book-recommendations

[mortal ore]

Bredon is usually the choice for more rigorous algtop

[wild blaze]

oh awesome thank for telling me

so bredon it is then

[lethal sentinel]

I remember reading a book called Gamma, exploring eulers constant by Julian Havil when i was in high school. Since then I have not really read more "light math books", as in not a textbook and rather light reading whenever. Anyone have any recommendations for similar books or some list of these? Preferably on a similar or higher level to the one i mentioned in similar subjects (analysis, number theory)

[wet sentinel]

this is late but lang

(maybe unironically tbh )

[midnight gulch]

i'm not sure about his undergraduate algebra book such but I think his undergraduate analysis one is quite good

i assume they are written in a similar way

[wet sentinel]

i am talking about the grad one

[pearl palm]

I’ve heard mixed things about that one,but have it nonetheless,what’s its strengths?

[wet sentinel]

i like it because it gets straight to the point and it also covers stuff that arent seen in intro courses in say group theory for example

one can use it without doing any algebra beforehand, but in the ring theory chapter for example there are some stuff which arent mentioned like euclidean domains etc..

[pearl palm]

What’s the prereqs? I looked it up before but can’t remember 😅

[midnight gulch]

well you know that's obviously irrelevant

[wet sentinel]

no thats not irrelevant imo

thats why i mentioned it

i mean i am using it for intro algebra

[midnight gulch]

have they taken a class in algebra before? i don't think they mentioned it

[wet sentinel]

lang says that someone who have read his undergrad LA and undergrad AA should be more than prepared, but he does start from the ground up

the ring theory chapter is missing some stuff which i think are omitted because he supposes that the readers have done intro AA

but the group theory chapter for example covers everything you see in intro algebra books and more

i am not saying its the best choice lmao

[pearl palm]

Sounds good,thanks for the advice

[wet sentinel]

in fact its a very tough choice

[midnight gulch]

why recommend it then?

[wet sentinel]

because i find it the best, tho others might not

[pearl palm]

I’m too far in now ever since I mistook it for a non graduate algebra book

[wet sentinel]

others would recommend D&F for example

i dont like that book

[pearl palm]

How come?

[wet sentinel]

i tried it and dropped it

because to me it sounded wordy

for others this might be optimal, especially since one would be somewhat new to proofs at that point in time

i was in the same position too lol, but i chose lang even tho its significantly harder

[pearl palm]

That’s cool

[wet sentinel]

so I find lang better, but most probably everyone else would definitely prefer a book like say D&F over it and that makes sense too

[pearl palm]

Would it be better to combine both and read them together?

Get both worlds at once

[wet sentinel]

ohhh so you are using lang?

[wild blaze]

you did lang first?

thats quite impressive no

what proof writing did you have before that

[pearl palm]

Not yet,my goal in mathematics is to one day finish the book. But I do have it,it’s on my shelf just collecting dust until I can get up there

[wet sentinel]

yes, i am still doing it. I used D&F, stopped using it from the start of chapter 2 since i found it too wordy/boring so i tried lang's algebra. It went kinda smoothly at the beginning till the section on normal groups where he started talking about the butterfly lemma etc.. At that point i found this particular part of the section very difficult so i switched to his undegrad book, but then i switched back the grad one because i felt that the undergrad one was missing many things

[wild blaze]

what proof writing did u have b4 it

[wet sentinel]

the only really tough time i had with lang's algebra was this section lol

[wild blaze]

interesting

[wet sentinel]

hmmm let me try to remember

[wet sentinel]

(other ones where tough but that was the thing i found the hardest at the time)

[pearl palm]

How long have you been doing math for? and proofs too?

[pearl palm]

This isn’t really a book question so sorry if that’s an issue 👍

[wild blaze]

curious abt this

i dont know how u could jump straight into lang

with no la or aa

[pearl palm]

Yeah

Wizardry

[wet sentinel]

a good part of the single variable part of rudin's PMA (I think up to and including chapter 6), and I have also done a bit of LA from werner greub's book and FIS book

but not much LA

tho all of this is self study

[wild blaze]

interesting

just rudin

[wet sentinel]

so i wasnt in a proper course thats why you will probably find a few random/weird things

[wild blaze]

thats impressive tho

[wet sentinel]

I dont think so

I mean i had a really hard time with lang, i cant deny that

[pearl palm]

Did you take an intro to proofs course/book?

[wild blaze]

how long have u spent

[wet sentinel]

as i told you at some point i quit the book and then came back

[wild blaze]

a lot off ppl use rudin as introductory tbh

although its rough

[wet sentinel]

no

[pearl palm]

Oh

[past dust]

should i continue with thomas calc for calc 3 (i think it's the asme as multi var calc) or switch to a multi var calc book

[wet sentinel]

i think people go for FIS or understanding analysis by abbott for intro, at least these are the ones which get recommended more commonly here

also i have to admit that i am stubborn

[wild blaze]

whats fis?

[midnight gulch]

how much have you done with lang? i think it can be useful as a secondary source to consult for certain definitions or proof, but as a main motivating textbook i personally see it as a terrible option

[wet sentinel]

often i choose tough textbooks on purpose, idk why lol

it kinda feels like challenging myself or something like that

[midnight gulch]

for undergraduate aa, i should say

[wet sentinel]

but thats stupid

[wet sentinel]

i have finished the first 2 chapters and jumped to the 4th, currently i am in the 4th chapter

[midnight gulch]

yeah, "challenge" is not itself a virtue if the goal is to learn math. but if you think it works best then all power to you

[wet sentinel]

i will go back to the 3rd (which is about modules) later but for now i want to try to get to galois theory asap

because i want to use it for something else like algebraic nt

but modules are very important so i might come back to them right after chapter 4

[wet sentinel]

yea thats true, and i admit its stupid. thats why i am not doing this anymore

but i liked lang's style, thats the only reason i am continuing with it rn

[wet sentinel]

friedberg, insel and spence. A linear algebra book

[wet sentinel]

i couldnt study continuously for a long period of time because of the circumstances at that time

[wild blaze]

oh ive seen that my bad

[wet sentinel]

i would say that it has been like 10 months since things got back more or less to normal so that i could study properly

even then i slack off sometimes often

the thing is that i came to a new country 1 year ago, so i had to learn the language and get into a uni etc.. so that took time

[pearl palm]

Do you personally find it hard to stay concentrated sometimes when you do math?

[wet sentinel]

yea sometimes, but also these days i am feeling tired for some reason. As in, sometimes i feel like i cant think properly

[pearl palm]

Oh

[wet sentinel]

its probably because i have been sleeping and waking up quite late for a while now

[wet sentinel]

what about you?

[pearl palm]

Pretty similar myself

Sometimes I’ll stay in line on it for a while and other times just can’t do anything

[wet sentinel]

i see

[wet sentinel]

i think that you could stick to thomas, i havent read it myself but tbh there isnt much difference between calc book

at least not much difference between books like thomas and stewart for example

tho there might be other opinions, so i suggest that you wait for other responses too if you want

[scenic sequoia]

Any good books on numerical analysis ?

[delicate bolt]

i really don't wanna be the one to ask, but, i would really like a book rec for whatever i can study after or as compliment to a course in pde. i'm about to enter my eight semester in chemical engineering and i took the differential equations class in 2024, so, i would appreciate any recs or if i should just stick to the basics or anything like that

[marble solar]

Churchill and Brown have some good books, with an applied side, on: fourier series, complex variables, and some transform methods. Walter Strauss' PDE book is also an interesting book for reading

[delicate bolt]

thank you, i really appreciate it!!!

[mortal iris]

Arnold's Lectures on PDEs are golden.

[delicate bolt]

let me see if i can find that one in my native language, because you are right, it does sound good, Especially since it sounds like it does cover pretty well the basis of my major, thank you so much!!

[gray gazelle]

Any suggestions to practice better problems on Linear Algebra?

Been reading David C Lay’s Linear Algebra and the problems aren’t that challenging

Although it is good cuz it is my first read on Linear Algebra, but I need something a bit more challenging

[slow roost]

Shilov seems tough

[wet sentinel]

maybe check greub if you want

[gray gazelle]

Ah alright.

[slow roost]

in Soviet Russia, algebra linearizes YOU!

[gray gazelle]

Yeah I gotto check other books. The proofs in Lay aren’t that rigorous.

[gray gazelle]

💔

[gray gazelle]

Hey, sorry for disturbing you, but do you have the link to Georgi Shilov’s Linear Algebra?

[remote sparrow]

https://bookstore.ams.org/amstext-54/

[slow roost]

I do not, but in my experience sometimes when googling the title of a book for information on it, the literal top result is an upload of the book in question

but also, it’s a Dover book, and they’re cheap

[scenic sequoia]

Shilov is king if you are willing to struggle

[mortal iris]

Shilov isn't as much of a struggle imo as opposed to a Hoffmann and Kunze

But Shilov is great

[hasty sluice]

Do you have some examples?

[slow roost]

Golan looks like another good challenging LA book

the one called like All The Linear Algebra A Beginning Grad Student Should Know (If They Want to Stand a Chance Working with Me)

[vital bane]

Tsiolkovsky

[slow roost]

Konstantin Tsiolkovsky?

[mint atlas]

Where should i start if I want to prepare for olympiads? Are there any good introductory books?

[solar jewel]

there's an oly math server known as mods btw

[viscid remnant]

@mint atlas This and Evan Chens Blog

[mint atlas]

Thank you!

[normal crystal]

no piracy on this server
<@&268886789983436800>

[rapid fjord]

please dont share pirated resources here

[vital bane]

дa

[alpine ridge]

Hi, can someone suggest a good resource for solving IMO/Putnam style problems? Not to compete, just curious on how they think. I've been stuck for days trying to solve an A1 problem

[frigid aspen]

Any suggestion on books for formal logic

[flint apex]

guess can anyone suggest me books i want to start with mathematics as a hobby or like i want to do olympiad in future

[vital bane]

What is your background?

[novel sluice]

This is more of a question about textbook recommendations, but what would be some good texts for one to learn about Projective Representations of Lie Groups? I know the definitions but that's like nothing in the subject, so I'd like to know about a starting point. There's a book for Finite Groups written by Karpilovsky, but that's about what I could find.

[solar jewel]

brian c hall's quantum theory for mathematicians

[novel sluice]

Thanks, I'll check that out

[desert oriole]

does springer use printforce?

[naive lava]

depending on the depth you wanna go

you can check out weinberg's 2nd chapter, it has an appendix on this stuff

or

yuji tachikawa has notes on AT, which discusses projective reps in terms of group cohomology/universal bundle

[ebon plinth]

"Games, gambling, and probability : an introduction to mathematics / David G. Taylor, Roanoke College, Salem, VA." Without link . For the interest ed

@shadow_ta

[amber beacon]

algebra books : i knew de morgan and dis tributed law and nothing else which book your will recommend me

[molten gulch]

Any beginner algebra book should be fine, many review naïve set theory as needed at the outset

Also <@&268886789983436800> username

[wet sentinel]

"RequestANewNickname"

[shell zealot]

Does Apostol 1 treat integrals as a limit of sums?

[mortal iris]

Yes

[thick gyro]

what books would be good for an introduction to number theory?

[solar jewel]

an introduction to the theory of numbers is a classic

[thick gyro]

by Hardy?

[solar jewel]

yeah

it has recent editions too

[thick gyro]

does this number theory require calculus as background?

number theory book*

[solar bluff]

Hey everyone
I am a student at University first year of my master degree in stochastic
I have a small background in linear algebra and analysis
I am currently trying to study mesure theory as one of the important material in my semster and i am struggling a lot

Any help YouTube videos
Books
Anything to help me study my test is coming and i still struggling to understand it even start with the proof and exercise

[molten gulch]

folland

[solar bluff]

What is folland ?

[solar jewel]

author's name

book's name is real analysis

[solar bluff]

And is it a good way to start for someone who struggle with proof ?

[solar jewel]

no

[solar bluff]

Then what should i do ?

[solar jewel]

try reading the book

I can't gauge your skill level

[thick gyro]

have you read through an intro to proof book?

[solar bluff]

No

But based on all of that i don't think i have enough time to read all these books my test is due in 10 days

[shell zealot]

Can you provide a review of Apostol 1? I'm a newcomer to calculus.

I'd like some theory before practicing calculus questions

[hybrid sigil]

I like Burton and Niven, Zuckerman, Montgomery (for slightly harder book). And I for some reason don't like Hardy's book, I tried hard to like it though 🙂

Also note that Hardy's book has no exercises

[stable night]

Are these books related to math or overall recommendations

[proud osprey]

You can ask about other kinds of books too

[shell zealot]

may I have a review of apostol 1 please?

[versed portal]

He first introduces integrals with step functions and uses that to go to more general functions

[versed portal]

in what sense?

[shell zealot]

As a first introduction to calculus before moving on to a problem book

[versed portal]

do you know calculus? and what do you mean a problem book? Apostol has lots of problems

[shell zealot]

Problems as in the typical manipulation questions

i've only got the basic idea

[versed portal]

what are those?

[versed portal]

like?

[shell zealot]

I have a list of formulae, and I plug them in by identifying problems into predetermined patterns

[versed portal]

well then apostol will be very different

[shell zealot]

Right, so I want the theory before moving into a problem book

[versed portal]

take a look at his book you will see that before any calculus you have field axioms order axioms etc

[shell zealot]

what prerequisites does apostol 1 have?

[versed portal]

I think if I understand you correctly your problem book is just full of problems where you don't really think just plug and chug. If that is the case I think Apostol would just be enough

[versed portal]

idk probably know how to write proofs but I think you can learn it on the way

A curious and determined mind

probably most important prerequisite

[shell zealot]

Thank you

how long will I need to go through it?

[versed portal]

idk I am still going through it

start reading and you will be able to make some sort of estimates

[shell zealot]

I did some preliminary reading

I need to read more

[versed portal]

ok

[shell zealot]

can one solve the unsolved problems of Apostol 1 with the provided theory?

[versed portal]

wdym?

[shell zealot]

exercise questions

[versed portal]

yes

[remote sparrow]

any springer books whose physical copies are on sale for $23.99 that y'all would recommend?

[ripe condor]

hi all is there a field/undergrad course in math that teaches how to formulate real world phenomena into mathematical models/systems of equations?

[daring wolf]

silverman ec

because elliptic curves are

[radiant marlin]

the field is called applied math

unless you mean something more specific

[wet sentinel]

what about the ring

[sage python]

Elliptic curves are excellent

[daring wolf]

true

[wicked fractal]

I recommend this too

Still waiting for my EC book

[craggy notch]

Okay can anyone recommend the best book/source for like basic topology

[solar jewel]

topology by munkres

[craggy notch]

Thank you!! I’ll go take a looksies

[vestal dust]

Can anyone recommend a nice abstract algebra book for beginners

[vestal dust]

Im currently reading this one

[mortal iris]

Good book. A bit dry in its presentation as opposed to a Spivak but solid nonetheless. Starts off from fairly basic things and is pretty rigorous. Close to no plug and chug. Not recommended if you don't have an inclination towards abstraction and proofs. It does develop the theory intuitively to begin with but the language is quite formal so a beginner will need to spend quality time to understand stuff.

[turbid quest]

I'm going into my senior year, and I am starting to realize how much I don't know for the title "Senior as a Mathematics major." One of the set of basic concepts or ideas I am especially ignorant of is the work of Euclid on planar Geometry, which sounds absurd to say. I have been looking it up for a minute or so, and it seems to be segmented into 13 parts, and each part has a collection of propositions that are proven. The specific version I was looking at was on claymath.org. I would appreciate it if anyone that knows about Euclid's work on planar geometry could help in finding textbooks that encapsulate or even translate his work. 🙏

Or is the version on claymath.org sufficient to study?

[wary nacelle]

What books are good for complex numbers in geometry?

Is the "Complex numbers from A to Z" by Titu good?

[solar jewel]

yes it's very good

[wary nacelle]

Thanks

[slow roost]

Lee’s Axiomatic Geometry is a nice modern treatment of that material, based on Hilbert’s reformulation

I think you can get a full translation of Euclid, too

[vital bane]

What books are good for becoming disciplined and doing all your work on time?

[turbid quest]

Okay I'll definitely look into this. Thanks

[turbid quest]

Nice bio btw 😂😂😂

[vital bane]

Titu mentioned

[wary nacelle]

Even if there were such books, i'd procrastinate reading them

[wicked fractal]

You think such a book would help? You'd just procrastinate reading it or even worse give you a toxic relationship with what you do

[gray gazelle]

there's discipline, and then there's tricking your brain. deadlines have a pretty real psychological effect. accounting honestly for your time can also help (because generally, no one is happy to write "scrolled bullsh*t for 2 hours" when they know they intended to do some work). it probably feels like discipline because you "know" you won't enjoy it. if you enjoy doing math once you're into it, but don't like starting it, you'll just have to make it easy to start. rather than pulling out a book, pulling out a laptop, getting a notepad or whatever, just have all that stuff set up on a clean desk, maybe even a problem on a screen visible from across the room, and you'll probably start doing it way more often. I'd consider this like tricking your brain with bait; if it doesn't work, maybe you can turn it into a game and lock certain rewards behind solving certain problems or something

there's definitely real answers to this problem, but idk if I've ever seen a whole book on it unfortunately
a deadline can very easily turn into a bunch of rest time + the minimum amount of time you can do the thing
if you add a reward at the end, or make it fun to start, or stay accountable to milestones, etc., that can change the situation mentally

[long cloak]

Is there any book about Conic Sections?

[mortal iris]

Books don't cut it, but a clever use of reinforcement is helpful in practice. Reward yourself properly for meeting your ends or incentivise to do so by conditionally avoiding some unpleasant chore. Beyond that it's about sticking to your word so hold yourself accountable. Helps when the chore itself is for another person or so, making you accountable for someone else if you're not accountable to yourself.

[mortal iris]

For an introduction, Stitz and Zeager's Precalculus (Ch 7 and 11 in particular). For more dedicated material, Pogorelov's Analytical Geometry (up until he goes into quadric surfaces).

[mortal iris]

I treat myself to biryani every week after successful completion of my weekly tasks that I set for myself. When I am unable to do them I don't get biryani. That makes me motivated to do them.

[muted quest]

A book recommendation for actual pre calculus concept building and problem solving

[mortal iris]

Stitz and Zeager

[muted quest]

How would you rate it's difficulty out of 10 I don't want anything that's very hard I am justa freshman in highschool

[molten gulch]

stitz zeager

[molten gulch]

Your year doesn't matter, book difficulty is subjective for the most part, it's free so just go take a look at it

https://www.stitz-zeager.com/Precalculus4.pdf

[muted quest]

Ohh thankss soo much @molten gulch @mortal iris

[trail void]

biryani with potatoes or without?

[trail void]

ngl i feel that fictional fantasy books help you more in regards to this than the so called "Practical" Books

but i guess you can read any book on habit if you want to get a practical routine

i did read "Atomic Habits" and despite some narratives i do not personally agree with, you are more than free to read that book.

[vital bane]

Are you Bengali

[vital bane]

They kind of do honestly

[vital bane]

Yeah I've heard of it, I need to check it out

[vital bane]

It's not exactly chores that I sturggle with, but consistently putting in effort and learning all the things I want to learn over the course of several months, things like measure theory, module theory, QM etc

I think the main problem is I've conditioned myself into procrastinating like browsing reddit, watching youtube, chatting on discord etc. that doing these things take 0 effort or even less than zero effort meanwhile putting in effort into things I actually want to do becomes very difficult

For the last two days I've actually been sitting down and studying properly so that's good but for the past 3 weeks I did essentially nothing all day long

[vital bane]

🥀

[vital bane]

Yeah being organized definitely helps

[trail void]

not at all

[olive wraith]

Yo

So?

[vital bane]

Parabolic curves and Hyperbolic curves when?

[compact ore]

i need a resource on conic sections

they never taught them at my high school

preferably something fairly fast paced—i'm in my 3rd year of math undergrad

it could be like a chapter of a different book, that's fine too

oh also quadratic forms seem to be important and related

[trail void]

scroll up a bit

[trail void]

.

[compact ore]

lmao

thank you

[trail void]

youre welcome

[mortal iris]

Depends on my mood. I am half Bengali so I did grow up on it but I'm also Half-Tamizhan and we get completely different kinds of Biryani down there. And I presently reside in a place where Hyderabadi (the supposed standard) is more popular.

[mortal iris]

You should give it a try. No other style of biryani it would work for (maybe to a degree Karachi's).

[mortal iris]

You need a digital detox.

[wet sentinel]

read math posts on reddit, watch math vids on youtube and chat about math on discord etc.. and your problem will be solved fr

[gray gazelle]

it's easier to start quick some random scrolling and get dopamine from it. ye, being organized makes it easier to get that same dopamine from succeeding math
it is 100% a psychological problem with psychological solutions imo

[vital bane]

I have tried it lol that's why I asked my follow up question

[vital bane]

That's what I used to do 🥀 instead of actually working through books to become better at math 🥀

[vital bane]

Yeah 100%

[vital bane]

Real

I gotta throw my phone and PC into the ocean

I'll send physical mail to profs asking for a summer internship

[wet sentinel]

i mean i am not one to talk

[vital bane]

no emails

[wet sentinel]

i am much worse

[vital bane]

Sure buddy

Keep thinking that

(I'm a million times worse than you 🗣️ 🔥 🔥 🔥 )

You stand no chance against me

[wet sentinel]

vro thinks that its a contest about who is the worst 🥀

[mortal iris]

Pretty sure Germans appreciate this lol. So try your luck there 😂

[vital bane]

Casual procrastinator meets competitive procrastinator

ranked procastination

[wet sentinel]

[mortal iris]

What a nice use case of the rank-nullity theorem

[wet sentinel]

a random and possibly a vague question, what are the prereqs of ODEs? what about PDEs?

[vital bane]

You mean rigorous ODEs and PDEs?

afaik for ODEs it's lin alg and anal on R^n and for PDEs you need some functional analysis

Wobolev Spaces

[daring wolf]

nothing

use noggin

[mortal iris]

ODEs: Real Analysis and Linear Algebra.
PDEs: Functional Analysis and ODEs.
(for rigorous exposure)

[mortal iris]

For an introduction, Calculus is sufficient. Linear Algebra is definitely helpful.

For both an intro and a rigorous exposure, knowing some topology can be pretty insightful too, especially when dealing with non linear systems.

[wet sentinel]

by intro here you mean numerical/computational?

[wet sentinel]

i see

[wet sentinel]

ohhhh i see

[vital bane]

use noggin mfs when I ask them to prove the generalized hodge conjecture

[wet sentinel]

well then what would be the prereqs of functional analysis

[vital bane]

some measure theory

[wet sentinel]

i assume intro RA and LA?

[wet sentinel]

[vital bane]

and LA yeah

LA is trivial

[wet sentinel]

well then what are...

[vital bane]

(I almost failed LA last semester)

[wet sentinel]

thats probably just intro RA

[vital bane]

Ja

[vital bane]

Understanding Analysis by Stephen Abbott

Yes, specifically that book

It's too based

[daring wolf]

LA is just QCoh(Spec k) where k is a field

[molten gulch]

Quasicoherence moment

[wet sentinel]

side note: someone asked me about ODEs and PDEs thats why i asked, ofc i wont study either of them

after all i am not analysis pilled :chad:

[vital bane]

Be like Grothendieck

be analysis pilled

[daring wolf]

real

[vital bane]

"Grothendieck is my favorite analyst"

[daring wolf]

Grothendieck did a PhD in functional analysis iirc?

[vital bane]

I think so yeah

he started off doing FA

[dapper root]

Tensor product

[daring wolf]

what i remember is like he broke some unsolved problems in functional analysis and then moved to algebraic geometry

[vital bane]

Grothenproduct

[daring wolf]

[vital bane]

More like Chmanono

[dapper root]

Before he really moved to AG he wrote Tohoku and changed homological algebra

[vital bane]

Grothendieck invented Touhou?? Based

[idle mortar]

the goat

[wet sentinel]

vro is on another level

[idle mortar]

I consider Dirchlet one of my favourite mathematicians because of this

Dirchlet Approximation Theorem
https://en.wikipedia.org/wiki/Dirichlet's_approximation_theorem

[vital bane]

Weierstrass Approximation Theorem solos it tbh 🗿

powerscaling theorems

[remote sparrow]

as it happens, perko's ODE book is on sale on springer

[wet sentinel]

ohhh i see, tysm for the info

[shadow vector]

does arnolds ODE book require analysis?

[indigo siren]

Read the Martian

It’s actually a fire book

[foggy quest]

For ODEs, you typically just need to know calculus, but you will be introduced to or need to know real analysis and linear algebra for some of the more advanced topics in an introduction like existence and uniqueness theory and vector fields. See "Introduction to Differential Equations" here: https://mtaylor.web.unc.edu/notes/math-524-second-semester-ode/

[foggy quest]

For PDEs you just need measure theory. You can learn topology and functional analysis on the way, since you don't need that much for PDE

[mortal iris]

Numerical work to some degree would still require functional analysis. By intro I mean linear ODEs and PDEs by well known equations (Waves, Heat, Schrödinger) as opposed to in full generality.

[mortal iris]

Better if you know it. But Calculus and Linear Algebra is sufficient.

[wet sentinel]

I see, tysm for the explanations and recommendations @mortal iris and @foggy quest. have a great day/night both of you

[thick gyro]

i'm late to this, but thanks

[odd cargo]

math problems highkey be spiking my cortisol

i get unimaginably frustrated at them because im stuck in this perpetual cycle of simple mistakes

no wonder all these mathematicians got vegeta hairlines

[frozen perch]

“Are you ever put into a depressed state when you can't solve a math problem? Well, there's more coming." - Tom Wieting

[odd cargo]

horrendous hairline

[half vigil]

how little time would i be able to complete hoffman kunze in

[odd cargo]

as fast as you want, but cant guarantee you'll "learn" much if you do.

honestly if you want to complete chapters very quickly, just jump directly to the questions in each chapter and if you dont get something, look through the chapters material

probably bad advice but its not like you're preparing for an exam or something

[half vigil]

👍

would you say 5-6 months is reasonable?

[odd cargo]

if you're consistent, you could finish any book in half a year.

[half vigil]

thank you

[vital bane]

Learn functional analysis to study PDEs ❌

Learn functional analysis to apply it to Algebraic Geometry ✅

[mortal iris]

https://tenor.com/view/vegeta-vegeta-rain-vegeta-sad-dbz-dragon-ball-z-gif-2167897810151461845

[remote vortex]

<@&268886789983436800>

[wet sentinel]

you are a real chad

[rapid fjord]

was it the "robe" user

[remote vortex]

Yes, forgot to use the reply feature

I mean, the anime GIF is also banworthy

[rapid fjord]

no worries, theyve been banned i believe

[sage python]

Well did Grothendieck intend to do AG? I thought Serre kinda recruited him for that

[vital bane]

I'm not sure

[chrome mica]

Hey, what do you think of calculus made easy? Of course I would then need a more "formal" book but just to start 🙂

https://www.reddit.com/r/interestingasfuck/s/HwAPXDZOr2

This bit sounded good

[rich sun]

Isn't calculus already easy enough

[chrome mica]

Also, I will see 3blue1brown😊

[chrome mica]

This explains more the why, I think

[obtuse estuary]

sure, why not? part of developing mathematically is understanding what books are digestible for you, both in treatment and style, and being able to understand that will help you find that type of literature faster in the future too

[rich sun]

I have not read the book, so don't take me too seriously, but just from what I have seen here, this seems like the kind of exposition that obfuscates the actual meaning of the contents in calculus in order to make them a bit more approachable

[chrome mica]

What do you mean "obfuscates the actual meaning"?

[rich sun]

It does not tell you the rigorous definitions and uses justifications that seem legit but are actually not

For example, I have seen this part of the book

"This justifies the procedure" when it really does not

[chrome mica]

Well, I don't know then🫠

[rich sun]

This might also affect your algebraic manipulation skills in a bad way

[chrome mica]

I want something that explains the intuition first

Better to just go with thomas or steward like they said in help

[flint crane]

Hey guys could u recommend me a good book on calculus 1

[rich sun]

In my opinion, Stewart does a better job doing that, but everyone has their own preferred treatment and style, as Bernefan mentioned

[rich sun]

Stewart's Calculus

[flint crane]

awesome ty

[obtuse estuary]

I think @chrome mica is trying to learn calculus -- unless I'm mistaken -- not analysis. If they are looking for an intuitive explanation in calculus, rather than a formal proof, then that level of rigour is not necessary at this stage (and algebraically, I see no tangible issues, although you may disagree).

This is pretty much the level of rigour we had in high school, and I studied on a relatively rigorous program. It didn't interfere with me stuying these concepts at a more advanced level, so I don't think there are issues with picking up this text as a supplementary reference, which was OP's initial intention

But, I do recommend Stewart's book as well, I think that is a great main reference.

[molten gulch]

I think Thomas or Stewart are fine at this level, if/when they inevitably wish for more rigour, a text like Amann and Escher, or Zorich, or Rudin, or Abbott, or whichever of the dozens of analysis texts piques their curiosity should be fine

[obtuse estuary]

Yeah, and if they want rigour at an already-accessible level, the 3b1b videos, as they mentioned, will probably do the job. But those recommendations are great too

[chrome mica]

Yes, I'm trying to learn calculus, then I will go to analysis

[rich sun]

Stewart is a calculus textbook (rather than analysis) and still treats limits adequately as opposed to the excerpt I sent, where they do not even distinguish between difference and differential quotients.

[molten gulch]

Mhm, personally I learnt out of thomas, liked it more than the excerpts of stewart I've seen, but if I'm being completely honest, I don't really like most calculus textbooks in general

Like even to look up calculus facts these days I look them up in analysis texts 😭

[daring wolf]

i don't like calculus texts because it's just too yappy

tl;dr

[obtuse estuary]

I completely agree, that reference isn't the best by any measure. But sometimes you can benefit from just being exposed to an idea in motion, even if its development omits details (but is logically sound enough to make you believe it is true). I think to have a meaningful discussion we ideally would know OP's background in math. The safest option is probably Stewart, but if that is too challenging, which could be due to gaps, etc. then I think the 1910 textbook isn't all that bad as a supplement

[rich sun]

I don't mind using (and would highly suggest to use) other complementing resources / references when learning calculus. But my first impression of "calculus made easy" in particular is not very good.

[wet sentinel]

only if there was a calc book by lang, things wouldve been different fr

[daring wolf]

i mean there is rudin

[wet sentinel]

so this is considered calc these days huh, i wonder what intro analysis looks like

maybe RCA?

[obtuse estuary]

Oh, I haven't read Thomas, is it that much better? I used Stewart for multivariable calc, but yeah, it's kinda weird to go back to (most) calculus books after having gone through analysis. I self-taught using khan academy though, since I couldn't get my hands on real books at the time

[molten gulch]

Mehhhh I just prefered the writing style changes (what small ones exist between calculus textbooks which are homogenized to hell and back anyway)

[wet sentinel]

imo all of these calc books are the same

whether its thomas or stewart or whatever

because there isnt really room to be different

[obtuse estuary]

Ah, yeah fair, respectable

[obtuse estuary]

equivalent up to understanding

[wet sentinel]

like in intro RA the author can decide to treat things more generally by doing things with metric spaces from the get go (for example rudin) or avoiding that (like abbott), but in calc textbooks there isnt much option

[obtuse estuary]

i think abbott does metric spaces in the additional topics section, right?

[molten gulch]

Spivak being the big exception to that hegemony

[molten gulch]

Let me check

[daring wolf]

real intro real analysis: papa rudin

[molten gulch]

yea he does

[wet sentinel]

yea, from what i have seen its just one section tho

rudin does have a full chapter on the topology of metric spaces

[obtuse estuary]

i like ross, he talks about metric spaces when discussing convergent sequences

[wet sentinel]

its chapter 2

[obtuse estuary]

oh

[wet sentinel]

and he then treats limits/continuity on metric spaces for the most part

[molten gulch]

[obtuse estuary]

I haven't read rudin yet, that is a task I plan to embark upon cry during my summer term

[wet sentinel]

spivak doesnt know what he wants from that textbook fr

a bit of calc and a bit of analysis, vro didnt want to write 2 textbooks so he decided to do a mixture

[chrome mica]

Lmao, no😂

[molten gulch]

There is

https://www.amazon.com/First-Course-Calculus-Undergraduate-Mathematics/dp/0387962018

[wet sentinel]

[wet sentinel]

@daring wolf look here

maybe this book is calculus on schemes just like the one you once sent?

[vital bane]

Abbott does too

Chapter 3

[chrome mica]

People in reddit and chatgpt recommend Abbot

[vital bane]

Yeah it's called "Topology of R" but like every theorem and its proof holds for a general metric space as well

just replace |x - y| by d(x, y)

[molten gulch]

Don't use GPT when you're literally IN A BOOK RECOMMENDATIONS CHANNEL 🤦‍♂️

[vital bane]

Don't use chatGPT for learning math 🥀

[chrome mica]

I had already used it before going here. But I want to see what people think

[wet sentinel]

lies oh i see

[vital bane]

Holy opencry gang

[hybrid sigil]

What does this emoji mean? I see it used quite often recently 🙂

[vital bane]

It's a wilted rose

[wet sentinel]

yea actually there is a gang and that disturbs me

[hybrid sigil]

well I can see that 🙂

[wet sentinel]

bring the copypasta

[chrome mica]

I think is sadness

[vital bane]

it's a meme, it means you're basically disagreeing with something

or sadness (but not genuine)

it's similar to the sarcastic usage of "💀"

[wet sentinel]

its left as an exercise to the reader to figure out the meaning of this

[chrome mica]

I like💀

[vital bane]

gang theory

ali what do you even do 🥀

I thought you were a grad student or something

[molten gulch]

He does n*mber th*ory

[molten gulch]

He's a first year I think

[wet sentinel]

i dont do

[vital bane]

first year of elementary school

[vital bane]

Me

[chrome mica]

POOR NUMBER THEORY😭

[wet sentinel]

wait fr?

lmao

[vital bane]

Lmao yeah

[wet sentinel]

no i just finished 1st year undergrad

[wet sentinel]

maybe the grothendieck pfp is giving me aura fr

[vital bane]

I thought I saw you helping out in one of the adv channels

maybe I misremembered because you always hang out in #advanced-lounge

[vital bane]

in Brazil?

[wet sentinel]

it might be one of the very rare occasions when a question is asked in #groups-rings-fields and #real-complex-analysis which i can handle is asked

otherwise you would see me in these channels but i would be the one asking not answering

[vital bane]

I should probably help out sometimes in those channels as well

[wet sentinel]

yea

[vital bane]

But I can't even help myself how am I gonna help others 🥀

[wet sentinel]

wait lets go to #serious-discussion or the other server or something because otherwise mods will ban us

[vital bane]

What is no access?

🥀

[wet sentinel]

nah you are a king

[wet sentinel]

ah you have studying!

it was discussy 2, alright then lets move on to the other server

[vital bane]

let's go to the gang hideout

[mortal iris]

Just refer to Paul's Online Notes if you're just starting off. They're solid. Though, I personally always recommend Spivak if you're gonna buy a Calculus book.

[rich sun]

this is apparently calc in 1910

[chrome mica]

Isn't Spivak too rigorous for a first dive in Calculus?

[mortal iris]

Honestly, it is not. It is pretty much the only way one should get introduced to Calculus as opposed to a myriad of misunderstandings stemming from a purely intuitive text that focuses on mindless problem solving. For one thing, Spivak does convey the intuition as well but more importantly does so with a healthy dose of rigor. Most of the problems are gentle (avoid the starred ones on the first go around as they can be pretty challenging) and working through the theorems in the text will help you understand Calculus better than any text like Stewart or Thomas and the likes.

The good thing is that Spivak doesn't expect you to have gone through a course on proofs. It is a beginner's Calculus text. The snowflake Calculus texts are only good for engineers and economists.

Another alternative is Apostol Calculus Vol. 1. I'm not the biggest fan tbf since I find the presentation dry, but it is at a similar level to Spivak and I did my first course on Calculus using it. Was hard but valuable. Had to unlearn a lot of the BS I assumed was factual in high school Calculus.

[remote vortex]

To be fair he does outline most of the ideas in the actual text

[molten gulch]

I agree, I just found it a touch funny out of context

[chrome mica]

What is the difference between Spivak and Abbot?

[daring wolf]

I'd just read rudin over spivak

or yeah abbott

[rich sun]

"myriad of misunderstandings stemming from a purely intuitive text that focuses on mindless problem solving" describes it well

[chrome mica]

Do you like my obsidian? :3

Yes, there is portuguese mixed with english, lol😂

[hasty sluice]

What do you use for latex?

[chrome mica]

Obsidian uses MathJax, which is a subset of latex

If it is inline I put stuff between $$, if it's in block then i put between $$$$

It's this that I use and I customized it https://obsidian.md/

[cursive burrow]

some book have integral chapters and rules all of it

[rich sun]

at least the author "apologizes" after all of this

[mortal iris]

Spivak's is a Calculus text. Abbott is an Analysis text. As such Abbott covers much more material than Spivak. Especially around Sequences and Series and some basic Topology on the real line. There's a little more time spent on integration too.

[chrome mica]

How is it that there is no Euler emoji? How can such a sin be comitted?😂

[mortal iris]

Just cos

[chrome mica]

NOOOO, I'VE FOUND ONE IN ANOTHER SERVER ALSO CALLED MATHEMATICS BUT I CAN'T USE IT BECAUSE I DON'T HAVE NITRO😭

[rich sun]

nice colors

[chrome mica]

Thanks 🙂

[rich sun]

btw do you know of a way to use \( \) and \[ \] instead of $ $ and $$ $$ in Obsidian's MathJax?

[chrome mica]

What do you mean? You want to replace the $$ by that?

[rich sun]

yeah, use LaTeX delimiters instead of TeX delimiters

[chrome mica]

Hmm I'm not sure you can

Oh wait, I found something https://github.com/loglux/fix-math-for-obsidian

Oh wait, it's not this...

[rich sun]

Yeah, but the reason that plugin has been developed is because of the same issue

[chrome mica]

Do you know a compendium of proofs? I know proof wiki but it seems very incomplete

I ought to collect them alllll ahaha (ok, not all but many)

[solar jewel]

maybe a group effort can accomplish this

[chrome mica]

Yeyyy

[rich sun]

For starters, have you checked loch's pdf #proofs-and-logic message or hammack's book of proof https://richardhammack.github.io/BookOfProof/Main.pdf ?

[chrome mica]

What I want is a wiki of proofs, not how to do proofs, I already have How to Prove It by Velleman 🙂

[mortal iris]

https://tenor.com/view/ash-ketchum-hat-flip-pokemon-gif-3660604446364397912

[chrome mica]

Yeahh

[umbral field]

a wiki of proofs? that exists https://proofwiki.org/wiki/Main_Page

[idle mortar]

a book for optimisation theory

:>

[solar jewel]

I have recommendations but can you be more specific?

[pine tundra]

Nocedal Wright might be the way to go, at least from what I've heard

[chrome mica]

What is that white square at the end?

[trail pier]

qed

[chrome mica]

And the black?

[trail pier]

you make it black when you understood the proof

it's like for the reader

[chrome mica]

So the white square is when you, for example, proof a case and then the black one is that the main proof is done?

[umbral field]

white square vs black square is purely a typographical preference

[remote vortex]

Someone here redefined the qed symbol to be a black and white version of

[molten gulch]

I think @tribal crow has the code for that, I forget, though

[vital bane]

Someone here redefined the qed symbol to be a black and white version of

[slow roost]

I like that it's also called a "tombstone".. like RIP me after the proof I just tried to read

[obtuse estuary]

April 2026.

[mortal iris]

https://tenor.com/view/the-undertaker-tombstone-piledriver-johnny-stamboli-wwe-smack-down-gif-10986044

[molten gulch]

<@&268886789983436800>

[desert oriole]

tuff

[desert oriole]

.

[wide musk]

hey what do y'all think about coxeter's geometry revisited

[runic rover]

what happened

[molten gulch]

A spammer showed up

[chilly willow]

Hello to everyone! I'm finishing Axler's Algebra and trigonometry and want to study Calculus. There are trillion books about calculus, but I'm deciding between these three: Serge Lang A first course of Calculus and Multivariable Calculus, Purcell Calculus or Calculus in Context by Callahan. If I had to start today, I would use Purcell's volume (its in my native language and it looks really nice). Should I use Lang's or Callahan's? should I use another one?

[bronze lava]

How much do you want to understand from the material vs just learn the techniques

Like do u want it closer to just what you need to know for applying it or something halfway to what a real analysis course would look like

[chilly willow]

That's an awesome question. The book I'm using to precalc, which is Axler's, is a mix between actually understanding and just learning the techniques, so I guess I want something similar. It might be more useful to learn the techniques first, though

[bronze lava]

The main sticking point is whether you want to see the real definition of a limit and work with it

[chilly willow]

what would be the recommendation? maybe I can try a book intended to ''understand'' and another intended to apply? and see whats better for me now

[bronze lava]

My recommendation would be one that isn't on the list (aops calculus). I opened the one you linked to and it's very much on the side of "here are these table of rules, apply them" and the first few chapters felt like filler junk tbh (everything up to where they defined the derivative by giving a table of rules)

It has harder problems but you can skip competition focused ones if you want

[chilly willow]

I have to clarify that I'm a beginner. I started with pre-algebra on may 2025 and now I'm just finishing precalc (maybe this context helps)

[bronze lava]

Aops calculus is a bc-calc level course textbook

Do you have any idea how deep you want to study math?

[chilly willow]

I'm starting a degree on economics next year, and a degree on maths too (in the first year I'm not going to learn proofs or anything like that)

[bronze lava]

I checked Purcell and it looks better than Callahan to me

[chilly willow]

Maybe I can start Purcell + AoPS?

[bronze lava]

I just checked and I would say level of rigour is aops > Purcell > lang > callahan

[chilly willow]

interesting, very good insight

[bronze lava]

I really really dislike Callahan's approach and I think if you want to go further into math it'll hurt

Any of the others are fine

[chilly willow]

Oh ok, thats good to know

thanks a lot

I think AoPS volume is very interesting, I'm gonna check it

[bronze lava]

the more rigour you get into early the less the jump will be later too

[wet sentinel]

stewart/thomas might be good too

[chilly willow]

My idea was to do something like Purcell > Proofs (Hammack) > Spivak

[chilly willow]

As far as I know, Thomas = Stewart = Purcell (i think)

[bronze lava]

2nd time around i would just get a real analysis text

[wet sentinel]

once you do calc i think it would be a waste of time to try spivak

at that point you would want to pick up a book on real analysis if you want

[bronze lava]

i have heardc that aops calc and spivak are pretty similar

[wet sentinel]

if you dont want to study math beyond calc, some linear algebra and whatever you need for you economics degree then you might as well avoid real analysis to begin with ig

if you are doing it because it might be useful for your degree then i doubt that it is

if you are doing it to enjoy/study more advanced stuff later which you enjoy and not for the sake of your economics major then sure

[chilly willow]

So, I'm doing this: I'm gonna use Purcell as my main textbook while testing AoPS

[chilly willow]

I'm studying both economics and maths

[bronze lava]

ye thats fine. you can also just read thru the first chapter of both and go with whatever hits your groove

[wet sentinel]

imo spivak is kinda useles, but thats just my opinion

mainly because its somewhere between calc and analysis more or less

[bronze lava]

i self learnt out of aops calc and it made intro analysis a breeze

[wet sentinel]

tho i havent tried it to see to what extent its mixed

[chilly willow]

why is different compared to the normal calc. book?

[wet sentinel]

but it sounds like a calc book is better than spivak and an analysis book is surely better

i am not sure about the calc book part but for the analysis book i can say that i am certain

[bronze lava]

mm the main reason is that it does not try to skirt around delta epsilon because its hard to understnad for ppl

a lot of calc books just try to teach u to go by intuition except real valued functions do not behave well at all and your intuition will lead you astray all the time

[wet sentinel]

ah i see

[hallow hull]

Hello

[slow roost]

yeah, it's in an awkward place of being way too hard for almost anybody to use as their actual first calc book, and too unorthodox to use as a real analysis book (and is consequently rarely assigned as the text for that course)

[vital bane]

Based Re:Zero fan, I hopefully finish reading Arc 4, 5 and 6 before April 2026 🙏

[slow roost]

but for someone who's gone through those already and wants to go back and refresh/strengthen their calc, it's an outstanding resource

[wet sentinel]

right

[wet sentinel]

hmmmm yea that might be reasonable

[ebon plinth]

You'll be unable to predict a recession and unable to pickup social cues afterwards

[chilly willow]

and?

[ebon plinth]

Don't worry about it

[chilly willow]

this is kinda offtopic but I don't even think maths are particularly useful to economics. Are to mainstream econ. but not to the discipline itself

[vital chasm]

There was a time where I had to dabble in mechanism design, and there was quite a bit of analysis in there

[chrome mica]

I hope you create some type of a more ethical economics because the current one sucks

Fuck you capitalism

[chrome mica]

You know what I'm excited to? I'm excited to start discrete math because when I was in my computer science degree I liked it very much (although my first contact was "What kind of math is this? It's so weird, lol")

[obtuse estuary]

🙏 🙏

[weary remnant]

Hey guys any precalculus recommendations? Not that watery a bit of balance between dry and something, also fun to do I don’t like stewarts or others because they overexplain

I would like for sourdrop to recommend his legendary recommendations @remote sparrow sorry for pinging

[vital chasm]

Khan academy and skip topics as necessary

[weary remnant]

Nah man I am in 9th grade

Khan’s precalculus starts at like something

Which I am not familiar with

Also I like the precalculus book which starts with like exponents and then etc

[vital chasm]

Idk what 9th grade does, not from where you are, good luck finding resources haha

[remote sparrow]

#book-recommendations message

[weary remnant]

Most reddit recs are crap

[weary remnant]

Will that be enough to do thomas calculus or spivak?

[remote sparrow]

yeah

[weary remnant]

I heard the trig is bad

[slow roost]

I just learned Axler has a precalc book that looks pretty good

it’s called Algebra and Trigonometry

his linear algebra book is extremely popular, so this one is probably also good

[weary remnant]

The solution manual is hard to find

Also the problems have no odd problem solutions like it said

Only exercises

[slow roost]

not having a solution manual is a problem of the past

you can get help right here… or by… other means

[rich sparrow]

hello, is there a good book about group theory, i started learn abstract algebra and i really like the group theory topic there!

[slow roost]

greetings! big-time, there are a lot of really cool books on group theory and/or other abstract algebra

my first one is a bit of an old-school classic, Herstein's Topics in Algebra

aside from the very awkward usage of reverse function notation in some places, like (x)f, I like it a lot

[rich sparrow]

same as in my uni book hahaha

[slow roost]

I also really like the newer classic, Dummit & Foote

it is rather wordy, but I like that

I also really like Aluffi's Algebra: Chapter 0

it's less wordy and has very elegant presentations of things

with categories!

[rich sparrow]

thank you! , all the books seems very interesting.

[slow roost]

sure thing

finally, if you're interested in looking at a more "hardcore" and comprehensive reference text, two big ones are Lang's Algebra and Hungerford's Algebra

some people really love them

[rich sparrow]

thank you!

[chrome mica]

What the hell? Why?😂

[slow roost]

he writes “Algebraists often write mappings on the right; other mathematicians write them on the left. In fact, we shall not be absolutely consistent in this ourselves”

I guess the notation was less standardized in 1964 than it is now

but it has the advantage of the effect of a composition of functions happening in order left to right, the same way as written

that way for example if $g_1,g_2$ are elements of a group of permutations of a set, then $g_1 g_2$ is literally “$g_1$, then $g_2$”

[hasty eagle]

ManifoldCuriosity

[hybrid sigil]

I also like those books suggested by Mr Manifold and use them to study group theory. Additionally I can recommend Pinter “A book of abstract algebra” for a gentler and shorter textbook. It’s very readable and has exercises grouped in project-like problem sets

[slow roost]

oh yeah, Pinter is nice

[glass trail]

hi , are there any recommended books i should get when trying to expose myself to linear algebra that may include proof based as well ?

as a first time learner , preferably books that help introduce it as a topic

[viscid remnant]

See pins

[glass trail]

ah ok, thank you

[viscid remnant]

<@&268886789983436800> trolling

[rapid fjord]

did someone beat me to it

or did they delete themselves

[livid lintel]

I think it's the latter

[ember karma]

Making it easy for us to find you, are we

[rapid fjord]

okay someone actually beat me to it this time

[viscid remnant]

Mods can read deleted logs

[real marsh]

Sybau

[ember karma]

I don't know why they think that pinging us and deleting their messages, even when we see them delete them, will help their case

[chrome mica]

First I'm gonna go through Strang's book then Linear Algebra Done Right by Axler

[unique arch]

[chrome mica]

One is for intuition and the other for proofs

What do people think of Jay Cummings Real Analysis and the proof book? (which has a weird name)

[daring wolf]

L

[wet sentinel]

might be a waste of your time imo

tho if you want to do both then do as you like

[chrome mica]

Why? I want intuition🥲

[viscid remnant]

Linear Algebra done wrong also follows an intuitive approach, yet somewhat rigorous (it advertises as a intuition focused book though)

[wet sentinel]

i would say that using FIS alone is good

[wet sentinel]

maybe try it and see if its hard or no

[chrome mica]

I would run away from such a title, lol, but i will see it x)

[wet sentinel]

i would suggest that over axler tbh

[viscid remnant]

The purpose of the title is to have a non traditional approach

[chrome mica]

What is FIS?

[wet sentinel]

tho i might be biased because i dont really like axlers LA book

[chrome mica]

Why?

[wet sentinel]

friedberg, insel and spence

you can also check #book-recommendations message

it has a list of LA books with brief descriptions/comments

[chrome mica]

It doesn't have one "this book is very good" and then I get very undecided 🥲

[wet sentinel]

well just pick up a book with not too much/major complaints and one which you find nice/suits your tastes

[daring wolf]

<@&268886789983436800>

[chrome mica]

How can I put a pink thumbs up? It's cute, I like pink

[gaunt vigil]

not a recommandation, but, is that normal that i can't track the books i bought on springer 4 days ago

[daring wolf]

yeah

i ordered 2 books Dec 14 and was able to track the books last Friday

[gaunt vigil]

💀

[daring wolf]

they send an email when it's possible to track your orders

[gaunt vigil]

ah ok thanks

[weary remnant]

I tried.. the other means.. So I think I can get help from you🙏

[muted quest]

Can someone recommend a book about binary sequence that starts from basics and ends at intermidiate levels?

[sacred lintel]

Hi, Im starting preparations for IOQM(Indian Olympiad Qualifier in Mathematics), do you guys have any suggestions for books I could use to prepare? Thank you !

[weary remnant]

Morse code

[weary remnant]

Aops

[desert topaz]

I wonder why this guy is still gray name tag

[remote sparrow]

he also has a precalc book titled Precalculus

🤯

[chilly willow]

Hi! I'm currently finishing Axler's Algebra and trigonometry. Great book, I recommend it. He also wrote a Precalc book but both have the same chapters really

[trail void]

i second this, it was more preferable for me at the time than szeged as the latter seemed more of a reference book than one to learn from, i feel the trig is done better in the szeged book though! ^^

[astral meadow]

Aaah sniped again damn

[split portal]

Rest in pasta

[desert oriole]

https://link.springer.com/book/10.1007/978-3-031-55368-4 mentions martin shkreli

[desert oriole]

springer print on demand usually takes a bit longer

[wicked fractal]

Yes don't freak out

(Although I freaked out one day before my book arrived)

Hilarious

But finally got the bad boy

[remote sparrow]

show binding

[weary remnant]

But umm the solutions manual?

[chilly willow]

it includes the solutions manual

[weary remnant]

Students solution manual only

The problems aren’t included not even the odd ones

[chilly willow]

yes, but if you are a beginner you should skip the problems

are giga hard, if you don't know basic proofs is very very difficult

[weary remnant]

Not really a beginner I just wanna get into calculus soon

[chilly willow]

imo start Axler's book, do the exercises and select some problems

but your main study should be the sections and the exercises, later you can come back to problems

[vital bane]

He also has a real analysis book about measure theory and integration titled Measure, Integration and Real Analysis

[tired echo]

im gonna mail the mailman dog poop and nobody can stop me

forbidden objects in the mail are just a spook

obstructing my liberty

my liberty to mail people dog poop

[mortal iris]

What the actual f?

[chilly willow]

have you worked the book? were you able to do the problems? I personally not, I don't have proofs background

[weary remnant]

What chaps you in

[chilly willow]

8

[weary remnant]

Damn

[vital chasm]

Its probably bad to skip problems
You dont have to solve them but at least spend time trying

[chilly willow]

yeah true

[vital chasm]

Your brain does process problems in the background

Quite miraculously people often find problems approachable the next day

After a good rest

[weary remnant]

I also have this book by dolciani and had the instructor solutions manual

[chilly willow]

but if like me you dont even know what is a logarithm or a matrix and you are short of time, doing the problems is very very hard

[vital chasm]

Yeah thats ok
Its an exercise in thinking

[chilly willow]

totally

I did some problems though

[vital chasm]

The problems are there to get you engaged in the material
Solving them is a bonus usually

[chilly willow]

it was extremely satisfactory

[chilly willow]

I would just do Axler tbh, you can ask me if you have doubts

the inequalities chapter is terrible btw

[weary remnant]

These are the contents of the book Idk if its the same as a precalc one

[weary remnant]

Dolciani is also a good one from what I’ve heard online

[tired echo]

the lorax was an extremist manifesto

[chilly willow]

this looks good, I think either one is ok

[tired echo]

the same tired pro tree talking points

[chilly willow]

just try both and see which one is better for you

[vestal dust]

whats some cheap linear alg/calc textbooks that below 30 dollars

[vital bane]

real

[vital bane]

real

[lean badge]

"open-source" "preserved" "tasteful"

[humble spire]

morris kline calc

[wicked fractal]

Binding?

[remote sparrow]

how are the pages held together i mean

are they glued together?

[remote sparrow]

example of what i mean

[molten gulch]

is this a GSM?

[wicked fractal]

This one looks fire

[remote sparrow]

yes

[remote sparrow]

at least it was cheap

technically you could get it cheaper with lulu

[wicked fractal]

I get anxiety opening a fresh book cuz of these bindings

[remote sparrow]

they're trash i know

if the binding breaks you can complain to springer tho

i made a complaint for a book where one page was partially illegible and i got a new copy

[wicked fractal]

is that a thing

[remote sparrow]

yeah

[wicked fractal]

Anytime?

[remote sparrow]

dunno i found stories where they could get a copy months out

just save ur order number

[wicked fractal]

I have it saved

[rigid trail]

free extra copies hack

[wicked fractal]

I haven't opened the book wide open yet

okay i did open it

It's fine (mainly because I'm very careful with opening books)

I remember my friend had a similar binding for a book

She opened it fast and rip

game over

[daring wolf]

LMAO

[radiant marlin]

arent hardcovers better tho

my softcover seems fine too

[remote sparrow]

depends

[remote sparrow]

try asking her to file a complaint

[radiant marlin]

why are they so much more expensive though

[remote sparrow]

which? sometimes they only cost a bit more

[radiant marlin]

ok this is biased because not a super popular book (and also not on the springer website) but idk if the binders don't hold better why would you pay more money for two pieces of cardboard

like at least >15 bucks more is what ive seen

[remote sparrow]

you can stuff it in your bag ig

the cover won't wear down as much with repeated shelving and reshelving

[mortal iris]

No. I'm way beyond doing Precalculus but I am teaching it and those problems are not hard. Anyways, any form of advice to skip all problems at the back is just bad.

[chilly willow]

he could try some, I maybe exaggerated a little. Still, if you are a complete beginner who just finished an introductory algebra book without a teacher, those problems are not going to be easy. Maybe they are easy in general, but if you dont have a clue about how to start or where, its quite hard

That's why I did some in my own too, dont get me wrong

[mortal iris]

And nobody needs a proofs background to work out the simplistic proofs of a Precalc text. You are not expected to be rigorous or have said background.

[mortal iris]

Regardless of ease, one should make an effort. Math isn't easy and avoiding harder problems is not a good way to do things. It's a different matter if they were out of pocket and impossibly challenging problems.

And if you're on a platform like this, regardless of whether you are teaching yourself, you can afford to seek assistance.

[somber shore]

Chat what’s a good book for calculating Lie algebras? I have turned to the dark side (theoretical physics) realized I didn’t know the necessary math to do stuff, and I need Lie algebras because that’s what people told me

[rich sun]

What does calculating Lie algebras mean?

[daring wolf]

tfw Lie algebra is just vector space along with Lie brackets and asking how to calculate Lie algebras

[daring wolf]

I suppose he means given a Lie group, evaluating its tangent space at identity

[odd cargo]

im honestly shocked at how good the british curriculum is

[tender cobalt]

suggest really nice topology books other than munkre, im trying to find different perspectives

[midnight gulch]

i just saw this newer book which is from a categorical perspective https://link.springer.com/book/10.1007/978-3-662-70602-2

looks pretty interesting, its also on sale

[tender cobalt]

holy shit

"basic course"

but includes sheaves

wildd

[midnight gulch]

it looks like it just introduces the basics of sheaves

[tender cobalt]

the book is so short!

seems like problem solving based

like the author teaches you concepts making you work through

[midnight gulch]

yeah, a lot of the CTM series is designed more for courses/self study rather than as a reference

[tender cobalt]

wow pretty cool

texts like this is what i was actually looking for

Reading and reading with scarcity of exercises feel like rote learning

[midnight gulch]

unrelated but apparently this isnt a new book and is just a translation of the original 2015 one in german

[chrome mica]

Guys, what book or books should I pick for axiomatic geometry?

Idc if it's useless, it seems cool

[tender cobalt]

oo

[tender cobalt]

The only book I know is by John lee

[chrome mica]

I know Euclid and Beyond and the one by Velema but I want to know opinions

[hybrid sigil]

Four Pillars of Geometry by Stillwell seems to give an interesting overview:

[chrome mica]

Why are there many geometries and not one?

[hybrid sigil]

I am also interested in this question. Currently it looks like this book, Lee “Axiomatic Geometry”, Hartshorne “Euclid and Beyond” and Moise “Elementary geometry from advanced standpoint” should be enough 🙂

[chrome mica]

What about Velema?

[hybrid sigil]

Not sure, got it too, and Greenberg “Euclidean and non-Euclidean Geometries”, but haven’t looked at them yet

It’s Venema, btw, not Velema

[chrome mica]

Ops😅

[hybrid sigil]

AFAIU because you can change one assumption independent of others and the rest still holds, so you get consistent systems with very different results. And moreover it turned out that those new geometries are even very useful in applications like in Einstein’s relativity

[chrome mica]

Thanks

I'm gonna watch this video, seems cool https://www.youtube.com/watch?v=lFlu60qs7_4

Altough I don't like "hidden universes", seems too mystical, better "hidden math worlds" or something

[hybrid sigil]

The assumption (or “postulate” in Euclid’s terms) that varies is basically the one that if you have a straight line and point not on the line, then you can draw one line parallel to the given line

But you can say - I can have many parallel lines instead of just one. Or you can say: I can have zero parallel lines, not one.

And see what happens 🙂

[hybrid sigil]

Yeah, but then you won’t get that many views on YouTube, will you? You need sensationalist titles and clickbait 🙂

[chrome mica]

I almost didn't click because of that lmao

[vital bane]

You could also say you can educate a wider audience this way if you named it "Origins of Differential Geometry" not as many people would click on it and therefore wouldn't get to know this backstory behind it

[hybrid sigil]

Fair

[vital bane]

This is one of the reasons I love Vsauce, he used to make these cool videos and title them with a really interesting title like "How hot can things get" or "" which will get lots of people curious and he'll use that as an opportunity to talk about all the science and linguistics and philosophy related to that topic

[remote vortex]

Sure, but "hidden universes" is definitely overselling it

[timber mesa]

clickbait is a necessary evil when doing science outreach

[gray gazelle]

Any good book recommendations on the following topics:

• Effects of War on countries & communities
• Breaking down the psychology of killers

[vapid owl]

Can you guys recommend me a book to understand real analysis better especially sequence, series and continuity?

[native cradle]

A few books I've used , and a few books I've heard a lot about

1. Abbott

I've heard a lot about real analysis via seqeunces and series

[vapid owl]

Thanks, I needed this since I have a real analysis course in this semester and our professor teaches us from Baby Rudin and we don't understand anything

[native cradle]

rudin as a book for your first RA course ?

Sorry for the emote

I'll be using rudin too, but for my second RA course

[vapid owl]

No no it's okay you don't have to apologize

[lean badge]

since when was rudin supposed to be introductory

[native cradle]

Oh, bartle and sherbert too

[daring wolf]

idek i used it for first real math book

lmfao

[native cradle]

Pretty old, but good enough for basic problems

[vapid owl]

Funny enough I also have a set theory course too and it is not as bad as the real analysis course and we are using the first journey through logic for our set theory course

and it gets even funnier our professor literaly skipped chapter 1 of baby rudin and just jumped right into chapter 2

[native cradle]

okay, so to summarise
I've used abbott for seqeunces, real valued sereis, continuity and differentiation. Pretty good bookd
I've used bartle and sherbert for everything mentioned above but series, also nice.

My prof had a copy of Real analysis via seqeunces and series, so it must be a pretty good book

[lean badge]

strangely my first-ever uni course (supposedly before calc in the sample plan) used enderton

[native cradle]

I also do have copies of Tao, but personally not a huge fan

[vapid owl]

one day our professor told us if we want pass this course ( Real Analysis ) we have to memorize everything

[native cradle]

Now apostle does have REALLY GOOD problems, but don't use it for the first half of the sem atleast

sorry for the info dump 😭

WHAT

😭

RA is about understanding structure

[vapid owl]

no no it's okay you don't have to apologize

and here's the problem even if we try to memorize the professor just modifies some of the questions of Rudin and if I try to understand real analysis I don't understand anything so it is a lose lose situation for me

[vital chasm]

for a text like rudin you'd spend most of your time reading the theorems and trying to understand it, at least make every line make sense, and try to play with the theorem (what if i drop this hypothesis, can we prove stronger things, etc), the exercises arent as important

the exercises in rudin arent exactly the best

just read through them and make sure you understand what the questions are

[vapid owl]

also another problem I have is that whenever I read the proofs sometimes I don't understand them or I just feel like they came out of nowhere

[native cradle]

Here's my advice: NEVER memorise anything but the axioms in RA

[vital chasm]

then you gotta ask for help

talk to your prof or friends or ask here

[dim pendant]

I would say that memorization in early undergrad isn't a big deal but it should be replaced with intuitive understanding with haste as one learns the theory better

But you definitely have to get going if you're struggling a lot

[native cradle]

It is a problem in a course like RA

[vital chasm]

yeah for rudin, its not possible to rmb it all

its exceedingly dense

[dim pendant]

Sometimes you really just can't compromise. It took me half of a course of real analysis just to understand properly the definition of a limit

I would've never survived if I just sat there and not allowed it for memorization

[vital chasm]

i still wouldnt push memorization as anyhting but a last resort i guess
at least it doesnt make me comfortable

[vapid owl]

our professor tried give us ways to memorize real analysis but it made things even worse

[native cradle]

Okay, when did your sem start

[vapid owl]

At the start of Fall

[dim widget]

Any good books for Lie Algebras + Differential Manifolds?

[native cradle]

I ask as I really feel you should try to understand, not memorise

[vapid owl]

I am trying but I don't know how

[native cradle]

Open a help channel here : )

What's a topic you don't understand

or even a definition, a theorm etc

[vapid owl]

I am going to start sequences, series and continuity

[native cradle]

Okay, and what have you done so far

[vapid owl]

I managed to learn the epsilon-delta definitions for sequences and I leaned the convergence for sequences

I learned them thanks to Youtube

[native cradle]

okay, cool. What about I give you a few questions in #real-complex-analysis and you try solving them using these definitions

and let's also see how much you understand them?

If not it's also cool

[vapid owl]

thanks

[native cradle]

Wait is that a yes or a no 😭

[vapid owl]

yes

this is a yes

[molten gulch]

I thought it was standard in a lot of places

[dim pendant]

Yeah it shouldn't be your standard approach to the material

[lean badge]

as the only reference for a first RA course tho...

[dim pendant]

But it shouldn't be something to avoid like the plague

Gotta do what you gotta do

[dim pendant]

Definitely lazy on the professor's part

[vital chasm]

Rudin with a good guidance from the lecturer is a really nice book

My analysis course used rudin and munkres, it went ok

[lean badge]

d&f vs a first course in abstract algebra?
(first algebra book)

[solar jewel]

d&f has a lot of information and no solutions

fraleigh has solutions (separate) and is slightly more suited as a first exposure

but d&f is fine too as a first exposure

[remote vortex]

Abbott's Understanding Analysis has a lot of exposition and nice exercises.

[weary remnant]

Is Algebra, Trig for the Practical Man by J.E. Thompson enough to do contemporary Calculus like stewarts today?

[trail void]

yes

aslong as it has logarithms and polynomial functions yes

[remote sparrow]

viro et al

singh

lopez

[remote sparrow]

it was when it was first published, but the caliber of students was higher then too.

[bronze lava]

I don't think being introductory is the same as being easy to read... It's not like it has crazy pre reqs

[willow basin]

What is the rationale for this?

[willow basin]

.

[tame tree]

completely disagree

[willow basin]

It'd be nice if the exercises weren't all just in the back of each chapter or were a bit more organized

[bronze lava]

"it is not as good/easy/whatever metric as other introductory texts" =/= "is not an introductory text"

[mortal iris]

If you're working with a text like Rudin then I'd recommend Zorich if you're interested in both utility and rigor at the level of Rudin. If not, just for exploring Analysis in a nice way even Cummings is really nice.

[mortal iris]

It's the one good thing about Rudin. The writing is abysmal. It's trying to flex brevity when it's supposed to be expository as an intended introductory text.

[wet sentinel]

its an introductory text in brevity

[mortal iris]

Introductory = Expository; Visual (wherever possible); Developing Intuition with Rigor using Examples and Counter-Examples; Motivating Applications. A few jokes here and there and a lively writing style helps.

[mortal iris]

Baby Rudin checks only the first out of all these requirements and not very well.

[bronze lava]

Those are good traits for one yes

[vernal tinsel]

What's a good recommendation on local fields?

[wet sentinel]

I mean he does give motivation sometimes like in chapter 7 about sequences and series of functions where he motivates uniform convergence by saying that we would like to preserve nice properties such as that the limit of a continuous family of functions is continuous etc.. , tho not applications

[wicked fractal]

Serre's local fields

[wet sentinel]

tho yea he rarely does that ig

[mortal iris]

No good mathematics text should be as far removed from applications as some of these idiotic standard texts are. They are very useful for a student to have some context for what they are doing and helps develop intuition for writing good proofs.

[wet sentinel]

well sure but also some topics are just not too much connected to applications depending on what you mean by that

[wicked fractal]

What applications?

[wet sentinel]

phone apps like call of duty

[bronze lava]

tbf a lot of real analysis 1 is stuff you've already seen applied (presumably you like most normal people took calc before real analysis)

[wet sentinel]

I am not sure if killuminati meant applications to other areas of math or to other sciences or both

[wicked fractal]

I'm purist as hell so I'm assuming applications in the mathematical realm

[bronze lava]

anytime a book interjects to talk about science = skip

[wet sentinel]

real

[mortal iris]

And not a lot of Calc courses do any applications either.

[bronze lava]

i am thinking of calculus being the application

[wicked fractal]

Are the real world calculus applications even fun? Lol nope

[mortal iris]

Both, especially the latter (both physical and social sciences).

[wet sentinel]

no

[mortal iris]

Is your first course in analysis fun? Also no.

[wet sentinel]

ohhh i see, yea i would say thats the job of calc books to be honest

[wicked fractal]

Yes.