Textbook Thread

Because I’m a fledgling autodidact and I’m interested in linear algebra.

Rudin is a meme is a meme

Recommended books:
Analysis: Baby Rudin or Introduction to Real Analysis by White if you can find it (I prefer the latter, it's rudin with more detailed proofs, GREAT book, but old and out of print, but it's better than rudin in every way)

Algebra: Nicholson is okay, but I hate algebra. Herstein's "Topics" is good. Not "Abstract Algebra" which belongs in a garbage bin.

Probability: a first course in probability theory, by Ross. Very clear, good examples and problems. I hear Durrett is good too

Seeking: a good book on mathematical statistics, preferably small and concise like baby rudin. Essentially a book of definitions, theorems and their proofs.

Somewhat related: I ran into a book a while ago that taught you by just giving definitions and a little motivation, then making you prove all the relevant results yourself (worth hints). It was really cool. Does anyone know math books like that? Would be a cool way to learn a topic

This book covers robot kinematics and dynamics very well

Also recommended

Linear state-space control systems / Robert L. Williams II and Douglas A. Lawrence.

Really develops from system dynamics all the way to optimal control, great book in my opinion.

Wouldn't be my intro to system dynamics, since it's briefly covered in 4he first chapter and focused to people aware of transfer functions, but after learning dynamics in Laplace domain with Ogata's dynamic systems I became very comfortable with state space in under a day

Both are highly regarded, pick either one or read both.

...

>Stop forcing that meme.
I agree, Rudin shouldn't be forced.

Seriously OP, how do you stay motivated with that autodidact shit?

Anyone got a copy of Elements of Electromagnetics 6th edition?

What's the best route to molecular computing? I'm guessing I need some background in organic chemistry and computer science (specifically, algorithm design). It shouldn't be too difficult to learn these because I'm a physics student. I guess some inorganic would be useful too if I don't want to restrict myself too much.
Ideally I'd learn the contents of a biochem degree but there's probably not time for that. I'll need to know about protein conformation & the details of how enzymes work.. plus studying psychopharmacology would help but that's a longer-term goal.
idk guys, help me out! at the minute I have:
Molecular Biology of the Cell
Physical Biology of the Cell
Protein Structure & Function
Chromatin
Molecular Computing

but I'm a bit more stuck on the CS side.

robotacademy.net.au/

Well, I didn't just decide to study robotics for the fuck of it. It's relevant to my studies (just not included in the curriculum, because my uni is shit), and I need it to have a marketable skillset.

Because i find it essential in mathematics to have great intuition in lingebra. Shilov builds insanely good image of lingebra, while the image you build with Hoffman, Kunze isn't guaranteed to be great (or good even).
Get both if you want, but get Shilov if you only want one book on lingebra.

I'm reading Intorduction to basic robotics and domotics with arduino, by Pedro Porcuna Lopez.
It's not much, but for begginers (like me) it works fine.

Is analysis at the level of baby rudin & linear algebra from incel friedberg spence enough to start studying functional analysis?

Yeah for intro level stuff like Introductory Real Analysis (renamed from "Elements of the Theory of Functions and Functional Analysis") by Kolmogorov and Fomin

If you haven't started reading, there's Shilov's 3 part series:
Shilov's Linear Algebra -> Shilov's Elementary Real and Complex Analysis -> Shilov's Elementary Functional Analysis

What are some great Mathematics books you think a high school/undergraduate student should do? If there are certain books that may benefit Physics students, that would be even better. Also, I have already checked the sticky at the top of the page and was wondering if you guys have some other recommendations.

what are you learning/want to learn?
find a consistent time everyday where you are studying auto-didactically and being productive. define what you want to achieve in the short term (finishing a textbook, lecture series) and break it into smaller pieces like reading 50 pages of a novel or working through a chapter of a textbook. make punishments if you miss a day and rewards if you hit a target amount of days.

these vids might help:
youtube.com/watch?v=GM_UlcLgZzI
youtube.com/watch?v=VY3iRItq7xM

the guy who made the videos studies languages by himself and has some good advice about time management and motivation. most of what he said can be applied to studying anything, not just language learning.

if you don't have a goal and you don't have a regular time you will probably spin your wheels because you won't make progress on a consistent basis.

also think about when you are studying how focused you are. being tired, trying to study after staring at a screen all day and distracted will attenuate how much you can focus and your mental gains.

While Rudin is (one of) THE reference book(s) for a introduction to real analys (weakness in lebesgue integral chapter), lot of people don't write (cause it is clearly implicated) that it is either suited as a ADDITIONAL book to something like let's say... a lecture, or a book for readers who have a strong understanding about maths, not necessarily the topics covered in the book already...
It certainly is not a meme, it is just terese as fuck.

Kolmogorov's Elements, if you can get your hands on it are amazing, even with the sub-par translation. Then there's bunch of soviet books targeted at highschoolers that are great for physicists (it's math, but with motivations in physics like Maxwell equations), but these are untranslated afaik and are rare even in yuropoor.
If you grind some math (when you finished all excercises in Dobrushkin), you can start reading the theoretical physics bible by Landau. Landau is definitely readable in highschool (not all volumes), contrary to what the underachievers would want you to believe. We were reading the first three volumes in our highschool physics club and, while certainly not easy, it was very understandable.
Basically, the soviet method produced exactly what you want- math-heavy books focused at physicists. Most of the american books that would rival the soviet ones aren't self-contained and require support from curricullum, thusare not readable by highschoolers. The only exception i know is an intro book on QM by Shankar.

Thanks for the suggestions. You've recommended many Soviet authors. I'll try to check them out, hopefully I can obtain some copies if I like them.

Real analysis: Old Classics would be Rudin, Apostol, and Papa Rudin. Newer texts would be Terry Tao's, and Pugh's. I recommend the latter two in conjunction. Pugh follows geometric intuition and gives some less than completely rigorous approach, but you learn how mathematicians think about doing analysis. Terry's is an axiomatic approach, starting with foundations making them a good pair because they approach the same material in a completely different way.

Complex Analysis: Stein & Shakarchi is common, and has loads of good problems but I didn't care for it too much. I really enjoy Ahlfors as a text. A good reference is schaum's outline. A lighter version of Ahlfors is Donald Sarason's complex function theory.

Topology: for point set, I think the schaum's outline is good enough. First Algebraic text grab Fulton. For differential the go to standard is Pollack - but I have no experience in this topic.

Linear algebra: Hoffman & Kunze is a fantastic text but a little dated. Something more recent is Axler's text - which is pretty good but avoids determinants too much. Halmos' finite dimensional vector spaces is a text you can't miss out on. I've heard good things about Advanced Linear Algebra by Roman

Algebra: Google Richard Elman UCLA lecture notes, they're free online and absolutely fantastic. If you want group theory use Rotman. Commutative Rings use Matsumora. Depending on your tastes you might like Lang or Hungerford. Dummit and Foote is a reference text.

Differential geometry: use schaum's as a first text, then spivak's calculus on manifolds. After that John Lee has a trilogy that's pretty good. Riemmanian Geometry by De Carmo is supposed to be the bees knees. Peter Petersen from UCLA also has an interesting text

Calculus: My love here is for spivak's text, but honestly the newer editions of Stewart aren't that bad.

how is intro to topological manifolds by Lee?
My background includes abstract algebra and analysis.

I'd suggest reading a book calculus on manifolds such as spivak's or munkres. Alternatively, Pugh's chapter 5 also has a good treatment of the subject.

I'm looking for Machine Learning textbook recommendations.

Yes. Some real analysis from big Rudin or others like Royden or Folland would be helpful. Kreysig has a nice non rigorous book for applications which might help to look through first. Reed and Simon is technically meant for physicists but it's rigorous and good. Rudin also has a book on functional analysis which I never looked at but is probably good. You also may need to look up some general topology from Munkres or Kelley occasionally.

Veeky Forums-science.wikia.com/wiki/Mathematics

Book of Proof by Hammack (people.vcu.edu/~rhammack/BookOfProof/)
Mathematics: Its Content, Methods and Meaning (Dover Books) by Aleksandrov, Kolmogorov, Lavrentev, Sobolev, Gel'fand, et al.
Visual Group Theory by Carter

c2v

Not OP, but from a former soviet country. Is there any way I can contact you to talk to you more about this? I am greatly interested in this approach to physics and would very much appreciate some guidance.

I'd rather not dox myself.
Anyway, i'll elaborate a little bit more on my (direct) experience with soviet method. I come from west of yuropoor but parents moved to russia because of work and i enrolled to school 57 where the soviet method is still used. Some materials we used are public, including few math textbooks for the regular class.
The standard curriculum is based on discovery through problem solving, i.e. we are given some problems and have to come up with the solution, for example when we were studying quadratic functions, we had to come up with a way to find the roots on our own. After few lectures, the standard method is given to us and explained by the teacher, followed by heavy drill excercises.
The specialized curriculum is much more individual, to the point that you someties get one teacher for two or three students. Otherwise it follows the same pattern of discovery, followed by formalization and heavy drills. Except the formalization step covers much more, in shorter time.
On university, i don't have experience with soviet method because i went to university outside of russia. But most of the textbooks i read are from soviet era and i place above 90th percentile, on an institute that's very competitive.
If you can read russian, an example of a modern highschool book that uses soviet method is Maтeмaтичecкий aнaлиз в 57-й шкoлe or Элeмeнты мaтeмaтики в зaдaнaж. Also, we used a *lot* of books by Kolmogorov in the specialized class and they were all worth the time.
For the physics, i'm not familiar with the specialized curriculum, but the standard curriculum was heavily relying on the math classes. We mostly had to come up with the formulas, identify what parameters are important, with some guidance from the teacher, this sometimes resulted in amusing situations where we were discussing Lagrangian mechanics before the standard vector-based Newton's formulation.

not the guy you responded to but what is Элeмeнты мaтeмaтики в зaдaнaж? google translate doesn't have an translation for зaдaнaж and зaдaнaж gives no results in google

thanks for your post, i was curious about your answer too

deeply regret not paying more attention to mathematics

thinking of getting aleksandrov
then spivak
this would take me a year, assuming i have estimated them correctly (i.e. nothing missing inbetween)

need help
i'm sure there's 100 paths but i just need a sensei to tell me what to do

Yeah, mistake on my part. Зaдaчaх - excercises. Haven't seen cyrillic or typed it on keyboard for several years, i'd better read what i write.
The title in english would be "elements of mathematics in excercises", not that it would help you find the book as it is not translated to english.

autodidact user here
Back in high school all of my teachers were lazy as fuck and I felt like I was wasting my time, so I decided to go the school's library and study on my own, and here I am. I dunno, I'm just motivated to do so. I guess that I wouldn't be autodidact on stuff I don't like, honestly, but it just happens that I'm interested in a lot of subjects.

One way to motivate yourself could be watching short videos on youtube, or, instead of beginning your study by reading a book (some books are very dense and not pedagogical in any sense), begin by trying to tackle some problems/exercises. That could help.

For y'all nerds? I recommend Jordan Peterson's latest book

That should be the other way around for better effect

Jesus christ, you guys must be really smart. Did you guys discover some alternate better ways to solve common problems? Did some sort of new discovery(no matter how small) ever happen in those classes?

it is translated in spanish though, thanks user! looking forward to study from it :)

So I'm currently going through Kleppner and Kolenkow's mechanics book. Great book, btw, for those considering it. Anyone have suggestions on where to proceed from here (in classical mechanics)?

Looking for a pdf of Freidberg's Ideal MHD, anyone have a copy they'd be willing to share?

how did you survive this long without libgen

libgen.io/_ads/61ADFCE7CF9DCB6C77E047D7C92478E5

My god... it's full of books.

Not really, of course all the student are pretty good, but it's not like we were a school full of geniuses, in fact i don't remember anyone who i could call that except maybe this girl that was freak in chemistry and was working with MIPT already when she was 14 (she anheroed recently and was a huge slut, but god was she smart).
We mostly figured out some clever (and some poor) tricks, for example in the case of quadratic functions most of us used the square trick because it was really obvious to everyone and we didn't know about discriminants then. Also many combinatorial problems were solved with graph theory, completely side-stepping the ugliness and some problems in analysis were side-stepped by number theory. As far as i remember, there were no novel discoveries, most students "independently" discovered a lot of lower mathlike linear algebra or some theorems in topology, fundamental group, measure theory, lots and lots of number theory because it was really fun playing with it back the (hate it now). I was really obsessed by what now know as twistor algebras for example. It could be said that if you didn't "independently" discover any notable result every week or so, you were among the weakest students and would probably leave in two years. I put independent in quotation marks because really we were guided towards many of thosr discoveries, and the rest was result of just playing with math.
Didn't know about that, i'll remember it, thanks. If it's highschool material you're after, i can upload some excercises i have still in my notebook from the physics class.

I'm , but not I'm looking for undergrad material to be honest, starting a math major this year, if someone ITT has a good source of analysis-related problems it would be great.

Also, I'm looking for a book that could get me into the intricacies of analysis than I can read before starting uni. I already know about Rudin (I bought baby rudin)

Can't help you much, we used course notes. But names i used to hear during that time were Rudin and Zorich.
If you know french, i highly suggest
math.ens.fr/enseignement/telecharger_fichier.php?fichier=5
math.ens.fr/enseignement/telecharger_fichier.php?fichier=117
math.ens.fr/enseignement/telecharger_fichier.php?fichier=4
Though they're not really introductory for an average student.

I know a couple. There is an old book by Joe Roberts which treats elementary number theory in this fashion, which was cool for the secondary reason that it was handwritten in calligraphy. Out of print now, sadly.
There's also Algebraic Geometry: a Problem-Based Approach which does elementary AG entirely through problems.

>Shilov builds insanely good image of lingebra
It felt strangled by abstruse notation to me. Took axler to see what was actually going on

youtube.com/watch?v=sqEyWLGvvdw&list=PL04BA7A9EB907EDAF

might be worth checking out before you go

Why did you find the notation astruse? It was very intuitive to me. I agree notation can make a great book good or even average, and since there's over 20 learning "styles" that work for different kind of people, it's inevitable that some great books will be less than stellar for certain people. But everyone i know that were suggested Shilov from me were thankful for it and agreed that it gave them an edge over the rest of their class.
I find this approach to be better handled by Tao. I've only read the first part (goes only up to Riemanm-Stieltjes i think?), but it is absolutely self-contained axiomatic approach. I'm more of an intuitionist but if that's what you prefer, give Tao a try.

If you want that complex shit, try find review papers on pubmed. Textbooks don't really delve too deeply into shit like enzymes, but if you need one any biochem book should suffice for proteins, like stryers biochemistry (Bible in this field).

Also
molecular biology of the gene by Watson is good

what about intro to real analysis by Bartle/sherbert

How is this book? Physics by Ohanian

I never see it mentioned. Im reading it at the same time as giancoli. A little less calculus but seems clearer to me

It's not good but it's not horrible. Honestly, anything that has "for engineers" or "for scientists" is subpar compared to just grabbing an actual textbook on the subject. At most it's good for a first time look at concepts.

What textbook would you recommend for an elementary general physics class? Or you would just reference books specific to a field?

Why not the usual Halliday, Resnick?

Don't fall for the spivak meme.

University Physics by freedman

Try The Molecules of Life for biochemistry. It introduces thermodynamics, structure and folding of proteins, among other things.
>Bioinformatics
I used Biological Sequence Analysis during introduction to bioinformatics class. You might want to look up a pdf of this.
>exclusively uses vi or emacs
At least there's a little bit of Chad in me. Maybe there's still hope...

Does anybody know of any good systems biology and synthetic biology textbooks?

I'm probably gonna take Advanced Calculus next semester but my university doesn't list the textbook it uses for Advanced Calculus because it's not a course being offered this semester. So Does anyone got a recommended book for Advanced Calculus?

>The term Advanced Calculus has come to mean different things over the course of the past century. During the first half of the 20th century, Advanced Calculus courses consisted of what's now commonly found in Multivariable and Vector Calculus possibly with some Differential Equations topics thrown in. Lately, it has been fashionable to call very watered down "Real Analysis" courses Advanced Calculus even though it's not advanced nor calculus and goes no deeper into analysis than a good rigorous calculus book does. Here Advanced Calculus means what the name implies, advanced topics in calculus (and tools from analysis) typically not found in the usual calculus sequence but still very useful for solving difficult problems in science, engineering, and mathematics.
>Veeky Forums-science.wikia.com/wiki/Mathematics#Advanced_Calculus

Could be literally anything. Post the syllabus.

I need to learn some laser physics. It doesn't need to be super deep or extensive so a good chapter or two in a broader book would be fine for now. Any suggestions?

What are good books for learning elementary geometry and probabilities/statistics? (I'd like to keep it as abstract as possible, so no "for engineers" edition pls)

>learning elementary geometry
synthetic:
Veeky Forums-science.wikia.com/wiki/Mathematics#Basic_Axiomatic_Geometry
modern:
Geometry by Brannan, Esplen, and Gray
Geometric Methods and Applications: For Computer Science and Engineering by Gallier
Geometry: A Comprehensive Course (Dover Books on Mathematics) by Pedoe

>probabilities/statistics
Veeky Forums-science.wikia.com/wiki/Mathematics#Probability_and_Randomness

gimme neuro/computational/cogneuro books boys

Grimmet and Stirzaker for probability.

funny how the same site that has resulted in me downloading 5 new textbooks in the past week is the same one that will prevent me from finishing any of them. FUCK IM NEVER GOING TO MAKE IT

I need a textbook for statics

Beer, Johnston, Mazurek & Eisenberg's book on statics is pretty decent. Published by McGraw-Hill.

Good luck on your studies!

Any textbooks on probability and statistics for computer scientists/engineers that isn't the error-ridden one by Sheldon Ross?

i need a textbook for combinatorics

Combinatorics: Topics, Techniques, Algorithms
Peter J. Cameron

(((((((((((((rigor))))))))))))))

>imperial metrics
come on

What do you want to learn? Topology or smooth manifolds? If topology, then Munkres' Topology. Otherwise other user is right. If you have the topology already, then Lee's smooth manifolds.

I skimmed through topological manifolds by Lee some months ago and thought it wasn't great, but at least it has theorems that are big lists that encompass most of the main properties of each construction, which I thought was quite alright. It isn't deep and topological manifold theory is not very interesting regardless.

seconding

>I used Biological Sequence Analysis during introduction to bioinformatics class. You might want to look up a pdf of this.
Thanks!

>Seeking: a good book on mathematical statistics, preferably small and concise like baby rudin.
The most Rudin-like statistics book I know of is Schervish's Theory of Statistics: it isn't exactly "small" but I think that's an inevitability for any applied subject (strip out everything but the definitions, theorems, and proofs, and you're left with a book on probability rather than statistics).

may be asking in vain here, but looking for texts on symbolic logic for self study?
also any reading on mathematical philosophy would be cool

Veeky Forums-science.wikia.com/wiki/Mathematics#Proofs_and_Mathematical_Reasoning
Veeky Forums-science.wikia.com/wiki/Mathematics#Introductory_Logic
Veeky Forums-science.wikia.com/wiki/Mathematics#Intermediate_Set_Theory_and_Logic

can anyone recommend a good book on botany? I want to learn more about mycorrhizal interactions and figured I need to know something about plants

I need to understand linear algebra and differential equations in order to understand my subjects, any recommendation?

Differential Equations with Applications and Historical Notes by Simmons

Want more theory: An Introduction to Ordinary Differential Equations (Dover Books) by Coddington
Want more problem solving: Ordinary Differential Equations
by Carrier and Pearson

when you guys study these books do you buy a physical copy or do you use pdfs/ebooks you get online?

If I'm interested in it, I'll download the pdf
If I like it, I'll borrow it from my school's library
If I really like it or know I'll use it as a reference forever, I'll buy it
>t. own Munkres Topology, Eisenbud Comm Alg, Hartshorne AG

I buy books when they're under $10.

cheers, yeah seems like molecular computing is a pretty new field. I'll browse papers once I have the basics down

thanks m8

for organic, try the oxford uni press "foundations of organic chemisty" - I'm finding it a pretty good introduction, but perhaps only because I already understand atomic physics in some depth (seems inevitable that chem books skim over the fundamentals in that respect)

My laser course right now (senior/grad level) is using "Lasers" by Thyagarajan and Ghatak. PDF of it should be easy to find and the book seems alright in my opinion. It starts on basic optics, simple QM, and then chapters 4-19 are all on lasers, different types, applications, etc..

looks cool, thanks

Does anyone know any book that goes in depth with set theory cardinality stuff? Or a book that explains rigorous combinatorics through set theory

The higher infinite by Kanamori