book-recommendations

[floral agate]

That’s what’s covered in my course I guess, Ik it’s a little vague, acc very vague

They might be better (it’s a bit longer but I hope a quick look might summarise where I am)

[remote sparrow]

even though you have a very small amount of experience with proofs, many intro to proof books would be okay for you.

In surname alphabetical order:
Proofs: A Long-Form Mathematics Textbook by Jay Cummings
A Bridge to Advanced Mathematics: From Natural to Complex Numbers by Sebastian M. Cioaba and Werner Linde
Introduction to Proof Through Number Theory by Bennett Chow
Book of Proof by Hammack (Very nice explanations, and the PDF is free)
Number Systems: A Path into Rigorous Mathematics by Anthony Kay
A Concise Introduction to Pure Mathematics by Martin Liebeck
Number Systems and the Foundations of Analysis by Elliott Mendelson
Foundations of Mathematics by Sibley (this was the book assigned for my intro to proofs class.)
How to Prove It: A Structured Approach by Velleman
Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand, Polimeni, Zhang (comprehensive and thorough, but a bit dull)
Proof and the Art of Mathematics by Hamkins (Good to learn from and also interesting to read even if you're advanced, though being organized by mathematical topics rather than proof techniques may make it more difficult to use as a reference for particular proof techniques)

Those are books specifically designed for a transition to proof-based math. Discrete math books are frequently used at other institutions, though, like Epp or Rosen (in particular, CS majors learn how to read and write proofs with such books). Sometimes there is no such course and students get put directly into a course like linear algebra or real analysis.

[floral agate]

The proofs topics for me are tiny, do you have any specific recommendations?

Read my mind 🤣

[remote sparrow]

you could also feel free to jump into relatively simple books that teach a particular field of math

for example, you could try Elementary Number Theory by Underwood Dudley

[floral agate]

I think those will be a really good read, from what others said proofs are very different, do you know any books that's like a calculus Intro, I find that topic really interesting from what I'm doing now?

[remote sparrow]

wdym by calculus intro?

like analysis?

i thought you'd learned calc already?

based on your screenshots

[floral agate]

Yeh I have, looking at the course content for degrees they seem to have some more but it doesn't give details, so I guess there's more to learn?

[remote sparrow]

there's multivariable calculus

differential equations use calculus

[floral agate]

I see

Do you have any recommendations for those?

[remote sparrow]

stewart or larson's calculus books have chapters on multivariable calculus. if you want something proof-based, try hubbard and hubbard's vector calculus or shifrin's multivariable mathematics. many intro to ordinary differential equations classes focus on analytic techniques, and my recommendations for those would be tenenbaum and pollard's ordinary differential equations (no coverage of boundary-value problems) or boyce and diprima's differential equations with boundary value problems. for a book that has more emphasis on qualitative and graphical techniques, see blanchard, devaney, and hall's differential equations text.

[tepid prairie]

That ODE book is amazing! (Morris Tenenbaum and Harry Pollard.)

[floral agate]

thanks for all those recommendations I will look into them, I’ve been rlly fascinated by mv calc because of its applications in applied maths and physucs and computer science, but I was never had the ability to follow lots of the tutorials I saw on it (I tried to run before walk I guess) so I’m rlly interested in that topic. I wanna see if I enjoy the proof based stuff to see if the maths part is for me or not or wether to just take comp sci which is why I ask

Thank you for all your advice I’ll look into them all, Thanks again for all the help

[remote sparrow]

comp sci has proofs too

[remote sparrow]

some other books like this would be hefferon's linear algebra (he has solutions to all the exercises and video lectures) or bona's a walk through combinatorics

plus hefferon's book is available free as an ebook

and cheap as a paperback

https://www.amazon.com/Linear-Algebra-Theory-Intuition-Code/dp/9083136604

i've not read this book but i've heard good things about this ^

[floral agate]

That looks rlly good cause it seems quite good fit between both maths and comp sci

[remote sparrow]

hefferon has some coding exercises and labs on his website

[sudden kindle]

Nice!

[remote sparrow]

https://hefferon.net/linearalgebra/index.html

[floral agate]

Thank you so much, I downloaded that one (it’s great that it’s free too) I’ll give that a read, I think I need to implement some concepts into my software project (in order to solve systems of equations) so it’ll be great to learn too

[remote sparrow]

there are certain less than legal ways to obtain ebooks for free that i won't mention, but yes, i'm a big advocate for free open source books

[floral agate]

It makes it a lot easier to learn it, some of the books I’ve seen In tbe past are rlly expensive

[remote sparrow]

any significant difference between 4th and 5th edition of friedberg, insel, and spence's Linear Algebra? planning to add either of these to my library

as in physical library

will go with a used copy of 4th edition if there's no huge change

actually scratch that somehow 4th edition is more expensive???

[ornate shuttle]

i have an international version of the 4th edition

apparently an entire chapter is missing in that version

im not sure why

[remote sparrow]

will take that into account when hunting for a copy of friedberg

[heady ember]

Ooohh yeah I see what you mean

The 4th ed doesn't have the chapter on canonical forms

[heady ember]

Hm nvm I actually found a 4th ed with canonical forms

[upbeat finch]

any analysis textbook recommendation for high schoolers

[heady ember]

Dami would say Schroder or Browder, probably

as a first course in real analysis

if you want smt easier than that you could try Spivak (single-var) or Abbott

[upbeat finch]

thx i will look it up :D

[coarse frost]

apostol is awesome

😌

[grand thistle]

rudin

[fierce hedge]

In almost all international editions, the last chapter is left out for some reason. (Probably to cut costs idk)

[coarse frost]

[gray gazelle]

Principles of Mathematical Analysis by walter rudin and don't listen to the haters or Anthony Sully Sullivan. Legit opened my eyes

[fierce hedge]

Would recommend Lang Algebra after rudin

[gray jungle]

is this the who recommends the worse book for highschoolers competition , in that case worry not i recommend stable homotopy and generalised homology by frank adam

anw jokes aside , and i know many people love to shit on this book here but for a highschool i think tao analysis would be a good start

[gray gazelle]

I never read that book but I've heard good things about it

[fierce hedge]

I am currently doing Tao's A1 and I would not recommend it to average high schooler as it's a bit slow paced + he leaves quite a lot of things to the reader. Then again, doing most of it would build a solid base for analysis and proof writing

[fierce hedge]

How much pre-requisite does one require to read that book?

[smoky zephyr]

probably a lot

[devout sphinx]

I know someone who loves those books

both lang and rudin

[remote sparrow]

Foundations shouldn't be separate from analysis imo, so i approve of tao's analysis. The onus is on the analyst and not the set theorist.

Tao as a book might seem slow going but Tao reports having successfully covered all the main results in a typical analysis course even when spending the first few weeks on constructing each number system.

[tulip saffron]

looking for recommendation about a ML book, for phd interviews and data scientist interviews.
My current choice is PRML. (I dont like ESL and ISLR a bit)

[fierce hedge]

PRML is very good, would recommend it over ESL

[tulip saffron]

thank you!

[mystic orbit]

Surprisingly, not a lot

[mystic orbit]

A bit of category theory which can be covered with a few chapter from riehl

And hatcher

[smoky zephyr]

how would you know

[mystic orbit]

The prereqs for hatcher are a bit of pointset (which can be covered with hatcher's notes on point set) and some group/ring/module theory

The abstract algebra can be covered by a few artin chapters or similar

[mystic orbit]

I did a bit of research and asked around

[hallow oriole]

get rudin

nah jk

dami would say schroeder im like 99%

[lime sapphire]

Why tf everyone simping for daminark's recs 🤔

Just recommend smth u personally think is good

[grave thorn]

Don't listen to other people

Get an "easier" book

[tardy walrus]

Would Tao’s analysis be a good recommendation?

I looked over it and it seemed relatively “easy”/simple

[remote sparrow]

depends on their skill level, but i agree, i find it quite strange to recommend a book like rudin without knowing anything about their background. just because a book is "less rigorous" and "intuitive" doesn't mean you won't get the same insight. arguably, part of getting good at math is learning how to formalize intuitions yourself. sure, not everyone shares the same intuitions, so picking an austere, rigorous book is something you can recommend to everyone without probing into someone's background, but that doesn't make it the best choice for someone. choosing a book is a highly personal decision.

[grave thorn]

Especially given Schroeder spends 2/3 of the book doing very advanced analysis

[remote sparrow]

tao's analysis is a pleasant read, but it may be difficult to use as a reference. also, a lot of things (some important) are left to the reader. YMMV on that. all textbooks make a tradeoff between being pedagogical and utility as a reference, however. further, some people aren't interested in foundational topics (like constructing out each number system up to the reals) and those sections may seem tedious to them. i think foundations should be covered in every analysis class, but when it should be taught is something i would allow to be deferred to the end of the course, as foundations historically came after nonrigorous investigation of calculus. some people like me prefer to build things from the ground up, but most people do not. to paraphrase zorich, people tend to "know" more than they can rigorously justify, and to be frank, there's no material harm, only a slight one philosophically.

i guess i don't really share the intuition that "rigorous" (or at the extreme end, Bourbaki-esque) books are the default "best" books to recommend to people. i mean, taken to its logical conclusion, we may as well ditch those rigorous books and just link them here: https://us.metamath.org/ or some other reverse math webpage. perfectly rigorous, but probably not very insightful to most people.

also, these rigorous texts might lull people into a false sense of security of what the frontiers of mathematics might look like. there are no neat solutions out in the field. also, a lot of informal experimentation happens in research. of course they've got a rigorous foundation so that their intuitions don't lead them too far astray. but research problems are rarely like textbook problems, and it may take years before a cutting edge topic is organized neatly into a textbook.

[sage python]

@grave thorn you do realize the reason I recommend Schroder is because I think it's on the gentle side

It looks advanced but then the first few chapters are like

Oh yeah some side commentary on why this is a step you should take in the proof. So even though it gets further it might be easier than even Spivak

[grave thorn]

tbh high schoolers don't have self control

They're gonna zoom through things to get through to the cool stuff

[sage python]

Browder I wouldn't recommend to a high schooler because as far as difficulty is concerned it's on par with Rudin

Like it's basically Rudin but slightly reorganized and with better multivariable calculus. But Schroder babies you at first

Schroder might not be as easy as Tao or Abbott, it might be easier

[foggy relic]

@sage python although it is more gentle, i think it does cover a similar amount of material to like pugh/rudin

but the excercises dont seem to be at that level of difficulty

for a motivated high schooler i think both browder and schroder work

[grave thorn]

And once they hit the cool stuff

It loses its coolness

[sage python]

Invictus yeah I agree it covers good amount of material. Like

That's the appeal

[foggy relic]

a good plan imo is Browder and then Schroder part 3

[remote sparrow]

are there philosophy of math books that are like hamkins' Lectures on the Philosophy of Mathematics? as in texts that are geared to practitioners of mathematics? i know hamkins wrote his book partly as a response to the lack of such texts, but i'm hoping there are others.

[lean pagoda]

I'm not familiar with Hamkins' text, but if you're looking for a survey text on mathematics, I found Mathematics, Form and Function by Mac Lane (yes that Mac Lane) to be quite enjoyable.
Knowing Hamkins, his book probably contains much more philosophical content, whereas Mac Lane only talks about it here and there. So it's only half a suggestion (but it's far from an ordinary textbook)

Wikipedia lists it as a philosophy publication, so maybe not entirely off the mark here

[fierce hedge]

I am confused by this statement. Is it easier or not? Also, easy refers to the readibility or how hard the exercises are or both?

[sage python]

I'm saying I don't know exactly how they compare, but it's plausible either way. While e.g. Rudin is obv harder than Abbott

[grave thorn]

Basic real analysis+basic topology is baby rudin

oh lmao

Well

I like "essentials of integration theory" by Stroock

Or you could go w/ kolmogorov fomin

[fierce hedge]

I have completed first few chapters of Artin covering Group Theory and basic Matrices. Should I move to proper, different books on abstract algebra and LA or just stick to Artin? I wanna cover things quickly.

[remote sparrow]

maybe think about Measure, Integration, and Real Analysis by axler. the ebook is free on his website, so it can't hurt to try it.

[livid summit]

any recs for an intro to differential geometry?

[remote sparrow]

do carmo is used by a lot of places, but it seems quite a few hold mixed feelings about it. tapp is nice. both mainly focus on R^3 rather than R^n.

like diffy geo of curves and surfaces

[wary compass]

could anyone recommend textbooks/sites that talks about implementing pseudo-spectral method in order to solve some problems related to quantum mechanics?

[sick wasp]

Hello
I basically know nothing about number theory and wanted to learn about it.
Is there any particular book that i should start with?

[heady ember]

Look in pinned

[weak violet]

not really asking for a book rec but i'm a highschooler self-studying higher math and i wanted to ask how do you decide on which book you should read for a particular subject
since people will suggest so many different books with so many different teaching styles and varying quality of exercises and for me it's hard to tell if the book is written poorly or if i'm just not being smart enough
and you can't really just skim a book either you have to really dig into it to see how you learn from it
so how do i filter through the variety of options to get to something that works for me?

[molten linden]

is defranza's book for LA a good choice

[heady ember]

I haven't really needed to decide between multiple books that much yet, but I guess just read through a couple pages and see which you like best

Like I originally tried LADR and Friedberg. I ended up choosing Friedberg because I liked its presentation more

[lime sapphire]

I think the way to go about it is to first skim through the contents of the books you're considering and narrow down the books to a couple or few that you like the look of (or even just one book in which case happy days)
Proceed to use them alongside each other and some number of pages in you'll realise you want to stick to one more than the other(s) or you may want to use more than one till the end

[upbeat finch]

ooh i read through the discussions above and i just downloaded the pdf of tao analysis.
the intro chapter gave quite a lot of interesting questions. the contents look attractive too. think i'm going to use it.
thanks yall for the recs and i'm gonna mark other books too!

[placid pollen]

This but the opposite. The thing is you're missing a good chapter on actual Topology. Check out Willard's General Topology book about neighborhood systems so that you at least know how to prove different metrics can induce the same Topology. Maybe it's an exercise in baby rudin but I find it easier to get with topology words than with inequalities.
Also realize that you can use the axiom of specification to get a set with any property from an existing set (most importantly through measure theory, the power set of a set), properties of sets like inclusion related to unions and intersections, and probably even sets elevated to a set exponent. But, do all of this having in mind how it will give you an insight to Papa Rudin. You have to close the bridge. Gamelin and Greene intro to Topology chapter 2 is a good way of getting started with topology for analysis and also realizing why some set theory will be important. Willard, and Kelley books have set theory in hand at the beginning of the book too but you will be unmotivated bored to read it as it is, if not for analysis IMO.
After a bit of topology and a bit of set theory, what Rudin does for his proofs in RCA will be a bit of review of basic topology and naive set theory, at least for the first two chapters

[brittle breach]

royden is ok, some like folland (but I find rudin easier)

and I second rain's rec of Willard's General topology, I bought just because of how well writing it was

[fierce hedge]

But Wilard only covers mostly point-set topology right? As in doesn't go much into AT and stuff (source: mse)

[brittle breach]

yeah, mostly stuff to do with analysis

[fierce hedge]

How does it compare to the standard textbook Munkres?

[brittle breach]

far better

I wasn't looking to study topology, but started reading because of how good it is

[gray gazelle]

what are good books to study calculus, discrete mathematics and linear algebra?

[fierce hedge]

For linear algebra you might wanna have a look at the pinned posts

[tawny copper]

Is it okay to talk about piracy in here? (related to math books I mean)

[topaz rune]

https://tenor.com/view/johnny-depp-pirate-pirate-salute-salute-intergalactic-pirates-of-the-caribbean-gif-25016099

[tawny copper]

I just wanted to find Lectures on the philosophy of mathematics by Hamkins. I don't know if someone knows where I can find it to download it (for free ofc).

my browser don't let me enter that site lol. Found it in Zlib though. Couldn't find it in Libgen

thanks

what are other places I can find free books and so on? I would have thought libgen was enough

sounds plausible

thanks

[gentle arrow]

piracy

[remote sparrow]

you could try burton's elementary number theory or dudley's elementary number theory.

[gray gazelle]

whats a good calculus book for self-study and practice?

[inner token]

@unkempt gorge https://www.people.vcu.edu/~rhammack/BookOfProof/index.html

Then you can focus on a particular topic of interest

After you get some basics of writing proofs

[unkempt gorge]

Alright, thanks:)

[remote sparrow]

stewart is usually cited as an excellent source of practice problems, but less usable as a self-study text. you could try looking through these websites for free resources and books: https://realnotcomplex.com/analysis/calculus.

https://personal.math.ubc.ca/~CLP/

another free calculus book

https://github.com/nculwell/MathStudy/

https://4chan-science.fandom.com/wiki//sci/_Wiki

https://www.reddit.com/r/bibliographies/wiki/directory

more book recs here above and below

https://aimath.org/textbooks/approved-textbooks/

[gray gazelle]

thanks a lot!

[gray gazelle]

Hello.

Any recommendations for texts to help one get better at various series summation techniques?
Say, for example, summations of expressions involving nCr or nPr, factorials, recurrence relations, etc.

[sage kelp]

So these 3 textbooks would cover the Calculus sequence?

[sage kelp]

I was also looking into the three Volumes of Calculus available at https://openstax.org/subjects/math
Haven't checked them out but I gather they should be fine

[remote sparrow]

looks like it

[sturdy shore]

I would assume any combinatorics textbook

I havent read any combinatorics books, but I have read Knuth's book and it has stuff related to summation

[gray gazelle]

It's true that one could just pick up a combinatorics textbook.
But if someone is more versed in the field and art of combinatorics, then they'd be able to give a finer recommendation, noting which texts have what weaknesses, strengths, and so on.

[sturdy shore]

yeah I don't have the depth to answer that

[gray gazelle]

No worries.
I may give Knuth a look.
Thank you.

[gray gazelle]

?

https://www.amazon.com/Art-Computer-Programming-Combinatorial-Algorithms/dp/0201038048

[sturdy shore]

no no

concrete math

[gray gazelle]

https://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025

?

[sturdy shore]

yep

[gray gazelle]

Thank you.

[sturdy shore]

honestly, it is on one hand a great book

but its exposition differs from regular textbooks and it kind of made me suffer

anyway, just give it a try

it is a classic

and definitely heavy on sums, if the sigma on the cover didn't make it obvious enough

[gray gazelle]

I'm seeing now that it's a classic.
Thank you for the recommendation.

[sick wasp]

Thank you <3

[rain birch]

Looking for some difficult books on ordinary differential equations

Something like berman with lots of problems

[twin fox]

how is the stewart's calculus book and the art of problem solving precalculus book for self study??

[oak inlet]

this looks really good

[livid summit]

fundamentals of physics by Halliday, Resnick and Walker is pretty cool

[orchid mortar]

Seems like some people don't like HR + Walker

Other possible books:
https://matterandinteractions.org/ (not free online, just a place where you can see related things)
https://openstax.org/details/books/university-physics-volume-1
https://www.feynmanlectures.caltech.edu/

[tame tree]

good enough

larson and stewart are generally good enough for a first pass through/learning the methods of calculus

accompanied by some youtube videos, paul's online notes, or w/e else

[twin fox]

thank you

[remote sparrow]

feynman lectures are not really usable for a first pass through general/survey/intro calculus-based uni physics

they're something to read and appreciate after having learned some already

other physics books that are comparable with HRW are university physics by young and freedman or physics for scientists and engineers by serway and jewett.

all three of these books are unfortunately expensive but if you're allowed to buy an old edition they tend to be significantly cheaper

and pretty much the same content

[zealous coyote]

Tao's analysis 1 starts off doing foundational stuff. If you want to know how to construct everything from scratch, that's the one to go for.

Rudin is more straightforward. I would give more details but it's been a long time since I read it

[remote sparrow]

just so you know there are a few books dedicated to constructing the number systems from scratch if you'd rather postpone that sort of thing. some of those books are: Foundations of Analysis by Edmund Landau, The Number Systems: Foundations of Algebra and Analysis by Solomon Feferman, The Number System by H. A. Thurston, and Number Systems and the Foundations of Analysis by Elliott Mendelson.

mendelson has the benefit of being cheap and covering both dedekind cuts and the cauchy sequence construction

[gray gazelle]

I need to read up on some probabilistic methods for determining if a number is a perfect square, mainly based on quadratic residues, can someone provide me some sources?

i'm having trouble finding anything

[gray gazelle]

I don't know how Tao covers things but it can't be bad. And I haven't really read Rudin, but I did read most of his real and complex analysis, and I hate his style of exposition. So I'd be more towards Tao on this one

[manic cairn]

Use spivak, not Stewart

[limber tiger]

I heard Tao was a really good writer for his analysis books

[fierce hedge]

I am currently doing Tao A1, the start is pretty slow compared to other books. It took me around a month to get to the meaty part. It starts off in Chapter 1 with some motivation as to why do analysis like changing sums and integrals, summing over various sequences etc. Chapter 2 is construction of natural number (yes it starts with 0) using Peano's axioms. Chapter 3 takes a detour where he teaches axiomatic set theory in particular he covers ZF (axiom of choice is covered later). Chapter 4 he introduces integers as formal difference of natural numbers and rationals as formal quotients of integers. Chapter 5 is reals as formal limit of rationals and also introduces exponentiation. Chapter 6 is where I currently am where he defines limits properly and gives an actual definition of real exponentiation.
As previous comment mentioned, it's really good if you want to real know you reals and sets axioms. Plus, exercises are pretty good and really force you thinking axiomatically. There are hints given and it's easy to find solutions to individual problems. Note: I have the 4th edition physical copy. If you use 3rd edition pdf be wary as it contains quite some typos although they are easy to catch.

Compared to that Baby Rudin does zero hand holding and you gotta suck it up and do everything on your own. Tao is much more friendly and mildly annoying cause of the pedantry

[remote sparrow]

He has a 4th ed. out now?

[fierce hedge]

Yes, it came out this year

[lime sapphire]

wow

31.50

[fierce hedge]

I think it's expensive cause it has to be imported from India. Here, it only costed me 17 usd for A1+A2

[dapper root]

Must be trash if it’s 31.50

[fierce hedge]

Is that low

[dapper root]

sigh

Unfortunately yes

[fierce hedge]

That better be /s cause the full book is in 2 parts and 31.5 is just for the first part

[zealous light]

It's not

Textbooks in the US tend to be way more expensive than necessary

International editions are typically much less

[remote sparrow]

ams, the official distributor for the hindustan book agency (the publisher of tao's book) has ridiculous markups on analysis i and ii

it's $62 for the former and $52.60 for the latter for non-members

i will be ordering tao's book to add to my shelf from amazon

[forest sleet]

The usual books like graduate studies in math series that the AMS publishes are very good quality at least

(meaning print quality, since that directly affects the cost)

[balmy phoenix]

i understand regular induction, but the next section was strong induction which is way overmy head.

so a recourse that slowly ramps up the difficulty of strong induction instead of starting at 100%

[dapper root]

Strong and weak induction are the same thing thoigh?

I’m unsure how the idea of weak induction could make sense but strong induction wouldn’t

If by strong induction you mean transfinite induction then that’s actually a bit more confusing and is something you just have to sit and stew on for a bit

[balmy phoenix]

i don't know one involved base cases made sense was fun. the next one didn't invovle base cases is absolutely no fun at all (and makes no sense)

[dapper root]

I mean the base case gets established in strong induction like

Assume P(k) for all k < n then prove P(n), that’s strong induction

Okay, if you can do this take n = 0, then there’s no k < n

So you’re simply proving P(0), so you have the base case

[balmy phoenix]

well this isn't the space to discuss my difficulties with it im lookin for a book and can open up a discussioon with ya over in proofs

[mossy portal]

Any good physics book that includes all these topics

I have 0 physics knowledge, well versed in calculus

[orchid mortar]

I'm sure all of these do

[mossy portal]

Found halliday and resnick so hard to read

I will check those out

[hollow peak]

Basically any intro uni level physics text

[wind pecan]

Guys, should I get quadrivium? I heard it's a good book.

[remote sparrow]

can you give a link to the book or drop some details about the author, publisher, year published, etc?

quadrivium is also a general historical term

https://en.wikipedia.org/wiki/Quadrivium

[subtle swift]

[rugged radish]

any good books that help u with this kind of math fractions algerbra? etc

[remote sparrow]

don't really think you need a book for this sort of material specifically. if you really want an outside resource, khan academy is good.

for these sorts of problems, you just need to make the units cancel

for example, for problem 1, 2.00 kg of cheese is 2.00 kg * (1 lb / 0.4536 kg) = 4.41 lb

(strictly speaking, pounds is a unit of force, but in the states it's common to conflate weight and mass)

the american unit for mass is slugs which i'm pretty sure nobody uses

[grand thistle]

wtf r slugs

[primal mica]

There are books on dimensional analysis out there, but I'm not intimately familiar offhand, however I know my department library has a couple sitting around.

Although I feel like such a concept might be more difficult to understand by book than just a dedicated lecture online or a few examples

[keen orbit]

What are some recomended physics books to start self studying physics

[fallow cypress]

there's multiple different conventions here

sometimes lb is mass and lbf is weight

[lapis sundial]

and sometimes you use real units

[night prism]

Feynmann Lectures

[drowsy heath]

GRE for Dumies

dummies

[tame tree]

Good website for used math books?

/retailer

[remote sparrow]

Amazon is a good first stop

[chilly edge]

any recommended books for calculus?

[remote sparrow]

Depends on your needs and background

[chilly edge]

for a first-year student

i got one by gilber or sumn but it contains 600++ pages bruh

[tame tree]

That’s gonna be typical of calc books

Needs hella exercises to cement the topic

@remote sparrow You recommended meckes' linear algebra book to me the other day, almost getting it, but i have to ask, is it proof based?

or mostly computations

[remote sparrow]

Proofs, but also usable by applied people. Defers determinants towards the end of the book.

Emphasizes matrices as linear maps

[tame tree]

alright

ill jump the gun on it and use it as a first pass through for the topic

later on i can just read more advanced ones if i want

[gray gazelle]

cal early trans by briggs and cochran is pretty solid imo

and for practice exercises you can use stewart's

[remote sparrow]

people also recommend larson's calculus. for free resources, see my previous post: #book-recommendations message

[sudden kindle]

Bump's Automorphic Forms and Representations book is growing on me. I kinda love chapter 1 now, wtf?

The more I progress in this book, the more I see the bigger picture and its all clicking for me why we're doing all this in the first place. It's kinda cool

[hollow shore]

https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/

this is a solid resource for calculus.

[chilly edge]

Is it recommended for a first year student?

[hollow shore]

yes

[chilly edge]

Ok thx

[gilded coyote]

Books for IOQM??

[hybrid sequoia]

Same question I think pre college mathematics is first choice of most out there and few others are like problem solving approach by Arthur Engel and mathematical circles

But I want a book that starts from very basics all the way upto Olympiad level in geometry
Cause I'm very weak in geometry I need some suggestions

[novel obsidian]

anyone have any good first course elementary nt course notes just so I'm caught up? I'd prefer not to read a textbook if I don't have to

[gilded coyote]

sAME HERE

[novel obsidian]

https://amosunov.files.wordpress.com/2018/11/mosunov-lecture-notes-on-number-theory1.pdf I found these notes, would anyone be willing to have a look if they're appropriate for a first whirl in number theory? thanks 🙂

[stray veldt]

looks fine

[whole canyon]

Any good documents on Newton raphson method?

[gaunt bobcat]

recommendation for ODE?

[remote sparrow]

intro or not?

many intro to ordinary differential equations classes focus on analytic techniques, and my recommendations for those would be tenenbaum and pollard's ordinary differential equations (no coverage of boundary-value problems or PDE's) or boyce and diprima's differential equations with boundary value problems (old editions are much cheaper if you want a physical copy). for a book that has more emphasis on qualitative and graphical techniques, see blanchard, devaney, and hall's differential equations text.

i don't know what goes on in an advanced ode class, but i've heard hirsch, smale, and devaney's differential equations, dynamical systems, and an introduction to chaos or arnold's ordinary differential equations are suitable.

[remote sparrow]

newton's method is briefly covered in many standard calculus books. however, a more sophisticated treatment would probably be found in a numerical analysis text. i've never taken numerical analysis, so i wouldn't know which book covers it.

[remote sparrow]

maybe kiselev's geometry volumes?

you can also check the following links:

https://github.com/nculwell/MathStudy/blob/master/GeomTopo.md

https://4chan-science.fandom.com/wiki/Mathematics#Basic_Euclidean_geometry

you can also look at olympiad problem books

https://web.evanchen.cc/geombook.html

evan chen has done a lot of coaching for olympiads

i've linked to his geometry book for olympiads

@gilded coyote

[heady ember]

Look in pinned

[warm glen]

im liking clark's "elements of abstract algebra"

it's basically a problem book covering groups, then fields/galois theory, then rings and ideal theory

[brittle breach]

Willard general topology

[remote sparrow]

Number Systems and the Foundations of Analysis by Elliott Mendelson, A Book of Abstract Algebra by Charles Pinter, and Elementary Number Theory by Underwood Dudley. The various math puzzle books would also be worth recommending to anyone.

e.g. those by Martin Gardner

jacobson's basic algebra i and ii might serve you, and they're dover books. basic algebra ii has the material you probably want.

people also recommend aluffi's algebra chapter 0

[whole canyon]

Ok, thanks for answering.

[sudden kindle]

@slim nacelle do you have any recommendations to learn about hilbert modular forms and galois representations?

Like good references

[slim nacelle]

Van der Geer's book on Hilbert modular surfaces

also Hirzebruch-Zagier's article on intersection numbers of curves on Hilbert modular surfaces

[sterile harness]

where should I study abstract algebra from? (introductory)

and what is the opinion on Contemporary Abstract Algebra by Gallian

[prime inlet]

https://www.amazon.com/generatingfunctionology-Third-Herbert-S-Wilf/dp/1568812795

only reccomending this for the funny name lol

[crimson leaf]

This book is also free online

My advisor said it's pretty good for a book just on generating functions though he doesn't like the name

[prime inlet]

yee, those options show up first if you google it

i dont even understand the math yet, still in calc 2

looks cool though

[remote sparrow]

try abstract algebra by judson (free) or a book of abstract algebra by charles pinter (cheap dover book). do note that pinter puts some key results in the exercises

[tawny crater]

It should be common courtesy to atleast highlight which exercises are fundamental

[remote sparrow]

https://www-users.cse.umn.edu/~akhmedov/MATH4281.html

i found some exercises

don't know if those exercises have those fundamental results but i'd trust a professor's judgment

could always read judson's book to see those key results

which is free

or just work as many exercises as possible if time is not an issue

you can read pinter to just understand stuff whoever reacted to rfish

and do exercises from a different book

[latent dagger]

can i get solution manual of Elementary linear algebra 12th solution anton

[idle bobcat]

Lebesgue measure ,integral etc book recommendations for beginners with solutions to problems ?

[remote ginkgo]

axler has a kinda fun book

i hate it tho

try big rudin

dont worry about solutions youw ill figure it out

[heady ember]

If you're looking for measure theory, look in pinned

If you're looking for an intro to analysis, i.e. baby rudin level, also look in pinned

[cedar ridge]

anyone got Differential Calculus on Normed Spaces pdf

[heady ember]

Just go to zlib or smt

[cedar ridge]

cant find on libgen, whats smt

oh, smthing

[gray gazelle]

Rotman or Fraleigh for an algebra text?

in general, what is considered the best introductory abstract algebra text?

[remote ginkgo]

neither

[remote ginkgo]

i like a combination of pinter and aluffi

[heady ember]

Look in pinned for Dami™️ reviews

[gray gazelle]

is that an introductory text?

[lime sapphire]

Why do u say its fun

[gray gazelle]

on a similar topic, would Herstein qualify as an introductory text?

[remote ginkgo]

its easy and exercises are cute

[remote ginkgo]

yes, both are

[brittle breach]

has anyone learned complex analysis from rudin

[fallow cypress]

Fraleigh is easier/covers less material but it's good for a first sem, Dummit-Foote is considered "standard" but can be dry, Aluffi contains more categorical perspective so it can be harder to understand but the tone is very friendly

[grand thistle]

RCA? im also curious because it seems to present a unified approach of real and complex analysis

[remote ginkgo]

ahlfors bro

[gray gazelle]

best intro book on combinatorics and GT?

[fluid stirrup]

I need a good book to help me grasp a solid precalc/algebra background. I'm taking precalc right now as a freshman in uni (i plan to move on to other calculus courses), and I'm lost since I havent taken a math class in what feels like forever.

[gentle arrow]

algebra by serge lang
(on a more serious note, i think khan academy is fine for hs algebra/precalc. do not use lang because while it is called algebra, it is not the algebra you are looking for and is for grad students)

you should also probably work on basic logic/proofs to be able to understand things better (hammack is a pretty good choice)

[fluid stirrup]

sounds good, and yeah khan academy / yt videos work well for me honestly, my professor just talks really fast and i sit in class for 2 hours not understanding a thing. i think what i really need is more of a book where i can work on a lot of problem sets

or if you have any resources where i can easily practice problems

[brittle breach]

I am in the middle of rudin the real analysis section, was wondering what does his approach adds and/is lacking from the usual approach.

[remote ginkgo]

what

ahlfors has no real analysis section

i have no clue. nobody actually reads the second half of rudin

[tough zealot]

they were joking about lang

[fluid stirrup]

yea ik lol, saw the preview on amazon and was very lost by the first chapter

[remote ginkgo]

love lang

i have the same birthday as him

[gray gazelle]

self dox

[remote ginkgo]

nope

you just self skull reactud

[fierce hedge]

Gallian?

[smoky zephyr]

skull issue

[coarse frost]

artin 😌

[hearty steppe]

I gotta check this out soon https://www.barnesandnoble.com/w/vortex-field-theory-with-new-principles-for-physical-unification-ying-ye/1142102907?ean=9798823111690&fbclid=IwAR1deSN4VOvY_WktzQtqN9B7CRbhAZC3bPB4yotcW774xvQTjNqOX8Ob2_U

I gotta level up quicker now 🤣

[wise crater]

pirate it

[shut shale]

hey, I'm looking for a mathematical statistics textbook. I'd like it to have problems and answers in the back or nicely worked examples in-line with the text. Could be paired with a MOOC or open-ed resource as a potential upside or have the worked examples distributed in the online resource while the text itself is more condensed.

[gray gazelle]

?

[remote sparrow]

try mathematical statistics with applications by wackerly, mendenhall, and scheaffer

[shut shale]

thanks, ordered this and I'll let you know what I think when I get into it.

[remote sparrow]

try a walk through combinatorics by miklos bona

he has a lot of exercises and he has solutions for all of the regular exercises (the supplementary exercises have no solution) in the book

[remote sparrow]

depends on your needs and background

and what you like in a book

[inner token]

Artin is freeee on the interwebs

[gray jungle]

Artin is great

but i would find exercises elsewhere

[wise crater]

dover's website?

[wise crater]

any books for learning bout universal algebra, with an emphasis on partial algebras?

[gray gazelle]

Recommend me some profound math books to read, for fun

[gray gazelle]

Universal algebra by George gratzer

[gray gazelle]

Set theory by jech

[wise crater]

thanks

[quasi sigil]

does aluffi have good problems?

[quasi sigil]

lol

[fallow cypress]

I've heard no, but I haven't tried them tbh

[summer moth]

Anyone have any good books that give you a brief but solid trigonometry overview of everything for calc along with a solid intro to calc?

[rose geyser]

Speaking of which anyone else finding dummit and foote wordy as hell

[warped cedar]

that's a common complaint

[night prism]

Yep

[plucky shell]

I require advice:

What would be better for someone who wishes to teach themselves Analysis,
Analysis I by Terence Tao or, Mathematical Analysis I by V. A. Zorich?

[zealous coyote]

I don't know Zorich, but I have some perspective on Tao

Tao's book also goes through how we construct the naturals, the integers, the rationals, and finally the reals. It explains a lot to do this, but the great thing is at the end you really know how everything is done.

If you're interested in that, Tao Analysis I is the book for you.

If you just want to know analysis, another book will do it faster.

[plucky shell]

Thanks, appreciate the advice!

[fierce hedge]

Zorich is more complete, does a lot more things but is significant time investment (if you will be doing both books). Tao is much more thorough and better if you really wanna know the fundamentals

[grand osprey]

How is apostol’s analytical number theory? I’m taking a course on it this year

[heady ember]

Not directly answering your qns but you can consider schroder and browder too

They are the top picks of Dami™️

[plucky shell]

Thanks everyone, appreciate the advice.

[heady ember]

Np

[worldly sequoia]

can someone suggest a good book to learn discrete math? rn im hoping to get more proficient at proofs

[heady ember]

You could try Rosen if you really wanted to. But it was very boring for the 20-30 pages I read. Which is why I switched to Enderton's EEOS (Elements of Set Theory). You could try this if you have an interest in learning more about set theory, particularly axiomatically. However, do be warned that hours may be needed to solve one question and you might not get anywhere even after hours. Similarly for the content, sometimes you'll get stuck. The longest I have gotten stuck so far was on the cartesian product.
Also, there is a saying "foundations first is active self-mutilation"

Well, now onto more normal proof recs. Personally I did Spivak chapter 1-2 exercises. They are elementary exercises, in the sense that you don't really need any new knowledge to do them for the most part. (First 2 chapters are on numbers) However that does not mean they are easy. They are good exercises that are challenging and can, too, take hours and you may make no progress after hours. But I think that its a good way to practice proofs. And if you like it you can continue on with the books

Also, if you haven't learnt the basic proof techniques yet, look at loch's summary of intro to proofs

#proofs-and-logic message

[hollow shore]

there is a very good lecture note which is based on spivak which talks about logic and proofs in the initial chapters

[lime sapphire]

perhaps this is what you're referring to? https://www3.nd.edu/~dgalvin1/10850/10850_F19/HCalc_notes.pdf

and yea i agree

its pretty good

[hollow shore]

yes yes

[lime sapphire]

like supplementing these notes with spivak is probs best combination you can find online for it

[remote ginkgo]

analytic

not the same thing

[hearty steppe]

I’m not sharing this book here just for me but this is a new book that I think some mathematical physics people in this server other than potentially myself will get to appreciate

Lots of people been trying to understand what the heck is going on with vortex points when we have some weird issues with further deriving quantized behavior in fluid flow problems and thermodynamics

So this is pretty exciting for a lot of people to check out I think 🧐

[wise crater]

I think its pretty neat how navier stokes is such a simple wquation but encompasses the phenomena you're mentioning

[hearty steppe]

Maxwells equations are like the first thing the overview mentions.

It is interesting we are coming full circle from E&M based derived behavior here which pretty much a lot of people have a hard time grasping the most when they’re learning physics *

It’s because you have compounding charge behavior happening with the electric field. The electric field is restricted from just being responsible for generating arbitrary voltages

And we haven’t even began to shed light on quantized electric field behavior here, but I was trying to imply that 😂

[gray gazelle]

i know group theory and some ring theory, haven;t touched fields other than the whole commutative ring definition

i think i'll just go with fraleigh tbh

[valid kiln]

Hey, I wanna learn math, what book should I got?

I've been searching, but I found none. They're all so unknown

[wise crater]

thats like asking "i wanna eat food, what food should i get?"

what kind

[white cedar]

depends on your level, what math you're looking to learn, how in-depth you want the book to be, etc

[valid kiln]

I will start from the very bottom

[zealous coyote]

Okay well I have

On a more serious note

We really need more information

Perhaps a basic book on mathematical thinking would be in order, but even that may be questionable

[karmic thorn]

Yeah, it's ideal that you specify your background knowledge with math and what your goals are (so that something catering to those goals can be suggested).

[hearty steppe]

I would eventually like to argue that there is not necessarily a right way to learn math if you can do math correctly

That being said I would not put past going through standard text books that give you an idea of the abstraction your dealing with

But I’m increasingly now having a hard time telling people to do what I did

Or… be like… yea so I spent this much time in analysis land and that much time in linear algebra land and… well you see how perplexing that gets?

And to be honest I didn’t really spend that much time rigorously learning linear algebra probably cuz I spent that much more time in analysis land and abstract algebra land for pretty much most of the stuff to just click when I look at definitions

[wise crater]

I thought lang did a well reccommended pre calc book and then other than that all you need for basics would be polya's how to solve it and maybe one of those introductory proof books

as far as "easy hit the ground running" sort of practical teaching books

[hearty steppe]

Chartrand and zhangs proof book I think is enough and you only have to do up to the relations chapter.

I mean if you want to do pure math, it’s not going to be enough clearly but… I mean. I don’t know what people want to do these days

[wise crater]

people just want to be able to count the sticks and stones in their backyard and then build stick spaces and stone extensions

simple as

[hearty steppe]

I don’t do pure math btw but I go thru pure math texts a bit here and there

[wise crater]

nothing's pure about math

its all tainted with physicality n shit

[zealous coyote]

Ah yes, the physicality of the zariski topology of affine 10-space over algebraically closed fields of positive characteristic

Very tainted

More pure pls

[wise crater]

are you saying algebraists are the most pure?

hot take

[gray jungle]

wait till you hear about cats

[zealous coyote]

No.

[wise crater]

i think you coukd find a physical analogy for the zariski topology, if i could borrow an analogy for varieties

[zealous coyote]

Lol sure, a physical analogy for a non-hausdorff space.

[hearty steppe]

Well actually I am not sure we can quite say that.

We can derive physicality with an area of mathematics that im currently studying known as dynamical systems

Topological dynamics anyone?

Brin and stuck chapter 2

I Gotta read that soon haha

[zealous coyote]

I think most so-called pure mathematics is somewhat inspired by—but ultimately divorced from—anything I would consider 'physicality'.

[hearty steppe]

You have no idea how excited I am to start that chapter but I’m getting through my Kolmogorov complexity reads first cuz I can finish them in maybe two months which would be quicker for me than the general dynamical systems texts I’m focused on

Brin and stuck is a hard book not gona lie but I been enjoying it

[wise crater]

yeah, i guess the thing that makes it seem silly is that people will still jerk it off about being the language of the universe, or being discovered rather than invented, which would make either all that meaningless fluff or your statement seem untrue, which it isnt i agree with you im just doing a funny but at the same time its silly

[hearty steppe]

I would hesitate to call it an “introductory” book haha

If you consider advanced undergrad in the first chapter then go straight to grad level introductory then sure

[zealous coyote]

I do agree it's questionable to call it the language of the universe.

Dare I say silly, yes lol

[wise crater]

maybe the final solution is to cave in the heads of philosophy majors

cant be told its unethical if there's no ethics

[zealous coyote]

Philosophy majors are probably the ones questioning this claim that it is the language of the universe!

[wise crater]

that sounds like the kind of arguement a philosopher would use...

maybe you're right though it should be the heads of the journalists running pop sci mags

[zealous coyote]

Definitely

Shall I fetch the crowbars?

[wise crater]

ay ay

[grand osprey]

Minor error, but u ofc knew what I meant. So any views on analytic number theory by apostol?

[gray gazelle]

@molten wave yo i got the pre uni role

but lost access to #discussion

[molten wave]

you got the studying role

[gray gazelle]

ohhh

nvm thank you

[hushed zephyr]

https://www.mathway.com/ if yall need help with math

[wise crater]

thanks!

[zealous coyote]

wow thanks

[gray gazelle]

Every time I look at this channel I think of non mathematical book recommendations and I get confused for a sec lol

[gray jungle]

you lied, it didn't help

[carmine lintel]

Lol

[remote sparrow]

try graduate texts like jacobson's, rotman's, aluffi's, lang's, etc.

[zealous coyote]

I have read most of fraleigh and I sincerely think it's a bad book if you've already done groups and some ring stuff. I agree with Sour Drop here.

[fallow cypress]

if you are already coming in with some background knowledge, then fraleigh is not the move

[bright siren]

Is it worth reading The Grand Design by Stephen hawking if I read A Briefer history of time?

[golden drum]

hey, so im currently a 12th grade student and want to learn like "extended" geometry. Idk if thats the right word for it but do you have any recommendations?

[wise crater]

read lockhart's geometry, breeze through the first section if you feel comfortable, i found it was a fun read at the end of highschool

[golden drum]

tysm will def check it out!

[fallow cypress]

I would ask in the physics server, check #old-network

[gray gazelle]

Well this thing can't do algebra obviously

[zealous coyote]

GPT3 does better!

[remote sparrow]

https://tenor.com/view/inugami-korone-processing-thinking-pondering-calculating-gif-24147534

woaw

[grave thorn]

no

honestly the vast majority of things in math don't have a "physical representation"

[gray gazelle]

Abstract algebra. And on that topic, would you personally buy Heifetz or Dummit/Foote?

[grave thorn]

I am not aware of "Heifetz"

[gray gazelle]

Did i spell it wrong

ill check

Herstein i mean i think i was thinking of the pianist

Or violinist

Or whatever

[grave thorn]

iirc herstein is slightly friendly for a begineer

idk for sure though

[gray gazelle]

Ive read people calling d/f a ‘classic’ while others responding that ‘its not at all a classic’ and that its inferior to Herstein. On the other hand ive read Herstein makes it more difficult than it is. Ive not read much elaboration.

[zealous light]

I wouldn't break the bank for buying any textbook unless you feel like physical copies are better for you for whatever reason

Or you know it'll be a reference book later

[gray gazelle]

Ah yeah

If hypothetically you had to choose tho between the two? Weigh the pros and cons? Ive found free pdf’s so access wont be a problem

[zealous light]

I've really only ever looked at d&f

[gray gazelle]

What you think?

[zealous light]

I don't think I can give a good opinion on it tbh

[remote sparrow]

try pinter or judson

both cheap as physical copies

[gray gazelle]

Thanks for the recs

Thanks all

.close

Nvm

[proud gazelle]

is linear algebra done right a good book for someone who didn't take a course in linear algebra before?

is it rigorous?

[sage python]

It's rigorous, fine for the first few chapters but it teaches you to think about determinants and characteristic polynomials like an idiot

[proud gazelle]

do you have a better suggestion?

that's suitable for self study

[sage python]

Linear Algebra Done Wrong seems decent. Friedberg-Insel-Spence is the standard, kinda long

People seem to like Halmos but I hear it's old and that reflects in the terminology

[remote sparrow]

#book-recommendations message

[remote sparrow]

you can read the preface or foreword or whatever and see how you feel about it

[wise crater]

dummit and foote i always come back to for reference if i dont want to read lang

I think Lang is pretty comprehensive, D/F also acts as a great reference. Hmm

[sturdy sail]

What book do you guys recommend for statistical mechanics?

It has to be reasonably mathematically rigorous, but still covering the main topics covered in early graduate courses.

[remote sparrow]

i've heard pathria and beale is good

though are you looking for a physics book or a mathematical physics book

i know some people here might make a big fuss about "rigor" in physics but even as someone who is studying pure math, it can't hurt to take on the physicist's perspective

[sturdy sail]

I'd like to see both perspectives.

I wouldn't mind reading a physics book.

[remote ginkgo]

lang

hate df

[remote ginkgo]

landau

[grave thorn]

lol to a physicist every function is integrable

[remote ginkgo]

defn of a function: something integrable

algebra by lang

enjoy

[grave thorn]

nlab

[remote sparrow]

if it agrees with experiment it doesn't matter

[grave thorn]

it doesnt though lmao (im talking about theoretical physicists)

[remote ginkgo]

this book is terrible. try shilov

[wise crater]

not really an algebra encyclopedia so much as a category theorist's idea of algrbra

[grave thorn]

hence the

[wise crater]

yeah... people might take you seriously though

[remote ginkgo]

i use nlab a lot

[sturdy sail]

What about a math-phys book on statistical mechanics tho?

[remote ginkgo]

and i dont do cat theory

[remote ginkgo]

the one where the author tells you to kys at the intro page is ok

but landau better

[grave thorn]

whenever you add "opinion" + "" it becomes a joke

[wise crater]

i do too, its easy to use as a reference for notation

[remote ginkgo]

yea

[manic cape]

i have heard decent stuff about kardar and pathria stat mech books too

[wise crater]

maybe to us regulars but newbs looking for advice wont regard it

[wise crater]

you got a functional analysis book you recc, pi?

[grave thorn]

I think the only time ive every used nlab is for the def'n of a Gelfand triple

its definition is garbage

[remote ginkgo]

ah yes combinatorial cohomology

[grave thorn]

i don't care about the "category of hilbert spaces"

i care about "hilbert spaces"

[remote ginkgo]

halmos
hilbert space problem book

:^)

[wise crater]

does it talk about sobolev spaces?

[remote ginkgo]

no

i dont actually have a rec for func analysis

i just know ppl talk about kreyszig a lot

[grave thorn]

use brezis for FA

[remote ginkgo]

but i only have rudin

[wise crater]

i'll note these down

[remote ginkgo]

theres another my friend references

his opinions are the best i have come across

[sturdy sail]

I like Salamon's book on fun anal

[wise crater]

i act like i'll be able to understand any of it lmao im still getting a grip with regular pdes and banachs original papers

[sturdy sail]

Pedersen "Analysis Now" is also pretty good

[remote sparrow]

is there unfun anal?

[remote ginkgo]

but his fun anal rec is really

interesting

[grave thorn]

probably nuclear spaces

[remote ginkgo]

its something very physics flavored

[remote sparrow]

https://www.reddit.com/r/math/comments/47sfjp/statistical_mechanics_texts_for_mathematicians/

https://mathoverflow.net/questions/4172/where-does-a-math-person-go-to-learn-statistical-mechanics

[remote ginkgo]

"where does a math person go to learn X physics topic"

how about you change the question

to "where does a math person go to become a physics person"

i think u rly just have to be both.

[manic cape]

no, physicists dont learn those types of things usually

[remote ginkgo]

wat

[remote sparrow]

it's better to think about physics like a physicist would if you really want to do physics

imo

[remote ginkgo]

yeah

like yes there is plenty of value in doing physics like a mathematician

[sturdy sail]

When you are doing analysis over:
https://encyclopediaofmath.org/wiki/Tight_measure

[remote ginkgo]

goodness gracious...

[wise crater]

where does a math person go to learna new language

[manic cape]

not significantly for the average physicist

[remote ginkgo]

physics school

[wise crater]

LEWD

[sturdy sail]

Ow man

you know it is true

[grave thorn]

I can't give a rec on stat mech but I do have this book on probability that goes over statmech as an application (maybe good as a supplement)

[remote sparrow]

@sturdy sail anyway you'll probably get more answers in the physics discord (linked in #old-network)

[grave thorn]

I also have a very theoretical book that goes over statmech as an application

[sturdy sail]

I will do that

thanks for all the recommendations guys

[remote sparrow]

[wise crater]

thats toooo much man!

[blazing canopy]

I'm looking for a comprehensive monograph on classical electrodynamics with a focus on the mathematical aspects from the standpoint of PDE and integral equations. Does anyone know if such a thing exists? There are plenty of resources on aspects of this topic at the research level, but nothing too comprehensive.

[grand thistle]

is it literally called "Analysis Now"?

funny name

[topaz rune]

In case you want to become criminal, mathematically

[zealous light]

Interesting (pdf downloaded from my institution)

[stable dagger]

where I can read blowup in differential equations?

and blowup for curves

[stable dagger]

Classical Electrodynamics
Textbook by John David Jackson

[topaz rune]

Like instability or what do you mean

[stable dagger]

yes, also it's called sigma process

[topaz rune]

Are you talking about stochastic processes?

[stable dagger]

for equation y'=y^2, y(0)=1/5 (y=1/(5-t)) you cannot expand solution beyond t<5

no, ordinary differential equations

[topaz rune]

In this context I have never heard about sigma process. But for (in)stability regarding differential equations most ODE books should cover this

[stable dagger]

it's advanced ODE, I read Vladimir Arnold "ODE", he talks about blowup there without deep explanation

https://en.wikipedia.org/wiki/Blowing_up

[wise crater]

why drugs, corruption, and tensors

cause they'rr useful!

[solid wadi]

Hello!

I am looking for literature that traces applications of mathematical stuff to real life, in the way that makes knowledge of fancy Mathematics readily appreciable from the economical, pragmatic point of view. Like, «why should I invest in this» point. For example, I want to read why groups are good, why cohomologies are good, why cobordisms are good… in terms of application. You get it.

I do not need an introduction to applied Mathematics here. But ideally not cheesy «groups are good for studying crystals and crystallographers use them a lot» stuff either.

[wise crater]

I liked reading some mathematical economics manuals, if only cause the interpretation of calculus was kinda neat

[solid wadi]

Would you have any specific titles for me?

[wise crater]

Mathematical Investigations in the Theory of Value and Prices by Irving Fisher its pretty short and you can probably pirate it

[solid wadi]

No need to pirate anything, it is on Archive already: https://archive.org/details/in.ernet.dli.2015.84061/page/n15/mode/2up.

Indeed it was written somewhere about 1892.

[wise crater]

yeah! its rather old timey

i imagine if fisher saw the insanity of the markets today the book would be a lil different

[stable dagger]

groups are used in tensor analysis, ODEs

many ODE books have groups in introduction

Arnold "ODE", Olver "Applications of Lie Groups to Differential Equations". Ibragimov "Elementary Lie Group Analysis and Ordinary Differential Equations"

[topaz rune]

Just read any physics or engineering book tbh

[stable dagger]

Algorithmic Lie Theory for Solving Ordinary Differential Equations By Fritz Schwarz

I think he wants application in math

[topaz rune]

Yes real life applications I think

Not different math that utilises the other concepts

[stable dagger]

oh ok

[solid wadi]

Yes, any Physics or Engineering book is going to explain some mathematics, but it will be mostly boring mathematics spread out at unnecessary length. I am not looking to learn how to do Engineering, but rather how to ground fancy Mathematics in pragmatic reality. So I was hoping there is a better fitting set of reading.

One could say I want to avoid doing the work of summarizing what I already know about how Mathematics is handy in daily life.

[stable dagger]

like to be useful for engineers as mathematicians?

[solid wadi]

Not sure I understand the question but the answer is likely to be «yes».

I know that Mathematics is handy for Mechanical Engineering, Radio Engineering, Software Engineering, and so on, but I know this because I have at least skimmed several books on these topics. I am looking for a more compact, but not trivializing summary.

[stable dagger]

not sure if such books exist, it's good to narrow it to some more concrete

[solid wadi]

Yep, me neither…

https://mathigon.org/applications — maybe something like this but a book.

[stable dagger]

why you don't want to pick up some specific area and dive into it?

[solid wadi]

I am already diving into specific areas!

[topaz rune]

Summary like ‘math used by engineers and scientists + examples’ style or what do you mean?

This will be hard to find when it should have any depth because the applications topics itself are very big

http://www-m6.ma.tum.de/~alt/alt-continuum.pdf

For example this is about continuum mechanics from a more mathematical POV. It is used in the mechanics of deformable bodies, fluid dynamics and thermodynamics

This is about linear systems as studied by control and signal processing engineers https://federico-ramponi.unibs.it/docs/linsys2014.pdf

Maybe also check out the applied mathematics series by springer

Tbh I don’t quite get what you are looking for though

[solid wadi]

Yes. Something like that.

The links you sent look good. I am somewhat unexpectedly captivated.

[topaz rune]

Ah, nice. I have tons of resources like these just hit me up with a topic and I can see if I have something about it

[stable dagger]

"Applications of Mathematics publishes original research papers of high scientific level that are directed towards the use of mathematics in different branches of science."

https://am.math.cas.cz/

[solid wadi]

Wow, this will be the first Czech web site I am to peruse.

[warm wedge]

hello, any recommandation for a graph theory book/pdf ? with a huge emphazis on algorithms etc

[stable dagger]

for mathematicians or computer scientists, programmers?

Graph Theory with Algorithms and Its Applications: In Applied Science and Technology
Book by Santanu Saha Ray

[warm wedge]

more for computer scientists i'd say

[oak phoenix]

Any math book recommendation for a class 10 student ?

the one i have is not sufficient already finished it

[stable dagger]

then read a book for another year or university math

[topaz rune]

Topic?

Just grab a more rigorous one of the same topic

[stable dagger]

https://en.wikipedia.org/wiki/Quantum_Magazine

[oak phoenix]

more specifically quadratic equation

[scarlet pumice]

Hi, I am planning on starting my bachelor of mechanical engineering soon but my math isn't that good. Does anyone have any book recommendations?

[stable dagger]

are you in first year or just plan?

[scarlet pumice]

just planning but I will probably start in 4 months or so

[stable dagger]

https://www.amazon.com/Stanford-Mathematics-Problem-Book-Solutions/dp/0486469247

https://www.quora.com/What-are-the-best-books-on-mathematical-problem-solving

[scarlet pumice]

thanks for the recommendations

[topaz rune]

Maybe worth a look or two

@scarlet pumice

You can find pdfs of it by googling

[remote ginkgo]

kreyzsig has a nice book

'Advanced Engineering Mathematics'

[remote ginkgo]

this book is useless

i bought it years ago and got nothing out of it

either you know the material already and it teaches you nothing new

or you don't know it and the exposition is too poor to learn from

not good even as a reference

[topaz rune]

1400 pages and it can’t teach anything? The ratings are pretty good

[remote ginkgo]

im aware

people have bad opinions though

[topaz rune]

Maybe it wasn’t for you

[remote ginkgo]

im approaching this from a statistical learning theory perspective

so its just like

guarantible

im evil like that

[remote sparrow]

what about boas or arfken

[remote ginkgo]

dunno them

[remote sparrow]

would that help?

[remote ginkgo]

bofas

[remote sparrow]

deez nuts

[remote ginkgo]

@topaz rune i also gifted copies of that book to multiple friends

none of them got anything out of it

kreyszig made a difference tho

[topaz rune]

I wouldn’t use a book this big as a copy, just pdf

[remote sparrow]

zill also has a big engineering math book

[remote ginkgo]

regardless

has too few actual computations and very little remunerative discussion

just not a good book

reviewers are just captivated by 'breadth'

[topaz rune]

Actual computations as in examples?

[remote ginkgo]

not actual mathematicians/physicists

yep

kreyszig is chock full of em

and covers the material in a much better way

try it out u will see what im talking ab

[topaz rune]

Too many examples can get annoying though

[remote ginkgo]

no it cant

[topaz rune]

I don’t use this book anyway I prefer shorter and more topic specific books

But that guy was about to start engineering and this book gives a good overview about the topics he’ll learn

[remote ginkgo]

i dont agree

i think its like

structure doesnt mimic actual engineering math

kreyzsig does

i think kreyzsig is just a better author in general

everything hes written is good

functional analysis from him is good

so is his diff geo book

hes just good

[topaz rune]

How so?

[remote ginkgo]

dont want to explain

detracts from the main point i mean to make anyway

[topaz rune]

Often engineering math is taught way too hand wavey and crappy, especially in the US

[remote ginkgo]

i agree

and i think the book u linked does precisely that

kreyzsig is more careful in his writing

[topaz rune]

Idk never read it but it does give a good topic overview and that was my intention

When recommending

[remote ginkgo]

ok i have read it front to back

its not good

i like what it wants to do

but the execution is crap

kreyzsig does it better

[topaz rune]

Does krezsig pay you to say this

[remote ginkgo]

no i pay kreyzsig

[topaz rune]

Btw can you link the book I wanna check it out

[remote ginkgo]

sure

[remote sparrow]

there's also a book called advanced engineering mathematics by michael greenberg. dunno if that's good

[remote ginkgo]

https://media.discordapp.net/attachments/1023025885172994048/1023225261770145823/Screenshot_20220924-093142.png

oops LMAO

wrong pic

[topaz rune]

Hmm I don’t really like the topic layout tbh

He does ODEs before linear algebra

[remote ginkgo]

2 bad

presumably you should study linear algebra outside this book

i have a list of books i actually recommend

kreyzsig is not on it

[topaz rune]

Yeah

Linear Algebra done right is fine even for engineers

[remote ginkgo]

no, it's terrible

http://sheafification.com/index.php/2022/08/14/the-fast-track/

here's the list

[topaz rune]

Doesn’t load

[remote ginkgo]

yes it does

[remote sparrow]

https://www.amazon.com/dp/1498777805
https://www.amazon.com/gp/product/0486612724/ref=ox_sc_saved_title_5?smid=ATVPDKIKX0DER&psc=1
https://www.amazon.com/Table-Integrals-Products-Daniel-Zwillinger/dp/0123849330/

these may be interesting splurge buys if an engineer wants to build a library of references

but not necessary

[solid wadi]

@remote ginkgo You have SSH problems. It loads only over HTTP.

[remote ginkgo]

what

ssh problems?

you're trying to connect over SSH?

[solid wadi]

Ah, SSL.

[remote ginkgo]

yes, there are no SSL certs

[solid wadi]

HTTPS.

[remote ginkgo]

hence i didnt link https

[topaz rune]

I have much bs turned off on my phone and it doesn’t load the page

[remote ginkgo]

i think your browser is messing up the url

[solid wadi]

This can be a problem. Some browsers do not like to connect without encryption.

[remote ginkgo]

ik

[solid wadi]

No, it is me who is messing up the URL.

[topaz rune]

Yep mine won’t

[remote ginkgo]

im too lazy to set up a cronjob

to renew ssl certs

:^)

[stable dagger]

just ignore if it has no ssl, press agree

[remote ginkgo]

need to get a webmaster to fix that for me

[topaz rune]

Send a screen shit here with the list @remote ginkgo

[remote ginkgo]

bc too lazy

[topaz rune]

Screenshot

[remote ginkgo]

kk

[topaz rune]

I see much landau lifshitz

[remote ginkgo]

ya

[stable dagger]

landau is not for engineer unless hydrodynamic maybe

fundamental physics mostly

[topaz rune]

Theory of elasticity volume is fine too for engineers researching or studying continuum mechanics

[remote ginkgo]

yep

engineers should know theoretical physics

[stable dagger]

AI researches is very progressive and it's need and payable

If i were good mathematician I would look there

[remote sparrow]

does anyone know if Analytical Mechanics by Antonio Fasano and Stefano Marmi is a good book for a mathematically oriented treatment of lagrangian and hamiltonian mechanics?

[topaz rune]

‘AI’ is just an umbrella term

Used mainly by marketing departments

Machine learning research pretty much boils down to optimization and data processing

[wise crater]

its topped out outside of a lot of work on what if

[bitter path]

does anyone have suggestions on a calc 3 textbook that isn't primarily focused on computations (i.e not stewart lol)? im somewhat familiar with proofs, logic, and set theory

[remote sparrow]

try hubbard and hubbard or shifrin's text

[crimson leaf]

https://ocw.mit.edu/courses/18-024-multivariable-calculus-with-theory-spring-2011/

[remote ginkgo]

you forget control

[remote ginkgo]

agreed on both

if they are married would you call them hubbard & hubby

[hearty steppe]

Hubby and hubby

[gray gazelle]

2-3 years

[gray gazelle]

How do you get the free time to do this whole list in 2-3 years

[remote ginkgo]

magic

[foggy relic]

carter new pfp?

dang

[remote ginkgo]

yep

highly draconic

[gray gazelle]

Any good introductory texts for getting projective geometry at a senior undergrad / early grad level?

[sick river]

Check out this projective geometry book. Most introductions are synthetic so for me I preferred this book when learning the subject the first time. https://www.amazon.com/Analytic-Projective-Geometry-Textbooks-Mathematics/dp/3037191384

[zinc jewel]

Hello guys! What do you all think of book called ''A survey in modern algebra'' is it a good book for highschooler?

[remote sparrow]

depends on your needs and background

pinter is pretty good for the average highschooler though

[zinc jewel]

just for like understanding algebra deeper

[remote sparrow]

abstract algebra or just that solving equations stuff

[zinc jewel]

i wanna find what i truly like in maths

[zinc jewel]

ig so

[remote sparrow]

which one

do you know what abstract algebra is?

[zinc jewel]

solving eq

[remote sparrow]

a survey in modern algebra is not appropriate for you

[zinc jewel]

i have read in wiki😂

i know there aint no eq but it still can be amazing

[remote sparrow]

do you know how to read and write proofs?

[zinc jewel]

kinda

not bad at it but not pro

i just wanna explore math yunno starting with algebra bc i like algebra but not the olympiad one

[remote sparrow]

well, i can certainly tell you that abstract algebra has very little to do with "solving" equations like quadratics (but it can tell you about the nonexistence of a quintic formula)

but nonetheless you would be better off with something like lang's basic mathematics if you're looking for a deeper look at algebra of the solving equations sort

[zinc jewel]

i dont really care if there aint no equations but like i just want to find something more than equations solving i mean i love it but

[remote sparrow]

as to your experience with reading and writing proofs, would you mind telling me what materials you've gone over already?

[zinc jewel]

olympiad math

and lots of lots a4 papers of writing why apple belongs to the 3rd path not 1st

[remote sparrow]

https://www.people.vcu.edu/~rhammack/BookOfProof/index.html

are you familiar with any of the methods outlined in this table of contents?

that's what i want to know about your experience with reading and writing proofs

[zinc jewel]

idk man im not learning in english nor i am learning the names

i mean

in like regions

[remote sparrow]

i've never participated in a math olympiad, so i wouldn't know

[zinc jewel]

😂

[zinc jewel]

oh

[remote sparrow]

i also don't know your native language, so i'm not sure how else i can further advise you

[zinc jewel]

ill just read it and see if i like it

but it is abstract algebra right?

with linear

[remote sparrow]

undergraduate abstract algebra textbooks may discuss linear algebra (a prominent example is artin's algebra text) but it does not need to

[zinc jewel]

i meant this exact book

[remote sparrow]

may you remind me what book you are referring to?

[zinc jewel]

A survey in modern algebra

[remote sparrow]

i've never read it myself, so i wouldn't know whether linear algebra is specifically discussed in the text

i do know what it is about

[zinc jewel]

ah man

[zinc jewel]

yess??

what is it about?

[remote sparrow]

it's an abstract algebra textbook, as i've previously implied.

[loud cradle]

birkhoff/maclane? it has about 200 pages (4 chapters) of linear algebra up to and including jordan canonical form

[remote sparrow]

and it likely has very little to do with the olympiad math you've already done

[zinc jewel]

i dont need olympiad math

[remote sparrow]

i know. but i tried to assess your background, and so far i haven't received a satisfactory answer. this could be due to your language barrier, but i do not feel i could in good conscience, with the information i have now, recommend you birkhoff/maclane's text.

[zinc jewel]

yeah all i can tell you is i have written a lot of prooffs in math olys

like not olys but preps for olys under teachers look ig

[gray gazelle]

Thank you!

[hasty eagle]

You already have the selfroles studying!, do you want to remove them? (y(es)/n(o))
(Tip: use ,iamnot to remove roles without this prompt.)

Removed the studying! role from you.

Session timed out waiting for user response.

Sep 25, 2022, 1:34 PM

[hidden apex]

Good math book for calculus?... i will start learning calculus next week

[solid wadi]

Differential and Integral Calculus by Richard Courant is a classic.

[hidden apex]

is it easy to read and understand?

i am dumb

[frigid burrow]

if you think you are dumb then you are looking for a book with a lot of examples and a lot of explanation
https://math.stackexchange.com/questions/322892/calculus-book-recommendations-for-complete-beginner
but to be honest, if you want to master calculus you need to change your mind about yourself being dumb :)

[solid wadi]

You can do it if you try. If something is not working, you can always ask on the Internet! Trying for a while and then talking to someone leads me to understanding every time I try.

Yo! I am looking for literature that talks about Abstract Algebra in concrete examples and problems. For example, instead of saying that a group is a set with such and such operations and laws, I want it to tell me about symmetries of physical bodies, Platonic solids, tilings, graphs, and then introduce stuff like stabilizers on these examples and apply the fancy abstractions to concrete problems, like say how to find solutions for Rubik's cube. There must be computational content and if some results are given without proof that is fine — I already have all the proofs I need. Ideally I want it to go on to other algebraic settings like rings, modules, fields, vector spaces, topological groups, and so on.

[hidden apex]

oh okk

[hidden apex]

i understand. i just every time want to finish theory as quick as possible(as these make me sleep) and then try a lot of problems

[solid wadi]

I see. Well, what I do when I want to learn something is blaze my own path — find something that can in principle be done with the theory I want to learn, and then try to do some chunk of it. So, you need a task that requires Differential and Integral Calculus that you want to see done. Say, you can try to build a robot.

Both Electrical and Mechanical Engineering need some integration. So you will have any number of problems on your hands right away.

[hidden apex]

👍

[safe aspen]

Anyone know where I can buy a license key for this book?
University Physics with Modern Physics, 15th edition

[pseudo zodiac]

carter visual group theory does some of this

[remote sparrow]

This probably occurred to you already, but i at least know there are dedicated group theory textbooks for chemists, and thus possibly for other scientists.

[topaz rune]

,iam dying

[hasty eagle]

Gave you the studying! selfrole.

[charred roost]

anyone have a good book recommendation for an introduction to probability for a mathematically mature student?

[remote ginkgo]

billingsley

[finite thorn]

I'm looking to get into combinatorics after I'm done with Artin's Algebra. What is a good book for Probabilistic Combinatorics and what are the requirements for that?

[remote sparrow]

i don't quite know any such books for that, but an introductory book to combinatorics that gives a survey of the probabilistic method (i.e. positive probability implies existence) would be A Walk Through Combinatorics by Miklos Bona. i also found a few syllabi for courses that do specifically teach probabilistic combinatorics (though they may or may not be suitable for your background), and they list a textbook. my limited search indicates alon and spencer's text is most commonly used. i also found a couple of miscellaneous PDFs.
https://www.math.uni-frankfurt.de/~acoghlan/probcomb.pdf
https://courses-archive.maths.ox.ac.uk/node/151
https://yufeizhao.com/pm/
https://impa.br/wp-content/uploads/2017/04/28CBM_04.pdf
https://math.gatech.edu/courses/math/7018
https://sites.math.washington.edu/~rothvoss/lecturenotes/ProbabilisticCombinatorics-15-MAR-2019.pdf

[finite thorn]

Thank you very much

I'll take a look at alon and spencer's

[old elk]

A first course in calculus Serge lang

[dim hound]

Anybody have a discrete math book that has a lot of good practice problems? Specifically in Set theory, logic and counting?

[unique ice]

kenneth rosen?

[dim hound]

Thanks, I'll check it out 🙂

[unique ice]

Just wanted to put this out there: I’ve read Claus Tondering’s Intro to Surreal numbers some years back https://tondering.dk/download/sur.pdf and I liked it

[dim hound]

Skimming through it, there seems to be a lot of really well explained proofs on it. So I'll check that out as well

Discrete is a lot harder than I expected it to be lol

[unique ice]

It’s v useful

[remote sparrow]

epp is a common alternative (though taking a glance at its table of contents, it doesn't seem to cover as many computer science applications as rosen)

hammack is adopted at some institutions for discrete math classes (plus its PDF is free)

concrete mathematics by knuth technically fits the bill but it's probably too hard for you

https://open.umn.edu/opentextbooks/textbooks/394

this free book seems to have good reviews

it'd help if you could send us a syllabus

[unique ice]

I am planning on doing it, we can do it if you want

[remote sparrow]

if you feel confident then go ahead

[dim hound]

We cover chapters 1-14 on Hammack's book of proof.

[remote sparrow]

common alternatives to hammack would be velleman's How to Prove It or chartrand's Mathematical Proofs: A Transition to Advanced Mathematics. books that i personally enjoyed were Foundations of Mathematics by Thomas Q. Sibley and Proof and the Art of Mathematics by Joel David Hamkins. do note that hamkins organizes his content by mathematical topic rather than specific proof techniques, so it may be difficult to use as a reference.

[dim hound]

I'll check them out. Thanks dude :^)

[plucky shell]

Any recommendations on books that would useful as I attempt to self learn knot theory?

[forest sleet]

Adams The Knot Book

[granite viper]

Knots and Physics; On Knots; Formal Knot Theory (Dover Books) by Kauffman

[forest sleet]

if you want more algebraic topology (don't think Adams' book uses it since it's an intro) I've heard Rolfsen recommended

[plucky shell]

I'll be sure to check them out, thanks for the advice.

[hollow dome]

Any good books for linear algebra?

[granite viper]

https://4chan-science.fandom.com/wiki/Mathematics#Linear_Algebra

[hollow dome]

Ty

[remote sparrow]

#book-recommendations message

#book-recommendations message

[gray gazelle]

Which proof book would be better for me? How to Prove it by Velleman or Transition to Higher Mathematics by Chartrand? (CS major but I want to really learn real/functional analysis)

[heady ember]

Rosen was too boring for me personally. I read only like the first 20-30 pages. But i mean if you like it, there's no problem continue using it.

then i tried Enderton and liked the pain and suffering

[shadow crown]

is isaac asimov an ok book

I just found it

it's kinda Babylon kind of numeral

it's like Roman numerals but different letter

[remote ginkgo]

yes

its a goqd book

[hearty steppe]

Hey if your learning knot theory, maybe try ordering some of these too https://www.tavernpuzzle.com

They’re really really really really really hard but I love them. I own two disentanglements and solved one so far

[lethal fox]

does someone know good introduction or overview to semidefinite programming?

[shadow crown]

oh wait it's actual name was

asimov on numbers