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/sci/ - Science & Math

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3179786 No.3179786 [Reply] [Original]

Consider me a highschool summerfag with absolutely no prior knowledge who wants to read some scientific shit.

Principia Mathematica is first on my list. What should I read next ?

>> No.3179801

some Feynman book

>> No.3179795

old book is old

>> No.3179805

Stupid first choice, start of with something comparably light, I'd advise Bill Brysons A short History of Nearly Everything. The Principia is a horrendously tedious book that you would neither understand nor enjoy.

>> No.3179834

>>3179801
Read the first few chapters of The Feynman Lectures on Physics, I liked it a lot.

>>3179805
What else would you recommend?

Just to clarify, I'm not a full retard (I hope), just have limited knowledge that I want to increase over the summer.

>> No.3179839

>>3179786
Somehow I don't see you understanding shit that's in Principia.

>> No.3179842

introduction to categories- may be somewhat difficult but work very slowly

what is mathematics (courant)

letters to a young mathematician- best book for high schoolers

>> No.3179846

Don't read the fucking Principia, Newton's take on calculus is horrible, and was already outdated by Leibniz's when he published it.

That book alone slowed down mathematics in Britain for centuries.

>> No.3179849

"Some scientific shit" is too general

Hell even "some biology" or "some math" would be hard to steer in a direction.

What interests you OP?

>> No.3179852 [DELETED] 

>high school
>probably doesn't know calculus or DEQ
>wants to read Principia

Yeah, it'd be more worthwhile to learn some math right now.

>> No.3179854

>>3179842
oh yeah, i forgot a few things

godel escher bach is great for beginners wanting to learn some logic/math

the first part of discrete math by rosen is golden with hard and easy exercises mix.

how to prove it by velleman

paul halmos's autobiography

>> No.3179856

>>3179786
why the shit would you read the principia, just study classical mechanics physics textbook and calculus

>> No.3179866

>>3179786
Try Hardy's Course in Pure Mathematics; it's a good intro to college math and the excercises are a good challenge.

>> No.3179870

>>3179786
Godel, Escher, Bach: Eternal Golden Braid.

>> No.3179871

>>3179849
Mainly math, physics as a close second and logic, but not that much. 'Some scientific shit' was more meant to be interpreted as science related books that you wish you read earlier because they helped you understand math/logic/world better.

On the second thought, I was being a bit vague. Sorry about that.

>> No.3179893

The Elegant Universe by Brian Green is a great book about quantum theory, you could also try some of Steven Hawking's books: A brief History of Time, The Grand Design. I personally find them a tad too chocked full of equations and mathematical proofs, but maybe that's what you want.

>> No.3179912

>>3179852
Eh, I guess you got that right. I know some basic derivative/antiderivative things, but what is that used for is beyond me. It isn't taught before university here, so I'd be delighted if you could recommend me a calculus book.

>>3179854
I heard GEB was something of a holy grail for beginners, I guess I'll have a chance to check it out. I read 'How to solve it' and damn, it changed my view on some things. That's the kind of book I'm looking for. Thanks a lot.

>>3179856
Fuck me, heard it was a good book. Seems that I'll have to wait a while to be able to understand it.

>> No.3179923
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3179923

Am I high or /sci/ is helping a underage b&?

GTFO faggot.

>> No.3179927

>>3179871

I think you have expectations that cannot be accomplished. Getting knowledge of what is really going on in this world takes, at least for me, years and years of study of science out of textbooks.

Then there is some great books out there but you only get the true and deep meaning of them when you have worked trough those years of studying and can see how great these minds are.

Nevertheless this is jsut my personal opinion, do whatever you like.

>>3179893

I once read a popsci book by Hawking, they are horrible, I never would anyone else to experience such...

>> No.3179935

>>3179871
>>3179871

I would say that ounce for ounce, the best scientific textbook was "The Art of Electronics."
It might be a little beyond you, but it's just basically simple circuitry and electronics once you boil it all down.

I read it on a whim when I was done with undergrad and realized just how much fucking electronics goes on in any field you go into. Best textbook I ever used.

>> No.3179995

"Stardust" John Gribbons

A nice, interesting introduction to Physics.

>> No.3180026

>>3179786
>Wants to read PM
>No prior knowledge

Reminds me of how nihilsts begin:
>Buy Der Einzige und sein Eigentum
>Stop at page 4

No, OP, try something else, start with the Feynman lectures. They're good.s

>> No.3180030

While this might sound stupid as fuck; I really wish this collection had existed when I was learning this stuff:
The Manga Guide to Calculus
The Manga Guide to Molecular Biology
The Manga Guide to Physics
The Manga Guide to Electricity
The Manga Guide to Statistics
The Manga Guide to Calculus

>> No.3180046
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3180046

>>3180026
I have some bad news...

>> No.3180037

>>3179927
It would be horribly stupid of me to expect to suck up all of worlds knowledge in 10 books. I was actually just hoping for solid foundations that will allow me to advance better. An obvious example would be learning university level math before university, so I can focus on other things.

>>3179935
I'm not that much interested in EE, but I'll be sure to put it on my reading list.

So far we have:
>GEB
>letters to a young mathematician
>discrete math by rosen
>How to Prove it - re-read
>eventually Feynman Lectures

Anything else ?

>> No.3180060

The Road to Reality by Roger Penrose is excellent, I recommend you read it.
It may seem boring, but I'd also recommend you learn how to use C++ or some other programming language. Knowing how to program is a huge part of science.
If you feel like watching something good torrent Cosmos by Carl Sagan, and watch Lawrence Krauss giving his lecture "A universe from nothing", which details the possible origin of the universe.

>> No.3180099

>>3180046

Does this bother you?

>> No.3180100

>>3180046
except his sage was used in the proper way, much like I am using it now.

>> No.3180110

>>3180037

Ok, it was just that I understood like you expect the worlds knowledge in 10 handy books.

Maybe something in the style of " Physics for dummies" then ? Or anything with "for engineers" in it. This post was not meant to sound rude but in these books they explain the stuff in much easier terms and the basic idea is better to grasp. When I started to study physics I left school with horrible notes and virtually no knowledge on math before entering university. I didn't know what a derivate does, I didn't know what integrals to, I couldn't even calculate most of them and I sure had forgotten everything on vectors but then I read a German book whose title translates as " Math for Physicists " and I worked it all trough in summer holidays and understood even integrals it was great and I got good grades in the first semester on university.

>> No.3180158

If I could go back, I'd learn Calc 1-3 cold, and work through as much Feyman Lectures as possible.

>> No.3180189

>>3180158
If you could, how would you learn calc 1-3 ?

>> No.3180261
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3180261

>> No.3180272

I thought OP wanted to read Russell's Principa. I almost died of laughter.

>> No.3180278

>>3180272
There's a different one?

>> No.3180281

>>3180030

Holy shit, not OP, but I like this :D

>> No.3180307

>>3180278
>>3180272
Newtons and Russells. Could be more though ?

>> No.3180313

It pisses me off how people use the work of heisenberg's, uncertainty to the application of particle physics, and use it philosophically to create the argument that things may or may not exist (the tree falling the woods scenario).

The two ideas are not all related. Stop quoting heisenberg you hipster douches.

>> No.3180318

"Emperor's New Mind", "Godel, Escher, Bach", "Classical Mechanics" by Kibble and Berkshire, "div, grad, curl and all that", "Introduction to Electrodynamics" and "Introduction to Quantum Mechanics" by Griffiths, "Statistical Mechanics" Mandl.

You don't need to complete the maths books before starting on the physics. For inorganic and physical chemistry Atkins is good, but I've never read any organic chemistry. I know nothing of biology.

Get some biographies like "Men of Mathematics" and "The Strangest Man" to inspire you too.

Don't run before you can walk, it will save you plenty of time and effort. I have to go now, good luck.

>> No.3180377

While we're on the subject of highschool summerfags who want to learn about shit, what are some books on neuroscience and astrophysics I could read? Those are the two fields I'm considering and I'd love to learn more about them.

>> No.3180588

>>3180377
Dunno about neuroscience, but be sure to watch Sagan's Cosmos

>> No.3180760

>>3180588

Definitely Cosmos. And if you can find them online - Brian Cox's Wonders of the Solar System/Universe.

>> No.3180859

>>3180189
To be honest, I'm not really sure what the best way is. I used Stewart in college, but there's got to be a better way. Maybe one of the Dover books (for rigor), coupled with something softer and friendlier?

>> No.3181126

Do not read PM. If you mean the math one, generally speaking, mathematics texts\papers in general can be critiqued in the following:

- They are necessary.
- They are enlightening.
- They are readable.

For (almost) every math paper, you may pick at most two. PM suffers from having only the first property. The PM you also may be referring to is Newton's, which actually suffers from having only the first property as well. Feynman's lectures have the latter two, making them pretty good.

Some other criticisms of books which have been suggested:

I'm currently reading GEB right now, and it is a great book, but I would hardly consider it great introductory material for science. If anything, it is a differing viewpoint from what is already out there (or, was, when he wrote it).

I would NOT recommend reading The Road to Reality. I had already learned most of the concepts in the book when I began to read it, and the way he presented them made me confused about the things I already knew! The way he teaches the mathematics (primarily beginning when he talks about spinors) is horrendous.

I do recommend Brian Greene, but after you read his work you should also read Lee Smolin's so as not to be one-sided. Take both with a giant grain of salt. But they do explain rather well what is going on in physics now-a-days. Smolin's also has the nice advantage of talking about how most departments "really" work. Or, at least, how mine does. Ha.

>> No.3181145

If you want stuff on biology, there's an assload of nature documentaries out there. Just pick up a few that seem to interest you (preferrable narrated by David Attenborough because he's awesome).

>> No.3181153

As for how to learn things. For calculus, my calculus classes are required to have some book authored by Sallas, which is not terrible, but Stewart is my choice text. I often will give my more advanced students "online" copies of the text so as to give extra credit reading or questions. It is an exceptional book, and if you go through it slowly and do lots of exercises, you WILL learn calculus.

I don't know how to do a lot of the ODE, PDE stuff required for more advanced non-pure physics, but there are a number of good books out there for both. In particular, MIT offers online courses for at least one of those.

As for pop-math, the two books I would recommend above all else are: Euler's Gem, and How To Solve It.

I don't usually recommend text books unless the OP specifically has something in mind that they love. Usually what happens is that they will buy the book, skim through it reading the theorems (omitting the proofs, mostly) and attempt to do 4 or 5 problems from the chapter before getting halfway through the book and quitting. Take note OP and others: I have never, in my life, completed a text book and understood the subject to where I was comfortable in less than three and a half months. Most take at least half-a-year. Make time for these things.

>> No.3181159

If you're interested in mathematical logic (which you should be, because it's awesome) I highly recommend Alfred Tarski's introduction to logic.

>> No.3181169

Everything and Nothing with Jim Alkalili or however you spell it.

It basically covers the history of physics

>> No.3181206

Do you guys know any book that includes something about elliptic geometry?

>> No.3181234

>>3181206

There are a number of good books on this topic, but it depends on how much mathematics you've already seen. A lot of them require more advanced mathematics, at least in some later chapters.

>> No.3181259

its not exactly mind blowing or rigorous, but if you're looking for a basic pick up on some subjects, theres khanacademy.com

>> No.3181261
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3181261

>>3181206
http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf

Free books are fun for the whole family.

>> No.3181265

Godel
Kant
Sagan

/Thread

Nigger nigger re nigger nigger

>> No.3181362

>>3181261

Have you read through this text? What do you think of F's presentation?

>> No.3181405

>>3181362
I've actually never read it myself, but I'm led to believe it's a fairly standard intro text for the subject.

>> No.3181523

>>3181405

I just have no idea what class this would be for. I'd use Atiyah and Reid for Intro to Comm Algebra + Alg Geom, which he seems to crunch into the first few chapters, but then I'd use Kirwan for Algebraic Curves. I don't know what level a student would have to be at to make any use of this book. Nonetheless, I'm enjoying reading it now. Fulton's "three paragraphs then some exercises" style certainly is attractive here.

>> No.3181764

Reviving thread.

Skip Polya's How to Solve It, read How to Solve It: Modern Heuristics by Zbigniew Michalewicz.

>> No.3181789

>>3179786
>heisenberg may AND may not have been here

fix'd

>> No.3182439

>>3179846
10/10.

made me rage

>> No.3182484

>>3182439

too bad he's correct. the horrible british mentality that sparked during the dispute over who invented the calculus dropped britain out of the head of the mathematically world for almost 200 years.

it wasn't until the 1900s with mathematicians such as hardy that it really returned. the majority of the 17/1800s was dominated by france and germany.

i would recommend books by Paul J. Nahin
such as:

Dr. euler's fabulous formula
Sqrt(-1): an imaginary tale

also a book called
E: the story of a number

and

The calculus gallery.

these are all books that require knowledge of calculus 1/2, but will deeply expand your knowledge and teach you much about the history of the mathematics as well as touch on many topics you wouldn't find elsewhere easily

>> No.3182487
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3182487

It's not the most math intensive book by any means, but reading flatland to me was a really eye opening experience and made me really think. I highly recommend it. (it's a very short novella)

>> No.3182589

>>3182484
Why shouldn't I read it?
What problems will I get if I do read it?

>> No.3183289

>>3182589
Brain poop smear.

>> No.3183294

Principia isn't worth it. A modern set theory textbook will do exactly the same thing without being written with archaic syntax and style.

>> No.3184277

>>3183294
Bullshit.

>> No.3184356

Russell's Principles of Mathematics is a good one.

It will kick your ass, tho.

QM and the Schism in Physics by Popper is a great intro to QM.

>> No.3184485

>>3184356
>Russell's Principles of Mathematics
>for a highschooler

Are you serious ?

>> No.3184653

>>3184485
Yes. I do believe I qualified my recommendation with an admonition, something to the effect of "It will kick your ass," no?

It's as lofty mathematically as all fuck, but it's the thing one should naturally read upon completing the Principia.

>> No.3184722

Psuedo-pop books; psuedo-pop books err'where.

>>3181153
>How To Solve It.
>pop math

What the fuck? Are you high? How to Solve it by Polya and the "Art of problem solving" by Tao are texts utilized by a voluminous amount of individuals who partake in Olympiads, Math contests and Putnam examinations. That book is far from Pop math. It's equivalent to the Bible in regards to it's usage in mathematical competition.

>> No.3184738

>>3184277

That poster is partially correct. Principia should be read at your own leisure when you have the time/already well versed in Calculus, not for learning. I'd know since I read/went through it last year.

The Geometry in that book is fucking groundbreaking, though. Dat celestial mechanics.

>> No.3185239

>>3184738
Since OP is long dead, I have to ask for myself, which book would you recommend for calculus ? Is there *the* ultimate book or are we stuck with something less good ?

>> No.3185796

>>3185239

First read Rudin "Principles of Mathematical Analysis" cover to cover (which I have yet to do myself, rigorous, standard college text for real analysis) and then read Spivak "Calculus on Manifolds" or Munkres "Analysis on Manifolds" (rigorous, standard multivariate analysis texts)

>> No.3185917

Start exploring journal and article collections like pubmed etc, understand the scientific method.

Watch interesting films which prompt ideas that you can explore. Be they philosophical, scientific or artistic. Gattaca being an example.

Read new scientist. Pick an article and explore it fully until you know every fucking thing about that topic and you can talk about it confidently

Read lots and lots and lots of wikipedia

>> No.3186520

bump

>> No.3188624

bump

>> No.3188710

>>3185796
you should probably start off with ross or courant (both called analysis). courant is only cryptic if you overcomplicate it yourself and don't read word for word. if you do the exercises and get the answer book, calculus proofs will be very clear and intuitive. the main thing is to think in "inequalities".

the best book to use before proofs is probably discrete math, rosen, even though people usually recommended a "real" proof book. rosen can be downloaded and has very good examples. the most important chapters are the ones about induction/recurrence relations. knowing about "assume, if, then, thus" etc. are extremely important for organizing your thoughts and leading yourself to an answer.

doing exercises will show that you don't understand a concept, and understanding them will increase your ability to reason with what is laid out in front of you, though this will happen slowly. also, if you're thinking about skipping discrete math (i don't recommend skipping induction, which is incredibly important for all things), ross walks you through proofs step by step. Read up to mathematical reasoning, and if you have time, counting/advanced counting/relations are important (but not so if you're just doing calculus)

finally, when going over proofs, do a 'structured' version. if something seems to skip over a step (assumes a theorem) WRITE THAT SKIPPED STEP somewhere! this patches the gaps in your reasoning very well. after a while, redo the proof by yourself, and follow this by doing proving theorems that follow from that theorem by yourself.

>> No.3188956

Shit, this thread is gold.

>> No.3188989

>>3188956
It's 2 days old. Keep it alive.

>> No.3189337

>>3188989
Making a humble bump.

Also, for whoever enjoys doing really heavy math problems, get some russian books. Demidovich is one crazy son of a bitch.

>> No.3189461

yo i'm gonna take commutative algebra at MIT next year, what's the difference between eisenbud and atiyah? atiyah is like 130 something pages but it's still pretty fucking expensive i heard but are good howerver

>> No.3189928

Bumping a good thread, GEB has made my reading list.

>> No.3189936

Entropy and Information is a good book, however I will stop reading it until I get some hold of Calculus (My high school doesn't teach it).

>> No.3189985

>>3185239

Start with a standard undergraduate text in Calculus, like James Stewart. From there, move forward into greater/better texts mentioned in the thread. Use Khan Academy and PaulsOnlineNotes as an aid. /sci/ is willing to help you out if you're really stumped/not searching for answers. It's not considered HW if you're doing self-study.

>>3188710
>>3185796

Are you guys fucking high? I'm not trying to insult either of you, but these books are too intense for someone to learn right now. Calc on Manifolds is a text that I read through for Diff. Geometry and that shit ain't "nothin 2 fuk wit." You're giving him too high of a mountain to climb. He has to start slow with slopes, climb upwards along hills and then, maybe if he feels comfortable, he can start climbing "mount analysis." Until then, he has to start from scratch and do the atypical/standard "plug'n'chug'' Calculus.

What you guys said is beneficial for someone who has already learned the rudimentary; but, he's just starting out. He needs to go through the Calculus series first, and then move forward into Analysis(of course, taking discrete math/standard proofing course is also necessary). You guys also haven't mentioned Abstract Algebra/Group Theory, which is ESSENTIAL to proof writing.