book-recommendations

[remote sparrow]

just checked my copy of jacobson

says it's from dover publications

[fierce hedge]

As lems mentioned, it is by W H Freeman and Company which is the original publisher and certainly not complaining about the hardcover

My only issue was that the page looks yellowish, the printing is not dark enough on the yellowish page and the next page contents seems to leak out a bit

[fluid bay]

just curious. anyone know what the quality of AMS books are like? Like graduate studies in mathematics books for example

specifically are the hardcovers case bound and not just perfect bound glued to some boards like springer's?

[remote sparrow]

[fierce hedge]

How's the print quality on the Dover edition you have? Can you send a picture? Cause if it's better than this one then I'll return this one for Dover edition.

[subtle mango]

i have one

not only is the cover ugly

it’s just glued

so like the glue on mine is just about gone

[fluid bay]

you are talking to me, right?

[subtle mango]

ye

whoever designed the graduate studies in mathematics cover design should be fired

[fluid bay]

damn, sucks to hear

[subtle mango]

i feel embarrassed every time i pull out that ugly yellow and blue mess

[remote sparrow]

after i finish my league game

[fierce hedge]

you play LoL

[fluid bay]

he's a gamer

[crimson leaf]

It seems weird that the two books from the same publisher have different covers though

[forest sleet]

the AMS graduate studies in math that I've bought before are sewn bound with thick paper

I don't have any with me right now but I can double check the library book tomorrow

[fluid bay]

are we talking newly printed books (from the past 5 to 10 years maybe), or older?

[forest sleet]

I bought one in the last year that was originally published in 2012 and I could see the stitching and count the pages in each signature (it was low iirc because the pages are thick)

[loud cradle]

same here, mine are all of pretty good physical quality, certainly better than the average springer book since they started doing crappy print-on-demand over the past decade or two

if you buy an old used springer book that's 20+ years old, they're much better made

(not useful for current titles obv)

[fluid bay]

well, that's good to hear, but also contradicts what @subtle mango said

[forest sleet]

hmm anamono which graduate studies in math book do you have with the glue binding? (if you don't mind sharing)

maybe it could be the really new ones? or really old ones?

I agree the new cover design looks bad

the proportions of yellow and turquoise and the big rectangle now are bad

compared to before

the spacing is not aesthetically pleasing

compared to

[fluid bay]

oh interesting, i thought all GSMs still looked like the latter

[heady ember]

I just scrolled through AMS' bookstore after seeing the above discussion out of curiosity of what books they have. I randomly stumbled upon a Linear Algebra book from Michael E. Taylor: https://bookstore.ams.org/amstext-45/
Damn is the content rather fast paced

What about that author

[heady ember]

[grand thistle]

morton curtis ❤️

my fav linalg

book

[gray gazelle]

Jesus

[grand thistle]

to be fair, torsion is mentioned once throughout the whole book in like 2 sentences

field characteristic is used like once or twice

[subtle mango]

knowing the odds by walsh

i bought it in like august this year

[subtle mango]

this is the cover design mine has

i’ll take a picture once i muster the willpower to get out of bed

[acoustic ridge]

Suggest a better book on exponential functions, growth and decay problems and a huge discussion on the constant 'e'....

[hasty turret]

Wdym by "better"

What are we comparing against

[acoustic ridge]

Many calculus books that talks about 'e'.

I've read many calculus books but none of them gave better explanation on it

[heady ember]

Read spivak

He has a whole chapter or at least section dedicated to the euler's number iirc

[acoustic ridge]

Oki ty

[gray gazelle]

Any self-study expert here on how to study two topics daily (calculus and discrete math in my case)?

Like do 5 pages of calculus and then 5 of the other, or do 1 hour of each, or do one topic one day and the other next day?

just do it when you have the time

[gray gazelle]

I have time, I just don't know how to balance them

5 pages of calculus and then 5 of the other, or do 1 hour of each, or do one topic one day and the other next day?

just do as much as you can, whatever you feel like learning more at the moment imo

I obviously want to learn same amount from both

it's kind of pointless to place like an upper bound of 5 pages

It's not? I can't just go around "meh today I feel like doing this much until im tired" or whatever, I need some structure to stay disciplined and make fair progress instead of relying on whatever is convenient at the time

that just invites procrastination

[hazy elk]

I like to stick to one topic until I take a long break/get tired/stuck on a topic. I think you'll get further just by doing what you feel like doing at the moment

[hazy elk]

For some ppl I guess, for others fixing the constraint makes you procrastinate

[gray gazelle]

It gives me a clear goal and makes achievement easier rather than relying on my emotions to guide me to "whatever I feel like"

[hazy elk]

you can still set a goal according to the topics each day and cover them accordingly

[gray gazelle]

I want to ignore emotions and do strict discipline schedule of balance between two topics daily, even if I don't "feel" like it

[hazy elk]

Like today I will learn graphs and fundamental theorem of calculus is a better goal than time limits/page count

[hazy elk]

Ok but don't burden yourself if you're just learning for your pleasure, it'll take the fun away

[gray gazelle]

You're still kind of setting a goal tho?

[hazy elk]

Yess

You have to still set learning goals

I mean I do

[gray gazelle]

I'm learning to advance into more fun math, there is nothing fun about elementary calculus and discrete math

I want to finish these topics as soon as possible to move onto interesting stuff

[hazy elk]

It could be fun, depending on the books and problems you're solving

[gray gazelle]

There is no way I'll ever say "today I'm going to have fun problem solving heavy computation 25 exercises in derivatives 🤪 "

[hazy elk]

For sure

So it's for school I'm assuming?

[gray gazelle]

I will never find calculus interesting

No it's self study

[hazy elk]

You don't have to do calculus like that I guess?

[gray gazelle]

I do to understand and move onto the advanced stuff

[hazy elk]

You can try Spivak or Abbott or something

Even Apostol

[gray gazelle]

Spivak require proof knowledge

[hazy elk]

Proofs aren't that hard

You can learn to write proofs in like a week if you want

[gray gazelle]

Yeah but they're still prerequisites, hard to dive into differential equations if you've never taken calculus i.e.

[gray gazelle]

No way lol

[hazy elk]

No one from my uni has ever taken a proofs class

We did fine imo

[gray gazelle]

You never did proofs and just dove into spivak?

[hazy elk]

I did Axler and never did proofs

[heady ember]

Spivak is probably ok as an intro to proofs I guess? Well, the first two chapters, that is.

He introduces induction and strong induction in the second chapter iirc

[hazy elk]

Never did calculus, just analysis

[gray gazelle]

as with everything, the hardest part is to start out

[heady ember]

Yeah

[hazy elk]

I mean in uni that is

[gray gazelle]

first chapter he assume you already know proofs tho

[gray gazelle]

impressive

[hazy elk]

It's not

[frigid flax]

thompson is pretty good for beginners

[gray gazelle]

you were born with natural ability to do proofs

[hazy elk]

I think you have a mental block

Noooo

Proofs are not some glorious difficult thing

They are just correct precise logical sentences

[heady ember]

I mean I didn't really know a lot of proofs stuff before I did Spivak chapter 1-2 or Enderton. Just needed to stare at the questions for hours sometimes, which is common in math anyways. Slowly but surely, I think I have improved.

[gray gazelle]

born with the ability to do proofs... good for you Smegma

haha

[gray gazelle]

he made it sound like it lol

[hazy elk]

For the record, I was not bragging

Just trying to convince you to give it a try

[gray gazelle]

what did you know about proofs before diving into it then?

learning how to do proofs is an experience, and we constantly learn new methods etc. of how to do that

enderton logic or enderton set theory?

you just need to get into it

[heady ember]

Well, I did know what direct proofs, proof by contradiction, inductioon are from my random ass math readings lol

[heady ember]

Also, he doesn't assume you know proofs already?

[heady ember]

Set theory, im doing it rn

My latex PDF is almost as long as the number of pages I have read so far

[gray gazelle]

So he shows small snippets of proofs and uses that to justify it's all you need to know now you're expert on proofs?

Like he doesn't even say what proof method it is

[heady ember]

Expert on proofs
Definitely not.

It takes years, probably, to become an 'expert'

[hazy elk]

High school geometry makes you do proofs btw

That's all a proof is

[heady ember]

I think these are wise words

Just give it a go if you want

[gray gazelle]

Is this from spivak?

[heady ember]

I mean you don't lose anything and you might find that perhaps it's not as bad as you thought

[heady ember]

No

Its from Schroder

[gray gazelle]

What book are you recommending me?

[heady ember]

I did you recomend you any book thus far

I was just quoting a small section from Schroder which I think is good advice

[gray gazelle]

Oh

[hazy elk]

#proofs-and-logic message

[heady ember]

Loch

[hazy elk]

Hey can you actually copy paste citation [4] for me pls?

[heady ember]

Sure

[4] R. Bjork (1994), Memory and Metamemory Considerations in the Training of
Human Beings, in J. Metcalfe and A. Shimamura (eds.), Metacognition: Knowing about knowing, MIT Press, Cambridge, MA, 185-205.
[5] J.Bransford, R. Sherwood, N. Vye, and J. Rieser (1986), Teaching Thinking and
Problem Solving, American Psychologist, October issue.

[hazy elk]

Thanks

[gray gazelle]

@heady emberSo he's saying bang your head against the wall and you'll be fine

[paper ice]

Bang your head against wall is suuch a disgusting statement

[heady ember]

[gray gazelle]

okay against the desk then?

c:

[paper ice]

I often learn more from thinking about text than actual text

[heady ember]

You need to be determined/persistent in math. It takes time. For example, I did a self-exercise (qns I thought of myself) the other day and it took me more than one day to complete it.

[subtle mango]

ive been contradicting my parents for my whole life

[heady ember]

You will get absolutely slapped, potentially on a regularly basis. In fact, if you're doing uni texts its probable. The pain is part of the experience and I guess you just have to learn to adapt/accept it as a whole package together with the fun times.

I still remember the last time I started learning about infinite cartesian products in Enderton it absolutely took me for a ride. I took more than a full day to understand it, even with the math discord's help. Even after that, I regularly thought of it which eventually helped me to digest and internalise it.

[subtle mango]

@forest sleet @fluid bay

[heady ember]

However, it is one of the most interesting parts I have done in spite of the time commitment

In fact, perhaps the time commitment made it all the more satisfying to understand it, I'm not sure.

[subtle mango]

true endorphins come from finishing a proof

working out is a scam

[gray gazelle]

@heady ember you're inspiring, this motivated me

I always feel like i'm the only person struggling and everyone in here just zooming through pages like it's nothing

[heady ember]

Nah lol

Everyone probably has their own struggles, even if you might not know of them

[fierce hedge]

Kinda too late to respond but the page quality is kinda slightly better. More importantly, I found a big reason to return the book, the smell.

[remote sparrow]

kinda slightly what

[fierce hedge]

slightly better

Anyway, the book smells awful. It's the most disgusting smelling book and it smells awful even from far somehow

[remote sparrow]

mold or mildew?

[thick nimbus]

Damn

[fierce hedge]

Nah, smells like chemicals

[remote sparrow]

huh

[thick nimbus]

Do y’all have any book recommendations for a beginner in Statistics. I’m high key struggling-

[remote sparrow]

do you know calculus

[thick nimbus]

No

[remote sparrow]

idk then

[thick nimbus]

Damn

[fierce hedge]

idk how to put it, (for the lack of better words) it smells like bad quality paper and a particular type of glue

Not even being sarcastic

[thick nimbus]

It do be like that

[fierce hedge]

If the Dover version is better than good otherwise i'll just get it printed on decent quality paper

[remote sparrow]

you have money to print several hundred pages on your own?

because i tried using lulu, but its process is very finicky

and i won't accept anything less than a bound book

[fierce hedge]

Nah, here in India there's a printing service which charges decently and has free delivery. For hard cover, the charge would be same as the book

[remote sparrow]

wtf

i wish such a service were here in the states

[fierce hedge]

But for soft covers especially for latex typeset, the price is half to 10% of the costs

[remote sparrow]

if anyone knows a good printing cum bookbinding service like lulu, please let me know

but obviously more convenient like numbpy is talking about

no spiral bound

no three hole punched books

actual paperback or hardcover

[fierce hedge]

I checked and for 600 pages (softcover) with good quality paper the cost comes out to be around 650 rs which is less than half the cost of the book

[gray gazelle]

lol?

[fierce hedge]

huh

[heady dirge]

Any recommendations for resources to study calculus as a kind of dumb person (😅) that explains things in a more practical and engaging way? I love math, but the way it's normally taught in school makes me (like most people) extremely bored and confused and mind wandering. I don't want to just learn the rules and do 40 practice problems, I want to be taught in a way that allows me to really get a good grasp of how the concepts work and how they are applied with easier examples. I'm not sure if I'm making sense so if I'm not please tell me

[modern stone]

Check out “Burn Math Class: and Reinvent Mathematics for Yourself” by Jason Wilkes

and 3Blue1Brown’s series on calculus

but, while the aforementioned resources build a good intuition, you still need to supplement them with a lot of exercises, as this is an essential part of learning mathematics

[fluid bay]

@anamono#0499 hate to ask u this but could u maybe take a pic of side of the book with it open to a page in the middle in the book to show how it’s bound?

Like this for example:

Also does your book have the new GSM cover or the old one (see washingbear’s message)?

[forest sleet]

Here's a library gsm book from 2008

The pages are yellower and I think thicker? than another GSM book from 2015

They are both sewn bound

Both of these have the old cover but the pages are definitely different paper types

Stitching

[limber tiger]

Triola, Essentials of Statistics, Pearson.
I used this when I took it but I barely used the textbook. The book is kinda made precalc.
Only offering this because there was no pther suggestions

[past linden]

what book do I go with for linear algebra

[gray gazelle]

What are you trying to flex

[next stream]

Big ups to this book, I wish there were more like it. I read it over spring break in gr 11, the fact that decent portions of the book are written as a dialogue made it pretty easy to get through quickly. It's definitely not rigorous but that's not that point of it, it succeeded in getting me hyped to study calculus in more depth afterwards though.

[forest sleet]

? Did you read the previous post history?

Someone wanted to see the spine binding quality of gsm series books

[foggy relic]

gsms are nice

gtms are dogshit

[forest sleet]

The picture shows it is bound using signatures and not just glue bound

[forest sleet]

Oh I guess it's not linked to the post history, but the post right before is continuing a discussion about book binding quality from yesterday

[thick nimbus]

Ah ok! Thank you!!!!

[gray gazelle]

In my life the best quality book I've bought was from Oxford University Press, the quality of the paper was just supreme

[fluid bay]

ty for the pictures btw washingbear

[grave thorn]

But I like the colors!!1!

[foggy relic]

based ngl

[orchid mortar]

by this you mean print quality?

[foggy relic]

idk about print quality but the binding is bad

[rare radish]

Im intending to self learn ODEs, what would you recommend as a textbook to do so?

[heady ember]

These are the recs I have heard people mention here

[willow pecan]

All ODE books are bad

[remote sparrow]

not wrong tbh

see giancarlo rota's rant about ode classes

https://web.williams.edu/Mathematics/lg5/Rota.pdf

[rare radish]

I have heard good things about DIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND AN INTRODUCTION
TO CHAOS but idk if its gonna be approachable

[remote sparrow]

https://www.amazon.com/Differential-Equations-Linear-Algebra-Books/dp/0321985818

any thoughts on this book?

[willow pecan]

It's a pearson book so probably not good

[remote sparrow]

idk, when i used this book, it wasn't terribly interesting, but i'm wondering if i should sell my copy to buy other books

[tropic shuttle]

Ey I'm new here. Literally struggling with geometry and got completely lost with perpendicular bisectors, reflections, and graphing. Would love recommendations to a text book or book of any sorts that is easily accessible.

[heady ember]

Friedberg be like

[crimson leaf]

Munkres, Freidberg, West, Artin, Royden, and Fraleigh are all Pearson books

[remote sparrow]

well, i hope we can all at least agree pearson books are severely overpriced

especially friedberg

[crimson leaf]

Yes ridiculous pricing

$120 for Artin

[hollow shore]

the local pearson books sold here have lots of typos and sometimes they even miss a chapter or two which is there in the original book

[remote sparrow]

see, i can understand asking $200 for stewart's calculus (although textbooks should be free ) since you'll use it for three semesters

but friedberg is only gonna be used for one semester

yet it's $170

[hollow shore]

stewart calculus 🤢

[remote sparrow]

advanced books should get cheaper since the audience gets more niche right

[heady ember]

The paperback 5th edition on Amazon is 35 USD

[remote sparrow]

as always, refer to principia mathematica by bertrand russell

https://www.principiarewrite.com/

there's even an updated version in the works

[mossy flume]

update to the rewrite you linked?

or do you mean that rewrite is the update

[remote sparrow]

the rewrite is the update

anyway the principia rec was a meme

although it is still of historical value to the philosophy of mathematics and logic

[mossy flume]

I wonder how the rewrite is going

Last git commit was Feb 22

And last written update was Dec 2021

[remote sparrow]

i'd imagine a project like this is a lot of work

and it could be this isn't really a high priority, at least in a way relevant to contemporary logic research

since the basic goal of russell and whitehead was to derive all of math purely from logic, but this project pretty much died because of the incompleteness theorems

[fierce hedge]

Thankfully there's Pearson India for cheap Eastern editions. I recently got FIS for 500 rs (around 6 usd)

[remote sparrow]

i've bought intl. ed. before, just jittery about them cuz of some bad reviews

also intl. ed. are hard to return i think

[fierce hedge]

Hard to return in what sense?

[shadow dust]

hello there!

I want to go through the math necessary for my point mechanics course very rigorously

anybody got recommendations on some a-z resource on vector mathematics

would it just happen to be a matrix course

[slim peak]

not Viorel Barbu's one

[mossy flume]

yea they seemed to be doing the rewrite just for historical value

[strange siren]

Hi does anyone have any free online pdfs of textbooks that would be good to self-study calculus from? I'm trying to get some good practice problems so I can review all of the calculus AB content and maybe more content if I have time

[remote sparrow]

#book-recommendations message

[frozen lark]

any good analysis 1 books?

[mossy flume]

I've been using Rosenlicht in my analysis class

I like it

[thick nimbus]

Does anyone have any online resources to learn college stats? I am absolute crap at it.

[subtle mango]

idk what college stats entails, but maybe khan academy

depends what kind of stats “college stats” is

[frozen lark]

thanks, do u have a pdf?

[strange siren]

I'm wondering if you have any advice about how to approach self-study. I was thinking to review main concepts and also do the corresponding practice problems and I have the next 21 days to review all topics covered within calc AB. do you think counting the number of topics there are to cover and dividing by 21 would be a good plan for topics to cover per day, or would you recommend a different approach?

[gray jungle]

Not a problem book but "The Banach-Tarski Paradox" by Grzegorz tomkowicz and Stan Wagon is a great read , one of my favorites.

[thick nimbus]

Both descriptive and inferential stats 🥲🥲🥲🥲

[gaunt path]

Any good book recommendations for a first read on algebraic geometry for self study. Also, my algebra might but be a little mediocre, but I'm willing to research what I don't know when it comes up.

[remote sparrow]

I don't think it's wise to go through everything. You should figure out where you're weakest and prioritize studying that most, then reviewing the stuff you feel confident in. For the stuff you feel confident in, try doing some more difficult problems.

[strange siren]

Hmm I see, so maybe proceed throughout the textbook and just go for the more difficult problems first, then move on if it goes well or lower difficulty if necessary, then review the basic definition itself if that doesn't go well?

[remote sparrow]

If you spend time on the hard problems in stuff that you're confident in, you might lose too much time and not study your weak points. Presumably you're studying for some kind of test. Only you know what your teacher tests like, but on average there will be mostly easy to moderately difficult problem and a few hard problems.

[remote sparrow]

#book-recommendations message

[buoyant vessel]

Hi does anyone know where can I access Basic algebra by Jacobson PDF

preferabbly for free

but if I need to pay for it, its fine

@gray gazelle

wuts up blitz

[heady ember]

Discussion on piracy is a little frowned upon here

but z- redacted

[buoyant vessel]

a lot of books are just open sources?

[heady ember]

Its physical copy is also decently priced on amazon

https://www.amazon.com/Basic-Algebra-Second-Dover-Mathematics/dp/0486471896

18 USD

[buoyant vessel]

like a lot of piano pieces too

i dont want hard copy

[heady ember]

No. Most math (text)books are not

[sturdy shore]

it is no longer that, now it's the library named after the first book of the bible

[heady ember]

[buoyant vessel]

[sturdy shore]

if you want to pay though, you probably can through dover

[heady ember]

Yeah

[sturdy shore]

whoops

https://m.doverpublications.com/0486471896.html

[buoyant vessel]

ok

[buoyant vessel]

what if i dont?

since its open source

??

[sturdy shore]

it is not?

[buoyant vessel]

oh ok'

then

ill just get the ebook

[remote sparrow]

tor

[sturdy shore]

if they used tor they wouldn't be asking this question in the first place lol

[remote sparrow]

could just check the wikipedia page tbh

[heady ember]

Yesterday

Today

(Schroder's analysis book)

[remote sparrow]

buy used

[crimson leaf]

I got mine on ebay for something like 30-40

[loud cradle]

allegedly "brand new in plastic wrap" although it looks a little battered in the photo

i recall amazon was selling ahlfors' complex analysis for like $250, twenty years ago!

old enough to remember the above

[sturdy shore]

overpriced textbooks: an expensive introduction

[loud cradle]

😀

[crimson leaf]

That one crazy guy at GA Tech keeps a pdf of Alfhors on his website

[loud cradle]

likewise zoomer! 😁

it's an ok book but sure as sh-t not worth $250 even today let alone back when $250 was worth something

interesting, it's been republished in a chelsea paperback for $60, that's almost reasonable

[remote sparrow]

i have an international edition of ahlfors

was very cheap

[foggy relic]

abebooks > amazon

[remote sparrow]

abebooks is owned by amazon, and frequently international editions also show up on amazon search

[foggy relic]

ye

[loud cradle]

i love when the photo on amazon's website says "not for sale in the US" right on the book cover, haha

[heady ember]

Only one available lol

[remote sparrow]

you will likely get it

[heady ember]

Yeah I just found this as well

[remote sparrow]

math books tend to be niche

[heady ember]

I meant only 1 new

No used ones lel

(since i don't live in the US)

[remote sparrow]

i think the supreme court determined the buying and selling of these books was legal

if you live outside the u.s. i have no idea though

i'm sure publishers can strongarm smaller sellers even if they have no legal basis though

[loud cradle]

oh nice! it always seemed dubious that any prohibition would be enforceable

[crimson leaf]

https://www.npr.org/sections/thetwo-way/2013/03/19/174757355/supreme-court-oks-discounted-resale-of-gray-market-goods

[loud cradle]

i wish there was an equivalent of spotify for math books

or i guess books in general

pay a monthly fee and access whatever you want, but you are only borrowing, not owning

[crimson leaf]

Looks like it was Wiley who had a big stink over someone importing and selling their international books

Personally I don't like not owning books or have some kind of control of my copy

[remote sparrow]

fuck DRM

[loud cradle]

yea for sure i like owning them, but i'd like to browse a wider range of them than i want to buy, and it would be cool if there was a way to do that which didn't involve dubious pdf downloads or visiting a large university library

[foggy relic]

why

i would never pay for an ebook

[remote sparrow]

internet archive sorta was until it got a little too popular during the pandemic and publishers threw a hissy fit

[foggy relic]

worldcat is a thing

you can basically get books from any library in the US for free

including participating colleges

[remote sparrow]

based

[foggy relic]

https://www.worldcat.org/

[remote sparrow]

the existence of dubious pdf repositories can only exist because knowledge isn't free in the first place

[loud cradle]

hmm, i found a copy of ahlfors complex analysis via worldcat at my local university's library, but it just sends me to the university library's web site, which requires that I have an account with them in order to borrow it.. am i missing something?

[foggy relic]

do you have a public library near you

there is a high chance they can get the book from that university via worldcat

ive gotten math books from far away states via worldcat

[loud cradle]

oh i see, i can get a "community borrowing" privilege from the university for $50, that's not too unreasonable

[loud cradle]

i'll double check, but i think the public library doesn't give you access to the university libraries (via interlibrary loan or whatever)

[foggy relic]

no harm in asking

[loud cradle]

for sure

[remote sparrow]

so worldcat isn't free?

[foggy relic]

it is

bungo is talking about something else

[gray gazelle]

Is a self-learner better off going through math books in the order they are provided at say a local college, or is a recommended list from an unidentified discord user with lots of roles superior? Genuinely asking.

[loud cradle]

yea i was talking about my local university's library, which is where worldcat redirected me... worldcat can see its inventory but apparently i can't borrow from it via worldcat

[remote sparrow]

somewhat false dichotomy

[loud cradle]

this depends on so many variables... maybe most importantly, what is your goal?

[gray gazelle]

Goal is to become a well rounded mathematician, to learn the basics and to have a solid foundation for exploring advanced topics. Is it better to research what books are used at a local college and go through them in order, or is it better to do research on what books are recommended by roled-up math enthusiasts on discord, and go through them in order?

[remote sparrow]

this is a false dichotomy

[gray gazelle]

Like imo I feel like listening to enthusiasts online is a good thing because many of them are grad students that have already put in the grueling work of experiencing what materials are good/bad + their own preferences, but then again local curriculum is most likely (hopefully) well vetted by current professors?

[sturdy shore]

the orders used by colleges are often designed with way more than mathematicians in mind*, so it is generally not optimal

[gray gazelle]

Can you explain please?

[sturdy shore]

a lot of math curriculum in first year, and some in 2nd year, is designed with a lot of attention paid to engineers

tbh I am not sure whether engineers even benefit from this system, but in the end you get very computation heavy texts

[gray gazelle]

Does that build a bad foundation? Or just faster for engineers but worse from a pure math perspective?

[sturdy shore]

it doesn't matter all that much, I would say worse from a math perspective but it won't kill you

also, even if everything were catered purely to mathematicians, you could still get more value out of a personally designed curriculum

just because courses in unis have to pay attention to prereqs for a whole class of people

for example, I am particularly fond of textbooks that either pair multivar calc + linalg (shifrin, hubbard/hubbard) or a book like artin that pairs linalg with algebra at an introductory level

but books like this are hard to fit into a university program, because they would generally require multiple semesters where the content is integrated

though some colleges use them of course

[gray gazelle]

If you reset everything you know besides what books you would recommend, and you followed your own curriculum of books from the start, would you be able to pass tests given for a college curriculum?

Sorry my questions are a bit dumb, I'm just wondering

[sturdy shore]

I would definitely need time to prepare for whatever is in the college curriculum, but I would argue it wouldn't take long

[crimson leaf]

You also at some point want to study specific things because you'll be interested in them, math becomes very non-linear

[sturdy shore]

oh yeah, once you've done the very basics you will necessarily have to follow your own path

[crimson leaf]

Like becoming well rounded after knowledge of proofs would probably be some basic analysis, number theory, abstract algebra intro, some form of discrete math and topology but after that the world's your oyster and you don't necessarily have to do all of those to do something else

[gray gazelle]

I've been looking at colleges again and it's really hard to know what program would be worth the money, have had bad experiences in the past. Self learning feels the best but finding resources is the hardest part.

[sturdy shore]

for math the resources are very easy to find I would say, hard part is not having a professor to help you out lol

[gray gazelle]

So I don't know if following online recommendations is any better than taking whatever curriculum local colleges force

[crimson leaf]

MIT OCW is probably the best single resource if you want structure and what not but I find sometimes the content is a little harsh or hard to get through without the instruction

Sometimes when just reading a book and doing problems you get stuck on something, the upside to having a professor is they may cover it in lecture and a very intuitive and understandable way, you can ask them specific questions about something, and if they teach the material often or have taught it before they likely have run into someone having the same trouble you're having on a problem or specific part and so they can give very good guidance or hints.

Like for instance my professor had me reading a paper for research and I was getting close to a certain topic and he was like oh yeah a lot of people who I've had read this paper got stuck at this so keep these things in mind when you read it and it'll make more sense

Worked like a charm

[gray gazelle]

I hear you. Education is really just optimization of resources

Having a professor definitely helps with that

[hasty turret]

Depends on the uni and country unfortunately

Sometimes the prof exists to tell you "refer to the textbook because I don't know jackshit"

[loud cradle]

on the other hand, the best profs can have lectures/notes that are better than any textbook (depending on subject of course)

[hasty turret]

I guess that's an occurrence that's more common than you expect

[hasty turret]

What would that look like for say computational LA

[loud cradle]

yea like i said, depending on subject. I'm thinkin in particular of the prof I had for honors abstract algebra, to this day I've never seen a textbook i like as well as his lecture notes

[hasty turret]

Ok that sounds good

[loud cradle]

imo though, the biggest advantage a professor brings is not only structure but enforced schedule

[hasty turret]

Ok,I think I can understand that

As someone who self learns math,I just don't do it because I don't feel like it, which means I don't get anything done mostly

[loud cradle]

unless you're very highly motivated, speaking from my experience at least, it's really hard to cover as much material on your own during the time frame of a semester or quarter, as you will be forced to cover if you take a formal course

[loud cradle]

the other related problem with self studying (for me at least) is it's so easy to get distracted by other subjects, like i'm cruising along making good progress on some topic within algebra, but then something raises my interest (maybe even a question on discord) about some analysis topic and then i go look at that instead

might be an attention deficit issue on my part though 😀

[crimson leaf]

Some courses are really slow though, I felt like calculus 1 & 3 were like that also computational linear algebra felt really slow

[loud cradle]

yea, particularly the lower level courses seem to be like that if they are designed for a wide audience of people from various majors

service courses or whatever

people who barely have a command of basic algebra trying to learn calculus etc

[crimson leaf]

Yeah...LA was interesting to say the least

[remote sparrow]

https://www.youtube.com/watch?v=g7MSfHEdxXs

https://www.youtube.com/watch?v=eGDtW3BZyyE

i thought these videos about self studying were neat

but if possible, "self" study is best done if you can find a group that wants to study with you

besides having a professor, having peers to communicate with is enormously helpful

[loud cradle]

i always get distracted trying to identify as many of the books behind The Math Sorcerer as I can 😆

[gaunt path]

Asked for a recommendation for an algebraic geometry book with no response. if anyone has one, it will be well appreciated!

[dapper root]

Read Undergraduate Commutative Algebra by Reid first

It’s not that long, and does a really good job at illustrating the geometry present in the commutative algebra

If you don’t have a solid basis in algebra you’ll get stuck really quickly

After that, there’s Fulton’s algebraic curves which are good, and a lot of people also really like the notes by Gathmann

[gaunt path]

I would say I know more than what one would know with a first course of group theory. Ring and feild theory is where I say I am lacking. I know the axioms, and maybe a little more.

[dapper root]

Group theory is, frankly, almost entirely useless for algebraic geometry

Ring theory and to a lesser degree field theory are what the entire theory is based off of

As well as modules over rings

[gaunt path]

this information is very useful, along with the book recommendations. Thank you

[gray gazelle]

Ping me one more time and I'm blocking you

[tulip horizon]

Are there any good books about reverse mathematics?

without the book reverse mathematics: proofs from the inside out
(because I already read that book)

[gray gazelle]

<@&268886789983436800>

[molten wave]

@gray gazelle that's not appropriate here

[lean pagoda]

There's a fairly recent book by Carl Mummert but I haven't read it yet. Other than that, the standard reference is the Subsystems of second-order arithmetic book by Simpson

[trail kernel]

is there a book that teaches linear algebra with bra-ket notation?

[muted acorn]

Ive been reading book on cfd and the author first presented figure on domain and boundaries of hyperbolic equaitons, then started talking about supersonic flow and somehow used previous information. So, i though about reading more about it since i didnt understand anything

Any recommendations?

[acoustic ridge]

Does anyone have the solution pdf of Calculus: Early transcendentals by James Stewart?

[buoyant vessel]

have anyone read the Awesome Polynomials for Mathematics Competitions

@gray gazelle

[gray gazelle]

I wasn't joking

[buoyant vessel]

blitz u gay

[crimson leaf]

Can we not use gay as an insult

[zealous light]

yeah let’s not do that

[crimson leaf]

Bourbaki

[carmine linden]

Any books for statics preferably with lots of examples

[muted acorn]

@gray gazelle Do you have any book on mind?

[muted acorn]

.

[gray gazelle]

No idea

[muted acorn]

:/

[tame tree]

Anybody familiar with A level maths have a good book that they would recommend? (Not further maths)

This is the one where they have papers 1 and 3 pure mathematics, paper 4 mechanics, and paper 5 prob and statistics

[tame tree]

ye im good on the learning math outside of it for fun, i plan to get to real analysis by that time, just need to make sure i study the right stuff and pass the papers

[remote sparrow]

https://www.amazon.com/Differential-Equations-Linear-Algebra-Gilbert/dp/0980232791/
https://www.amazon.com/Differential-Equations-Linear-Algebra-4th/dp/013449718X
https://www.amazon.com/Differential-Equations-Linear-Algebra-4th/dp/0321964675

thoughts on these three books?

[sage python]

Wonder if they're about differential equations and linear algebra

[remote sparrow]

i'd say they are with probability 0 <= p <= 1

[violet shuttle]

almost surely

[violet shuttle]

Shankar's Introduction to Quantum Mechanics

it's also how i first learnt linear algebra

[trail kernel]

alr thanks I'm gonna check it out 🙏

[violet shuttle]

note that there's only one chapter on linear algebra

[warm glen]

does serre's linear representations require anything more than group theory and basic linear algebra to read

with basic to me meaning nothing beyond eigen stuff

[broken meadow]

thats what the first segment of the book seems to require yes

u probably could not do the 2nd and 3rd parts

without more math

[warm glen]

damn

what would i need for those

gonna study rings and modules next quarter

[broken meadow]

i dont remember exactly atm oogissimo

[warm glen]

ah well i'll just read the 1st part for now and see what trips me up later

[remote sparrow]

https://www.amazon.com/Modern-Mathematical-Logic-Cambridge-Textbooks/dp/1108833144

A book released this year

Dunno anything about it, but i'm putting this on everyone's radar
Discord search keywords for posterity: Modern Mathematical Logic Joseph Mileti

[orchid mortar]

Talks about model theory, , is that what pure math students who take a course in logic have to know?
Wonder how many logicians we actually have in here, but it's certainly not me

[trail kernel]

my linear algebra skills are pretty good, but I'm still having some trouble with bra-ket notation, so I think that's fine

[remote sparrow]

Just noticed @fallow cypress is using this book. Feel free to give your thoughts on it.

[trail kernel]

is this a book for undergrads or grads?

[remote sparrow]

Requiring only a modest background of undergraduate mathematics, the text can be readily adapted for a variety of one- or two-semester courses at the upper-undergraduate or beginning-graduate level.

so comparable to enderton or ebbinghaus

[trail kernel]

alr sounds awesome

I'm probably at the level of a mid-undergrad (math undergrad ofc)

[heady ember]

Are you a highschooler?

[trail kernel]

1st year in uni

but I'm not studying math

[heady ember]

Ah I see

Nice

[trail kernel]

it's a software dev degree

[heady ember]

I see

[gray gazelle]

Can anyone recommend an intro book for category theory?

[remote sparrow]

i heard eugenia cheng's The Joy of Abstraction could work for undergrad

[trail kernel]

lawvere and shanuel's "a first introduction to categories" is a pretty cool nonstandard way to learn category theory

I also enjoyed milewski's "category theory for programmers"

[mystic orbit]

I recommend the article on Stanford's encyclopedia of philosophy as a brief intro

https://plato.stanford.edu/entries/category-theory/

You can decide whether you need more afterwards

[violet violet]

Can I get the PDF file of modern mathematical logic (Cambridge mathematical textbooks )

[remote sparrow]

the author has his draft copy available here: https://mileti.math.grinnell.edu/MathematicalLogic.pdf

[violet violet]

Ok thanks

[alpine rover]

hi, can anyone recommend an introductory book on number theory?

i've done a bit of analysis and abstract algebra, but i have virtually zero experience with number theory

[fallow cypress]

it's great

it was not finished when I read it though

it stopped a little bit before proving the first incompleteness theorem

also some of the sections are skippable (most of ch 1?)

I like how he develops propositional logic so much before moving on to first order logic

[plush terrace]

do you guys have a good recommendation for ode’s?

I’m not good at proof based books, so an easier read would be better!

[frigid flax]

elementary number theory by underwood dudley

or elementary number theory by David burton

[crimson leaf]

Number theory by Andrews

Nice dover book

[willow pecan]

All ODE books are bad

[coral narwhal]

coddington intro to ode

[alpine rover]

zill

reads like stewart calculus

[winged mauve]

Any good recommendations on series and summations?

[plush terrace]

eyyy I was planning on getting that one too

Saw it on the math sorcerer

[plush terrace]

Stewart’s book worked for me, but that was Calc 2. Idk if you need higher level stuff

[slim peak]

Not Viorel Barbu's one.

[winged mauve]

That will probably suffice. Thank you. I assume this is stewarts calc book?

[remote sparrow]

if you have some experience with abstract algebra and analysis, An Introduction to the Theory of Numbers by Niven, Zuckerman, and Montgomery could work for you.

[remote sparrow]

i don't really like the way andrews starts with basis representation

the combinatorial proof of the chinese remainder theorem was really neat though

[remote sparrow]

#book-recommendations message

it might be wise to avoid coddington's intro to ODE, as it's more rigorous. it is a good reference that more modern ODE books point to for full proofs of certain theorems.

also, coddington has two books, an introductory one and an advanced one. the introductory one is reprinted by dover, which makes it cheap. it could be useful to buy it if you want a reference for some proofs.

edwards and penney has some proofs of existence and uniqueness of solutions in the appendix

boyce and diprima doesn't

edwards and penney's latest edition apparently has additional emphasis on computing and modeling

it could be interesting

william trench has made his two differential equations books (one with and one without boundary value problems) available for free online

unfortunately, most ODE books are expensive besides morris, tenenbaum, and pollard and coddington's

costs can be significantly mitigated, however, by buying used

that said, as others have said, ODE books are generally fairly uninspired, to put it lightly

https://web.williams.edu/Mathematics/lg5/Rota.pdf

you may find this essay interesting

[warm glen]

when do you need algebra and analysis?

im reading the book rn barely got started on ch 1 so im actually wondering

[remote sparrow]

https://math.berkeley.edu/~ribet/115/

first seven chapters are elementary apparently; there isn't any strong need to really know some algebra or analysis

though chapter two has some sections that involve algebra

9 and 11 mention lim inf and lim sup

so a little analysis background is needed

[remote sparrow]

https://www.youtube.com/watch?v=EE7KpcReYw4

interesting book recommendations (more in the description)

there's a slant to taking a historical approach and studying theory for applications

[gray gazelle]

Music recommendations: https://open.spotify.com/artist/2x5UG8NI2Tvyf5aYVFRncv?si=QFeP_7ZdSpK1s3uxSwOJ0g

[foggy relic]

[daring ravine]

Not history per se but james newman has a set called “the world of mathematics” that’s pretty broad

Missing some newer stuff though

[grave thorn]

Arnold is good

[winged mauve]

Maybe A history of mathematics by Carl Boyer?

[remote sparrow]

i believe i already mentioned that

katz also has written a history of math textbook besides his sourcebooks

https://www.amazon.com/History-Mathematics-Source-Based-Approach-Textbooks/dp/1470464993

there are these two books

[winged mauve]

Oh nice

[spare ridge]

https://tenor.com/bpAWv.gif

vi arnold be like

[winged mauve]

What about a good prealgebra book?

[remote sparrow]

https://www.amazon.com/hz/wishlist/ls/305T0IS17NSKY?ref_=wl_share

i've made an amazon wish list

[willow pecan]

Amazon bad

[remote sparrow]

i've already bought some items not on the wishlist, like rudin's PMA

[remote sparrow]

true!

but it is convenient

so i will use it

my wish list isn't really a recommendation per se but i guess it's kinda like a compilation of books people think are good?

i'm not gonna dump all my money

this is something i'll chip away at over time

if anyone feels they want to add something to this list, let me know

[zealous light]

Smh it doesn't have evans

[heady ember]

[remote sparrow]

Idc that much about pde tbh

[sage python]

Feels like there's a lot of redundancy here no?

[remote sparrow]

It's the insatiable urge to hoard books

[gray gazelle]

Will you read any of them

[remote sparrow]

Yes

[zealous light]

Fwiw it has Strauss in there so that's why I pointed out the lack of evans

[willow pecan]

Called out

[fierce hedge]

No topology books? Have you already purchased Munkres or something?

[sage python]

Rotman and Hatcher are both there

[fierce hedge]

Ah, okay for some reason Chrome wasn't showing the first 10 entries I opened it in firefox

Damn, that's a hell lotta books

[novel obsidian]

Actually on the topic, does anyone know of any good online bookshops, I'm in the market for a copy of rudin and artin

Or maybe a better question is where do you all buy your books from

[fluid bay]

i feel like most of the time i buy a book, its when I randomly find a good deal browsing ebay, and not when I actually need the book kek

[heady ember]

I bought Linear Algebra by FIS and Nathan Jacobson's Basic Algebra I yesterday

[fierce hedge]

Same, finally a legit copy of Jacobson

[gray gazelle]

If I want a physical copy I just use a library

[fierce hedge]

Yeah but it's nice to have some books plus won't have library access after uni

[gray gazelle]

I don't use physical books that much

Anyway

[heady ember]

:hifive:

[heady ember]

I don't think any public libraries in my country has any semblance of a wide array of (uni) math textbooks

[fluid bay]

not in my country either (united states). only university libraries

[strange crater]

Beginner post hs book recs?

[hollow shore]

assuming you have seen calculus before, you can have a look at this
https://www.jirka.org/ra/

[remote sparrow]

i already have hubbard

[remote sparrow]

munkres is on the list

[fierce hedge]

Yeah, I could only see the first 10 entries

[foggy relic]

a ton of this is redundant yeah

[heady ember]

No Lee intro to topological/riemannian manifolds?

[fierce hedge]

It would be a good library

[remote sparrow]

which is the point

expensive, to be sure

it's a long-term thing

i'll prioritize getting books that jive well with me first, but other perspectives from different books are welcome

and it's not like the list is fixed

[river tangle]

guys any good books for basic chemistry?

not organic

[remote sparrow]

my high school used Chemistry: The Central Science, then switched to zumdahl's book later in the year but not sure if they like zumdahl better or it was just the cheapest new book at the time

that's an intro college level book

[sage python]

@remote sparrow so where are you at now and do you have any leanings re your mathematical interests?

[foggy relic]

@remote sparrow look at dover, tons of good cheap books

if you want to amass book for the sake of it

[remote sparrow]

i've had algebra and real analysis. topology, mathematical logic, and axiomatic set theory aren't offered as undergraduate courses. although i would really love to learn some axiomatic set theory and math logic (currently, i just have enderton's books). complex analysis is technically available, but it's not offered on a regular basis. highest on the list would probably be gamelin's book. i'm aware of dover and own a few myself. i have morris, tenenbaum, and pollard's ode book, shilov's linear algebra, and dudley's elementary number theory book. i have counterexamples in analysis, topology, and a smallish book constructing the number systems by thurston. i also have willard's topology book. i'd say right now my interests are slanted to foundations of math.

[heady ember]

Enderton

[fierce hedge]

Are all of these purchased new or some are printed. I am just buying those books for which the pdf available is not of good quality. Rest I'd get printed

[foggy relic]

@remote sparrow how many of those books have you read

And which ones did you like

[remote sparrow]

All my dovers are new

[remote sparrow]

Dudley, morris, and thurston are good. I flipped through counterexamples in analysis as a reference

[foggy relic]

try ireland rosen, im currently reading it and its very nice, i think you will like it

[sage python]

Sorry I intended to respond sooner but uh

Calc proctoring

[foggy relic]

least forgetful calc proctor

[astral sorrel]

Im studying math seriously for my GED. Where should I start?

[random sundial]

Who has read Euclid?

[upper crypt]

Hello, I bought some books on ams. I want to track my shipment ,but I know only order number. In this case how can I check my shipment?

[timber rampart]

Any decent books on studying Differential Equations and then Real Analysis?

Given a foundation in Calculus I to III

[winged mauve]

ODE & PDE?

[timber rampart]

Yes

Starting with ODEs

[winged mauve]

I have the dover books (intro to linear algebra and diffE, Intro to DiffE) and the Zill book. Ive seen the Zill book recommended a few times in here

As for analysis i was recommended Real Analysis by Bartle

[thorn cloak]

Hey all, just finished a standard intro to linear algebra class and was wondering if there were any good books about more “advanced” or “abstract” linear algebra. I’m taking multi var next semester but still want to continue learning a more theoretical class, but don’t really have any other prereqs but linear algebra haha. Any book recommendations? I’m thinking of Linear algebra by Friedberg, Spence, and Insel

[heady ember]

What does your linear algebra class cover

Without that, we won't really know what would be "more abstract" to you

Does it cover vector spaces?

Oh yeah Friedberg is good, rather friendly as well. Many people here like it, including me, though I haven't done that much of it.

[thorn cloak]

To a degree yes. We did basically everything up to eigenvectors and diagonal matrices

[heady ember]

I see

[thorn cloak]

We didn’t cover orthogonal stuff but I was planning on self studying that chapter

[heady ember]

Fyi you can check out the linear alg recs in pinned

[thorn cloak]

Oh I didn’t even notice that! Tysm

[heady ember]

Np!

On a random note, my physical copy of Friedberg is coming in two weeks time
(I have been using a digital pirated copy lol)

[thorn cloak]

Ah nice lmao! I like physical books more but they are so expensive nowadays

[heady ember]

Yeah

~~How to get cheap physical books:

1. Get a copy online (piracy)
2. Print it out
3. Bind it
4. Profit~~

[remote sparrow]

someone please figure out to print with lulu

[remote sparrow]

where do you go to bind your books

speaking generally

[grave thorn]

Is Bogachev's Gaussian Measures a good book?

[heady ember]

I haven't actually print out any books yet

But I would bind them myself, probably

[remote sparrow]

seems like a hassle to do that

and maybe even expensive

for binding anyway

[heady ember]

I'd probably just need some glue (which I already bought) and some backing for the hardcover

[winged mauve]

Print at work = Free
3 hole punch = ~10$
3 Ring binders = between 5 - 15$

[heady ember]

Print at work doesn't necessarily work I think

I mean I doubt your employer would be happy about you printing out a 500 page book using company resources

[thorn cloak]

Idk you can find 500 pages of printer paper for like 5 bucks at target

[heady ember]

I think sour was talking about self-binding

[winged mauve]

I work for a place that prints a lot of paper. And they let me print out a couple of books already lol

[remote sparrow]

not interested in 3 hole punch

i'm interested in paperbacks or hardcovers

[crimson leaf]

I might try to bind one myself

[hollow shore]

just buy an ipad lmao

[remote sparrow]

it's easier to cross-reference multiple books with physical

ipad and e-reader's advantage is less space for fiction

i'll grant that much

ipad is harder on the eyes than an e-reader

[hollow shore]

physical books take up a lot of space

that's why I am considering getting a tablet

[remote sparrow]

for academic purposes, physical is still king imo. fiction you can make a different case i suppose. though i don't really want to buy electronic copies of fiction if i want to somehow support an author since i can't abide by any sort of digital rights management, nor do i tolerate only being licensed to view a book rather than owning it outright.

[hollow shore]

I too think likewise in regards with fiction

[heady ember]

~~A hardcover book is also an excellent weapon for self-defense ~~

[remote sparrow]

i don't think understanding analysis is very helpful for that purpose

nor ladr

they're both pretty slim

stewart's calculus is fucking heavy as hell

literal doorstop of a book

that would work

[heady ember]

Dummit and foote hardcover would probably work too

[remote sparrow]

yeah but it would only last one or two hits at most with its shitty binding

[heady ember]

[golden bear]

Is tao's analysis 1 a good book to start to refresh my analysis background?

[heady ember]

lmao

[remote sparrow]

ye

[golden bear]

thanks

[vital bane]

that could will kill someone

[fierce hedge]

I'd prefer getting shot in the foote

[heady ember]

[faint nebula]

Just read Berserk

[fierce hedge]

Just purchased Shifrin, what the hell is that binding

[heady ember]

[grand thistle]

yea

the best weapons i have on my bookshelf are lee’s smooth manifolds, dummit and foote and stewart

feynman’s lectures also are up there

they heavy af even if they’re not hardcover

[heady ember]

Lee

[forest sleet]

if it's <500 pages it isn't too bad to sew it and bind yourself

assuming it's a normal sized math book so you can print 2 pages per side of a standard size sheet

(4 pages per sheet of paper)

I don't quite have all the proper details for binding down right but it is usable still

[crimson leaf]

There's a lot of resources though, it seems to be a hobby

[sage python]

@remote sparrow Here's my take on what I'm comfortable weighing in on.

• Gamelin's good for complex analysis, you can see my thoughts on other books in the pinned post. Similar for grad level real analysis. Big Rudin covers both (though I think is suboptimal for either subject alone).

• For undergrad level real analysis, either Browder (Baby Rudin + Spivak Calc on Manifolds but better) or Schroder (more gentle and arguably "pedagogical" but organized worse for refencing purposes).

• Can't go wrong with most choices in functional analysis, I think Einsiedler-Ward is particularly nice for its connections to other areas of math. Brezis is good for linking to PDE which is the main client of the subject

• Kriz & Pultr does everything* and is prob the book I'd pick for "one stop analysis shopping".

• Lang is probably the king in algebra books. If it's rough going try D&F which is much easier (to the point of being boring) or Jacobson (good exposition, less standard topic selection)

For topology/geometry, you already have a point-set book. Then there's algebraic topology, differential topology, and differential geometry as your "main" areas, though there are a lot of topics under these umbrellas and different sources can make different choices. I'll have another post for that entirely

*Okay by everything I don't mean it subsumes Big Rudin or Einsiedler-Ward or whatever, but it touches on a lot of topics that you otherwise can't find in one place: obvious contenders like topology and multivariable calculus (through measure theory), but also differential equations, complex analysis, manifolds and basic diffgeo, calc of variations, and functional analysis

[heady ember]

Im already gonna be getting like 3 math books for myself already. But today I saw needham's Visual Complex Analysis (paperback) at 18.40 USD which is seems to be a steal. Should I get it?

[willow pecan]

If you want it

[heady ember]

Ah well I wanted it but my mum said no
(which I can see why, since I am already getting 3)
(Im a highschooler so can't exactly pay without someone's help kek)

[bold knoll]

I'm reading it now and I have to say that I feel pretty overwhelmed with the material.
I'm just in the section on differential maps and I find myself re-reading definitions many times over. It doesn't feel productive and the exercises are so few and are pretty far into the chapter.
Are there any exercises or recorded lectures that can help?

I do understand everything I read so far but it takes such a long time to feel comfortable with everything that I'm certain that I'm doing something wrong.

Also, there aren't any examples of manifolds at all which makes it harder to bridge the abstract with the concrete.

Actually, they mentioned the identity map and spheres once but it's not much.

[gray gazelle]

It's probably going to get worse

Those parts are the easiest to understand

But it's probably not an introduction type of book

Reading it is a choice of suffering through it to understand it, or picking an easier intro

[bold knoll]

I like the abstract approach of the book.
I tried a GR book before, I could follow it but it was technical and lacked the rigor I'm looking for.
Which is common in physics...

[bold knoll]

I'm willing to do so, but I want to be sure that I won't waste a huge amount of time by reading a book like that.

[gray gazelle]

For physics right

[bold knoll]

It's different from learning from lectures.

[gray gazelle]

I don't think it's a big waste of time if it's related to your courses

Especially pseudo-Riemanian manifolds are relevant in physics

[bold knoll]

I'm not in university right now.

I just really want to learn GR.

[gray gazelle]

It's okay. Just go easy on how you approach it and come back to it

[bold knoll]

If you say so, I guess I'll trust the grind.

[gray gazelle]

Reading math books isn't easy, so don't get discouraged. Obstacles are to be overcomed.
People that say you are stupid or anything, they know nothing about how this world works

[gentle spade]

wait they right books bout maths?

write*

[gray gazelle]

Of course lol

There's more literature than there is subfields of math

And there's a huge amount of subfields of math

[gentle spade]

damn

[hollow shore]

where did you get it from?

[normal pawn]

Guys

Recommend me some books in precal and cal

[heady ember]

Spivak

[fierce hedge]

Got it from Flipkart

[hollow shore]

I see

[fierce hedge]

There's one on Amazon also but it's 40% more expensive

[vital bane]

do you have the prerequisites for the book?

[bold knoll]

Yes, I know topology and real analysis.
With linear algebra I think it's pretty much it.

[vital bane]

perhaps you will enjoy

fyi i havent gone through it, i just think you'd like it

[vital bane]

I mean I've only skimmed it but you're right

[lime sapphire]

i wish there was a higher quality pdf of schroder out there 🥺

[fierce hedge]

same

[brittle latch]

anyone have thoughts on massey basic course algebraic topology

[gray gazelle]

What books are better Folland's Real Analysis book?

For learning basic measure theory and functional analysis

[rapid lily]

Real and Functional Analysis by Lang is an alternative.

[sudden kindle]

Munkres or Spivak for calculus on manifolds?

I read and used munkres in undergrad but will be teaching a course next sem which uses Spivak by default

Thinking about if I should change books to go with something I'm more used to or stick with Spivak because it might be better

[calm pagoda]

i just started reading capinski & kopp - measure, integral, and probability as someone recommended it to me and its good so far

[sudden kindle]

I used it too in undergrad

Was my first intro to measure theory

It was good for me, tho I remember my prof complaining about some typos?

There's also Axler's new book on measure theory. Havnt read that but might be worth checking out

[calm pagoda]

Oh shit yeah

i should read that cause linear algebra done right is my fav textbook

[remote sparrow]

schilling is recommended in pins

but it could be too elementary

axler's measure theory book is legally available for free online

i saw bass on amazon

it's super cheap

[calm pagoda]

Realy

Oh wow

measure.axler.net

haha

[gray gazelle]

i think i'll just go with Folland it seems to cover the things i need for now and the presentation doesn t look too bad at first glance

[vestal coral]

Now that i discovered this chat

Someone here do know a practical mathematics book to train calculus?

Basic calculus

[remote sparrow]

hubbard's book can be used, at least according to the authors, if you use the appendix. the appendix has proofs of all the more sophisticated results. alternatively, consider using zorich

[sudden kindle]

stackexchange says

i havnt heard of Hubbard & Hubbard before

or Zorich

[remote sparrow]

hubbard doesn't hide the proofs, just relegates them to the appendix

https://link.springer.com/book/10.1007/978-3-662-48792-1

https://link.springer.com/book/10.1007/978-3-662-48993-2

@sudden kindle check ToC

chapters 7 and 8 of analysis I covers functions and differentiation of several variables

that doesn't mean you have to get both

volume ii is formally independent from volume i

[slender cargo]

Hubbard and Hubbard is for a different audience I feel like

[remote sparrow]

volume ii just uses differential forms instead

dami recommends browder's chapters on multivariable calculus

[grand thistle]

what abt amann and escher’s Analysis II?

i love their writing style and i think they cover analysis on manifolds in their second book though i’ve only read their first

wait actually calc on manifolds might be Analysis III

yeah it is

and seems like they do it very rigorously

[vital bane]

if nakahara has proofs (but sometimes omits long proofs) then yes!

[brittle latch]

bump

also wondering about suggestions for books on fields and modules

just finished a course on groups and rings that didnt have a textbook

but it's a grad class so ig anything at that level

[broken meadow]

Dummit and Foote

[brittle latch]

ive heard mixed things

how are the exercises

[broken meadow]

They're fine

people are always judging a book that is ultimately just fine

and also obviously you aren't bound to one book

so 🤷

[brittle latch]

ig that's true

though ive never tried to study out of more than one at a time

[neon tiger]

Can someone suggest books on advanced limits

For practice

[formal bronze]

What are advanced limits?

[neon tiger]

Limits that are at a competition math level

[heady ember]

You can see if Spivak has ones you find suitable for you I guess

[gray gazelle]

reading posts on #books, i have to comfort with proof based math, and basic linear algebra for some chapters
so i have done linear algebra but i'm currently learning mathematical proofs: a transition to advanced math authored by gary chartrand, albert d. polimen, and ping zhang by myself

so if i have finished my mathematical proofs: a transition to advanced math, will i be able to get started with basic algebra i?

i just wanna learn it by myself

[willow pecan]

Sure

[mossy flume]

Learning proofs by yourself is hard

Because IMO it's invaluable to have someone read your writing

[gray gazelle]

感谢你 :)

[willow pecan]

You can always ask for proof feedback in this server

[gray jungle]

The server here can be helpfull in that regards

i got very valuable critique while i was still learning the basics of proofs here

[gray gazelle]

why thank you ^-^

it's surely hard to do it by myself

even starting to learn something by one's self itself is already hard though

T^T

[mossy flume]

True

[gray gazelle]

it feels good to be able to start learning something and everyone welcomes me to discuss here

you don't know how emotional i am rn ;w;

[gray gazelle]

writing proofs is easy you just repeat few words over and over again
technique? Proof by induction and by contradiction is all you need to know

well, sometimes transfinite induction (for the more advanced in set theory)

[gray gazelle]

cool, i'm still learning proof by contradiction

the first 5 exercises told me to disprove the statements

once you learn that, logic rules are cool to have in mind to remind yourself what it is about
I don't mean anything complicated, just like when is implication true/false and so on

[hasty eagle]

Blitz

[gray gazelle]

gotcha

i feel pretty confident to get to learn algebra

everyone needs to learn a bit of algebra

but analysis is very cool too, even if it looks complicated at first

at first i found it so intimidating

that's why i was reluctant to start doing so

it's intimidating for me too

[restive falcon]

yeah you should learn some analysis even though algebra is better

[gray gazelle]

I see a false statement right here

which one?

analysis is superior to algebra

ok...

but i love both

<3

[restive falcon]

you're on the wrong side of history

[rich sun]

analysis and algebra go hand in hand

[gray gazelle]

i think i have to save my money to spend it on the books (print books)

tysm for your advice

alison and blitz <3

also ange and spamakin <3

[mossy flume]

Wrong

[gray gazelle]

i feel even more welcomed here

^-^

and also, special thanks to cofe cube

<3

[gray gazelle]

Analysis is like wine that matures, whereas algebra is like bread that gets stale

It's tasty when it's fresh

[ornate saddle]

Any introductory and rigorously explanatory book recommendation for Calculus of Variations?

[cinder trellis]

But when analysis and algebra work together in a subject though 🤌

[rich sun]

It's like dipping bread into wine

[remote sparrow]

people like gelfand

@gray gazelle if you find jacobson too difficult, you can try using pinter

just make sure you do a lot of exercises; a lot of material is in there

you can google syllabi to see what problems you should do

[gray gazelle]

It's a classic for sure

[ornate saddle]

[icy knot]

My Amazon wishlist is similar to @remote sparrow . For some reason I have this insatiable urge to buy more math books that I will never read or work through. I will post mine, if anyone is looking for suggestions on what books to look at.

[odd summit]

IA MARON?

[remote sparrow]

https://tenor.com/view/gigachad-chad-gif-20773266

[heady ember]

[heady ember]

Set theory is cool too

~~Read Enderton's Elements of Set Theory ~~

[fallow cypress]

does anyone have any good resources about the metropolis-hastings algorithm

[fallow cypress]

in particular I want to understand where this magical ratio comes from

something something detailed balance?

[fallow cypress]

wait nvm I think I get it

[fierce hedge]

My mom asked me this morning, "when are you gonna read all these books you bought?"

Some day mom, some day

[fierce hedge]

Good algebra book for quick revision of groups, rings and fields?

[remote sparrow]

are the pinned algebra recommendations not good enough for you?

[fierce hedge]

I mean, it takes me a lot of time to convince myself to stick to a particular book

So, if someone had a recommendation for a quick book, it would be nice otherwise I'd stick to Herstein I guess

[remote sparrow]

lang

[fierce hedge]

I take back back my question

[remote sparrow]

try knapp

looking for more people to review it

[fierce hedge]

I guess I can take one for the team

[remote sparrow]

you can at least try the book online

it's free

[fierce hedge]

even though I already bought Jacobson

yeah, I have a better adjusted copy from the biblical library

[heady ember]

I bought my copy of Jacobson 's Basic Algebra I a couple of days ago as well

Will be arriving next week

[fierce hedge]

I am thinking of buying either Schroder or Browder. Yet to decide between the two

[remote sparrow]

buy both

[fierce hedge]

I wish I was rich

[heady ember]

I bought Schroder of Ebay for US $30

but the shipping fee was US $20

Still cheaper than Amazon tho

[remote sparrow]

i saw an offer for schroder at $35 dollars in very good condition on amazon

you never know

[crimson leaf]

I got this for $37 w/ shipping and tax ignore the top left that's where I dropped it

[remote sparrow]

that looks really good

how's the binding

[fierce hedge]

Here, I have almost always seen the new book cheaper than the used ones

The only super cheap books are the one for IIT prep

[heady ember]

I went to Amazon's website and the only one available in where I live is >$100

[remote sparrow]

unlucky

just wait

@tame tree TIL elizabeth meckes died in 2020 https://thedaily.case.edu/remembering-professor-of-mathematics-elizabeth-meckes/

[tame tree]

Wtf

Way too soon

[heady ember]

Its unlikely there would be anyone reselling Schroder in my country. Even finding a uni math textbook on local online stores is rather suprising

I mean, there are a few from some uni students every now and then but even then those are books I never heard of

[blazing canopy]

For finite difference specifically I like Leveque's book on finite difference methods. For general numerical analysis I think this is difficult to answer because what counts as undergraduate level is not very standard for numerical analysis I feel. One of the popular books is by Burden and Faires.

[willow pecan]

Burden is a bad book

I would also recommend Iserles’ book

Cengage

Also it’s like

Intro numerical analysis is not a very coherent subject

[willow pecan]

#❓how-to-get-help

[orchid mortar]

!help

[hybrid sparrow]

Please read #❓how-to-get-help

[neon tiger]

someone please suggest on olympiad level algebra thatll also help me in other places like exams

this is because what i usually study for in math is at a higher level than what is being taught in my class

is this a good thing

cuz sometimes i cut down the time i spend on other subjects like english and social science

so im getting bad marks in those subjects (bw 80% and 90%) is this fine

[late quartz]

what book do i need to study for algebra

like self study

[formal bronze]

Linear algebra or abstract algebra? For abstract algebra I would suggest 'Abstract Algebra' by Dummit and Foote or 'Algebra' by Artin.

For linear algebra I have only used Hoffman and Kunze.

[neon tiger]

someone

[heady ember]

Be patient

[gray gazelle]

it can be high school algebra