book-recommendations

[floral lantern]

I think people will be more helpful there

[tired hound]

hmm I just tried but didn’t get an answer

[median fossil]

I'll add Folland as well as notes by David Skinner (see also the biblio recs in it)

[vital bane]

What about "Quantum Field Theory for Mathematicians" by Robin Ticciati?

I saw that book in a library once and flipped through it becuase it's QFT

not sure if it's good or not

[median fossil]

I does have "Definition", "Lemma" and "Proof"

The small bits I looked at were alright

[grim delta]

basic, like for calculus

[thorn hinge]

Books that have a chapter on pointed spaces, smash products, wedge sums?

[sharp jasper]

Just ask the question. If it's not the right place people will let you know but a lot of people here have experience reading math books.and might be able to answer your question

[wraith cave]

what books should i use before going into real analysis?

i have a bit of vector calculus down and any linear algebra required for it

but basically nothing past that

[tender cobalt]

I think you can start learning proof based linear algebra before that

it'll build up your familiarity with pure math concepts

[wraith cave]

yeah i was thinking of having:
abstract algebra
proofs
more linear algebra

but i have 0 clue on what books to use for those

[tender cobalt]

if you are starting with abstract algebra and arent much familiar with proofs

i suggest Paul Aluffi's "Algebra: Notes from Underground"

or hungerford's introduction to abstract algebra

both of these dont assume any linear algebra

and if you are starting with linear algebra, there are two excellent books: Friedberg Insel Spence's Linear Algebra and Sheldon Axler's Linear Algebra

Friedberg insel spence one is much more comprehensive than axler and the exercises are also nice

[wraith cave]

thank youuu

[bleak carbon]

hello

i am starting tensor calculus and analysis , manifold calculus i have no ideas about book what do i do

[rigid trail]

You just need some proof writing experience

Then you can take real analysis

[naive lava]

spivak has a very nice book on these types of stuff

[vital bane]

Spivak CoM?

that's not really tensor calculus though

that's just analysis on R^n and manifolds embedded in R^n

[naive lava]

yeah but - and hear me out here - vectors are just n scalars and tensors are just n vectors

unless you wanna deal with isometries and such

[bleak carbon]

humm ok

then what is am i buying then ?

suggest

[naive lava]

maybe you should start by watching eignechris' youtube videos

[bleak carbon]

thank you very much

[bleak carbon]

i am doing it
watching video is good but don't you think ill need sth to read dwell on to get a deeper understanding in subject
humm what do ya all think

[vital bane]

Axler 4th ed seems nice

for isometries

3rd ed is mid honestly

[celest steeple]

We're doing a book report in ELA, and I asked if I could do it on a non fiction math book. My teacher said it had to be fiction. Do y'all know of any fiction books about math.(Looking for late highschool/early college books but otherwise would work).

That may not be a thing, but I was just throwing it out there.

[normal crystal]

https://kasmana.people.charleston.edu/MATHFICT/browse.php

[celest steeple]

Thanks! It's a great list, but how can I read them?

[slow roost]

do you mean how can you acquire books from that list?

you can't on that site, it's just a list of books that have been published, so any of the usual ways

[celest steeple]

I see.

Thanks.

[rapid echo]

What math skills is required for running a business of mirror

[onyx spire]

I was reading a book that was supposed to be an introduction to analysis but it had me completely lost when it introduced fields and axioms. Are there any books that explain it nicely?

[molten gulch]

what book were you reading, if you don't mind we asking?

[onyx spire]

i think it was called introductory algebra and analysis by geoff smith or something like that

[molten gulch]

Ah, I believe a standard choice for analysis that goes a bit slower is "Understanding Analysis" by Stephen Abbott

If you'd like to learn about rings, fields, etc... properly, I'd say look into an abstract algebra text too

[onyx spire]

thank you, ill have a look at it

[floral lantern]

I really would not worry about it for the purpose of analysis

Basically the big thing that matters with R is that R is complete

The field stuff isn’t super necessary to get at this

[onyx spire]

ah ok, i'm basically just trying to go beyond my school stuff for uni applications and i was reading the first book but i didn't really understand it hence me asking. any topics you think i should have a look at. I don't really know much outside of the A-Level maths curriculum and some basic stuff ive read in a couple books so i dont know what is out there in maths thats a bit more abstract

[floral lantern]

I would start with linear algebra - if you’ve taken a computational class (I think A-level does some), you can read a more abstract text.

Axler is the de factor recommendation for abstract linear algebra, but Friedberg Insel and Spence is also good, as is Hoffman and Kunze (a little old), and to be honest a lot of other books.

[onyx spire]

and are books the best way to learn this stuff or should i look for courses online and slightly more interactive ways.

[floral lantern]

Axler and FIS are the most common, though.

Books typically

[onyx spire]

is computational like iteration and approximating roots?

[floral lantern]

You need to have a certain method of reading a book - when you see a theorem, first try to prove it yourself. If you can’t, read a little of the proof and try again, etc.

[floral lantern]

For linear algebra it would look more like row reducing matrices or finding square roots and stuff.

[slow roost]

solving actual linear systems of equations, finding inverses and determinants of actual matrices with given numbers, etc

[onyx spire]

i think thats where i struggled with the first book, i was just reading it and sort of skimming through the proofs and exercises

[floral lantern]

Yeah, you really need to get used to just going slowly and expecting to at best maybe do 5 pages a day.

[stuck fjord]

OK THOMAS’ CALCULUS

THOUGHTS

I HAVE A FRIEND WHO WILL SELL HIS TO ME

[naive lava]

Buy if cheap

[stuck fjord]

20 dollars…

Steal?

[rigid trail]

yeah

[stuck fjord]

Ok wait so we got

Berkey calculus

Thomas calculus

[rigid trail]

really doesnt matter as long as you end up learning calculus

[stuck fjord]

And stewart

[rigid trail]

$20 is a great deal for a full calculus textbook

[stuck fjord]

Ok and larson and edwards

Sorry my friend has like 10 textbooks

All are like 20

Which one? Do i get

[stuck fjord]

Yah but he got like 10

[rigid trail]

Why does your friend have so many calculus textbooks 😭

did he need to relearn the stuff 10 times or something

[stuck fjord]

Dude ion even know

[rigid trail]

i mean maybe he'll let you flip through each

[stuck fjord]

He just hella rich ig

[rigid trail]

i don't think it makes a huge difference which you pick

pick whichever one you want to read most

[stuck fjord]

Ok i might go for thomas jgl

Ngl

That shit looks deep and spicy

[rigid trail]

although i didnt use any calculus textbooks so maybe im missing that one of them is ass or something

pretty sure thomas is respected

[stuck fjord]

Oh…

[rigid trail]

ive looked at stewart before

i havent looked at the others

[rigid trail]

thomas should be good i just don't know anything about the others

[naive lava]

Nah that's about 19 dollars more than what I'd pay the most

[stuck fjord]

Ok heres the selection yall

Oh wait i cant send images

[stuck fjord]

Can i send u all the textbooks he has and u tell me which is best…

[naive lava]

Sure, why not

[stuck fjord]

TY GOAT

[rigid trail]

i'm looking for an introductory complex analysis book that wont cost me a liver. is that too much to ask for

[naive lava]

İsn't ahlfors dover nowadays?

[rigid trail]

liver

[naive lava]

Whoa

İ just checked it

[rigid trail]

im a broke student. will i have to resort to pdfs then

[naive lava]

Don't your library have something along these lines

[rigid trail]

uh mayyyybe
good point i'll check

[remote sparrow]

no, in the U.S. he's being reprinted by AMS Chelsea, but there are international editions floating around (which i own)

[naive lava]

he's been dead like 70 years now

dover should print

[signal badge]

iirc churchill & brown is pretty affordable (the used ones at least)

[remote sparrow]

#advanced-analysis

if it's possibly more related to pdes, #advanced-pdes

[foggy quest]

the one here is free: https://mtaylor.web.unc.edu/notes/complex-analysis-course/ It's great

there is also piracy

[remote sparrow]

if you asked this yesterday, there was a working 50% off code for springer...

i would have recommended gamelin

[naive lava]

+1 for gamelin

also, hear me out, Remmert

[remote sparrow]

i saw the softcover go for $16 before

i didn't buy it at the time though

periodically certain softcovers go for $16 on springer but it's hard to tell which and when

[naive lava]

46 usd rn

it's a german book, so, it's a bit different in the way of writing, but i like it

[open dove]

Hi! Which book would cover the floyd warshall and other different algorithms applicable on graph? I just checked Introduction to Graph Theory, it doesn't have it. Graph Theory by Reinhard is also doesn't have it.

[signal badge]

One of my friends is using Applied Combinatorics by Alan Tucker

That book seems to cover graph algorithms

[livid lintel]

<@&268886789983436800>

[open dove]

Thank you!! I think it has Floyd Warshall algorithm, let me check and get back.

[open dove]

I wanted to understand the proof of Floyd Warshall, but they gave it as an exercise

[signal badge]

😂

[proud bloom]

Any good book you all would recommend to a beginner doing math? something short, without that many prerequisites. (no, i am not looking for motivation books, just cool topics)

[tender river]

combinatorics!

you can look into Bona's walk through combinatorics https://www.amazon.com/Walk-Through-Combinatorics-Introduction-Enumeration/dp/9814460001

[proud bloom]

i am not a big fan, but I haven't had proper exposure to it. what book do you recommend?

[tender river]

what kind of math would you say ure into

therez calculus, number theory, algebra, linear algebra etc

logic and proofs even

[proud bloom]

I like programming, but I have never done anything mathy or theoretical, so maybe something about that? Many topics have a lot of prerequisites (say, category theory), though.

[proud bloom]

i will do those either way, i am just looking for some new topic to explore

[tender river]

categories are introduced in a second or a third algebra course so you could explore that space

you wanna look for introductory abstract algebra books, theres gallian's contemporary abstract Algebra thats pretty readable if youre beginning math

[proud bloom]

alright, thank you, will check both of them out

[tawdry pewter]

Any tips on how a person can actually study from textbooks effectively?

[naive lava]

i like going over all the theorems myself

[tender river]

Halmos

"Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis?"

[tawdry pewter]

Wow

[stuck fjord]

Thomas Calculus retrieved 😋

[foggy quest]

Does CLRS cover them?

[remote sparrow]

according to the table of contents, it's chapter 23.2

at least for the 4th edition

[foggy quest]

Competitive programming books cover Floyd warshall

[frosty kettle]

weird request, but are there any conversational math books on complex analysis?

[karmic tangle]

I'd recommend Aluffi's Algebra: Notes from the Underground

it's supposed to be a first-encounter-with-algebra kinda text I think and it also introduces categories right from the start as a kind of organizational framework for algebra

Also hello guys, could anyone please recommend me some books on enriched/higher categories with exercises?

more so enriched than higher, ideally to supplement a course mainly I feel like I could benefit from doing exercises

[torn blade]

how does this differ from algebra chapter 0

[remote sparrow]

it doesn't really use category theory, but rather it makes gestures to it

[plain apex]

any free online books for learning multivariable calculus?

[hearty meteor]

https://open.umn.edu/opentextbooks/textbooks/780

I've been using this one. Pretty thorough.

[plain apex]

thank you!

[sudden kindle]

.

[karmic tangle]

Chapter 0 is aimed at late undergraduates/early graduate students afaik

From what I've seen of Notes from the Underground it seems considerably more "friendly" for someone who has not yet had an encounter with proof based math

[remote sparrow]

https://www.rxddit.com/r/math/comments/1j2e7g8/springer_yellow_sale_march_1_30_june_2025/

[cursive storm]

My brain just automatically solve the problems each time I come up one

Imagine being asked 1+1

[hollow shore]

is there an analysis books megathread here?

[naive lava]

https://mathematics.gg/books

[torn blade]

#book-recommendations message

we should have threads on different subject areas lowkey

[hollow shore]

I found a course following Rudin https://ocw.mit.edu/courses/18-100b-analysis-i-fall-2010/

Okay ig I shall begin my proper Analysis journey

[naive lava]

i wish something like this existed for math folk too https://physics.stackexchange.com/questions/12175/resource-recommendations

[tough egret]

I highly recommend Johar's The Big Book of Real Analysis. It's packed with examples, extra notions from algebra, differential equations and an intro to measure theory, and it has hints to problems.

It's recent and not well-known so I promote it whenever I can

[hollow shore]

is there a one semester long course plan following the text?

[merry sphinx]

oh im gonna bookmark this, thanks

[tough egret]

There are two-semester and a three-semester plans, one semester would be a bit short considering how much material there is

[hollow shore]

can you share links please?

[tough egret]

Sure! https://link.springer.com/book/10.1007/978-3-031-30832-1

I have been through all of it on my own in like three months, but it took me about 10, maybe 12 hours per week which is not realistic if you have other courses (or a life)

[hollow shore]

I meant the course pages with a schedule

with problem sets

[hollow shore]

oh it's built into the book itself!

[tough egret]

The first one is missing :

Yes

The problem sets are quite amazing, they range from simple computations to guided demonstrations of theorems, sometimes quite exotic ones

[hollow shore]

Okay. Thanks for the suggestion.

[tough egret]

My pleasure!

[acoustic dove]

anyone knows what book i should buy next after rosen's elementary num theory? Just preparing

[topaz geyser]

Any online book pdf or YouTube channels to practice for the grade 12 Euclid contest?

[clever tiger]

Any book recommendations for introductory linear algebra

[molten gulch]

Computational or proofs

[clever tiger]

Whatever is easiest to understand

It's way out of league but I heard it doesn't require too much for prerequisites

[molten gulch]

What have you learned so far in maths

[clever tiger]

Algebra 1 and some algebra 2 and geometry

[molten gulch]

Overall computational linear algebra isn't too difficult IMO assuming you've learned up to say precalc

[clever tiger]

Along with complex concepts thanks to the internet

Concepts*

[clever tiger]

Alright

I'll focus on that for now ig, thanks

[rigid trail]

What do you need linalg for

[unborn jackal]

hoffman kunze linear algebra

dont use strang it is ass

id do real analysis parallel to it cause knowing some integration/differentiation might be helpful for some examples

[merry sphinx]

Howard anton, pretty good intro book imo

[molten gulch]

There's also Friedberg but it also has a decent bit of proofs and theory

For pure intro I've heard anton and strang are decent

[river holly]

I've been wanting to learn more math for a while now, but it's difficult because I don't know where to start. Formally, I've been up to a high school calculus class, but on my own, I've done a ton of stuff without any real structure. I'm not really looking for a book suggestion, but it's related to finding a book. How could I determine my level of math to know what books would and wouldn't be right for me?

[mortal ore]

Start with a book on proofs

If its all stuff you feel confident with, move on to linear algebra

If you can easily do everything there, most to abstract algebra and analysis

Just keep going with more and more stuff I guess

[river holly]

I'm not looking where to start because I already have a good (if possibly incomplete) knowledge of some of the stuff that comes after calculus. I did complete it 2 years ago, after all. I want to determine where I am so that I can know where to go from here.

[mortal ore]

That would mean you are looking for where to start

You're looking to find out what point ur at so u can start learning from there

[river holly]

That's a very long and boring way to determine where you are.

[river holly]

I don't really like reading, so I'd like to cut down on as much redundant stuff as I can. I want to start (or at least begin close to) stuff that is new to me.

[mortal ore]

i mean studying math on your own while also not liking reading

thats a rough combo

i guess you could do the opposite thing

pick up a textbook you think youre ready for

then if ur not, you could go down a step

[surreal heart]

frankly you're not going to make any meaningful progress without some redundancy, you'll have to fill in the gaps eventually. I also recommend hiido's first recommendation. if a whole section looks like something you understand well then just skip it

[river holly]

That's why I didn't start right after I finished calculus. I thought I needed to jsut start liking reading more, but I'm seeing that that's not a thing you can force.

[surreal heart]

also if you want to do math rigorously, especially without a mentor, you're going to have to read, might as well accept that up front. reading textbooks isn't really that much reading though, most of your time will be spent doing problems and taking notes etc

[mortal ore]

youll probably like reading if its a topic you care about

i used to not like reading but i started reading a lot more after i read things that i found meaningful

[river holly]

I'm not saying I won't read. I just don't want to read something I already know.

It's just boring.

[surreal heart]

yeah I'd just accept that you'll have to do that sometimes. it's not such a bad thing though, you'll get a deeper understanding of it. it's very hard to have completely wasted time while studying

[mortal ore]

i would go with the opposite method then if anything

just pick up a book you think you may be able to handle

if you cant, go down a level

[river holly]

I don't know what I can handle.

[surreal heart]

just take a shot, you'll never know if you don't try lol

[mortal ore]

so then the "reading something you already know" thing isnt something that actually exists

the level right after calc 3 is mathematical proofs

then linear algebra (though this can depend)

then after that abstract algebra and analysis

[river holly]

which I'm both pretty confident of.

[surreal heart]

your predicament right now is "I don't want to read anything I already know, but I don't actually know what I already know". unless you're willing to compromise, you're not going to make any actual progress. just pick up a book and start studying

[river holly]

That is not what I said.

I don't want to read a whole book on something I already know.

[mortal ore]

i would go through some problems in a textbook for proofs and linalg

[surreal heart]

then don't lol, you'll know before you're done with it if you already know it all

[mortal ore]

if ur right about ur confidence then you should be able to tackle these problems easily

[river holly]

Where are some problems I could attempt?

[surreal heart]

in a textbook...

[river holly]

Now I'd like some recommendations. I don't have any textbooks.

[mortal ore]

theres Linear Algebra Done Right

or Strang's Linear Algebra

[river holly]

I'll try that one

[surreal heart]

if you want to go for analysis instead I believe Abbot is a pretty good choice (haven't read it myself)

[mortal ore]

im using abbot currently

i like it

i used Gallian for abstract algebra, though its pretty bad with group actions

[surreal heart]

I'm using Fraleigh, but that should probably come after linear anyway

[mortal ore]

yeah

im actively studying linear algebra

im in a weird spot mathematically rn honestly

that spot where ur so so close to taking some high level math courses

[river holly]

Is Abbot the entire name?

[mortal ore]

Abbot's Undergraduate Analysis

i think thats what its called

[surreal heart]

Abbot is the author's name, it's titled "understanding analysis"

[river holly]

thanks

[mortal ore]

oh understanding might be it

i always get lang's undergrad alg textbook mixed up

[surreal heart]

it's definitely this

[mortal ore]

@river holly its Abbot's "Understanding Analysis"

my apologies

[torn blade]

Abbott is literally peak non-fiction

[surreal heart]

but if you look up Abbot analysis you'll get the right thing

[river holly]

ah, alright

[mortal ore]

yeah his textbook is pretty mainstream

[surreal heart]

it's common to refer to math books by Author's last name

[surreal heart]

eh you'll get there, it's not like you're not doing valuable math, and I think everyone reaches into some higher level math before they formally get there at the start of undergrad

[river holly]

That doesn't seem like a good idea. Most authors have multiple books, no?

[mortal ore]

very true

[river holly]

I can't imagine they write one and just stop

[mortal ore]

the awkwardness more lies in how accelerated math is going to become very soon

[mortal ore]

honestly not really

i mean they do

[surreal heart]

not on the same subject, and even if they did there would be one that is clearly the intention

[mortal ore]

but not all of them are super mainstream in one area

[surreal heart]

9 times in 10 when you refer to a textbook the context already makes it clear which field you're talking about and at what level, which probably already narrows it down to exactly 1

usually it's like "which book in X field is good/interesting/bad/whatever" and there are really only a handful in any given field that come up often. actually the author names are far more unique than the textbook names lol

[waxen sandal]

Yeah almost every Calculus book is named Calculus lol

[river holly]

Math books really need better names

[surreal heart]

that's probably the reason it started. if you asked for good linear algebra books "FIS, Strang, Axler, Hoffman and Kunze" is a much more useful list than "Linear Algebra, Introduction to Linear Algebra, Linear Algebra Done Right, Linear Algebra" lol

[river holly]

You can do so much in a title, but they just waste the creative possibilities by naming it after the subject.

[mortal ore]

im going to name my undergraduate algebra book "Industrial Society and its Consequences"

[river holly]

give me the Math book. The book named Math.

[surreal heart]

the industrial revolution and its consequences have been a disaster for the human race

[waxen sandal]

Your algebra book is now on a watch list

[mortal ore]

oh crap i forgot, a well known mathematician already wrote a book called that

[waxen sandal]

What about the linear algebra book by Anton?

[surreal heart]

yes there are many more good books than the ones I listed 😅

if you're actually asking, I've heard it's pretty good and very beginner-friendly

but I have never looked at it

[waxen sandal]

I had heard about it and saw it at a used book store the other day so I picked it up

I'm not taking linear algebra for probably another year lol

So I have time to pick another book if I need

It was $5...

[surreal heart]

that's a great deal!

[waxen sandal]

Yeah this used book store near my house sells a bunch of math textbooks for like $5 - $10 so I've been going by every few weeks on the hunt lol

[river holly]

I actually don't know of any math textbooks at book stores

or libraries. My area is just not that big for math.

I actually don't know of any book stores at all.

[waxen sandal]

You should never really buy a math textbook new

[river holly]

Even if I did, I have no money and no transportation.

[waxen sandal]

Always go used

Amazon or thriftbooks has good deals on used textbooks if you have no local used book store

[river holly]

I guess, yeah. Buying a book and waiting for shipping feels like too big of a commitment to try out a book I might immediately realize I don't need.

And with my extremely low amount of money, I can only do that like 4 times before I have nothing.

[waxen sandal]

A lot of textbooks are in the public domain and free online. You could alwaysd read a bit from a PDF before committing to a hard copy

[river holly]

I didn't know that

to determine if a book would be good for me, is there somewhere I could view the questions?

[waxen sandal]

If I was you I would find some books that are free and in the public domain for the topic(s) that you are interested in and read and attempt the questions in one of those books and then if you find a topic that you want to study just get a used hard copy of one of the modern textbooks for that topic

[foggy quest]

if you are willing to pirate, you can read a pirated pdf and then buy a hardcopy if you think you need a hardcopy.

[waxen sandal]

Yeah I didn't want to suggest it but that is always an option

Just know there are legal ways with tons of books in the public domain

[river holly]

I didn't want to directly bring it up either, but I was thinking it.

I literally have no money to buy textbooks with at all.

[foggy quest]

If you are a student, check your universities subscriptions. You may have legal pdf access already

[river holly]

I am not a student.

[foggy quest]

e.g. Springer link

[waxen sandal]

I just assume all books online are in the public domain😁

[river holly]

I would like to be a student, but I can't afford it.

[waxen sandal]

Not sure if I have ever pirated😅

[river holly]

Same here. Plausible deniability.

[waxen sandal]

You can't get financial aid?

[river holly]

I've looked into it a lot, and the only aid I qualify for pays only to tuition and nothing else.

The main expense to me would be housing. I also don't know how I'd be able to be accepted to anywhere without going to a community college first, which doesn't even have housing.

[foggy quest]

do you live near a state school?

[river holly]

no

[waxen sandal]

You should look into scholarships

[river holly]

I did

many times. I don't qualify for anything I found.

[waxen sandal]

Did you apply to any?

[river holly]

no

I honestly couldn't even find out how.

[waxen sandal]

I would apply to anything that sounds like you could remotely qualify for

[river holly]

I couldn't find anything I even remotely qualified for.

I barely found any anyway.

Is there a list I could use?

This is getting off topic. Should we move channels?

[waxen sandal]

You can find a scholarship for almost anything nowadays

You gotta think there are people who donate money to scholarships as a racket to write off taxes

It isn't as hard as people think

[river holly]

Where should I look?

[vital bane]

I'm just worried about the book being sold in a bad condition like torn up and stuff

[remote sparrow]

the used books i received haven't generally deviated too far from the stated condition

[vital bane]

Have you ever checked this out? I was reading a few pages in the preview and it seems quite well written

[remote sparrow]

no

[vital bane]

What do you mean you haven't read every book ever written? My view of Sour Drop has shattered...my life is a lie...

[remote sparrow]

[steady zodiac]

how is S.L.Loney for coordinate geo?

[orchid palm]

not sure where to ask this, but should I take discrete before delving into modern algebra?

[remote sparrow]

the basics of elementary number theory are pretty helpful; don't think combinatorics or graph theory are directly as helpful

[vital bane]

yea 100% you should learn basic number theory before doing algebra because a lot of group theory is basically just number theory

[frosty kettle]

the only problem i have with that book (personally) is that god awful typesetting (i think arihant's one is much better at this, though)

the problems are pretty good, i havent done the entire book, just some sections i needed.

[torn blade]

what from basic number theory, exactly?

oh wait i didnt realise what u meant by basic number theory

yeah no ur right

[gleaming turret]

O need recomendation for books tô study the basical tô advanced math

(My english is bad, m sorry, im a Brazilian)

[naive lava]

how basic to how advanced?

[gleaming turret]

Starting unto the basic

Tô calculs

[gleaming turret]

Starting into 2º grau equations

(The equations é dont know the name in english, if it have baskara fórmula

[molten gulch]

the quadratic formula is generally introduced in early high school algebra courses

[gleaming turret]

it´s sadness

[viscid valve]

Let's say I wanted to learn math, from about as basic as I can do, to some of the hardest applied maths, what would my roadmap for that look like? I know I'm not exactly asking for books, but I will possibly later on, once I have a good read on what my learning journey would look like

Noting heavily that at the moment, I'm not looking into doing pure math courses, so you can leave anything like that out of the picture

[sharp latch]

Just like pure math, applied math is highly specialized, so it depends on what area you’re interested in

[viscid valve]

Got it

Also I'm not sure if I was using the right terminology, but generally I meant like, computation math, so not proof math

But I'm assuming your point still stands, right? It depends what I'm going for and still goes far?
(Also should be noted that I'm a beginner in math still, so I'm not sure what paths even exist, is there anything I should try first, is mainly what I'm wondering?)

[naive lava]

What's your knowledge level?

[viscid valve]

Honestly, I don't even really have a dedicated level. I had started learning calculus a bit, but my foundational knowledge feels very weak, so I'd prefer to start from square 1, wherever that is, and up to whatever anyone recommends I go with for now. Like I don't know enough about math to really understand what paths exist yet, or what I'd want to do

[naive lava]

Roadmap should probably look something like this for the basics: high school -> calc -> linear alg -> diff eq

These cover the basics needed

Then you can specialize

[viscid valve]

Alright thanks!

[merry sphinx]

you should make sure your algebra is solid before calc though, a lot of calc students will make mistakes bc they arent as good as they should be with algebra

[viscid valve]

Yep, that's why I was asking in general

Wanted to start a bit further back, then properly go into it

[merry sphinx]

you can probably find some harder algebra qs online

and see what makes you uncomfortable

work on those and then move on to lims/differentiation

[brazen epoch]

Why linear algebra after calculus?

[naive lava]

Idk that's how it's taught in my uni

[merry sphinx]

you can do them both in tandem

[austere harness]

preferences?

[fresh skiff]

College algebra,
Whenever i see algebra alone (without college in front) i consider it abstract algebra lol

[gleaming turret]

starting learning pre-algebra and simple equations

to calculus

i´m starting in the world of the math

[austere harness]

language?

english or pt-br?

[tender cobalt]

does anyone know any supplement for roman advanced linear algebra

[gleaming turret]

preference to pt-br

my native language

but english i can traduct into the google

whatever

[waxen sandal]

I started in the same place as you and these are the books that I used:

1: Schaum's Elementary Math
ISBN-13: 978-0071762540

2: Elementary & Intermediate Algebra by Sullivan, Struve and Mazzerella
ISBN-13: 978-0134556079

3: Pre Calculus by Stewart, Redlin and Watson
ISBN-13: 978-1305071759

If you have no algebra experience I HIGHLY recommend the second book. Most people will recommend a college algebra book to start but if your going on to calculus you'll get all of the college algebra that you need in a pre calc book

[merry sphinx]

for me it depends on who im talking to, if im talking to someone who knows barely anything about math if i say "algebra" to them it'll mean hs algebra
if im talking to an undergrad student or the equivalent, algebra means AA

[gleaming turret]

thank you bro for the recomendation

i will search them in the web

[waxen sandal]

No problem! Self study is a fun and super rewarding journey. The most important thing is that you build a solid routine that you can stick to consistently.

[haughty kindle]

Hello guys

Im in grade 7, Can someone please recommend for me any books to start with practice math olympiads.

I'm in grade 9 lvl, if that's matter

[hollow peak]

Algebraic Geometry, Robin Hartshorne

That was a joke just to be clear

Art of Problem Solving has a series of math competition workbooks

[haughty kindle]

js interesting, is this book bad or something?

ok

now I understand💔

[molten gulch]

It's a very difficult book with many prerequisites and most people don't even dare touch it until grad school

[grim ore]

its a really dense book, and as Ryan stated, yeah most people dont approach it. But there are plenty of alternatives which practically have a book of around 200-300 pages dedicated to just a 50 page chapter of that one text

idk i like hartshorne to a degree, but i still find it humourous

imo its honestly just a compendium of theorems back to back to back

[naive lava]

If you manage to solve all problems inside there, you get 1 million dollars

[molten gulch]

smells like rudin

[naive lava]

Don't you dare

[grim ore]

atleast rudin has actual whitespace 😂 and more dfns

[molten gulch]

LMAOyeah

Okay we gotta go for a bit, DSA midterm

[grim ore]

gl!

[molten gulch]

Thx

[naive lava]

Polya has a book on problem solving, titu andressacu (I hope I spelled it right) also has various nice books on problem solving

[covert bane]

Does anyone have any good summaries/overviews of markov constructivism, constructive analysis/bishop constructivism, and locale theory? (not necessarily all in the same book ofc)

[errant matrix]

i am taking linear algebra and i didnt take calculus

[spiral sky]

Can anyone recommend a book on rep theory that has a lot of big picture perspective (interested in characters and irred reps)? Also speaking of AG by hartshorne what's a good seq to understand moduli spaces (and chow groups (maybe)). Finally a similar guideline for matroids maybe (any book w detailed theory and/or big picture would be appreciated)

[waxen sandal]

The only prerequisite for computational based linear algebra is basic algebra but I think proof based linear algebra demands a way higher mathematical maturity

Calculus is used as a random benchmark for mathematical maturity

I assume calculus can be put as a prerequisite for even computational linear algebra purely as a mathematical maturity benchmark

Some schools will gatekeep these courses harder than others

[mossy flume]

idk what you mean by big picture perspective but any rep theory text would cover characters and irreducible reps

Fulton Harris is a standard recommendation

and what I would probably go with

[spiral sky]

By big picture I mean it's relations to other areas

[mossy flume]

As far as matroids, this survey has some references: https://arxiv.org/abs/1409.3503

although admittedly I can't say much as I haven't looked into this too deeply despite it being on my reading list for a while

[spiral sky]

That looks pretty good thank u! Also, i think there's a counterpart for alg combinatorialists lol

Is that the same whitney from whitney embedding thm? Thanks again!

[mossy flume]

This would probably be the resource still (as alg combinatorics is pretty closely tied to alg geo)

I can ask Katz next time I see him if he has any more pointed recs lol

[floral lantern]

I'm not sure about applications, but Pavel Etingof's book https://math.mit.edu/~etingof/reprbook.pdf provides a very unified view of representation theory that does quivers, groups, algebras, lie algebras, etc. all at once.

[spiral sky]

Very nice rec thanks I can see the smooth built up I'll dive into the details in spring break

[fresh skiff]

Makes sense

[molten gulch]

I almost always mean abstract algebra when I say algebra, and that's in ANY context

[fresh skiff]

Yeah same goes for me.

[old elk]

Some monstrou, do you know of a book that talks about algebra and Lie groups, how to operate them and many examples are left

[fresh skiff]

Did you read D&F?

[old elk]

Groups and Lie algebra, as far as I remember D&F do not have that.

[stiff crow]

do you guys have any book suggestions for self studying linear algebra?

[fresh skiff]

Oh yeah it doesn't cover

[minor glen]

I am a self-taught person and I have finished studying the book "Understanding Analysis". I want to continue learning mathematical analysis. Please recommend me a few books suitable for self-study. It is best to bring the answers. You can recommend more books. I can read them one by one if I have more time.

[remote sparrow]

#book-recommendations message

[tropic thistle]

learn math in one big fat notebook

[remote sparrow]

https://www.rxddit.com/r/math/comments/1j46mgo/popular_math_youtuber_the_math_sorcerer/

[naive lava]

apperantly, the way to become a genius in math is to use ai

[still panther]

the way to become a genius in math is to read the contents page of a thousand math books

[fast portal]

https://tenor.com/view/made-up-making-things-up-misinformation-spreading-misinformation-lying-gif-5615616319157116451

[still panther]

can also scroll the pictures if they have any

[remote sparrow]

hello hyouka hater

[minor glen]

So, is this person a liar?

[remote sparrow]

the math sorcerer? i guess so, but his old vids were okayish

[minor glen]

His book introduction videos were great from what I recall—I used to follow his recommendations for beginner-friendly books, and they were all quite good. However, his channel appears to have stopped sharing book-related content, and I find that somewhat disappointing.

[still panther]

would his books review be better if there was another person in the room yelling "kininarimasu" and pointing at the book before he opens it

[remote sparrow]

i don't think they would get worse

actually that would be a funny gimmick he could milk for a while

[still panther]

trve

[mellow wren]

Knapp Lie groups

[remote sparrow]

https://tenor.com/view/yugioh-anime-omg-wtf-cant-unsee-gif-5159766

light mode

[night flare]

Recommend a book for beginner (Integration)

[vital bane]

interesting, I didn't know AGers cared about matroid theory

[vital bane]

"Inside Interesting Integrals" by Paul J. Nahin

[night flare]

Thx I'll definitely try it

[heady ember]

https://tenor.com/view/warhammer-gif-19055033

[heady ember]

Pauls' online math notes, Khan Academy, etc

[remote sparrow]

do you know calculus

[night flare]

Alr thank you

[remote sparrow]

#book-recommendations message

[spring night]

i was gonna rec this but u already did it haha

[true granite]

is there some commutative algebra books suitable for beginners? atiyah is too hard for me. or if I should read algebraic curve first?

[spring night]

yes

[remote sparrow]

https://stat110.net

[remote sparrow]

maybe try reading Undergraduate Commutative Algebra by reid

[true granite]

thanks, I'll try it

[stable flicker]

For a harder one and more reference-y use Grimmett and Stirzaker

Once/if you do finish GS the probability world is your oyster

[stiff crow]

thank you so muchhhh 🙏

[vital bane]

iirc D&F has a comm alg section, you could try checking that out as well

[dense plover]

Whats a good trig book?

[true granite]

OK, I know that book

[novel hound]

There's a free book by Kleiman and Altman which aims to be the new and improved Atiyah: https://dspace.mit.edu/handle/1721.1/116075.2

worth taking a look since it's free and includes solutions to all exercises in Atiyah

[spiral sky]

what are your thoughts on amann I, II and III analysis books? Self contained? Self study material? Motivational content? historical views? algebraic perspectives? I've been meaning to buy all volumes bc royden/kolmogorov is good and all but i feel amann has a similar style of kuratowski closure axioms, or maybe in the spirit of raeburn, williams functional analysis stuff, maybe recommend some analysis (measure/functional) that has cat/algebraic language (i.e d/dx explicitly saying is an action of lie algebra on C^inf(M) smooth functions) maybe asking this is too ambicious

[frank pendant]

What could be a good book for a person that isn't that good at math but wants to **understand **(not just learn) each concept and grow a Hobby out of it?

[spiral sky]

this is really awesome it reminds me of ash modern algebra

[mossy flume]

how much abstract algebra have you done?

[spiral sky]

art and craft of problem solving by paul zeitz

[mossy flume]

typically commutative algebra texts assume you have a good basic abstract algebra background

and the motivation to learn commutative algebra comes from algebraic geometry and algebraic number theory, which are subjects you learn after learning basic abstract algebra well anyways

[spiral sky]

i wish there was a newer version though i like the lmodern font (for atiyah)

[spiral sky]

btw will u get vakil's book printed? it has the most beautiful math book cover ever lol https://www.amazon.com/Rising-Sea-Foundations-Algebraic-Geometry/dp/0691268665/

[mossy flume]

Maybe one day

[stiff crow]

I mean what do you want to learn?

[frank pendant]

A bit of everything, maybe more on highschoolmath, calculus may be too tricky for me. So geometry, trigonometry, algebra etc. The main point is to have the concepts well explained, as in schools you don't have time to go to deeply into details and mainly remember formulas or principels just by doing problems.

[true granite]

thanks 🥹

[true granite]

group ring module field and galois theory, but don't know much about exact sequence and tensor product

[mossy flume]

yea so I think perhaps spending more time on more basic abstract alg would be a better use of time

otherwise you'll probably run into prereq issues with most commutative algebra texts

[mossy flume]

maybe this book is fine though idk

I definitely wouldn't look at Kleiman Altman or Atiyah Macdonald tho

[true granite]

when I read comm alg, can I learn algebraic curve in the same time? because sometimes, I can prove the theorem of comm alg , but I still can't understand what it is saying

[stiff crow]

how much mathematics do you know up to?

[proud bloom]

Lots of books on undergraduate theory of equations, but a lot of stuff from theory of equations is used in high school/olympiads, is there a good book that does a good mixture of both? (rigorous enough that it doesn't feel purely assumption-based, but still applied enough that it will teach me a thing or two i can use in hard problems)

[dense plover]

What's a good trig book?

[remote sparrow]

printed? you mean purchase a copy? also, if you subscribe to the princeton university press newsletter, you get a 40% off coupon code

the code is PUP40

[mossy flume]

$150 on PUP 😭

oh wait that's hardcover

oh you can't order the text there yet anyways

[frank pendant]

I know algebra pretty well as well as 1st and 2nd degree functions. Now I am studying trigonometry. As for geometry, I find it pleasant and not extremely hard.

[stiff crow]

if you want to really understand the entirety of trigonometry:
https://www.stitz-zeager.com/szct07042013.pdf
make sure you can do these algebra problem:
https://www.bethel.edu/undergrad/academics/math-cs/placement-exams/basic-alg-skills.pdf
if you’re able to do most of them and you know a good amount of trigonometry you can definitely start learning calculus.
i would prefer Stewart’s calculus for independent studying

[molten gulch]

<@&268886789983436800> last link is to a pirated textbook

[stiff crow]

is it?

💀

it was first link that popped up when i searched it

[quick hornet]

i doubt a calculus textbook is officially hosted on some random AWS instance

[stiff crow]

my bad:
this also works then
https://www.amazon.com/Calculus-James-Stewart/dp/1285740629

[molten gulch]

That is ALSO pirated

[quick hornet]

"patemath.weebly.com" is even sketchier lol

[stiff crow]

💀

[molten gulch]

You will not find official textbooks for free

[stiff crow]

oh

[molten gulch]

Do yourself a favour and just post the proper amazon link

[signal mountain]

(mostly)

[stiff crow]

alright 💀

[quick hornet]

to my knowledge, stewart's copyright isnt enforced anymore fwiw

like you can find it on archive.org

[signal mountain]

there are some authors who release their textbooks for free like axler, but this is far from common

[quick hornet]

which is questionably legal but if they wanted it taken down itd be taken down by now

[molten gulch]

Personally I'd feel it too risky

[stiff crow]

i mean i would think so, there are like 7 pdf on the first page if u search up

[quick hornet]

yeah because every school in the universe uses stewart and not all of them are totally compliant on following textbook copyright

a lot of course webpages that illegally host textbook pdfs, and many of the links are exposed to search engines

if publishers started going after schools for this itd be terrible PR

so they dont

but it is technically piracy

stewart himself is rich off of his textbooks lol

[modern ruin]

i should write a textbook

[quick hornet]

stewart is, i believe, the only person who has became rich off a textbook

like not even math specifically

across all fields

he's the only one

even other "standard" texts like CLRS for intro algorithms

dont ask me how tf stewart did it

[mossy flume]

I will write a book and become the second person to do it

[cursive orbit]

what baffles me is how everyone decided to use stewart

like I don't think it does anything particularly like

innovative

[foggy quest]

is the majority of their profit from online homework software?

[cursive orbit]

probably, otherwise nobody would buy the textbook

my university has a "special edition" of stewart that comes with an access code to the homework software and half the time people get a question "wrong" its because they forget to put a space between a comma and a number

[remote sparrow]

i think it popularized, if not invented, the early transcendentals approach

[sleek python]

Maybe we should ask stewart

[merry sphinx]

ik they edited the link but its funny to see that in response to an amazon one

[remote sparrow]

he died a few years ago

in case this is not a joke

[sleek python]

Oh

Should have asked him earlier then

(but seriously )

[grave pilot]

book recommendations ❓(Non fiction hopefully electronics related autobiography works)

[surreal token]

#book-recommendations

[sacred sorrel]

book recommendations about what?

[cursive orbit]

@dim sierra

[dim sierra]

Hi

[neon walrus]

Naked statistics by Charles wheelan

[vital bane]

https://measure.axler.net/

[gray gazelle]

hefferon.net

[remote sparrow]

https://stat110.net

https://linear.axler.net

https://services.math.duke.edu/~rtd/PTE/PTE5_011119.pdf

there are many examples

https://wiki.math.wisc.edu/index.php/Algebra_Qualifying_Exam

also i found someone who worked out solutions to some algebra quals at uw madison

[waxen sandal]

I finally found a "Like New" copy of Stewart Calculus 8th edtion on Amazon!

I've been looking everyday for like 2 months lol

I don't get what is so good about the 8th edition compared to the 7th or the 9th but the FOMO made me buy it

[gray gazelle]

have you heard about our savior gilbert strang?

[waxen sandal]

I have heard of Strang yes

Where do I sign?

[remote sparrow]

where did you hear that the 8th edition is better than the 7th or 9th editions

[waxen sandal]

I've been looking at the used sales of all 3 of these editions for the past 2 months

The 8th edition sells the most

That doesn't mean it is better

It's just the most popular

Or maybe amazon has more 8th editions 👉 👈 😅 😢

[remote sparrow]

there could be some inertia with regards to linking to the newest edition (but it's been about 5 years since the 9th edition came out...)

also i think the 8th edition is the last one solely authored by stewart

the 9th edition has two new authors

[waxen sandal]

The 8th also has those two authors

The 7th was the last by him alone

The 8th must have barely any edits by the other two authors because it was right after he died

He died December 2014 and the 8th edition was published May 2015 so in those 5 months I doubt they added much

Unless they started while he was on his death bed which would be kind of grim lol

[old elk]

Thanks, the book looks excellent, I should add it to the algebra section.

[boreal star]

Someone got a really good book, that has theory and some tough problems in Multivar-Calculus. I have studied div/grad/laplacian operators curl integral multivar integrals volume functions

[rigid trail]

im curious too actually

[remote sparrow]

try hubbard and hubbard or shifrin

[boreal star]

Theodore Shifrin right?

[remote sparrow]

yes

[boreal star]

And for hubbard i could get find only the vector calculus linalg and differential forms book, is that it?

which one do you think is better btw?

hubbard is pretty damn costly on amazon tbh

[rigid trail]

pdf.

[boreal star]

Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds Hardcover – Import, 22 January 2004
by Theodore Shifrin (Author) This one? @remote sparrow

[boreal star]

Yeah I ll look for that too

[remote sparrow]

https://matrixeditions.com/

it may be cheaper here

[remote sparrow]

that's the correct title

[misty harbor]

I'm thinking of getting the "hitchiker's guide to calculus'; is it any good?

[scenic sequoia]

Why not just get spivak calculus ?

[spiral sky]

Thanks for the info I didn't know this and I'll spread the info

[naive lava]

mit ocw

[remote sparrow]

not a course, but shifrin has lectures

[vital bane]

https://www.khanacademy.org/math/multivariable-calculus + http://www.damtp.cam.ac.uk/user/tong/vc.html

the latter is not necessarily a online course but eh close enough, it has lecture notes and problem sets

[spiral sky]

Are there notes or course purely oriented for diff geometry on multivariable calculus?

[vital bane]

what does "diff geometry on multivariable calculus" mean?

do you mean differential geometry of curves and surfaces? if so Shifrin has a book on that

so does Tristan Needham

[spiral sky]

Basically just the things you'll see generalized in diff geometry but on multivariable calculus. And yes thank u I'll check them out

[vital bane]

https://math.stackexchange.com/users/71348/ted-shifrin

here

and

[spiral sky]

I wanted to get that book but it's so expensive. I guess I'll just kill my eyes w the pdf

[vital bane]

you can print out PDFs

Oh wait there is also Andrew Pressley's Diff Geo of Curves and Surfaces book

[spiral sky]

Besides the cover (which already explains a lot) it has awesome content in there

[remote sparrow]

this one has solutions in the back

[spiral sky]

It's def a big plus for self study material

[remote sparrow]

they're not always 100% complete (there may be some gaps you'll need to fill) but they're there

[spiral sky]

Ash abstract algebra has solutions as well, and someone recommended a commutative alg here and it had solutions, as for analysis royden has solutions. They're all gems imo

[coral narwhal]

@remote sparrow how do you know about so many books?

(not doubting just curious)

[spiral sky]

Thanks! I'll def check them out bc lee is good but just takes too much time since I'm new in the subject

[remote sparrow]

idk a topic catches my eye and i wonder if there's any good books on it

[vital bane]

Have you learned real analysis, abstract linear algebra and some basic point set topology?

[spiral sky]

That's the soul of a self-studying student, same here that's why my analysis is engineering level but my alg goes along w my degree lol

[vital bane]

that's probably why you're struggling with Lee you gotta be good with analysis on R^n before you start studying diff geo of manifolds like a math student

[spiral sky]

Lin alg is my fav of all of them, real analysis I never had a course on, but I had to learn some tools for ode, diff geometry and topology had a course but barely up learned top spaces, took munkres and finished the book, but I need more practice

[vital bane]

you finished all the munkres exercises? based

[spiral sky]

I wish when I say finished the book meant finished the material, as for exercises I had done almost nothing

[remote sparrow]

[vital bane]

There's your problem

Let me show you something from Munkres

This is from "A Note to the Reader" in Munkres

[spiral sky]

My top prof said there are some challenging problems on there (but this was after) and this kinda scared me away from the exercises even more

[remote sparrow]

there's a better pdf fyi

you can preview books before you download them

so you don't keep shitty pdfs

[vital bane]

If you only do what you can do, you will never be more than you are now.

[remote sparrow]

munkres is basically standard everywhere; there are surely hints or solutions to a subset of the exercises on the internet

[spiral sky]

Yes I read this, this applies to every single course obviously but I kinda got away w it in algebra, but still solving problems is not natural

[vital bane]

that's sus

what book did you use for Linear Algebra?

and when you say "Algebra" do you mean Abstract Algebra?

[vital bane]

nevermind you did

[spiral sky]

The very first one was gallian, but then maracino or something like that, then hungerford (ug version) some artin stuff which was good for lie theory

[remote sparrow]

saracino

gallian

[spiral sky]

Exactly

[remote sparrow]

reminds me too much of a calculus textbook

[vital bane]

what's wrong with Gallian??

Gallian is awesome

Anyway you gotta do exercises to actually learn the material You need to start from Real Analysis, then Re:do Munkres (solving as many exercise as you can) I recommend Understanding Analysis by Stephen Abbott for Analysis, do lots of exercises from Abbott too

[spiral sky]

I like gallian but my fav is ash book I also wanted to check bourbakis book but it has bad reputation, wanted to check it bc it actually starts from group actions which is very nice imo

[vital bane]

after that you will have a much easier time with Lee

[remote sparrow]

https://www.youtube.com/watch?v=eGDtW3BZyyE&pp=ygUgemFjaCBzdGFyIHVuZGVyc3RhbmRpbmcgYW5hbHlzaXM%3D

[remote sparrow]

you can look at shahriari

[vital bane]

@merry sphinx

[remote sparrow]

does group actions pretty early

[vital bane]

so does

I need to actually get back to grinding this soon or else I'm cooked

[remote sparrow]

i heard dummit and foote doesn't integrate group actions very well into the rest of the book tho

[vital bane]

cap

[remote sparrow]

like the treatment exists but it's somewhat independent

[spiral sky]

Heard aluffi is also good but never checked it out

[vital bane]

Baseless slander I say!!

D&F, Abbott and Munkres are the holy trio no one shall slander them

[spiral sky]

It's really fascinating how u see group actions even on analysis

[vital bane]

huh

group actions in analysis?

bro has already started doing Harmonic Analysis

[spiral sky]

Never seen harmonic analysis lol

[remote sparrow]

d&f isn't my first choice to recommend to a beginner

[spiral sky]

Does HA has group actions?

[remote sparrow]

i think pinter is pretty goated for that purpose

[spiral sky]

I found the notation on D&F somewhat confusing. I think it's more of a referencial book

[remote sparrow]

it makes a fine textbook too

[vital bane]

notation for what?

it uses pretty standard notation though

[spiral sky]

Charles pinter?

I'll have to look I forgot

[remote sparrow]

yeah

#book-recommendations message

[spiral sky]

Omg I'm late for class gtg haha

[naive lava]

rudin mention WHAT THE FUCK IS EXPOSITION RAAAH

[grim ore]

?

[dense plover]

Is trig by loney good?

[fallen pivot]

Can u guys recommend any resources for self study for high school government olympiads

[merry sphinx]

ive watched this like 5 times

[gray gazelle]

i posted this yesterday

but here it goes

hefferon.net

[near jewel]

For groups, rings and fields, how is the book "A first course in abstract algebra"? I feel it got a weird "tone", or is it so with abstract algebra?

[slow roost]

what author?

[near jewel]

John B Fraleigh

[full cairn]

Fraleigh is great 👍 very beginner friendly

[spiral sky]

I also thought it was kinda unfair to say "first course" but then I realized how much there's to know after groups,rings and fields, made more sense the "basic" "algebra for beginners"

[coral prawn]

Hi, I got a question regarding gilbert strang's linalg book. It recommends some previous exposure to MVC before reading it. Is it really necessary?
I'm also wondering if HS students who haven't been exposed to rigorous mathematics would struggle with this book, as I've heard its moreso on the "applied" side of linalg.

[sick minnow]

Hi everyone. I delved into advanced mathematics a while back (undergrad chemical engineering), since then i took more managerial roles in strategy and analytics. I plan on taking a stats and probability program next year, but till then I'd really love to dabble in "applied" mathematics to brush off the rust. Any recommended books or online programs as such?

[remote sparrow]

@modern ruin is there anything you feel hatcher treats better compared to bredon? opinions about the quality of the exercises between each?

[remote sparrow]

strang has written a few linear algebra textbooks. which one are you talking about? also, in general, multivariable calculus isn't a logical prerequisite for linear algebra

[coral prawn]

intro to linalg 6th ed

but if he has written more beginner-friendly linalg books, I'd prefer those

[remote sparrow]

chapter 9, linear algebra in optimization, does use multivariable calculus

[remote sparrow]

the book you mentioned is supposed to be the easier version of Linear Algebra and Its Applications

[coral prawn]

Ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

I see, alr alr

[coral prawn]

noted

how rigorous is it? Would a HS student who doesn't have previous exposure to rigorous mathematics struggle?

[remote sparrow]

linear algebra isn't a subject that you need to worry too much about being too nonrigorous, but expect to mainly work with matrices and row reduction more than abstract vector spaces in strang

[coral prawn]

kay, thanks :D

[sick minnow]

In reference to this, and some googling, I'm thinking All the Math You Missed: (But Need to Know for Graduate School) (https://www.amazon.ca/All-Math-You-Missed-Graduate/dp/1009009192/) or The Princeton Companion to Applied Mathematics (https://www.amazon.ca/Princeton-Companion-Applied-Mathematics/dp/0691150397/), though I do worry they may be a tad advanced given i've been away from such topics for over 15 years. Any thoughts are appreciated!

though i think even if one of them is a tad complex, I could use it as a guidance and then cover the topics via other sources or online. Just not sure which to pic (aim is to brush up on general topics of math, perhaps leverage it in business/analytics context, and it won't harm if it preps me for a stats/probability program i intend to take next year)

[novel hound]

You may take a look at Kreyszig Advanced Engg Maths. The ode, pde parts are good. I'm not familiar with the other parts but there are sections on linear algebra, numerical analysis and on prob and statistics (very basic) which may interest you. Not sure it's the best option for you, but skim thru the ToC to see if it interests you.

[vital bane]

What do you plan to study?

you're going to enroll in a statistics and probabiltiy course? and after that you want to study some applied mathematics?

[pliant wadi]

As a person who's gone through 60% of that book, I think that's a valid opinion

D&F is a fantastic book but it's mostly encyclopaedic in nature imho

[drifting osprey]

Hey guys can someone suggest a good book on linear algebra which clears the basics and have a decent amount of problems to solve

[still panther]

idk i cant stand D&F

literally anything else is better

Hungerford is better, Aluffi is better, van der Waerden is better

D&F is the Hatcher of algebra

[naive lava]

Linear algebra done right is good

Hoffman and kunze is also nice

[full cairn]

Now you need to explain why Hatcher is the D&F of alg top

[drifting osprey]

Thanks 🙂

[vital bane]

FIS is better than Linear Algebra Done Right

FIS as in Friedberg Insel Spence

[heady ember]

That's suprising coming from you

I thought you would shill Axler's LADR

[torn blade]

honestly ive never found an abstract algebra book ive actually really liked

one thats really in sync with my way of learning / understanding it

i just learnt from lecture notes

[vital bane]

What?

No, I've been pretty outspoken about my distaste for Axler's hate for determinants

it caused me some trouble while I was preparing for entrance exams

[heady ember]

Yeah but you did like the other parts, no?

[vital bane]

they were alright

But overall I give the book a 6/10 (Axler LADR 3rd ed)

FIS is so much better

[naive lava]

and 4x the length tho

[vital bane]

wdym?

FIS is like 400 pages

Axler is 320 something

[naive lava]

my axler is like 220 pages

[vital bane]

but bigger book = more topics = more knowledge

[vital bane]

2nd edition moment

[naive lava]

whaaat

[vital bane]

4th edition is 400 pages

[naive lava]

why

how

[vital bane]

he includes multilinear algebra now

[naive lava]

[vital bane]

proper treatment of determinants now

finally

[naive lava]

i should learn that at some point lol

[vital bane]

yea let's go through Werner Greub's Multilinear Algebra

[naive lava]

orrrr

I can read my lang

wait is multilinear algebra just tensor shit

[tender cobalt]

I actually like FIS more than axler now

It also has computational problems which is really nice

and the exercises go from easy to hard

[vital bane]

I know right it's so fun

[tender cobalt]

unlike axler the exercises are crazy hard

Also axler isnt as comprehensive as FIS in my opinion

have you seen Lax's linear algebra @vital bane

[vital bane]

eh I wouldn't say crazy hard, I mean of course I was struggling with a lot of exercises in the beginning, but as I got more experience the exercises didn't seem very difficult (except a few)

[vital bane]

Peter Lax?

[tender cobalt]

Yea

[vital bane]

didn't know he had a LA book, I've only heard of his FA book

[tender cobalt]

Its so concise it covers spectral theory in first 80 pages 😭

[naive lava]

Functional analysis guy writes a la book?

[tender cobalt]

ohh

[naive lava]

I need to check that out

How many pages

[tender cobalt]

yeah i guess

only like 300

it also has solutions

[vital bane]

first 80 pages?

[naive lava]

What comes after the first 80 pages lol

[tender cobalt]

more stuff

it got vector calculus 😭

[naive lava]

220 pages more content

[tender cobalt]

some matrix theory

[vital bane]

non-archimedean spectral theory

[tender cobalt]

convex functions

[naive lava]

[naive lava]

[vital bane]

is this what you mean?

[tender cobalt]

yea

[naive lava]

He wrote a fing prequel to his other book lmao

[tender cobalt]

Man its rigorous and it got a lot of applications as well

[vital bane]

interesting book

I shall have to check it out

[tender cobalt]

IT HAS LORENTZ GROUP IN APPENDIX AS WELL AS FAST FOURIER TRANSFORM

😭

[naive lava]

My library has 3 of them

[naive lava]

Ngl Fourier is the best application of linear algebra ever

So im glad

[heady ember]

Actually that's why I want to do some LADR after FIS lol --- to see if there are interesting exercise not included in FIS.

But time is limited 😔

[tender cobalt]

oof

FIS has special relativtiy

[heady ember]

I do like one analysis exercise a week because of enslavement

I have regularly found FIS to not have sufficently many interesting exercises tbh

[vital bane]

do HK exercises after FIS

[vital bane]

2 years = 104 weeks = 104 exercises

[tender cobalt]

@vital bane hypothetically speaking if i manage to finish roman in 1 year

what subjects' prereq do i get my door open to

[vital bane]

don't hypothetically speak

first do it, then ask 🗿

[tender cobalt]

this my question

i think i can start functional analysis after it☠️

[fresh skiff]

You will need AA

[vital bane]

you need measure theory for functional analysis

[fresh skiff]

You need MT and RA

[tender cobalt]

so i need you? 👀

[vital bane]

Once you finish it you will be able to answer it 🗿

[fresh skiff]

Lol

[tender cobalt]

i kinda dont like hearing abstract algebra

i prefer just saying algebra

or modern algebra

cuz it is algebra just more advanced

😭

[fresh skiff]

I prefer algebra as well (but writing AA is much easier lol)

[naive lava]

really?

[fresh skiff]

@tender cobalt have you studied algebra?

[fresh skiff]

I think so!

[vital bane]

I don't think so, though you will need AA for harmonic analysis

[fresh skiff]

Ohh

Maybe not a strict prerequisite, but will be helpful

[vital bane]

Anti-Aircraft missiles

AA

[naive lava]

then i'm cooked

[fresh skiff]

Wdym

[naive lava]

I'm taking FA without much of the prereqs this semester

and now there's one more prereq

[tender cobalt]

not yet

[fresh skiff]

Oh, for FA?
I don't think so you need algebra (but some of linear algebra)

[tender cobalt]

Wait he meant u need AA for Roman linear algebra

[heady ember]

https://tenor.com/view/i-need-more-power-animefan27-kagenou-cid-the-eminence-in-shadow-kage-no-jitsuryokusha-ni-naritakute-gif-26866118

That is nowhere near enough

[tender cobalt]

FA is needs lot of linear algebra

[vital bane]

and a lot of analysis

[naive lava]

aaaaah i see

okay okay

[vital bane]

same

[tender cobalt]

i am planning to start real analysis after finishing my linear algebra and topology grind

[fresh skiff]

I see,

[fresh skiff]

Top => real anal
Is something not common

[tender cobalt]

i know

but real analysis will go smoother if i know top + lin alg well right

[heady ember]

You don't really need lin alg for intro analysis

[fresh skiff]

Maybe, also depends what book you will use

[tender cobalt]

i mean the grad one

by real analysis

[fresh skiff]

Grad real anal = MT

[naive lava]

you're gonna use metric space topology most of the time

[tender cobalt]

yah

[naive lava]

so that's a lot easier

[heady ember]

If you wanna learn multivariable analysis or DG, then I believe lin alg is indeed important.

[tender cobalt]

yeah

DG is my goal

[naive lava]

but seeing things from a topology pov helps a lot

[tender cobalt]

So I am trying to build good foundation in topology and linear algebra

[naive lava]

you immidiately see how it generalizes

[fresh skiff]

Read spivak's books

[tender cobalt]

also analysis is just special case of topology and linear algebra

[tender cobalt]

big af :(

[naive lava]

[tender cobalt]

I aint wasting my time with intro analysis to get the "motivation" for topology

[naive lava]

isn't analysis just the art of taking limits

[tender cobalt]

yes

and limits is just topology open sets stuff

[naive lava]

non cont functions

[tender cobalt]

I think in munkres topology book there's a section named "A Nowhere Differentiable Function"

[molten gulch]

it does

[vital bane]

no

analysis is the art of inequalities

triangle inequality, cauchy-schwarz inequality, holder's inequality, strichartz inequality, and a billion others

[naive lava]

Minkowski and holder, take it or leave it

[tender cobalt]

how to master these inequalities bro

it gets me stuck always

[rigid trail]

get to grinding

[tender cobalt]

is steele's Cauchy Schwarz master class a good book for mastering these inequalities 🤔

[rugged ether]

Hello, i want to ask if there are some recommendations for university probability and statistic materials / videos that might be helpful for univ courses

[gray jungle]

knowing topology without real analysis is like knowing grammar without ever reading a book, or studying music theory without listening to a single song.

you can do it but whats the point

[tender cobalt]

differential geometry / manifolds would be the song

algebraic topology would be the song

😭

and the other way around, analysis would be the song

[sick minnow]

the certificate is just a stop gap as then i intend to either delve into a full on masters in probability and statistics, or business strategy - so am trying to develop my math in these areas. when asking chatgpt about the math topics that would serve in both, I received this list:

• Optimization & Game Theory
• Probability & Statistics
• Econometrics
• Calculus & Mathematical Modeling
• Network Analysis & Graph Theory
• Machine Learning & Data Science (Emerging Importance)

therefore not sure what direction to really take for now ;p

[drowsy thicket]

Yeah that sounds weird, it seems like a lot of the examples one would normally bring would fall away, like that metrics induce a topology

[fresh skiff]

true

i usually find counter example by thinking about real line

in top

[near jewel]

If you look at the master that you're planning to take, it usually would have a path that you can look at (maybe it's the sequencial of a statistics bachelor).

[wise imp]

one fish two fish red fish blue fish by dr seuss, phd is rly good for super complex addition u guys should check it out

[strong rampart]

Hi guys,
Any recommendation about math books that a physics student should read.

thanks

[royal bloom]

very very vague question, you'll need to be more specific

[strong rampart]

Actually, i wanna read and go deep more about math that a physics student will need (bachelor, master, phd)

analysis/algebre

[keen grail]

yes I want to know the answer to this as well

[signal badge]

You have experience with proofs?

[strong rampart]

in school what we read is analysis 1 (study of a function/integrals (simple)/equation diff (solving 1-2 equation degree)/ the sequels )

series

our math program are really weak that's why i wanna read math my self

[rigid trail]

multivariable calculus?

[strong rampart]

sample knowledge about how we can derive a function with 2 variables (because we use it in thermodynamics)

[keen grail]

I agree this is the best apporach I mean in less then three months I have mastered 90% of a course

[strong rampart]

what course ?

[keen grail]

back then it was algebra

I know pretty basic really

I took it back then somewhat early

geometry took me a bit longer i think

math classes does teach stuff in a slower pace I useally make sure I read stuff throughly and do lots of practice

[signal badge]

Could try and read Abbott's Understanding Analysis for a taste of rigor, if you're uncomfortable with that read Hammack's Book of Proof or something similar

[keen grail]

I know this is far different from physics

[rigid trail]

okay you probably should learn some more multivariable then

it's very important for physics

[rigid trail]

it's so much better at uni level

the pace is a lot faster

much better

[keen grail]

do you have any recomeded uni? for wanting to learn more about math?

[rigid trail]

whatever is most affordable tbh

[sick minnow]

try khan academy if u wanna fill some gaps

[strong rampart]

any books recommendation

[rigid trail]

although a lot of unis have pathetic math programs unfortunately

so i suppose
whatever is affordable and has an okay math program or better

[signal badge]

Oops, I thought they were university students. My bad

[keen grail]

khan academy is good aleks or IXL are better at grasping the whole course I think idk

[rigid trail]

stewart, khan academy