas/

>>	Anonymous Wed Nov 2 18:42:29 2022 No.14956649 >>14952408 No man, you gotta like learn how to tell logic stories from the heart, bro.

Anonymous Wed Nov 2 18:59:24 2022 No.14956685

>>14956649
>be me
>phd professor, almost getting tenured
>spent years dedicated to maths, learning the craft and how mathematicians work
>get tenured, can troll anyone i want now
>student asks how mathematicians prove and read proofs
>"you just do it from the heart kid, there really isn't any method to it and nothing you do will make you better, just go with the flow. You either have it in you or you don't, sorry.", I say, as I hide my 2 copies of books that teach how to think like a mathematician

>>	Anonymous Wed Nov 2 19:07:36 2022 No.14956701 File: 65 KB, 165x236, 4t5ios.png [View same] [iqdb] [saucenao] [google] >>14956685 >books that teach how to think like a mathematician post those books, NOW.

>>	Anonymous Wed Nov 2 19:49:21 2022 No.14956798 >>14956701 no

>>	Anonymous Wed Nov 2 19:54:14 2022 No.14956809 >>14953104 this but unironically

>>	Anonymous Wed Nov 2 20:00:11 2022 No.14956826 File: 106 KB, 606x454, FHDrbSMXoA4A-fg.jpg [View same] [iqdb] [saucenao] [google] >>14956798

>>	Anonymous Wed Nov 2 20:17:40 2022 No.14956871 >>14956826 funny meme, here it is https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X/ https://www.amazon.com/How-Prove-Structured-Daniel-Velleman/dp/110842418X/

>>	Anonymous Thu Nov 3 06:49:41 2022 No.14958081 >>14953743 do you have pdf for this title? if so, could you upload it?

>>	Anonymous Thu Nov 3 12:46:54 2022 No.14958476 >>14952408 How to prove it by Velleman

>>	Anonymous Thu Nov 3 13:17:39 2022 No.14958521 >>14952408 >I am decent at Math, but recently started learning how math proofs work No you're not.

>>	Anonymous Fri Nov 4 03:15:11 2022 No.14960012 >>14958081 Unfortunately, this book hasn't been scanned or uploaded online, so I bought a hard copy. Personally, I thought it was worth it, but I also was motivated by needing to pass my classes.

>>	Anonymous Fri Nov 4 03:20:21 2022 No.14960021 >>14960012 Huh, looks like the book isn't available new anymore. I bought it for $35 new on Amazon but now copies seem to be going for $100+. What a shame.

>>	Anonymous Fri Nov 4 03:23:56 2022 No.14960028 >>14960021 Wait a minute, some guy on ebay is actually selling it for $5: https://www.ebay.com/itm/155133758457

>>	Anonymous Fri Nov 4 07:04:12 2022 No.14960347 >>14960021 author died some years ago and seems most of his titles are still available on his university webpage except this one.

>>	Anonymous Fri Nov 4 07:53:12 2022 No.14960408 >>14952541 >neither did like 80% of graduates. western "education" system

>>	Anonymous Fri Nov 4 07:59:47 2022 No.14960414 K bye

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