book-recommendations

[lusty ermine]

can someone recommend me a good book for using the characteristic curves method for a pde

Abdul-Majid Wazwaz , Partial Differential
Equations and
Solitary Waves Theory

I was recommended this before but was kind-of hard

I skimmed through some haberman, Elementary applied partial diff eqs but again, im trying to solve an exercise of this kind:

2u_x + 3u_y + 5u_z - u = 0
u(x,y,0) = x^2 sin (y)

[tender river]

<@&268886789983436800>

[finite gale]

Read #rules

[fierce hedge]

The fuck

This is against the rules, remove this before you get banned

[finite gale]

I thought it was just a muted

Also apparently mods are asleep

[fierce hedge]

shush

[finite gale]

if we're quiet the mods will never wake up

[fierce hedge]

I meant shush about the ban thing

[hearty steppe]

I’m hardly here cuz I don’t actually study math 😂

I just go through math books somewhat

[sterile pelican]

Before I left a handful of servers you were poking around Munkres' Topology before

[hearty steppe]

Oh yes that is a great book, unfortunately it goes far too deep in the woods than necessary for me and I was able to pick up on a lot of topology outside of Munkres.

I didn’t struggle with it, I just moved on to more challenging texts, and texts I needed to prioritize more time with.

[sterile pelican]

Ah I see

I am poking around other books at the moment, currently doing 6 books with some friends.

It makes me go slower than usual though but hey different maths to poke around with at least

[hearty steppe]

Ahh well I go through one book at a time usually and I’ve been able to complete each book within a matter of 3-6 weeks. Depending on difficulty of the text.

There are far more math and physics based texts that are not accessible or relevant to me in terms of level of exposition so at least I try to be honest with that level of humility. Despite the concepts I look at, any given time, I’ll have limits interpreting based on the abstraction involved in the exposition.

So I didn’t like Brian C Hall’s texts as an example. Didn’t like Artin, although I didn’t really need to go through an abstract algebra book for what I’m learning although there are abstract algebra texts I didn’t struggle with but I didn’t bother completing any of them

[sterile pelican]

It's better to go one by one to be fair, I only did this because I am kind of greedy :^)

I am currently going through Anderson & Feil's Algebra book it is quite my favourite

I hated a lot of analysis books out there but Bloch seems to be good enough for my level, though he is quite dry

[hearty steppe]

I tried finding a bunch of Lie Algebra books and most of them I couldn’t work through, but I found some that seem manageable but I haven’t worked through them yet, just skimmed them

[sterile pelican]

The other 3 books I only do once a week which are Cox's Ideals, Varieties, and Algorithms, Hodges' mathematical logic, and Hrbacek's set theory

Which is why it is manageable...sort of

[sterile pelican]

can't help you there bud but I am sure people here can do something about it

[crimson leaf]

Erdmann Lie Algebras is probably the most accessible math based Lie Algebra book I've seen, it's for undergrads

[silver stirrup]

TYSM - really appreciate it

oh one other thing, is there a specific edition you'd recommend? I see that a lot of the newer editions are quite a bit longer and cover more topics

[mossy flume]

IVA my beloved

I gotta dive back in

[gray gazelle]

hi I am Answw
I am preparing for JEE Advanced 2025 😅
Can anyone suggest me some books for Jee

Maths books*

[gray gazelle]

Thx but I solved some questions of cengage
And I would say that they are above moderate level but not above extreme....... or at extreme level......

Never heard of that book
But I'll try it 😄
Thx for the suggestion

Btw you got any books that are above extreme lvl for practice?

[lilac copper]

well you dont start with extreme

[lilac copper]

yeah the second one I recommended, it has some easy problems at the start of each topic, but as the numbers increase the level increases too.

[gray gazelle]

From beginner to extreme lvl?
This will help me alot 😄

[lilac copper]

yes

you are self studying?

[gray gazelle]

Hmm..... nah
I study in pw

[lilac copper]

ohh

try to get coaching materials of some other institute

[gray gazelle]

I have coaching modules ,dpps and other study materials of different institutes

[lilac copper]

then try to solve them first.

some are really good

then jump to other books

[gray gazelle]

I am doing coaching modules and other books at the same time

[remote sparrow]

if you're going to use a pdf, it doesn't matter

since you can just read the latest edition

if you're going to buy a physical copy of burton, i wouldn't buy the seventh edition, which is the latest edition. even used, it's still wildly expensive. the book is also poorly made. i would just get a used copy of the sixth edition. dudley is available for a very low price from dover books.

[final sluice]

yo my linear algebra is so shit, i took a computational linear algebra course and then a proof based linear algebra course and the texts we used were lay and axler respectively. i didn't have enough mathematical maturity back then lol so i skimmed the textbook, attempted the exercises w/o reading, etc and it was a disaster. any recommedations for a linear algebra proof-based textbook that's not axler?

i can always read axler again but i'm kind of interested to see if there's anything else

[civic python]

Friedberg and spenze, is usually recomended here i think

You could also try Paul Holmos: Finite dimensional vector spaces

[final sluice]

looks good, i'll check them out

thanks

[zinc lantern]

Anyone have a good AMC 10 prep books recommendation

[swift dome]

https://artofproblemsolving.com/wiki/index.php/AMC_10_Problems_and_Solutions , just solve problems from there, rearrange concepts, and without wasting time, tackle problems. This will help you improve fast

[dry oxide]

Are there any books that primarily focuses on non-convex optimization? I gleefully went through a chunk of Stephen Boyd's Convex Optimization book and it got me curious if there are other similar books that solely focuses on non-convex optimization problems and algorithms

[cold elbow]

anyone have any books for exponents and log

[median saffron]

I don’t think there’s a book specifically for that

Just look into some algebra books probably

[cold elbow]

alrighty

[cold elbow]

are there any good algebra books i cant fijd any 😭

[fierce hedge]

you can check algebra recommendations in pins as well as in #books
My bad I thought you wanted abstract algebra recommendations

[dark tulip]

No they are not looking for abstract algebra book

for exponents and log
I'd say any precalculus or (high-school) algebra book cover these topics

[fierce hedge]

Ohhh, my bad

[cold elbow]

oka ill search for them

[sterile pelican]

Basic Mathematics by Serge Lang or his Short Calculus book does cover exponents and log

[subtle fractal]

any good hard(bmo to imo level) nt books and or polynomial books

[sterile pelican]

Gelfand's algebra book might be enticing enough for you, his section on polynomials are fun, but I am not sure if it goes well for imo or bmo

[hardy field]

where is true general

[fallen orchid]

Hi people, Can you help get better at algebra by naming an book for it??

[dark tulip]

Abstract or high-school ?

[fallen orchid]

high school

[dark tulip]

Gelfand's algebra or Stewart's precalculus

You can try AoPS intermediate algebra as well (for more challenging problems)

[fallen orchid]

tysm

Have a nice day

[tawny copper]

Hojo Lee's collection of problems (its really really good)

If you want explanations, go to MONT. Andreescu is also a nice choice

For algebra idk, but you can always go to the math olympiad discord server and search for algebra problems, since there is not a lot of theory (except maybe in inequalities, where you should go to texts just about inequalities)

But you can always go to general math olympiad books, like Mathews, Everaise, Engel, etc

[gray gazelle]

any recommendation of a good math list of books

[vital bane]

@misty glen might know

[dusk wind]

why is memorization bad for learning maths?

[gray gazelle]

is there any simplified euclid elements that is nice to go through

[gray gazelle]

i think memorisation is bad without understanding, but without remembering things there isn't much left

[tawny copper]

Hartshorne (Euclid and beyond)

But if you read Hartshorne, you should read Euclids book along

[dusk wind]

you need to remember a lot of proofs though in general, if you don't use the math then you'll forget, so there needs to be application

[gray gazelle]

Also, in my opinion, having some sutff that we didn't understand in memory is useful for asynchronous learning

[dusk wind]

you could go hard on math for years but if you go on a sabbatical for like a year you might forget

[tawny copper]

Euclid is still readable, but the presentation is rough since its theorem after theorem. But if you know where everything is going then its nice

[gray gazelle]

I find it a bit boring or maybe difficult, so I wonder if there is something simpler i.e less rigurous, but similar ?

[dusk wind]

are you really going to explain difficult proofs to a layman student

[tawny copper]

There is another one, the author is called Artmann, but its very historical

You will probably find it more boring, I did find it boring

[gray gazelle]

i'm looking for something that is kinda easy to refresh, but i hate high-school like books

[tawny copper]

Do you want to read Euclids book or you just want to learn euclidean geometry?

These are two different things

[gray gazelle]

2. However when i took a look at euclids book, i though there was beauty, and that would make easy to sit and read

but it got quite heavy right after first pages

[sterile pelican]

The point of maths is to develop a sort of mental landscape of the topics you studied. While memorising some theorems/axioms/proofs are good it goes hand-in-hand with understanding. Lastly, forgetting is just as important since you would see the same idea from a different light in more advanced book, which further develops your intuition

[tawny copper]

Yeah. I think you should go to read some section on Euclid once you know what its about

[dusk wind]

so embrace forgetting some of the concepts sometimes? That is an interesting take, thanks for this

[gentle arrow]

memorization cannot take you far in proofs

[sterile pelican]

I am not sure if Chmonkey is a cat lover or a "Cat" lover :^)

[gentle arrow]

[sterile pelican]

So like a Category Theorist :^)

[gentle arrow]

we do not talk about category theory

[sterile pelican]

Ah so a cat lover

I love cats by the way :^)

[tawny copper]

@gray gazelle I think you could try solving geometry problems from math competitions. Its more fun this way in my opinion

And id you cannot solve the problems its fine. You will probably realize what "is missing" and when you read the theorem you will understand its motivation

[gray gazelle]

interesting

yes sure, i find quite difficult to know where do i need to go for what i want to learn ha

i think a book full of examples + theorems could be nice

so the abstract and the concrete

[gray gazelle]

do you know if any of this books could be good as an introduction to geometry, but are also somewhat dry and not a mouthful (or very repetitive) https://www.amazon.com/s?k=geometry&crid=XFNVXTMB4XYK&sprefix=geometry%2Caps%2C257&ref=nb_sb_noss_1

[sterile pelican]

Brannan would be my favourite but that is definitely not for a highschool/early uni level student

I do read stuff like this then poke some constructions though: http://aleph0.clarku.edu/~djoyce/elements/elements.html

The other is Euclid's Elements Redux by Callahan but I did not read it myself

[misty glen]

Jorge Nocedal Numerical Optimization, it doesn't focus solely on it, but there are references and chapters on non-convex problems

basically you develop algorithms for convex problems and then modify them for non-convex problems

also surprisingly enough accelerated proximal gradient with restarts is an extremely efficient algorithm for it's simplicity and generality - it can solve both convex and non-convex problems, can tackle reformulated non-differentiable (but convex) problems or simple non-differentiable functions for which prox operator is available, it can even handle constraints if you can project onto the feasible set cheaply (and you can do that for a large number of them - linear equalities, norm balls, simplex, non-negative orthant, PSD cone, etc)

you can read about it here https://my.siam.org/Store/Product/viewproduct/?ProductId=29044686 (the chapters 6 and 10 are actually free and that's enough for the entire algorithm) and read about restarts here https://arxiv.org/abs/1204.3982
boyd also has his own monograph on proximal gradient https://web.stanford.edu/~boyd/papers/pdf/prox_algs.pdf (the moreau decomposition is surprisingly powerful, make sure to not skip it, it allows you to compute some of the operators like for 2-norm or infinity norm in just a couple of lines)

Beck's book even explains how to adaptively select step lengths, which you should also modify to make sure you start off with previous value of the step length divided multiplied by 2 or something like that, so that you don't waste a bunch of extra iterations decreasing it from 1 all over again and instead only do 2-3 backtracking iterations

[crimson leaf]

I second this book, Dr. Wright has a couple good books imo

[dry oxide]

Thank you! I greatly appreciate all of this!

Going to add these to my to-read after I finish Bellman's dynamic book

[lean kettle]

I bought this geometry a book a while ago to relearn geometry that I forgot: https://www.amazon.com/gp/product/1934124087/
I found something disgusting in one of the pages and got a full refund for it though.
I'm wondering if I should buy another copy of it or get a different book. This book was quite a bit more advanced than what I remember in high school.
I'm not too interested in geometry, I'm just trying to get a good foundation to move on.
Any suggestions?

[gray gazelle]

Could be good to implement book sharing in discord

[crimson leaf]

Depends on what you want but this book is more so aimed towards students trying to do competition math. What did you find though that got you a refund?

[lean kettle]

I'll tell you in PM if you want, don't want to say it in here because it is really pretty disgusting

So do you have any recs for a geometry book that just gives a good foundation? Don't want to do geometry competitions

[crimson leaf]

Your best bet is probably to just use Khan Academy

Plus it's free

[lean kettle]

I don't like video resources, would rather just read because it's faster

Don't mind paying money either

[crimson leaf]

You can try something llike this if you prefer reading a book https://open.umn.edu/opentextbooks/textbooks/508

I read a bit of it when I started undergrad and thought it was pretty good not too hard

[dusk wind]

there's not much on geometry at that level

maybe worry more about trig?

there should be really good videos on yt
https://www.mathplanet.com/education/geometry
https://www.youtube.com/playlist?list=PLmN1jmOiJEf6vN3Pyoy5Dtnr5VPfQEuDS

not every video on a math subject is long, if it's past 20 mins then eh

Khan Academy and pen/paper can't be beat though

[lean kettle]

Yeah I'm going to focus more on trig, but that's alongside algebra 2

[lean kettle]

Can't find this one anywhere except Amazon

[dusk wind]

there's lots of good algebra resources everywhere, it's geometry that's scarce, a lot of trig uses geometry anyway

[lean kettle]

In America we learn trig alongside Algebra 2, as in it's not even its own course in high school it's taught alongside Algebra 2

Is that not the case where you're from?

[dusk wind]

I honestly wouldn't remember as high school was a blur

[lean kettle]

I do need to learn trig in-depth, that and combinatorics are 2 I'm going to spend a lot of time on

[dusk wind]

all I remember from 'algebra 2' is linear algebra and coordinates

when you do a search for math resources though there's tons of algebra content

[dusk wind]

we learned trig but that was a seperate class I think

[lean kettle]

I wonder how important is a good base in geometry to learn trig effectively?

[dusk wind]

who knows, I think that geometry is very important in the long haul and it can be very useful,
but if you learn trig it can solidify those geometric concepts.. of course if your algebra is strong it can affect in other areas too

most good trig books will do a review so if you do practice tests on khan academy or elsewhere you can gauge,
there is also the ALEKS math placement test you can try, there is a free trial/paid options and gives in depth stats

[lean kettle]

Ok thanks for the info

Not sure which 1 to go with out of these 2
https://www.amazon.com/Geometry-School-Course-Serge-Lang/dp/0387966544
https://www.amazon.com/Geometry-Israel-M-Gelfand/dp/1071602977/

The yellow one (by serge lang) has some section on vectors which would be useful for me
The Gelfand one is newer, only came out a few years ago

[sterile pelican]

I would prefer Lang to be honest while I do like Gelfand's Algebra and his Functions & Graphs I think his Geometry is better as a second exposure, as the vocabulary looks a bit more advanced based on the content page alone.

[lean kettle]

Ok thanks

[storm fossil]

Is there any Abstract Algebra textbook that's approachable for someone with just high school algebra to play with? It doesn't need to be overwhelmingly rigorous. Really, I just want to get a better understanding of the primary operations (addition/multiplication).

I can obviously add and multiply lol, but I want a better understanding of what's really going on.

[remote sparrow]

https://www.amazon.com/Symmetry-Mathematical-Exploration-Quantitative-Critical-dp-3030516687/dp/3030516687/

[storm fossil]

@remote sparrow Thank you 🙂

[remote sparrow]

https://maa.org/press/maa-reviews/symmetry-a-mathematical-exploration-0

[sterile pelican]

You think Nat would like Pinter though, Sour?

I do think a high school students would like Pinter from what I know, while he or she is learning some proofs

[remote sparrow]

i have recommended pinter many times in the past, but it still isn't good for someone that only knows high school algebra

[sterile pelican]

Oh if Nat's level is only high school algebra, which I didn't read his post :^), then I do agree

[storm fossil]

In case this helps anyone, I found a book that is exactly what I needed. I tried the Symmetry Math book, but it wasn't precisely what I wanted. (Which is my fault though, my comment was pretty vague.)

I've always wanted something that starts from the beginning. Defining natural numbers, defining what addition actually is, and so on.

Terrence Tao's Analysis I is exactly what I've always wanted. You can find it online. I'm not sure if the later chapters require advanced math or if the axioms alone are sufficient, but at the very least, the first chapter should be approachable by anyone that can read English.

Hopefully that helps someone. Thanks for the recommendations though, Sour and Kani. 🙂

I'm sure they do, but the only one I've read so far is the one by Tao. Seems well written. So, I can't comment on the others.

The slowness is preferred. Slow book for a slow dude. Fits me well.

Thank you for the recommendation. I'll save it.

[remote sparrow]

https://www.amazon.com/Number-Systems-Foundations-Analysis-Mathematics/dp/0486457923

this book would be better suited for you

https://www.youtube.com/playlist?list=PLBh2i93oe2qtbygdXz4u6Mkh7c_hMLBA8

this playlist may also be helpful

[gray gazelle]

are aops books good for algebra? (The Basics And Beyond series)

[gray gazelle]

Anyone got Discrete and Combinatorial Mathematics", by Ralph P. Grimaldi

[desert herald]

Hello guys, I'm looking for a book recommendation on graph theory for a CS student. I am planning to do my bachelor's thesis in that subject so I'm trying to better my knowledge in the field. I was looking at Combinatorics and Graph Theory by Hariis, Hirst and Mossinghoff but not sure if it is adequate for my level.

[ember kettle]

What are some good books on probability theory, that are not just school textbooks?

[tulip blade]

Idk what you mean “for a cs student”. The book introduction to graph theory by douglas west is good.

[charred estuary]

dual enrollment discrete math next summer before hs senior year - should i supplement learning with Rosen or Grimaldi which one is better

or does it like not matter

[remote sparrow]

if you know which professor you'll take discrete math with in advance, maybe google their syllabi

or email them to ask what their assigned textbook will be, if they do assign one

rosen or epp are good though

don't think i've looked through grimaldi

[fluid aspen]

Where is the channel that recommends online resources such as free courses (edx, khan, etc) or video channels (Prof Leo, Organic Chem Tutor, etc)?

Looking to learn alg, geo, trig, and calc.

(I’m rusty in everything as a returning student)

[remote sparrow]

i do not believe such a channel exists

[fluid aspen]

Skull

Massive skull

So instead of an engaging and informative video series showing how stuff works from big names like Prof Leo and Organic Chem Tutor, this discord recommends giant books of esoteric knowledge?

This in spite of the fact that humans learn far more by audibly listening and visually seeing concepts in real time than by just bare reading?

[sterile pelican]

I learn by bare reading then doing exercises, just see what works for you. For me textbook is king

[remote sparrow]

i don't think the lack of such a channel means that no one cares to recommend lecture series in this channel

[remote sparrow]

that is true, which is why schools exist, so that you get the benefit of a lecturer

however, as material becomes more advanced, video series becomes less adequate

a video cannot respond to real-time questions

and you may not follow an instructor's idiosyncrasies or intuitions for a subject

[upbeat vine]

The more active members of the community are at undergrad-grad level, at which it's rare to find a lecture series devoted to a topic

Not to mention, learning a proof is very difficult in a lecture because if you get stuck at a detail, you might won't be able to skip it

[remote sparrow]

lectures also become less about working the material more or less in full like in lower-division classes, and more about explaining a given topic in broad strokes so that you can better understand your book or the instructor's detailed notes

[sterile pelican]

In my view reading then doing the exercises to communicate with people is the most important

I had only one or two good lecturers but always had great tutors

since tutors actively talk to you about the solutions you did

[remote sparrow]

probably the next best thing to sitting in a classroom is finding a group of people willing to study a book with you, preferably with one or two people experienced in the topic and collaborating together

[sterile pelican]

Yeah this is a great approach

It helps fill the gaps of your understanding

[remote sparrow]

in any case, sooner or later your book will become the primary source of understanding. math is not a spectator sport

i try to recommend books suitable for self-studiers

[sterile pelican]

It is better that way

Velleman was that one book for me before that is great

And Lang actually is good too, especially his high school and calc books

[remote sparrow]

moreover, you are not just doing "bare reading" from a book. you should be working the exercises, or perhaps filling in a gap in a proof.

i'm not really aware of any lectures for plane geometry, and i presume if they resemble U.S. high school geometry, they're worthless anyway

your only recourse is a decent book

fortunately geometry is a very visual and hands-on subject

my uni's math education program has a basic geometry class as a required course, and i believe this is one of their course texts: https://www.amazon.com/Classical-Geometry-Euclidean-Transformational-Projective/dp/1118679199

there is a solutions manual to accompany it

it does assume prior familiarity with high school geometry

hmm looking through the book it might be a bit advanced for someone at your level

take a look at kiselev's geometry books instead

huh, i just found this geometry book by lang

https://www.amazon.com/Geometry-School-Course-Serge-Lang-dp-1441930841/dp/1441930841/

[dusk minnow]

not just bare reading, you also do exercises to engage in the maths yourself

[remote sparrow]

a few people have remarked that it treats geometry in a somewhat nonstandard fashion

but the reviews are quite favorable

https://www.amazon.com/Geometry-Ray-C-Jurgensen/dp/0395977274?ref_=ast_author_mpb

i hear this book is a little bit more standard

i'll have to check the pdfs of lang and jurgensen

ehhhh jurgensen seems pretty lame

https://www.amazon.com/Everything-Need-Geometry-Notebook-Notebooks/dp/1523504374

the big fat notebooks are presumably notebooks and not meant to substitute an actual text

they cover the standard topics in a standard way so that's nice

i'd probably suggest picking up this book along with the lang book

the lang book has a solutions manual as well

for algebra and trig, you can just watch khan academy

pick up a book like stewart's precalculus (any edition will suffice) as a reference and a source of additional problems

you could work through lang's Basic Mathematics if you're particularly motivated and willing to do proofs

but if your only goal is revision, i don't think it's necessary

calculus you can also watch videos, but reading your book becomes a bit more important

there are also tons of practice workbooks out there

[remote sparrow]

also, books are not always read linearly

jumping around is common for me

[sterile pelican]

This is a wonderful book but it is not exactly standard

[mystic orbit]

need source for this

[remote sparrow]

books are also used as "references"

[mystic orbit]

I honestly believe books are the most efficient way for people to learn

[remote sparrow]

that is, if you forget something, you look it up there

[mystic orbit]

it just might not be the best way for everyone

[remote sparrow]

guess we don't need universities then

[mystic orbit]

I didn't say that

[sterile pelican]

I am a devout book learner

[sterile pelican]

Nah you need unis for the connections

[mystic orbit]

the social factor is obviously very conducive to learning

[small perch]

There are universities, where less attention is on lectures and more on textbook, self-learning with help and program from university

[remote sparrow]

most students do not join mathcord, let alone seriously engage in the community, let alone have the initiative to independently seek out a book for self-study, let alone even commit to a book for a sustained period of time. there is a lot of self-selection here

[small perch]

I think that's rather problem of limited number of people, who can choose this way.
I personally prefer to study on my own and just write exams, but that's technically difficult, universities usually left you with 10 times bigger amount of homework and all you can afford is no time except for course. But still, I know some of people who ended with 5.0 as average grade on "self-study"

[remote sparrow]

in fairness, i barely recall theorems about circumscribing, inscribing, isosceles triangle (probably need some better examples since implicitly in the back of my mind they're ingrained and intuitive, and i'm probably not even thinking of the even more forgettable material), etc. and other fairly esoteric material because i never use them outside of the context of that class

so maybe lang's treatment is for the better

lang's book probably won't help you pass an average class in high school geometry, but she doesn't need to pass a class

just relearn/revise basic h.s. geometry

[tawny copper]

By school you mean university right?

[remote sparrow]

looking through your message history, it seems that you are actually in a calculus class right now

https://tutorial.math.lamar.edu/

this will be useful as a just-in-time intervention. as you practice more calculus problems you will also consolidate more of those basic skills.

[remote sparrow]

yeah

[mystic orbit]

I don't understand

ofc my opinion is based on my own experience

besides

I did say it might not be the best way for everyone

but learning straight from a book is the most efficient way

[fierce hedge]

This the classic visual learner thing which was debunked recently where it was shown that you need a mix of audio, visual and other things to get the best outta it.
So just do all the exercises to engage all of it

[mystic orbit]

coz you're learning at your own pace

you don't have to wait for anyone

nor do you have to constantly revisit stuff coz people are moving too fast

[tawny copper]

I disagree, the best is to learn 1 to 1 (given that the person teaching actually cares etc)

Specially when you do more serious math, and not just undergrad math

[small perch]

Most of the book are written in not so good way at least in some sections (writing is hard), and you better to have some people who you can ask about sections you are not sure. For example there are imho wrong proofs in Rudin, although that's almost best book on calculus.
Also learning 1 to 1 As @tawny copper wrote is better, but it is less affordable

[mystic orbit]

I mean instead of spending only your time you're spending two people's time lmao

[tawny copper]

Yeah, books are definitely the most reliable

But its not the most ideal situation

[mystic orbit]

can you really call that more efficient?

[tawny copper]

Why would people learn math and then not share it with other people?

I dont understand your reasoning

[mystic orbit]

[remote sparrow]

darq, what books have you read? and besides, in what sense are you using efficiency here? total labor time? or efficiency in you personally absorbing material

[mystic orbit]

where did that come from?

[fierce hedge]

Excuse me, there are wrong proofs in Rudin

[tawny copper]

Like there is zero chance of someone getting into research level math without someone guiding them.

[mystic orbit]

you think the only way people share math is on one on one sessions?

[mystic orbit]

oh

[remote sparrow]

didn't you say you worked through hubbard? that's an exceptionally well-written text

[mystic orbit]

[remote sparrow]

lots of books aren't amazing

[tawny copper]

Oh, so you meant 1 to 1 sessions are inefficient in general? I read your comment wrong

[mystic orbit]

hubbard, artin, baby rudin, folland, spivak calc on manifolds, aluffi

uhhh

[tawny copper]

Ofc this is not reliable lol

[mystic orbit]

hatcher's pointset and hatcher's AT

oh and lee ITM

there are prolly more

I haven't read all of them tho

actually I didn't finish even half of most of them

[tawny copper]

But next best would be a small class

[mystic orbit]

croqueta I think I misinterpreted you too

like, if what you meant by "1 on 1" is just asking people with more knowledge to guide you from time to time than ofc

ofc that's more efficient then just brute forcing books

I thought you meant like, tutorin

[mystic orbit]

I'm very happy with most the books I picked tbh

except perhaps spivak and rudin which were super terse

[tawny copper]

I am talking about a class with just 1 student

[mystic orbit]

yea, I disagree then

[tawny copper]

Not a student asking questions to an expert, because in order to ask good questions you need some knowledge already so its kinda pointless

[tawny copper]

Next best would be a class with few students

If then you are comparing books to a class with idk 30+people where the professor doesnt know a single name and just delivers the lecture then I might agree

But I dont think I have had good lecturers on topics I didnt know about already so idk

But anyway, for an average undergrad student, books are the most important. That I agree with, just saying its not the best

[mystic orbit]

that's my experience as well

[wheat ledge]

hello guys

https://quizlet.com/explanations/textbook-solutions/algebra-structure-and-method-book-1-1st-edition-9780395771167

im looking for pdf of this book

id be grateful if anyone has it & can share!

its called Algebra structure and method book 1 - 1st edition

[heady ember]

People can't share it here

Piracy is against tos

[sterile pelican]

No arrrr-ing about here guys

But you know one book I was surprised no one mentions is Anderson and Feil's A First Course in Abstract Algebra, it is a great algebra book if you learnt Velleman's How to Prove It

It's a bit unorthedox though he starts with rings first

[fluid aspen]

https://www.scienceoutside.org/post/pushing-your-teaching-down-the-learning-pyramid

[mystic orbit]

this puts lecture above reading

[sage python]

Ngl I prefer lectures when available

[fluid aspen]

Use the non-stem part of your brain; channel the right half of the brain~ listening and viewing video lecture is considered engagement especially if you’re following along with notes~

[mystic orbit]

Use the non-stem part of your brain
there's isn't one

jk

the teaching part is very true tho

I actually need to do more of that

[fluid aspen]

Agreed; I’ve found that to be super true myself.

[jade plume]

anyone could recommend a complex numbers book? Basically to do exercises in a first university year level

[sterile pelican]

What's your background?

Did you do multivariable analysis?

[jade plume]

I have worked quite a bit with complex numbers, so I'm looking for a mid level book

[finite gale]

This doesn't answer the question, but first year university level sounds like they haven't done analysis

[jade plume]

We didn't work so much on that topic, so I assume I don't know what it is

[vital bane]

spivak

[warm briar]

any good books for learning advanced trig

[novel obsidian]

what do you mean by advanced trig

[gusty hull]

this might be out of topic but i dont know where to ask this question ,whats the best way to study physics?

would flashcards help?

[remote sparrow]

if you have trouble remembering some basic concepts, flashcards are one way to help you memorize them

but better than that is doing some problems

[gusty hull]

i have a very hard time doing past papers

i think i need to learn the fundamentals first

i like using flashcards so ill use that

[finite gale]

i think it is better for stem topics to do a bunch of problems than forcing yourself to memorize thigns

[gusty hull]

im just doing a general physics course in hs

[mystic orbit]

BURNN

[vital bane]

still understanding the actual concept is far more efficient than memorizing stuff

physics and math are the best because you can just derive everything from first principles

no need to remember 200 different names and shit

[mystic orbit]

you do

especially if you're an algebraists

[gentle arrow]

hi darq

[mystic orbit]

cat bread!

[tawny copper]

Andreescu has a book on trigonometry

[tawny copper]

Andreescu has a book on complex numbers

But honestly, if you are comfortable with integer/rational/real numbers already you just need to know i^2=-1, nothing else

[dusk wind]

there are studies that show watching lectures can actually lead to coasting through the video (laziness)

when you read a book ofc you need to do the exercises to actually get anything out of it and this is true regardless of learning preference
and if you take things to the extreme, skipping classes to study on your own might produce a higher tradeoff than turning your brain off for hours
falling asleep during a lecture or video series, at some point you'll use a book anyway

there's no best book or series because everyone teaches/learns differently

[storm fossil]

This might be off-topic, so just let me know. I've found various sites like AbeBooks, but I'm curious if there are any even cheaper ways of getting textbooks (to purchase, not rent). This isn't for courses, so ISBN matches are irrelevant. Just grabbing textbooks for my own learning and enjoyment.

For example, do professors ever have a stock of copies of their textbook (similar to their journals) that they'll send you? Since many of them aren't paid for the book, I imagine they don't care if you buy it.

I've gotten my hands on several journals by just emailing the professor. Most of the time I'd just pay for the shipping or something.

[remote sparrow]

buying used books from amazon is generally the best way

i don't believe authors generally have the rights to distribute copies of their own textbook if they're signed with a big name publisher

[storm fossil]

Makes sense, I'll check Amazon. The times I've gotten them, the books have often been obliterated with highlighting and notes, unfortunately. Might just have to focus on specific sellers on there.

Thanks 🙂

[remote sparrow]

i don't really find writing in books problematic

[storm fossil]

It's the highlighting that usually gets me, not the writing.

[remote sparrow]

i would prefer a clean copy to be sure, but there is far worse damage that could be had

[storm fossil]

Last request (going to head out so I can't respond for a bit): does anyone know of another book similar to Calculus Made Easy by Thompson, 1910? I'm a big fan of this book and writing style. Don't really care about the older English, but I mean the more conversational style.

Calculus for the Practical Man is another example, but I dislike that book.

Just a conversational, but serious textbook (not a pop-science math book). Calc 1 ideally.

[dusk wind]

not sure but try one of these
https://www.mecmath.net/calculus/ElementaryCalculus.pdf
https://www.whitman.edu/mathematics/calculus/calculus.pdf

for even cheaper books consider free or open source

[full egret]

I need something for finite linear games, which is something quite specific lol

[vital bane]

yea but algebraists are cringe

[gentle arrow]

would you say that in front of chmonkeys face

[maiden halo]

You can check bookfinder.com for prices. And I've actually had good luck getting some books on eBay

[gusty hull]

yea i have an easy time with math which should mean im good with physics but im having a hard time with physics 😕

[gray gazelle]

What are some modern alternatives to Baby Rudin that takes the reader from somewhat rigorous Calculus to being able to dive into Functional Analysis?

[remote sparrow]

physics is just mushier than math. the difficulty comes from choosing the right model, which isn't something governed by axioms or precise definitions

[sterile pelican]

I had always wanted a maths oriented book on physics. So far the book that comes to mind is Gregory's Classical Mechanics but I got no clue on quantum mechanics

[vital bane]

mushier? what does that mean

precise definitions are there, that's called reality and experimental observations

[remote sparrow]

i don't really know any functional analysis books as the topic doesn't really interest me, but a good progression from baby analysis to measure theory would be abbott -> carothers (with baby rudin as an additional source of problems) -> axler's MIRA

[sturdy shore]

pretty sure just abbott into axler would work fine

and 2nd half of axler (or of most measure theoretic analysis books) is already intro to func anal

[gusty hull]

thats what makes it hard, there is a set of rules but so many infinte scenarios to apply the rules to

[mystic orbit]

True!!!

[mystic orbit]

@dapper root you're cringe

[vital bane]

@coarse frost

[coarse frost]

suck shit ty

[coarse frost]

also why are you pinging me, im not an algebraist

[mystic orbit]

????

did you just tell me off for no reason then?

[vital bane]

he's a closeted algebraist

[sterile pelican]

Why fight when you can have both :^) have you not heard of GAGA? :^)

[tawny copper]

Lady Gaga ???

[gray gazelle]

I've been looking at GF(2) because of CRCs in computer science, so something that will help me learn the general concept of finite fields and/or polynomial division in those fields

[tawny copper]

Rudolf Lidl "Introduction to finite fields and their applications" maybe

[gray gazelle]

£129

[tawny copper]

You should be able to find a pdf I think

But if you dont dm me

[sterile pelican]

https://en.m.wikipedia.org/wiki/Algebraic_geometry_and_analytic_geometry

🤓

[gray gazelle]

yeah the only version I can find is the 1986 one not the 2012 one

[coarse frost]

yes

coz telling you off is fun

fuck you

:)

[coarse frost]

??

[mystic orbit]

suck a dick

[coarse frost]

no

:)

[fierce hedge]

@moderator

[jovial parrot]

Everywhere I go in math servers

I see horny people

Even in book recs???!!!??

Of all places

[mystic orbit]

wat

[sage python]

amukh I don't think you're correctly reading the tone of that message

[jovial parrot]

Wdym

[fierce hedge]

The fuck you mean? It was clearly phrased as an insult

[jovial parrot]

I see

Y r u swearing at me

[sturdy shore]

sometimes I forget there are underaged people here

[fierce hedge]

I know amukh is underaged but he behaves so degen that I froget

[nova breach]

Probably a bit below the normal recommendations around here. Are there any good high school algebra (algebra 1 and 2. Note: I’m in the States, so I’m referring to that curriculum) textbooks that are conversational, short, and well-written?

Pretty much every high school algebra textbook seems designed to make kids hate math because of how boring they’re written. Super cliche, classic textbook style for children that are unreadable.

I’d like to find something for students that is written in a style like undergrad/grad books like Spivak, Abbott, Strang, etc.

I’m teaching adults at a local church and I’ve found that the typical high school books are terrible pedagogically.

Something <600-800 pages, well written, conversational, but rigorous. Good explanations of why things work rather than brute force “here is the product rule, don’t question it.”

Things like khanacademy exist, but I’ve had very bad experiences with students who use khan as a primary or even secondary source.

Sorry for such a long request, just figured I’d be clear in what I’m looking for and why.

Thanks

[tiny osprey]

Hey I’m a sophomore in US doing Ap Precalc 4 and am aiming for Ap calc BC next year
But am currently struggling and have C in my grades but there has only been 1 test.
I need a book which will help be study for at least 3 hours everyday so I can improve my grades and knowledge

I would appreciate if u could suggest a book

Thanks 😊

[nova breach]

@tiny osprey I'm not familiar with AP Precalc 4. Is it just the usual precalc course in the US? What's the curriculum?

[finite gale]

college board really trying to scam even more people

smh

it's probably the same as the usual curriculum

there's only so much you can change

default recommendation is khan academy

as for a textbook, any text for material before calculus is pretty much the same

so it doesn't really matter, they'll all hit the same things, roughly the same way

[finite gale]

aops books might be decent candidate

but otherwise im not really sure if books written in a style for undergrads are suitable for high school level students if you're somehow saying khan academy isn't a good fit

[remote sparrow]

"Conversational" and "short" conflict with each other somewhat. You may find Lang's Basic Mathematics useful. However, some topics are nonstandard. Is this part of an accredited continuing education program for adults, or simply an informal study group? If the former, some more standard books may be in order, even though they might not satisfy the criteria you laid out. I think there are some books which teach algebra to college level students. This course is usually called college algebra (not to be confused with modern or abstract algebra). Blitzer and Stewart are a couple of authors worth taking a look at.

Tangentially, you may be interested in a series of books by Hung Hsi-Wu that presents a vision of pre-college mathematics which is both rigorous (i.e. has precise definitions and proofs) and accessible to a pre-college audience. These books are not meant for students, but rather for education research and professional development. Perhaps you could look to these books for inspiration, however.

[nova breach]

Not part of an accredited program. These are remedial adult students that are trying to learn so they can eventually attend college or technical schools.

I wouldn’t necessarily say that conversational and short are mutually exclusive. I consider Spivak’s Calc, Strang’s stuff, and Abbott’s stuff to be pretty short while being rigorous and conversational.

There is a substantial difference between undergrad textbook writing and books written for high school. Typically, high school books written specifically for the class offer no real explanations and virtually never written with the student in mind. They’re written for the teacher, so they’re hardly readable for self-reading.

I don’t see any good reason Algebra 1 and 2 textbooks should be 1,000 pages of only examples and no written intuition or conceptual understanding.

College Algebra textbooks are likely too difficult. Needs to start at a remedial Algebra 1 level and build intuition and conceptual understanding.

The class isn’t often enough that I can be exclusively responsible for building that intuition. They need to be able to read a serious text that covers why the product rule exists, why addition and multiplication are associative, etc., why rise over run exists, what square roots actually mean, why based on the previous rules it makes sense that subtracting from one side must also be subtracted from the other, and why division is often the last step.

There are plenty of these books for undergrad courses, just not sure if anyone has written the same style of text for high school algebra

[finite gale]

I would recommend you check out aops books

[dusk wind]

lmao people come here asking for 'conversational' math books and it's like bro what does that even mean

maybe stop looking for textbooks or try non US material/courses, chances are if you stick to the usual stuff you'll only find rehashed content from exhausted tutors

[dusk wind]

either point them in the direction of Khan Academy or teach them using your own tools
or.. you'll have to go digging in the past a bit and find anything 500 words or less

why not simply write your own book based on the most important materials or just teach strictly for exams instead

[tiny osprey]

It’s the course u take if u want to take Calc BC the next year

If u want to take AB then it’s Precalc 3

[nova breach]

It means math textbooks that are conversational. Some of the key words here are: math; textbooks; conversational.

Conversational typically means that one feels as if there's a conversational tone.

If you need more definitions, I can recommend some resources.

[random hill]

Any book recommendations for studying Lie groups? (assuming an adequate understanding of manifolds and algebra, but suitable for building intuition, so preferably with examples and comprehensive exercises)

[dusk wind]

perhaps tiktok has what you're looking for

find your favorite algebra youtuber and hand out worksheets

[nova breach]

An algebraic expression consists of one or more numbers and variables
along with one or more arithmetic operations. Here are some examples of
algebraic expressions.

5x 3x - 7 4+p/q m × 5n 3ab ÷ 5cd

In algebraic expressions, a raised dot or parentheses are often used to
indicate multiplication as the symbol × can be easily mistaken for the
letter x. Here are several ways to represent the product of x and y.
xy x · y x(y) (x)y (x)(y)

In each expression, the quantities being multiplied are called factors, and
the result is called the product.

An expression like xn is raised is called a power. The variable x is called the
base, and n is called the exponent. The word power can also refer to the
exponent. The exponent indicates the number of times the base is used as a
factor. The expression xn is read “x to the nth power.”

VS

Even though we do not know how much he had at first we can let it be represented by an algebraic symbol, say the letter x. If then x is the number of dollars which he had, what he spent was \x and what he had left was also \x. The amount he earned, being twice what he had at first, is 2x. This added to what he had left after his purchase amounts to five dollars. Therefore,

\x + 2x = 5.

This simple symbolic statement is the statement of the entire problem. In order to solve the problem we must find the value of the unknown number x. To do this we add the \x and the 2x and obtain 2 \x. The symbolic statement then is

2\x = 5.

From this, of course, it must be that x = 2. That is, the boy had two dollars at first.

If you're struggling to find which one is more conversational, let me know and we can go over some English workbooks.

[dusk wind]

I'd just write down the equation and not bother to read either

chances are your students wouldn't either

[nova breach]

As for TikTok, no, I'm more busy with my research and teaching adults mathematics for free. But do go on with your high-roading. I'm sure you're doing very important stuff.

[dusk wind]

I mean afterall, such genuises are writing these textbooks it should be easy to teach it to anyone right

[nova breach]

That's wonderful for you. I'm more interested in teaching math than I am having them rep-out the quadratic equation.

[dusk wind]

there are really great resources on youtube to help fill in those gaps

most already have the aptitude anyway

[nova breach]

And for quite a lot of math subjects, there are equally good math textbooks that are substantially more rigorous. It isn't a stretch to wonder if one exists for high school algebra.

[dusk wind]

also you're not the only one that has taught math for free

[nova breach]

Anyway, I'd continue this conversation, but anyone who starts with: "lmao people come here asking for 'conversational' math books and it's like bro what does that even mean" is insufferable. So, I'll be ending this chat.

[dusk wind]

what's insufferable is your inability to access youtube for this 'conversational' tone you seek

[sage python]

@dusk wind nasty attitudes are not appreciated here

[remote sparrow]

@nova breach What are you doing is commendable, but I don't believe such a book exists on the market yet. The closest thing might be writing a book based on Hung Hsi-Wu's books on pre-college mathematics. I encourage you to take a look at his website; it's very interesting: https://math.berkeley.edu/~wu/. Here are a few articles of his which stood out to me:
https://math.berkeley.edu/~wu/AE2020A.pdf
https://math.berkeley.edu/~wu/teacher-education.pdf
https://math.berkeley.edu/~wu/lecture.pdf
https://math.berkeley.edu/~wu/wu1999.pdf
https://math.berkeley.edu/~wu/ICMtalk.pdf

FWIW, Axler has written books on college algebra, algebra and trig, and precalc. The college algebra text meets your length requirement.

https://axler.net/

[nova breach]

This is the most likely option. I doubt I'd finish it for this group, but maybe the next one. I could at least write some weekly lecture notes that are a bit more rigorous and just have them stapled or something.

Thanks for the resources. Probably my best option.

[gray gazelle]

anyone recomend a differential geometry book for a first time learner? the goal is to use it for general relativity, so i'll need to know a good amount (especiallt riemann manifolds). I've got all of the prerequisites as far as i know, was looking at Loring Tu's book

also if there's any other advanced math i may need for general relativity let me know

[nova breach]

Do Carmo's Riemannian Geometry is still considered pretty good. I don't think it's as rigorous as it could be, but that's just a difference in pedagogical styles, I think.

If I were to pick one, I'd go with Peterson's. It's also free on UCLA's website, so there's no harm in at least looking at it. https://www.math.ucla.edu/~petersen/DiffGeo.pdf

[nova breach]

What level of GR? Is it an undergrad class? A lot of GR undergrad classes don't have particularly crazy math prereqs

[gray gazelle]

it's for a personal research project, the physics just requires the math. let me send some examples of what i'll he working with

[nova breach]

@gray gazelle Since I'm not sure of your background, I'd say to make sure you understand vector calculus and linear algebra well beyond just doing problem sets for class.
Specifically, if you feel very good in both of those, then I really suggest reading Calculus On Manifolds by Spivak. I'm partial to Spivak because his style resonates with me, but any alternative book would be fine here. I would caution against the sort of books that people suggest by saying "I prefer this book because it doesn't focus so much on proofs." GR is hard and physicists who don't understand the math at a fundamental level don't understand GR.

GR is fundamentally a science of vectors, tensors, and Riemannian Geometry. If you're weak in any of these, you're just capped on the level of understanding you can achieve. So, if you don't feel awesome with any of those three, I think it'd be really worth taking some time to go through them. Spivak is 150 pages or so, but you should work through it slowly. It's not the end of the world if you don't understand everything, but being exposed to the ideas and trying your best will do a lot for you.

Other than that, you need SR and you need to be comfortable with Hamiltonians and Maxwell (granted, some of this is going to be in a SR book or other physics book). I can recommend some physics books if you're missing those prereqs.

I really can't stress the vector stuff enough though.

[lean kettle]

Is it realistic to be able to finish this book before the end of the year cover to cover with 30 min a day?
https://studylib.net/doc/25763888/geometry-a-high-school-course---pdfdrive--

[nova breach]

What's your math level? Are you just reviewing for fun, are you in high school?

[gray gazelle]

i taught a vector calc class so i'm solid with that

my linear algebra class was proof based and very in depth, so i think i've got that down too

[lean kettle]

I'm relearning it, it's been a while since I took geometry in high school so I forgot a lot of things

[nova breach]

With those two, you should be more than fine to continue with Spivak and Do Carmo.

[gray gazelle]

i am in high school for the record, so this would be completely for my own purposes

i'll check out spivak, it's the one i've heard the most so far

for GR i think i'll use carrol because i know him lol

[remote sparrow]

would a diff geo of curves and surfaces book be okay with you?

or is that too simple

[gray gazelle]

i think for the applications i'm doing i might need something more advanced

not sure though, obviously i've never tried either

[nova breach]

It's definitely doable. I wouldn't feel the need to rush. 30 minutes a day is probably fine for review, but imo you should spend more time to understand it. High School geometry is "simple," but I think it's always best to spend at least an hour on the subject a day with reading and problem sets. Now until the end of the year is basically an entire semester, which is absolutely doable for high school geometry.

[lean kettle]

Ok thanks

[nova breach]

Which books are you thinking? You can get pretty advanced with curves and surfaces. I can think of a few grad level texts at least.

[remote sparrow]

https://maa.org/press/maa-reviews/differential-geometry-of-curves-and-surfaces-2

just a basic intro one

like do carmo

[gray gazelle]

the one i sent is a grad level curves and surfaces i believe

[remote sparrow]

only some real analysis and linear algebra is assumed

[gray gazelle]

i've got both of those

do i need any abstract algebra

for any of this

[nova breach]

"Need" no, but it's useful.

[lean kettle]

Also quick question: @nova breach
in my high school we had Algebra 1 -> Geometry -> Algebra 2/Trig -> Precalc
In the pre-university category I see we have #prealg-and-algebra and #geometry-and-trigonometry
So is "Pre-Algebra" considered equal to Algebra 1?
Is "Algebra" equal to Algebra 2?

[gray gazelle]

i know rank 2 tensors like the stress tensor and stuff but that's all i have from that class

some multilinear mapping goes along with that

[nova breach]

I'm new to this discord, but "prealgebra" typically refers to arithmetic and some basic algebra like multiplication and basic intros to one step equations.

Algebra in the pre-uni context is probably referring to Alg 1 and 2

[remote sparrow]

The author has also followed the majority of textbook authors (O’Neill being the most well-known exception) in not using differential forms. For a first pass through the subject, I think this is a good decision — especially if, like Tapp, you are consciously trying to emphasize the geometric content of the subject.
If your vector calc class already covered differential forms (maybe from a book like Hubbard or Shifrin) then this book might be pitched a little too low

[lean kettle]

Ok thanks

[gray gazelle]

i feel like they never specifically mentioned differential forms but it was a pretty deep class, can you give an example

is that like k forms

[remote sparrow]

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

[gray gazelle]

ok yeah we did those

[nova breach]

I don't really see any other sensible direction than just jumping into differential geometry. The books I suggested are good, but I know some people don't like Do Carmo's style. Like I said, it isn't the most rigorous text in the field. I think it + Spivak would be more than sufficient for any purposes you have, but there are other texts that people like.

Assuming you have the physics prereqs as well.

[gray gazelle]

which are?

i have some good physics background as far as i know

[nova breach]

Really depends on what you're doing, but at the minimum a college physics course that has the basics of classical mechanics, maxwell's equations, and some "physics math" that's pretty much going to all be covered in one of those subjects. Doing GR without SR is for sure a mistake.

So, I'd say any college physics text, anything that covers maxwell, maybe an applied math textbook for physics, and SR.

I know of some courses that let you jump into GR with only Calc 2 and college physics. I think it's a terrible mistake, but it can be done.

[gray gazelle]

i have classical mechanics with pdes unofficially and officially i have vector calc based electromagnetism, thermo, optics, and taking modern physics next sem

i saw lagrangian density show up in GR earlier, so i've got stuff like that (lagrangian/hamiltonian) and maxwells eqs

[nova breach]

Unless you're doing some truly mindblowing stuff, I'd just grab a SR textbook, work through it alongside your differential geometry text, and you'll be fine.

Having Maxwell will help with SR, so you won't be completely out of the loop.

[gray gazelle]

should i do sr before gr?

i've also got some field theory stuff in my toolbox which could help

[nova breach]

Yes, it's the order in which Einstein discovered the theories and it's the order that is taught in uni. And it's just fundamentally needed for any rigorous GR texts.

Doing GR without SR would almost certainly be a mistake and likely very frustrating.

[gray gazelle]

oh cool, i didn't know that

while i'm here, do you recomend a sr text? i've got a gr already

[nova breach]

https://www.amazon.com/Geometry-Minkowski-Spacetime-Introduction-Mathematical/dp/1441978372

This is a pretty serious textbook, but appropriately rigorous in my opinion. Probably difficult to work through alone, but if you trust yourself to ask for help online or a teacher/professor, you should be fine.

I know that Carrol also has a SR book, but I have no idea if it's any good. Might be good enough if you plan on using his GR book.

[gray gazelle]

i also talked to wald this morning

he suggested i use his book obviously but it might be too tough for me

i'll research Carolls SR and if it's no good i'll check out the one you send

thanks so much for your help

also i love springer books

[nova breach]

I've not read Carrol's books, so I can't say how it compares. But given his public image, I would expect it to at least be more approachable. If I'm not mistaken, he's a philosopher of physics or something (can never remember the title), so he's probably going to go out of his way more to help with the conceptual understanding.

[gray gazelle]

i've got 2

[nova breach]

Yeah, Springer is generally great.

[gray gazelle]

carrols GR is just a slightly easier version of Walds

[nova breach]

No worries. Good luck on your studies. It's hard stuff, so don't get frustrated if it doesn't come as naturally as the math. Intuition with advanced physics can get pretty messy. You'll do fine with your math background though.

Gl 🙂

[gray gazelle]

i wish there was ppl around me who knew about this stuff so i wasn't going in alone

but it's ok

[remote sparrow]

i enjoy the content of some springer books, but i despise how poorly the books themselves are made

[gray gazelle]

i'm the opposite

the covers are so pretty

i like having a bunch of books that are the same size and color

[remote sparrow]

idc about the covers, but rather the binding

[gray gazelle]

susskind has a special relativity book too, im taking his class next year so could talk to him about it

[gray gazelle]

yeah it is pretty ass

ur right there

[loud cradle]

unfortunately they went to print-on-demand some years ago and so the print quality can be pretty terrible if you get a bad specimen

the quality control is terrible

[gray gazelle]

yikes

[finite gale]

The only thing I care about is the pdf has bookmarks

[tardy acorn]

Yoo

[loud cradle]

i bought and returned fully four copies of one title before eventually buying a used copy which was fine

[gray gazelle]

i must be getting lucky

my real and complex analysis books are springer

[loud cradle]

it really seems to be a question of luck, often they're fine

[gray gazelle]

thomas calculus best textbook ever frfr

[loud cradle]

but if you're dropping like $50-100 for a physical book you'd hope that the success ratio would be close to 100%

[gray gazelle]

i will never and have never bought a springer book for more than $20

used books are always better

[remote sparrow]

#advanced-lounge message

return or nah

[gray gazelle]

jesus that's awful

[loud cradle]

with the bonus that used books if old enough will probably predate the print-on-demand era and they'll be better made

[remote sparrow]

yep

[loud cradle]

ugh, that's horrible

i have a decent copy of hungerford but it's at least 10 years old when their QC wasn't as bad

[gray gazelle]

my book collection is getting pretty sexy

[loud cradle]

i'd return it if they send me one in that condition

[gray gazelle]

i've got like 10 math/physics books and the rest are AP exam study guides lol

[remote sparrow]

[loud cradle]

noice

[gray gazelle]

and my 2000 page SAT book

that one is stupid

[remote sparrow]

time to gamble on getting a decent copy of hungerford

[loud cradle]

ugh horrid

[remote sparrow]

[gray gazelle]

any Wiley haters here

[remote sparrow]

waw when did i get active

[gray gazelle]

because i can't stand how thin the pages are

[remote sparrow]

dunno, my only wiley book is schroder

[loud cradle]

persevere, that book has been around for ages and iirc it's not like there are newer editions with more/better content

so just get a used copy if the new ones are crap

[remote sparrow]

that one was used

lmfao

[loud cradle]

ah sigh

i hope whoever sold it didn't rate it any higher than "tolerable" condition

[gray gazelle]

the semiconductor one

?

[remote sparrow]

they put it as "good"

well my order was also delayed

[loud cradle]

ha they had to spend some time breaking it before shipping

[remote sparrow]

the real analysis book

[gray gazelle]

oh gotcha

i have boyce diff eq

[remote sparrow]

i have the 10th ed

[gray gazelle]

mine is 8th

[remote sparrow]

my profs said they didn't like newer editions so that's the one they mandate

[gray gazelle]

my lin alg book was first edition lol

and real analysis

[remote sparrow]

what books are your lin alg and real analysis ones

[gray gazelle]

bronson and ross

[remote sparrow]

no clue about bronson

[gray gazelle]

it's meh

[remote sparrow]

ross is kenneth ross?

[gray gazelle]

yes

i used others to supplement but prof required those

[flint dagger]

is there such a thing as a bad math book?

[left cloud]

yea these are known as serge lang books in the biz

[flint dagger]

"Bourbaki group"

[sterile pelican]

Not all of Lang's books are bad though I do like his Basic Mathematics, Caluclus, and Geometry books

I haven't looked at his undergrad books though and I know his infamous Algebra book, which is good as a reference but not as a textbook

Bourbaki books are the same thing too and that they are good as a reference book

[flint dagger]

a lot of them were retitled poorly it seems

[sterile pelican]

Retitled poorly? You mean Lang? I see no other culprit than Spivak's Calculus book

[flint dagger]

looking at reviews 👀

these people are brand new to me

[sterile pelican]

Well I cannot say with those reviews I can only say from what I did

[flint dagger]

so.. I'm developing my calc fundamentals.. I've been trying to find a book that's focused on application

[sterile pelican]

Then Lang is not for you

[flint dagger]

is this moreso an engineering route of books?

[sterile pelican]

Lang?

[flint dagger]

no

[sterile pelican]

Lang is not for engineers

[flint dagger]

my inquiry

lang is interesting to hear about, never heard of him until 5 mins ago

he's got some aesthetic yellow books

[sterile pelican]

Thing is my approach is I would learn books like Lang then pick up an engineer book, but that is probably not for you. I felt like knowing the maths first and foremest before applying them, but I heard of Cox's Calculus book

[flint dagger]

the math educationn is coming anyways.. I just really hope that I dont get stuck in a position where I dont get to use the math

I gave up my hairline for math this year -.-

I did see these kinds of courses open up after passing your first calc class.. Maybe get to play with application in a chem class

[sterile pelican]

https://www.amazon.com/Calculus-Context-James-Callahan/dp/0716726300/ref=mp_s_a_1_2?crid=38MJS529KNNP8&keywords=Cox+calculus&qid=1694670035&sprefix=cox+calculus%2Caps%2C282&sr=8-2

It’s called Calculus in Context which is more application based

I only know it’s the same author who wrote my favourite AG book for undergrads

[flint dagger]

I might be picking that up

[sterile pelican]

Let me know later how it’s like

Read the content page first and if possible the preface and see if you agree with the author

[flint dagger]

Np

I’ll reach out when it happens

[mystic orbit]

@remote sparrow is now active yoooo

you can post images now

[hollow shore]

there is this book in the library that I am not sure if I should borrow

the mathematical mechanic by mark levi

is it about applications of math in physics?

[alpine rover]

you can always borrow it and return if you don't like it

[magic perch]

any recommendations for an introductory group theory book? My course is using Jacobson but its not ideal lol

[gray gazelle]

Dummit & Foote.

[tawny copper]

I like Jacobson II

[distant spear]

I liked Herstein

[remote sparrow]

some people like hungerford

[unborn estuary]

Hello, was wondering if there are any substitute to Luenberger book on optimization?

[loud cradle]

<@&268886789983436800>

[broken meadow]

they got banned but the bot didnt delete the messages

ill delete them manyally

[alpine rover]

Pinter

very intuitive and gentle

[hardy yarrow]

which books do you recommend for self studying the entire ap calc bc curriculum?

[finite gale]

Stewart or khan academy both work probably

[hardy yarrow]

wait whats the difference between the early transcendentals version and the regular one?

[finite gale]

I think it's just a version difference?

[hardy yarrow]

apparently it introduces the logarithm and exponential function earlier but not as rigorously i think

also ive heard older versions of stewart are better than the moder ones, so which one is best?

[mellow wren]

I mean AP calc isn't really going for rigor

[hardy yarrow]

true ig it aint real analysis

[mellow wren]

if you're going for rigor usually it's found in some real analysis book

[hardy yarrow]

i tend to want to figure out how the math works, but i feel like id be slowed down and be behind the rest of the class

[hardy yarrow]

do u know which stewart version is considered best bc ive seen comments on how the modern versions are as good as the older ones

[mellow wren]

idk I used some rando version if I'm gonna be honest
I sorta just showed up to the exams without looking at the book much
But I think any one of them will be good for you

[hardy yarrow]

thanks

[narrow relic]

Cooperstein, An Introduction to Groups, Rings, and Fields (https://centerofmath.org/textbooks/groups/index.html)

[hollow shore]

you can try out artin but if it's too terse you can stick to gallian

http://euclid.nmu.edu/~joshthom/Teaching/MA312/homework.shtml

if you do gallian, this course page consists of homework assigned from it

if you want psets for artin, check the mit ocw course page of Algebra I

[heady ember]

Look in pinned

[fierce hedge]

what?? Jacobson is NOT an intro group theory book smh

[gray gazelle]

It is an intro to algebra, which covers group theory

So it is an intro to group theory if you consider only the 1st chapter

[finite gale]

Well regardless there's a book review of aa texts in pinned

[fierce hedge]

There's a difference between can be considered and intended for it. Jacobson is a grad algebra book

[gray gazelle]

No it isn’t

[fierce hedge]

[gray gazelle]

Jacobson himself says the exposition only requires a semester Linear Algebra and it was taught to Yale undergrads

Unless you’re doing basic Linear Algebra in last year it is not grad level

Basic Algebra II is grad level

[finite gale]

I don't really understand the point of this conversation; there are "grad level" texts that have become standard in first courses to undergrads

E.g. d&f

[sterile pelican]

I see d&f as a "grad" book though not a good first course book

[fierce hedge]

I meant to say that it's too dense for an intro to abstract algebra book

[sterile pelican]

Yeah there is no way it's an undergrad book

[gray gazelle]

Subjective. I used it alongside DF.

[fierce hedge]

It can be but book prefaces intentionally downplay the prerequisites, for example I think according to riehl's book's preface you require very little to do it but in reality it requires quite a lot of courses under your belt. Similarly, Rudin is can be used for a first course in analysis but that's not what is done for the average intro analysis class

[sterile pelican]

I agree I hated Rudin to the very bone for that :^)

[finite gale]

I think using Rudin for a second course is even worse than using it for a first course

At that point you're literally just wasting time

[sterile pelican]

And honestly as a first course using d&f is just too dry. I learnt algebra through Anderson & Feil and that was a great way to start for me

[fierce hedge]

Lmfao, that's actually a fair point

[gray gazelle]

I agree that the level of conciseness one likes varies. I actually preferred Jacobson to DF (although apparently the former is more advanced) because DF gave way too many examples and trivial results (in the big scheme of things) Jacobson is nice and concise

[finite gale]

Also Rotman > d&f

[fierce hedge]

Rotman

[gray gazelle]

I do think that books at the level of Pinter/Gallian are a waste of time for almost everyone though

But I agree that tastes vary with good books

[sterile pelican]

I think Pinter is good for a highschooler, and Gallian is garbage

[fierce hedge]

That's a bit of hot take ngl

[finite gale]

At least you aren't using lang for a first course

[fierce hedge]

[gray gazelle]

Lang looks scary

I will never read it

[sterile pelican]

You know what good idea let me try that to my friends who are interested in algebra :^)

[fierce hedge]

lang is what I show to my relatives when they ask what do you study in maths

[sterile pelican]

Then I follow up with Hartshorne

[remote sparrow]

are we talking about grad rotman

[sterile pelican]

I actually never read Rotman

[finite gale]

I was assuming yes

[fierce hedge]

Jacobson being nice is the general consensus, hell the book is also cheap enough to buy but I felt it was a little dense for my liking. DF and Jacobson are kinda like the opposite ends of spectrum. Rotman is somewhere between and perfectly fills the algebra void.

[gray gazelle]

Isn’t there a rot man reading group

[sterile pelican]

I was tempted to read Aluffi at some point

[finite gale]

Where is lang on this spectrum

[gray gazelle]

Most concise and dense

[gentle pond]

I'm using Gallians book for my intro to Abstract Algebra, is it really that bad?:(

[flint dagger]

Hey Kani, what do you study?

[sterile pelican]

I am actually a software developer, currently unemployed and job hunting, but I self study maths

[flint dagger]

java gang?

[fierce hedge]

I think so, yeah. In any case the grad book is almost a copy of his UG book with proofs cut short. I think it's pretty fair, you can always look up the UG book when needed

[sterile pelican]

You mean Java hostage

[gray gazelle]

Python

[flint dagger]

its got bells and whistles everywhere

behold! my javadocs!

yeah... im feeling a bit held hostage by java

[sterile pelican]

Back when I worked at the government job javadoc is a fairy tale

[flint dagger]

alright to move to dm? dont wanna stray off topic

[remote sparrow]

do you have the first or second edition of grad rotman

[fierce hedge]

nope, I started a knapp group although we did switch to rotman later

[gray gazelle]

Did it end

[fierce hedge]

I have a second (indian) edition physical copy

[remote sparrow]

2nd ed. is out of print so the prices are really jacked up

[fierce hedge]

Everyone got busy with exams so it's currently on hiatus

[gray gazelle]

Aluffi seems good I wish I knew it existed 7m ago

[hollow shore]

don't listen to them. It's good for a gentle intro to group theory. You can do the first 11 chapters and move to smth like artin or rotman.

[fierce hedge]

yeah, I kinda had to scour the whole Indian book market to find a single copy

[gray gazelle]

Or you can just start at Artin

[hollow shore]

it could be a little terse at first

[remote sparrow]

[gray gazelle]

Working hard on a good textbook is better than letting your brain rot

[hollow shore]

once you dip your toes a little bit you can shift

"good" textbook depends on who you ask

[remote sparrow]

i'm assuming if people are asking for a book rec, they're not in a classroom

[fierce hedge]

I'd say try the book, look at ToC, do some exercises and then decide for yourself. It's very subjective anyway

[finite gale]

Well the book rec you get from here depends on who you ask

[gray gazelle]

Ye

It is not like everyone’s read every book

So always investigate yourself

[fierce hedge]

@remote sparrow on a positive note, since the book is so old the Indian edition also has very good paper quality like surprisingly good.

[gray gazelle]

Where do you guys keep your physical book collections, did you buy shelves ?

Finding it hard to keep organized and I only bought Jacobson’s two books

[remote sparrow]

i have one my dad bought

the other shelves a neighbor was giving away

[hollow shore]

there is a university here which sells international editions of springer books for good price

they use normal post so I am worried if the book would get stuck in shipment

[fierce hedge]

university "sells" ??

[hollow shore]

yeah

IISc

[fierce hedge]

oh yeah, what are you buying from there?

[hollow shore]

maybe browder

and axler too

I got to know about this from a dude who wrote an article about how he got books like engel's problem solving strategies when he was preparing for inmo

[sterile pelican]

Hot take here I do think doing algebra then linear algebra is an interesting path :^)

[gray gazelle]

I mean it works, but it is certainly not optimal

[sterile pelican]

I do agree

You don't get into the fun stuff yet

[gray gazelle]

Yeah I think Linear Algebra + Analysis gets you the farthest the quickest starting from HS math

I wish I did that instead of just doing Algebra only

[sterile pelican]

Definitely but I had always wanted to see how it goes

[gray gazelle]

I mean it works, you will know Algebra, I think a few people in this server did that, i.e learned Algebra and still hasn't formally taken Linear Algebra

[sterile pelican]

I had always wanted to see someone do that because there is one LA book by Berberian that sort of needs algebra first

Freidberg is the standard but it feels so dry

[gray gazelle]

Wait till you see HK

The Dummit and Foote of Linear Algebra

[sterile pelican]

HK? I misinterpret that as Hong Kong :^)

[gray gazelle]

Hoffman & Kunze lol

Hong kong would be an Analysis book I feel like

The country gives off that vibe

[sterile pelican]

I feel like it's mathematical physics their AG stuff tends to be applications to physics

[gray gazelle]

This is $8, what does it do that requires Algebra

[sterile pelican]

I recall he just assumes you know fields and integral domain in the first chapter

Let me find the first few pages

[gray gazelle]

Looks like a good medium difficulty Linear Algebra book

I don't think you need to actually know the Algebra though

he collects what you need in the Appendix

[sterile pelican]

I tend to treat the appendix as a review of what you know really

Like how he defines vector spaces off the bat it's just nice to know fields

I think no one in the right mind would approach this book without some of that background given we have like Freidberg for example

[fierce hedge]

ah yes, my intro LA book

[sterile pelican]

How was that book numbily? I never read it :^)

[fierce hedge]

The equivalent of Rudin as your first book, maybe not as bad

It's dense and abstract. Like everything is done on abstract vector spaces

You won't see any matrix manipulation even

[sterile pelican]

Isn't that just an algebra book at that stage? :^)

just treat it with the language of modules then bam an algebra book

[fierce hedge]

I mean linear algebra is algebra but like you still have groups on which you can think concretely

I don't remember anything concrete in the book but that might just be my memory

[sterile pelican]

I mean true of course

[fierce hedge]

FIS is much more approachable but it's slow and gets boring

[sterile pelican]

it's just so dry

hence why I considered Berberian

[gray gazelle]

Try Shilov, looking over the TOC it looks really cute and I read through the first 3 chapters one weekend and it is surprisingly well-written. I personally used HK as a first cours ethough

[sterile pelican]

I heard good things of Shilov

[gray gazelle]

The determinants section is very well-written, but I'd recommend supplementing complementing it with another standard book's chapter when you get later into the book.

And I'd probably get off Discord if you really want to learn math

[fierce hedge]

btw I'd recommend to search for the courses online and see the recommended readings, notes and assignments

usually they also have additional stuff and it really helps

[gray gazelle]

brilliant recommendation, i often ask myself "what does uchicago/princeton use for this course"

when i want to learn something

LOLL

[fierce hedge]

I have multiple copies of whole course websites saved just in case they yeet it later

[sterile pelican]

Why get a course when you can just own a mini library of maths books? :^)

[remote sparrow]

doesn't hoffman kunze start with matrices?

[sturdy shore]

HK definitely does not shy away from matrices

[clever seal]

Is there any Group Theory book with lots of questions along with solutions?

[finite gale]

if you want a lot of questions, there's always dummit and foote....

[lilac copper]

@gray gazelledont spam stickers!

[gray gazelle]

ok

sorry

[finite gale]

if you want to spam stickers go to #chill

[lilac copper]

no why

dont spam anywhere

[fierce hedge]

I checked and it indeed does it a bit later my bad

[humble mantle]

is it fine if i do the Gilbert strang's linear algebra course instead of the book?

I'm currently doing spivak, do you have any recommendation for first time learning multivariate calculus?

Mulltidimensional Real Analysis Vol 1 and 2 (Duistermaat, Kolk)
Calculus on Manifold (Michael Spivak)

is any one these good for first time learning?

or perhaps a course would be better than a book to visualize the concepts of multivariate calculus?

[remote sparrow]

i'm assuming you're talking about spivak's Calculus

you know, you could do a combined book on linear algebra and multivariable calculus

two choices would be either hubbard or shifrin

you could also do linear algebra and multivariable calculus separately

#book-recommendations message

i have some suggestions for linear algebra textbooks

after doing some linear algebra, you could do hubbard or shifrin, skipping the linear algebra parts

munkres and spivak are standard choices too, provided you have some real analysis and linear algebra under your belt

[heady ember]

Isn't HK just as long

[humble mantle]

that would be absolutely great, as I have limited time

[humble mantle]

spivak for multivariable calculus?

[remote sparrow]

spivak has a book called Calculus on Manifolds

[humble mantle]

is it fine for first time?

[remote sparrow]

it's pretty hard if you have no guidance

[humble mantle]

i see

[remote sparrow]

could use it for some extra problems though

[humble mantle]

also, do you think I should do the gilbert strang's course on linear algebra?

[remote sparrow]

dunno

[humble mantle]

can someone answer this as well?

[ocean mulch]

Munkreas

But tbh, it didn't help me much, it helped my roommates tho.

No books I have found present a decent intuition for multivariable calculus. But then again, if I have to write one, Idk how I would present my intuition either, without linking YouTube videos...

From my experience, visualising multivariable calculus is easiest when you have some exposure to (classical) differential geometry. No need to calculate anything, just need to see how and why things are essentially the way they are.

[fickle whale]

I was just wondering if anyone could give me any opinions on this textbook, based only on the ToC

Chapters and sections marked with an asterisk mean that it's additional material that's safe to skip

[wheat trout]

Is this a book on the maths you need for general relativity?

[fickle whale]

A certain approach to them

A New Approach to Differential Geometry using Clifford's Geometric Algebra, I think is the title

I just remember it as Snygg Diff Geo

[wheat trout]

I have very limited knowledge in physics. I think a textbook should be judged based on whether it suits the reader's needs, and in this case, it is possible that the math about general relativity is better approached in this way. You could try to ask this to some students in physics.
I skim through the contents, it seems that it still covers curvature, parallel transport, geodesics, gauss-bonnet etc. According to the name of first few chapter in clifford algebra, the book tries to give some intuition for curved spaces. Maybe if you like intuitions or such, this book will be nice.

TBH, I am a bit tempted to read parts of this book. I have already forgetten most, if not all, of what I have learned about Riemann geometry.

[blissful shore]

I wonder what is Qibla problem

[orchid hatch]

can someone suggest me a good book for permutation and combination and probability

[sterile pelican]

Probability nothing beats Blitzstein's, but are you looking for undergrad?

[orchid hatch]

pre college level basically for entrance examinations and olympiads

[sterile pelican]

Oh can't help you there then

[orchid hatch]

ok

[wicked vale]

Hi guys. Is there anyone here who can introduce me a few books that exclusively or professionally deal with logarithms and exponential functions?

[magic moth]

has anyone here read apostol's calculus?

[gray gazelle]

pisagors inheritance

(not 100% of the name cause i personally translated the name from my og language)

[next yew]

I want to learn these topics

The easiest way would be appreciated (youtube,book,site)

[remote sparrow]

is enderton's Computability Theory: An Introduction to Recursion Theory good?

[loud cradle]

first read and understand axler

[prime oak]

whats a good second text to read for algebra?
i used artin for my courses so something beyond that

[loud cradle]

dummit and foote?

[magic moth]

can someone recommend a book on geometry, with its target audience being undergraduate math majors?

[jolly vault]

can anyone recommend a good pre calc book or course?

[remote sparrow]

https://www.amazon.com/Classical-Geometry-Euclidean-Transformational-Projective/dp/1118679199

requires prior experience with high school geometry

[magic moth]

should be no problem then

[remote sparrow]

stewart's precalculus book

[magic moth]

@remote sparrow have u read apostol's calculus?

[remote sparrow]

not in depth

[magic moth]

i get the feeling its not a really good introductory textbook

[remote sparrow]

for calculus?

[magic moth]

for analysis

[remote sparrow]

well it's kinda not intended as an analysis textbook

[magic moth]

i wouldnt call that a calculus text book

tbh

[heady ember]

Try looking through Schroder for a gentle intro to anal, maybe you'd like it

[remote sparrow]

it is for very prepared students

not for the average student

[magic moth]

sherbert is my standard at the moment

[remote sparrow]

abbott is good

[heady ember]

you might be suprised at the approachability of Schroder

[magic moth]

ill look into it

but i still consider myself a newbie at math so

[remote sparrow]

i feel more specialized books are better than schroeder

[heady ember]

In what ways? just curious

[magic moth]

give me the complete name of the author

found it nvm

[sterile pelican]

I like Bloch's The Real Numbers and Real Analysis but it is quite dry compared to most other books, but it is great for self study. Also be sure to read the preface as he has different paths for you to take

[magic moth]

ive been checking schroder's

the proofs area really clear and it also touches on a lot of background from the other numerical sets

its a pretty dense book

would have to read it with care

[tame storm]

whats a good calc book for an undergrad to self study

[magic moth]

@sterile pelican i love that he gives both the dedekind cut and the cauchy sequence construction of R

[remote sparrow]

schroeder is all right for single variable analysis (although he doesn't really motivate the subject well in the name of conciseness), but i think just moving on directly to axler or schilling for measure theory is better. alternatively, you could work through carothers after schroeder as preparation for the more sophisticated folland or bass.

[heady ember]

I see

[heady ember]

How complete do you feel is his multivar anal?

[prime oak]

applied arithmetic geometry

[sterile pelican]

I always wished analysis books covers this and this one is a rare gem

[remote sparrow]

i mean it gets to stokes' theorem, which is pretty much what most multivariable calculus textbooks have as their culminating result

imo it's better to get more background and work through something like tu's An Introduction to Manifolds. schroeder is also not ideal for people on a math education track or those looking to just teach a standard calc 3 course at a community college.

[sterile pelican]

I do think Rudin covers Dedekind cuts however I felt like Rudin is not a good intro book

[magic moth]

there are cuts in abbot

their just not called dedekind cuts

[heady ember]

I see, my plan was do Schroder as a stepping stone to learn more set theory and maybe read Lee in the future (after learning other basic stuff ofc)

[magic moth]

and their an exercise

[sterile pelican]

Ah a wasted chance! I do hear Abbott is a good book though

[magic moth]

Schroeder ordered sets looks promising

[magic moth]

i mean when i saw the dedekind cut definition it did help

cause i did the proof from abbot exercise

but i Will priorize sherbert

and look into all of those to get deeper into real analysis if i have the time

i need to get to numerical analysis

[prime oak]

what do you mean its perfect and comprehensible

i especially recommend working through every problem

they are very easy and if you cant solve them in under 5 minutes there is something wrong with you

[sterile pelican]

To each their own but when I first read Rudin I understood nothing from it, and it lacks motivation to explain why. I definitely felt there is a better first book of analysis out there, and it wouldn't be Rudin for me at least

I am actually unsure if this is sarcasm or seriousness now I think about it :^)

[fierce hedge]

Most likely sarcasm

[remote sparrow]

there is a section explicitly titled "Dedekind Cuts" in abbott on page 298 of the 2nd ed.

[magic moth]

i'm still at series

i mean sequences*

but boch's introduces the concept much earlier

abbot is a great book too i read it as a supplement to sherbert

[sterile pelican]

Bloch is a bit weird though he puts series and sequences at the end

So a lot of your proofs are elementary constructions, which can yield very long proofs at times

[copper axle]

Hi! can anybody recommend an analysis book for first/second year physics undergrads? thx!

[dapper root]

Maybe Abbot’s Understanding Analysis

[copper axle]

Do physics student halve to learn stuff like abstract algebra if they want to study some theoretical topics

I'm not sure what maths topics I have to learn

[remote sparrow]

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

check "Applications"

[copper axle]

Sure thx

[remote sparrow]

https://www.reddit.com/r/Physics/comments/k6unj/is_abstract_algebra_that_useful_in_physics/

[copper axle]

Sure seems like that I have to learn some

[sterile pelican]

studying abstract algebra for physics is like investing for the long term :^)

[copper axle]

taking a degree in physics is like taking half a degree in mathematics+applications+practicals😵‍💫

[sterile pelican]

just study maths then focus on mathematical physics

[copper axle]

My first year undergrad course include physics + chemistry + materials BRUH I'll be running out of sleep