/sci/ - Science & Math

>>7426799
bump, for same

>>7426799

I'm very interested in small scale hydroelectric generation.

Anyone know of good books on the topic?

I guess I should read an introduction to power systems as well.

Would appreciate help with either.

>>7426799
Spivak's mechanics?

>>7426799
ARNOL'D
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>>7426799
Ol' Spivvy literally wrote books by the name of physics for mathematicians.

>>7427013
>introduction to power systems
Power System Analysis and Design by Glover might be what you're looking for.

Sets, Logic and Categories
Gives a short introduction to concepts related to the title such as:
Isomorphisms
Ordinal Numbers
Formal Logic
Gödel's Theorem
Axiomatic Set Theory
Maybe some computability/turing stuff
Category Theory

For anyone comfortable with the material in Categories for the Working Mathematician or Handbook of Categorical Algebra, I definitely would recommend Sheaves in Geometry and Logic by Mac Lane and Moerdijk. I finished it last month, and found it to be very engaging and accessible while still presenting an admirable amount of rigour that you would expect from Mac Lane. 9/10, would recommend.

advanced electromagnetism
(for an EE, I have basics of EM down ie plane waves)

>>7427153
Sounds like a book that tries too hard to shoehorn in various topic. Those books normally suck. It's better just to get the `classic' books in their respective areas.

In what order should the 3 books authored by John M. Lee be read?

Also, what's the best introduction to differential geometry for someone who knows nothing about the subject? I know there are a ton of introductory books out there, but which is the best and smoothest for a beginner?

>>7427177
Following books, in order, start where appropriate:

>Electricity and Magnetism by Purcell/Morin
>Introduction to Electrodynamics by Griffiths
>Modern Electrodynamics by Zangwill
>Classical Electrodynamics by Jackson

>>7427205
Try Spivak

>>7427205
There is no good introductory book in differential geometry out there.

Is what every grad student, postdoc, and professor has told me.

>>7427209
>Classical Electrodynamics by Jackson
ahh, I had downloaded the pdf of that book, it is very physics major based. Relativistic charges and whatnot. I'd still want to learn about those, I am actually considering continuing with straight up applied phys grad study.

can someone compare the Jackson's EM and Balanis's EM textbook

>>7427348
I've never read or done exercises from Balanis but from what I remember it is more practical, i.e. suited for engineering or applied physics. Jackson is more for theoretical or experimental physics grad students. If you read Jackson and do the (absolutely grueling, demoralizing) exercises then absolutely nothing in the field of electrodynamics will ever come as a surprise or be 'new' to you, but it might be overkill for what you need.

>>7427414
May I ask what you do / study?

>>7427431
I have a bachelors in physics and took a couple grad classes as a senior (GR, E&M) I got a C in E&M which used Jackson, really cheated myself and didn't get much out of the problem sets.

>>7427159
seconding this- it's awesome(ly easy to read) and the content is very cool. easier than johnstones Topos theory by a longshot. I'm incorporating some of it into my research now.

Want to self study physics. I took the advanced intro courses at my Uni, but didn't pay attention and got Bs in both.

I was thinking about working through Young rigorously. Is this a good idea? If not what should I use.

Also, what should I move onto after I've mastered classical mechanics

>>7427526
What's your background?

>>7427532
Third year computer science undergrad with limited math knowledge.

I've gone through baby Rudin, and learn a decent amount of Linear Algebra for CS stuff. I also know VERY basic ODEs

However I would want something as rigorous as possible

>>7427532
>>7427546
pls respond

>>7426799
Please could people recommend me some books relating to signals, filter circuits and various audio circuits. I would also like to learn how to solve problems relating to these subjects with a programming language. I've just finished my first year of an EE course, I know how to program in C and I'm currently learning C++ if that helps people to narrow down their recommendations. Any help would be appreciated, thanks.

>>7427585
>signals
>filter circuits and various audio circuits
>programming language

dawg, that shit is all over the place
what do you mean by 'signals'

> I know how to program in C and I'm currently learning C++ if that helps people to narrow down their recommendations.
if you want to stay on an EE path and not become a programmer, it really matters not what languages you know and the way CS students learn such languages will be completely irrelevant. You don't need to know objects and whatnot, you need to be able to write algorithms and do scientific computation. Most codes are write are just a single file for example.

For EE, just torrent MATLAB, its visualization capabilities is going to be far more useful than the fast execution times of real programming languages.

>>7427546
Okay then.
>Mathematics

First you'll have to get gud at ODE's and PDE's, unfortunately I don't have many good recommendations for those subjects, however for PDE's I'd recommend Strauss "Partial Differential Equations".

You'll need a mathematical methods book as well, I used Riley, Hobson and Bence "Mathematics for physics and engineering"

I'm guessing you've done some multivariate calculus, so reading "Div, Grad, Curl and all that" should be sufficient to understand a lot of physics, it might leave you wanting in a few places however.

You'll also need to be versed in tensors, I used "A students guide to vectors and tensors", however I'm loath to recommend it since I thought the tensors part (the whole reason I bought it) was lacking, that said it'll give you an adequate understanding of the subject. I've heard "A Brief on Tensor Analysis" by Simmonds is pretty good.

You'll also need to be versed in Lagrangian and Hamiltonian mechanics, again I used a "students guide to Lagrangians and Hamiltonians" and again I found it to be so so.

>Electrodynamics

In order, I'd go:
Purcell "Electricity and magnetism"
Griffiths "Introduction to electromagnetism"
Greiner "Classical electrodynamics"
Jackson "Classical electrodynamics"

That last one is pretty hard, so be careful with it.

For an alternate and more interesting take on EM I can whole heartedly recommend

Baylis "Electrodynamics: A Modern Geometric Approach" It uses something called "Geometric algebra" and explores it using that formalism instead of the usual vector algebra.

>Quantum mechanics

Griffiths "An introduction to quantum mechanics"
Grenier "Quantum mechanics: An introduction"
Shankar "Principles of quantum mechanics"

>Thermodynamics

THERE ARE NO GOOD BOOKS ON THERMODYNAMICS

>Statistical mechanics

Bowley "Introductory statistical mechanics"
Greiner "Thermodynamics and statistical mechanics"

>Fluid mechanics

Chorin "A mathematical introduction to fluid mechanics"

cont...

>>7427546
>>7427572
>Want to self study physics.
why? what's your end game?

>>7427640
to know a lot about physics

to gain a better understanding of the world.


I don't know what a fucking Gluon is

>>7427634
a very nice post, I am not criticizing your post
but >>7427546, it will take sooooooooooooo much time. Do you want to learn physics to understand meme physics, or do you actually really enjoy physics enough to learn the sufficient math for it? If latter, shouldn't you have picked what you would enjoy as your major/career?

What's the best Intro to Physics for an auto-didact who just wants to learn the basics/fundamentals (maybe go onto other topics if I get interested) I do not have alot of knowledge (as in the actual formula and equations behind it) on the subject but I don't want something so basic I don't learn anything. Cheers in advance.

>>7427648
I just don't have money for a college education, so I'm sticking to something that I'll be able to pay off student loans with.

>>7427646
>I don't know what a fucking Gluon is
people who do phd, ever get to that point
that is like 10 years worth of effort
unless you stop everything you do, be a neet physics enthusiast, you'll never get there

>>7427653
Classical Mechanics by Goldstein

>>7427657
well I may as well start and give up later.

I'm a weird person. I honestly do want to study physics for 10+ years on my own time. If it doesn't work out, then so be it.

>>7427634
also I was waiting for the second post, but just so you don't get discouraged, thanks so much for the recommendations.

>>7427513
Johnstone's Elephant is great as a reference, though.

>>7427661
alright, stick to books that have a solution manuals, since you wont have anyone to ask questions to
also you can ask your questions no physics/math stackexchange

>>7427659
Cheers mate

>>7427672
would it be weird to just hit up a physics professor and ask for guidance?

I might be going for a MS in Machine Learning if I can convince a company to pay for it, and I've still got 2 years here left in undergrad

>>7427672
>solution manuals
This is a bad advice.
If you understand the content then you will know that your solution is correct if you don't understand it then you should reread the chapter and think about it until you have understood it.

>>7427681
bullshit advice, solution manuals are instrumental

>>7427681
Ignore this guy, he's fantastically retarded. Solution manuals guard against stupid math errors, and can reinforce the learning of new material.

>>7427634
cont...

>Special relativity

French "Special relativity"
Woodhouse "Special relativity" This more mathematical than the previous, as you'd expect being part of springers undergraduate mathematics series.

>Quantum field theory

Some people might recommend Griffiths here, I don't I hated it.

Lancaster "Quantum Field Theory for the gifted armature"
Greiner "Field quantisation"
Greiner "Quantum Electrodynamics"

>General relativity

Hobson "General Relativity: An Introduction for Physicists"
Shutlz "A first course in general relativity"
Woodhouse "General Relativity"
Wald "General Relativity"
Misner "Gravitation"

>Advanced mathematics (inb4 mathfags)

There's so much I could put here, but instead I'm going to direct you to Peter Szekeres "A Course in Modern Mathematical Physics". It's breath is astounding but unfortunately isn't that deep, use the references pages at the end of each chapter to go further.

>Supersymmetry

Okay I shit you not Labelle "Supersymmetry demystified" is a great place to start provided you know some QFT, use the references to delve deeper.

>Speculative theories

Zwieback "A first course in string theory"
West "Introduction to strings and branes"

There if you follow that you'll be upto date (more or less) with modern physics, unfortunately to go through this list will take a few years, if time isn't an issue then I recommend you go through it step by step. However if you don't have time do the following:

>Read the first listing in each category
>If a category has a book by Grenier in it, read that as well.

That should see you though. Good luck.

>>7427681
you can never go through an entire textbook without the solution manual unless you have a lifetime to invest on it

>>7427692
Thanks, man.

I'll be making that EM drive in no time


So to clarify, "Classical Electrodynamics" by Greiner differs enough from "Classical Electrodynamics" by Jackson to warrant going through both of them?

>>7427634
>>7427692

quality posts m8

>>7427701
Jackson has no equal

Is Asimov's Understanding Physics good for a layman?

Does anyone want a copy of that AAMC book, The Official Guide to Medical School Admissions?

>>7427711
but this also means you don't need to do jackson unless you want to specialize in EM

>>7427701
Jackson is a lot deeper than Greiner it's also more terse. To put it in perspective when I learnt EM my lecture referred to Jackson as "the bible of classical EM", in some ways unless you really really really want to understand every facet of classical EM, you can probably skip it without any loss in continuity.

>>7427716
Fair enough

Is there a good R book out there? I've heard about R Cookbook but it seems to be more of a hodge podge than anything

However it is worth nothing, if you want to deal with EM to some extent, you might want to go through jackson only to know what is in it so that you might use it as a reference later on

>>7427740
If it is worth nothing, I will not be taking this advice. Thanks for the heads up!

>>7427629
Haha, yes my response is a bit all over the place as I am very ignorant of the topics I've mentioned and need to learn more before I choose a set career path. By signals I mean analysis of signals (sorry for the badly worded question). I have experience with matlab but I thought it would help me to develop my progamming skills to learn to apply C/C++ to a real problem. But if you feel it's wasted effort I respect your opinion and if no one can recommend relevant textbooks then I will just use matlab. Thanks for your response and I hope I have been able to clarify what I was trying to say.

Best mathematical methods for physics book?

>>7427692
>Zwieback "A first course in string theory"

This book is shit. It assumes the reader doesn't know general relativity. It spends half the book doing string mechanics.

String theory for undergraduates is a stupid idea. Learn everything to a graduate level, learn QFT, then learn string theory. Learning string theory that soon is a waste of time.

>>7427692
>GR
>No Carroll

Come on man

>>7427634
>THERE ARE NO GOOD BOOKS ON THERMODYNAMICS
Really? Shit...

Any recommendations for more classical algebraic geometry, e.g. quasiprojective varieties? A professor gave me Shafarevich, but it's really not sitting well with me. Damn ruskie.

>>7427159
I've only read the first three chapters, but I agree that it's awesome stuff.

As of late, I just hit chapter 8 in Rotman's "Introduction to Homological Algebra". It's pretty good, I've found it much more friendly than Weibel, although there are a few too many typos.

My Fluid Mechanics book for next semester is getting absolute shit reviews on Amazon. Anyone have a rec for me to actually learn? Is >>7427634 good?

>>7428203
I just started Hatcher (having studied a good deal of category theory at this point, I want to get into modern homotopy theory); what other prerequisites will I need before trying to dig into Introduction to Homological Algebra?

>>7428251
Chorin and Marsden is good but you'll probably want some physical intuition to go with it so I'd say try Acheson.

>>7428289
You don't even need algebraic topology background for it. Obviously you should be really comfortable with groups, rings and topological spaces, but he goes over modules and pretty much everything else you'll need along the way. I thought his introductory section on sheaves at the end of chapter five wasn't as nice as most of the other parts of the book, so you might benefit by making yourself comfortable with them by the time you're 300 pages in. Not that skipping that stuff would make a big difference, but I think that the sheaf cohomology section in chapter 6 is the coolest part of the book so far.

As an aside, I'm a couple weeks away from submitting what will hopefully be my first publication, and the topic is in categorical homotopy theory! We classified the formal CW complexes you get from a specific model structure you can put on Grothendieck toposes. It's essentially baby's first research project with some support from my advisor, but I'm pretty happy about it, it was a lot of fun. So yeah, that subject is really rewarding.

>>7427159
>Categories for the Working Mathematician
Any prereqs for this? I dealt with categories a bit in Aluffi's Algebra but it mostly served as a setting in which to examine and explain the ideas of groups and rings.

>>7427689
>>7427690
>>7427697
Engineers detected.

If you can't even learn by yourself from a textbook you may as well give up right now, on living.

>>7428432
>Any prereqs for this?
What a dumb question. How about you download it and read the introduction for yourself?

>>7427634
>THERE ARE NO GOOD BOOKS ON THERMODYNAMICS


Holy shit is this true. This statement alone confirms that you know what you are talking about. Awesome posts by the way.

reading a standard math textbook:

>Preface
>No one reads this shit nor cares about your wife and how she allowed you to be a bad husband and write a shit book instead of spend time with her.
>Introduction
>Useless motivation, get to the point
>Chapters
>Theorem
>No proof provided. Author says it's obvious and relates to previous shit theorem 1.56
>Another useless theorem
>Outline of the proof but leaves the meat of it to the reader
>Another shit theorem
>No proof provided
>Well over a dozen homework problems that require techniques to prove it which are not covered in the book and require background material from a more advanced class
>New chapter
>Shitty forced quote at the beginning that only vague relations to the material covered
>Another shit theorem
>No proof provided
>Repeat till the end of the shitty book
>Go to Amazon
>Read how everyone rates the book 5/5 and how some old fucker from Harvard used this book in the 1960s
>Read about one guy stroking his dick and cumming in the book in 1975.
>See people recommend the book that obviously never read it

>>7428083
I found Carroll to be a confusing and bad writer. The only reason his book should ever be consulted is for the section on QFT in curved spacetime.

Logic: Techniques of Formal Reasoning
by Donald Kalish, Richard Montague, and Gary Mar

Excellent book with solutions for many of the exercises at the end of the first 8 or so chapters. It starts from modus tollens/modus ponens and ends with developing theories from analysis and number theory as examples, assuming nothing of the reader but a brain

Any recommendations for a book to help me learn intuitionistic/trivalent logic? No need for babby logic books since I already have a couple and I'm pretty comfortable with standard sentential and predicate logics.

>>7428499
>Richard Montague
Aw shit. I didn't know he did a textbook. I'll look at it despite my above comment! Babby books are always nice to help cement stuff I already know even further.

>>7428486

This tbh.

Any math books that are less terrible in this way? If I were an author it would be:

-Table of Contents
-Acknowledgments in the form of a list of people who gave actual help with the book, one page, no details on what they helped me with, no wifey (unless she actually helped me with technical aspects of the book), no kiddies. And only because they would get needlessly buttmad tbh.
-Main text: Definition, Theorem, Proof, minimal clarifying notes, then examples. One half page of "bird's eye view" before each chapter. And when I say proof, I mean PROOF, step-by-step, even little details filled in.
-End of book: really, really thorough index

>>7426799
Theoretical minimum by Lev Landau.

>>7428506
>Any recommendations for a book to help me learn intuitionistic/trivalent logic?
Get a book on suicide instead.

>>7428528
Anon, pls. This is a no bully thread.

I just want to ignore the law of excluded middle!

>>7428530
http://www.amazon.com/Introduction-Many-Valued-Fuzzy-Logic-Derivation/dp/0521707579/
Same chick who did the Logic Book. I will say that Kalish/Montague blows that book out of the water though. Might be too hard for the general plebs

>>7428533
Thanks! I'll see about grabbing a copy in some form.

>>7428530
Go suck an unexcluded cock, faglord.

shankar compared to griffiths for intro to QM?

Reading griffiths now, thinking about picking up shankar too but not sure if there's a point. Noticed a lot of the MIT lectures coincide with griffith's analogies and solution steps, but MIT has shankar as a textbook for the course.


memes

>>7428412
Oh, that's great! Congratulations! And, thanks for the information regarding the book. I have already added it to my library, and will probably move onto that next, unless I feel like returning to Leinster's "Higher Operads, Higher Categories" (it felt like it was becoming obtrusively sterile, and higher categories should be very natural objects, I think).

>>7428432
>>7428472
What a rude response... this is a discussive thread on textbooks, and perhaps the best place to ask a question about prerequisites.

I read Mac Lane with fairly little trouble as a Senior in high school, with only some knowledge of model theory, formal logic, set theory, and commutative algebra. The more you know, the more exercises you will be able to do, and the more examples you will understand. However, you only really need some understanding of set theory and ring theory, as most examples are given in the category of sets, with functions; or the category of modules over a fixed ring, with homomorphisms.

Learning the language of category theory is becoming almost necessary for any serious pure mathematician that wants to study something other than analysis, and even many analytic tools are made more clear when categorified (plus, you aren't going to REALLY get de Rham cohomology without a little category theory).

>>7428509
But then you would have a textbook dry enough to burn in a rainstorm. The best textbooks are the ones that find a solid balance between moral discussion of the constructions and theorems, rigorous proofs that are not sterile, and a small number of fundamentally helpful examples, perhaps with each relating to very different areas of mathematics.

>>7428486
>>7428509
Don't blame it on the writers if you're to stupid to even read a book.

is an operator on a smooth manifold known as a "smooth operator"?

>>7428251

Fundamentals of Fluid Mecahnics by Munson
Or if you are more advanced find Landau's text on it.

>>7428486
Hint: you might not be a mathematician... and that's not a bad thing

>>7426799
MATTER & INTERACTIONS I

>>7427714
Anyone?

>>7428509
I wouldn't mind a math book that proves the theorem explaining why they got to that demonstration, instead of trying hard to be as impersonal and dogmatic as possible

>>7428509
I would prefer reading a textbook like this, it could possibly be so good as to serve as a reference guide as one moves into more advanced areas.

>>7428509
What kind of books do you read ? I have rarely read a book that was not like this and as >>7428639 said, it can get pretty dry

>>7428709
>>7428652

A standard textbook like this may be fine in a class where the professor takes the incomplete proofs presented in the book and completes them in lecture and discusses the proof techniques used and reasoning behind them and then from there answers and clarifies any questions. At this point the students in the class (that paid attention) could go back and fill in the details to the other proofs and be able to do the homework assignments. This is pretty standard at any university math class. Maybe even an independent study class where the professor guides the students through the areas she struggles in.

But:
These books don't serve so well the students that aren't in a university setting or don't have access to other classmates or professors to clarify points, or check their work. The newb math student might think he has the correct logical reasoning and correct proof but might be missing a step here or there that doesn't necessarily follow from the axioms. This student will blindly just continue through the material having no idea if they are truly understanding the concepts or not. Maybe they get stuck on a problem and can't figure it out and the "hints" section says check theorem X but they do and they can't deduce it further. A typical university student will be able to present their work to the professor and get guidance "Use theorem X, do similar argument we did in class set k equal to this and derive from there to get your result and boom student is done. But the student NOT in university doesn't have this opportunity. In more recent times this has changed with the invention of stackexchange though, but stackexchange is no substitute for an actual university professor lecturing on common theorems/proofs and from there giving out assignments. The former student will be ahead of the student that is still stuck on the most ~basic~ incomplete proof they don't understand that the former student's university professor proved in class.

Are there any elementary number theory books that would fit a non-mathematician who's only had calculus?

>>7429218
Yeah, all that you've said makes sense if it is restricted to introductory books, that's my main problem with baby Rudin, which is an introductory book on basic stuff that is too hard to follow for most students.

But if it's an advanced book it is assumed that the reader is mature enough to complete most of the proofs in the book and at some point most proofs share the same pattern and it gets boring reading through all of them.

>>7429225
Number Theory - Andrews

>>7429233
>Yeah, all that you've said makes sense if it is restricted to introductory books, that's my main problem with baby Rudin, which is an introductory book on basic stuff that is too hard to follow for most students.

That's my main point. I wasn't arguing for higher level books that assumes a more mature audience. I had baby Rudin and similar books in mind while writing that.

>>7426799
>wants to know physics
k, lmk when it do

Apostol or Spivak for calculus?

>>7429233
Thanks.

Are there any books that go over physics but for lay people? I'm interested in the subject, but I don't know if I've got the time or mathematical ability to get much out of a textbook. Any advice?

>>7429290
Apostol

>>7429218
>The newb math student might think he has the correct logical reasoning and correct proof but might be missing a step here or there that doesn't necessarily follow from the axioms
Maybe if he's a retard. Anyone aiming to be a good student of math, I mean not just get a 2.0 for a bachelor's by taking the easy classes, should at least be able to work through baby Rudin.
> Maybe they get stuck on a problem and can't figure it out and the "hints" section says check theorem X but they do and they can't deduce it further.
Everybody gets stuck on problems. The only people who succeed are those that don't give up. You can't expect to solve every problem in an hour, sometimes you have to think about it in your spare time through the week.
And I'm not sure where you get the idea that professors necessarily flesh out proofs.

>>7427634
>>7427692
Great picks, except for Zwieback. It doesn't require the proper prereqs and therefore doesn't give you a good development of string theory.
I agree with "Supersymmetry demystified" the cover looks pretty childish but it is actually a very good resource on the topic.

What do you guys think about lambda calculus as a mathematician?

Any book recommendations?

>>7430228
The basics of the notation can be useful if you want to do some computability theory or related fields, simply because other people use it, but it's not really something worthy of study in itself for the sake of mathematics.

>>7427634
>THERE ARE NO GOOD BOOKS ON THERMODYNAMICS

What about Fermi? I heard it's pretty great.

What are good books on set theory, is Halmos fine?

>>7430389
probably, what is your math background?

>>7430473
Nice try NSA.

>>7430477
I don't get it. Is it a recruiting thing or something? Or are they keeping an eye on the l337 h4x0rs?

>>7430389
No, it's shit.
Try Enderton, Devlin and Jech and Hrbacek, in this order.
Enderton is great for a first introduction, Devlin is cool because it has non-well-foundedness and Jech and Hrbacek is a nice introduction to more advanced topics.

>>7430507
but then again who the hell wants to go through set theory

>>7430510
cool people

>>7430495
The NSA wants to know which IP address belongs to who.
Normally you can see the city from the IP address but with such personal question they can quickly reduce it to very few possible persons.

>>7430525
Ah very clever, I can tell you're well educated. What was the last name of your high school math teacher? If you don't mind me asking.

>>7430510
>mfw yet another set theorist complains about me calling a proper class a set

>>7430228
May as well just study HoTT.

>>7430683
Well, if they're not using Grothendieck universes at this point, they probably deserve to be ignored. Don't let them rustle your jimmies.

>>7430931
>mfw yet another algebraist raves about Grothendieck universes near me

>>7430933
Hey, you can dick around in an implicit universe all you want. Someday, however, you'll put on your big boy pants and enter into the world of reason... see you then!

>also, not restricting yourself to internal set theory
>not just working with model-theoretic foundations, building up categories, and then defining ETCS to work in
It's as if you are trying to climb over a mountain with no gear, when there is a tunnel with perfect architecture leading to the other side. Don't hurt yourself anon.

>>7430940
>mfw a category theorist exhales air near me

>>7430953
Jesus... Set theorists are to mathematicians as mathematicians are to STEM, I guess. Let's run a test by you: do you accept AC when you do your work? V=L? I have pretty small amounts of respect for constructivists that don't also study computer science.

>>7430956
Set theorist are to mathematicians as Topologist are to mathematicians. What is your point?

>>7431734
My point is you are winding yourself up in unnecessary loops of archaic, dry rope if you are not using modern approaches to set theory.

>>7431757
I'm not even the initial person you replied to, but all set theorist I know are 'modern mathematicians' that cross-pollinate in other areas of pure mathematics.

>>7431764
Whatever boner.

>>7429779
You missed the entire premise of the argument. Reread it, think about the point.

Are Dover books (mainly math) any good?

>>7433334
Yes.

Is Spivak's Calculus on Manifolds worth reading?

>>7433334
Nice book, reading through it right now.

As for myself, I wanna ask a question, I'm a Chem undergrad looking to get decent at Math so I did a proof book, going through pinter and courant because my calculus grounding was Stewart.

I just ordered this book because it was pretty inexpensive. Anyone used it before?

>>7433334
Most of them are great, and they're only about $5-$10.

>>7433570
Do you know multivariable analysis? If not, it's a wonderful and short book. I'm especially fond of the notation he uses.

>>7433591
>Anyone used it before?

Yeah I learned GA from it, I can recommend it if you've already had some exposure to linear algebra if not then it might be a bit of a struggle. You shouldn't stop at that one book, Macdonald wrote a follow up to it on vector and geometric calculus which is pretty good as well. After that you could go with "Electrodynamics: A Modern Geometric Approach" by Baylis which applies GA to electrodynamics, it's basically an intro to the Spacetime algebra and the algebra of physical space. Now after that you could attempt Geometric algebra for physicists, which goes from classical mechanics through special relativity ending with a discussion of a gauge theory of gravity, it's impressive in scope but pretty heavy going.

>>7433630
Thanks for the advice mate, I also bought the second book to save on shipping so I think I'll have some fun with it. I'll definitely check out Baylis but I'll keep that last one in view, not sure I have the time. But thanks for the suggestion, I know what to do now.

What textbook should I take for introductory meteorology?
1) The Atmosphere: An Introduction to Meteorology by Lutgens/Tarbuck/Tasa
2) Meteorology Today ин C. Donald Ahrens
I'm not a meteorology student or worker, just want some good basic understanding of weather and meteorology.

Does anybody know a nice introduction into linguistics, especially phonology and morphology, for people with a maths background?

>>7435773
You might find something interesting here:
http://www.its.caltech.edu/~matilde/CS101Winter2015.html

>>7428109
Start with Reid.
Then man up and start scheme theory.

Hey guys, Undergrad here.
Looking for good books in Physics, Chemistry and Mathematics

>>7436149
Ain't that the most vague question in the thread? Could you be a little more specific? What's your background?

Anyway I'd recommend Book of Proof for anyone starting out in Math, and old editions of Halliday and Resnick for Physics. For Chem I think Pauling's Gen Chem is pretty good, better than what I used at least (Chang). Feel free to correct me though /sci/, I haven't exposed myself to the vast majority of intro books.

>>7436149
Hello Mechatronics undergrad. I need math textbooks on dynamical systems and physics books on whatever hamiltonians and langrangians are

>>7436155
Well Im just looking for good books to start out in those fields.
My background in all the subjects covers most of the basics(Indian Syllabus, if that helps?).
Im pretty proficient in Math and Physics. Thanks for the reply though, will definitely check those books out

>>7436165
I'm gonna hazard a guess that you're gonna try for the IIT-JEE or Indian Olympiads or something, forgive me if I'm wrong.

I know a lot of the Indian students that come here study a good amount of Physics before coming applying. The culture of preparing for Physics and stuff really young in India astounds me, and I was really intrigued by the resources you guys use. I take it that you've heard of Irodov's book? I was pretty skeptical about the old Soviet texts that you and your peers may perhaps be accustomed to, but I ordered myself some of them and they seem pretty good.

I think on top of Halliday you might wanna do Irodov's problems in General Physics afterwards assuming you haven't done so already, it's pretty tough.

>>7436156
I wouldn't start on dynamical systems until you are well acquainted with analytical mechanics (the Hamiltonian and Lagrangian formulations).
There are plenty of good texts on this, such as this one: https://homepages.dias.ie/ydri/Goldstein.pdf

>>7436170
Yeah im past the JEE phase and the Irodov book has amazing problems. I'm a massive fan of international books as they do good on explanations, so would love to get some great books for a Pure Science undergrad course, sorry for the vagueness !

>>7436172
So when I master this book what dynamical systems book should I get

>>7436156
>>7436172
>First course in CM
>Goldstein
I hope you're hella good with your Mathematical Methods anon or you're gonna suffer. Maybe something lighter first like Morin or Kibble.

>>7436201
Thanks, I'm pulling a math minor with my engineering major but this shit looks scary. I'm resolved to learn dynamical systems though so we will see

>>7436218
Yeah no problem, indeed it looks scary, and if that anon pulled it off in a first course he must be pretty good.

I thought I was hot shit and I tried to self-study Goldstein but I couldn't get past the beginning chapters. There's a reason it's upper-division/graduate level Physics.

>>7436201
I wasn't recommending that as a first course in CM, but as an introduction to Hamiltonian and Lagrangian mechanics that would allow one to move on to dynamical systems. If he's looking to study dynamical systems, he presumably has already had an intro to classical meccano.

>>7436254
Ah ok, sorry, misunderstood you mate. Goldstein is one hell of a book, maybe I'll finish it one day.

I'm a programmer but I'm really interested in getting into more theoretical CS as well as math. I'm learning/have learned a good bit of Haskell for functional programming, though I don't know too much category theory. I'm reading A Book of Abstract Algebra (Pinter) and Topology (Munkres) right now to learn about some more math stuff. Any recommendations?

>>7436260
Depends what you mean by theoretical CS. Have you read Sipser and Introduction to Algorithms? They're the standard textbooks in computation and algorithms.

>>7436260
Are you asking for a category theory book? Because Categories for the Working Mathematician is canonical.

But Munkres is boring. Learn algebraic topology as soon as possible.

>>7436578
I'm not too far into Munkres yet but it looks like the second part is on algebraic topology, is that any good?

>>7436612
It's not the best. For instance, it lacks (co)homology, which is ubiquitous. Most people would suggest using Hatcher -- it's free on his website.

The first couple chapters of Munkres give a solid foundation, but the rest of part 1 is more specialized. That said, if you get through countability and really want more point set topology, then keep going.

>>7436612
For a first exposure to the fundamental group it is great.
And I disagree with the other anon, point set topology is great and very useful, and you shouldn't rush to learn algebraic topology, take your time learning the basics.

Anyway, since you're a programmer interested in topology you'll probably like Vickers' Topology via Logic, it develops a kind of algebraic version of topological spaces (frames and locales) and some ideas useful in computer science, it's basically Johnstone's Stone Spaces for babbys with applications.

Bumping to prevent pruning