book-recommendations

[heady ember]

Cant you go to a printer store or smt? I mean I presume it'll be cheaper than buying a printed book, or at least not more expensive

since buying a book from somewhere means manufacturing costs + book license fees + some more cost to make profit I assume

Proof by assumption

[solid idol]

kkk. will check some stores near buy. Thanks!

[heady ember]

np

[woven forge]

Does anyone know this book by callahan?

advanced calculus a geometric view

unfortunately I hated that book

oh

now is it visible?

[gray gazelle]

ye

[marble solar]

I'm gonna chime in here and say

The best Complex Analysis book is Marshall's

Stein and Shakarchi is really great, except for chapter 2 with the toy contours

I refer to S&S for their great exercises and problems

But the exposition is sometimes lacking

Ahlfors is also really great, but it starts off with a lot of geometry

Rudin's Real & Complex is amazing, but it's Rudin

So hard to read

[hidden rain]

sure

i have it

[karmic thorn]

Late response but you can probably find a printing service that can print it with cover for you at a nominal price.

[solid idol]

Kkk

[karmic thorn]

If you're still tied then you should look for books on discrete math or introduction to proofs that fit your budget.

(I have no clue about costs because I almost exclusively get them printed)

[hallow oriole]

say, how do you go abt doing this? like, do you own a printer or something? or is there a place you can go to print it? and what do you do with the loose papers after?

oops sorry for the ping

.>

i forgot to turn it off

[karmic thorn]

No worries

There exist printing services that allow you to upload PDFs, customise printing options (quality/size of paper, book cover) and get them delivered

[lime sapphire]

i've always wondered how this is a thing cus does it not violate any copyright laws?

[karmic thorn]

[stray veldt]

it doesnt

at least not in the EU

if you legally own a pdf (or book) you can make as many copies for private use as you want

[lime sapphire]

right

[karmic thorn]

Over here copyrights are good as non-existent for personal use in practice at least, even if not in principle

[tame plaza]

https://tenor.com/view/ours-communism-bugs-bunny-communist-gif-24069854

Russia:

[karmic thorn]

At least the printing services can dodge the bullet on grounds of "we don't monitor the contents of what we print to respect privacy" or something along those lines

[stray veldt]

oh yeah, the printing services might break the law 🤔

they certainly cant keep the pdf

[dense furnace]

Any calculus book recommendations

[hallow oriole]

spivak's calc, apostol's calc, lang's calc

are all recommendations i've seen

stewart is also good for exercises 👍

[dense furnace]

Thank you

Any you recommend more than the other outta those options?

[hallow oriole]

well

stewart is the only one i have personal experience with

lots of exercises

probably good as a supplementary material

i've also heard spivak's probably isn't the best for an intro to calc

so i would recommend apostol or lang more

[dense furnace]

Thx

One more question do they both go over derivatives?

[hallow oriole]

a calculus book that doesn't go over derivatives isn't worth glancing at

[dense furnace]

I wouldn't touch it

[sage python]

Apostol is just Spivak but written a bit worse, organized funny, and old school

If you aren't on a time crunch and you want to do proofs Spivak is perfect for a first course tbh

[hallow oriole]

really? someone told me spivak was just not good as an intro

[subtle mango]

what kind of calculus book doesnt do derivatives

[hallow oriole]

probably a really shit one

[shadow forum]

i would like to see one such book tbh

[hallow oriole]

i bet i could make one 😎

[subtle mango]

smth like teaching integrals then saying "the concept of derivatives follows trivially from integration, left to reader as exercise"

[hallow oriole]

the concept of integration follows trivially from derivatives ofc

[sage python]

Valley: it's harder than most

And it's only of much appeal if you want a fairly theoretical treatment

[hallow oriole]

would you say it's a good choice for someone who wants to shore up their calc foundations and learn multivar?

[subtle mango]

im planning on using spivak to relearn calculus 3 after i finish linalg, just to get a better idea of it aside from R3

[sage python]

Hmm, based on how you're talking valley it feels like you'll want something more condensed, given that you already know computational single variable calculus

Have you done linear algebra yet?

[hallow oriole]

nope, but i plan to self-study it with strang's linear algebra and its applications

although i'm also told ladr and ladw are good choices

so i'm having a bit of choice paralysis

[subtle mango]

ive heard ladr is flawed

[hallow oriole]

also i wasn't sure whether multivar before linalg was better or the other way around

[hallow oriole]

how so?

[subtle mango]

gonna be honest, not sure

but ive heard people suggest ladw over ladr

[warm glen]

for linear algebra i like the book by morton l. curtis

it's entirely proof based

[hallow oriole]

ladr @subtle mango #math-discussion message

this is sloths commenting on it

[subtle mango]

aha

[hallow oriole]

idk much abt it but seems pretty convincing

[subtle mango]

i'm using H+K rn

[sharp solar]

Hello. I'm a half computer science student (rather not explain right now) and I want to strengthen my mathematical foundations/fundamentals. I have had a course on discrete mathematics as well as kind of "introduction to mathematics for CS" modules, but these introduction modules basically only touched on a number of topics. Moreover, my knowledge of calculus from school is basic and pretty 'rote', application of rules, etc. without a solid understanding as to the why.

So now I basically would like to ask whether I should start with 'mastering' linear algebra or calculus first?

(or something else)

and given the channel, suggest a textbook on said topic 🙂

[gray gazelle]

under what topic do we read about double summations and stuff, and can some recommend a book for it

[sage python]

@brittle latch ask here, you were interrupting an active convo

[fervent lava]

Real analysis. I recommend seeing the last section of chapter 2 of abbot understanding analysis.

[dense furnace]

Really?

[untold plover]

I FOUND THE BEST BOOK

[glad prairie]

[gray gazelle]

Anyone got a book recommendation for analysis? Going to be taking it next semester and would like to get ahead—would like to build some intuition beforehand

[runic hatch]

The usual recommendations I’ve seen are Rudin and Apostol; both are decent, although Rudin is more terse

[gray gazelle]

Again, my goal is to develop intuition, not rigourously prove concepts. Would those two still be your recommendations?

[lapis heart]

watch some videos not read some books

[gray gazelle]

What videos?

[rugged seal]

any recommendations for Measure theoretic probability preferable with exercises and solutions.
it should have a brief introduction to measure theory (Measures, measurable functions, fubini, radon-nikodym etc.) and then use it for probability

[gray gazelle]

Why?

https://link.springer.com/book/10.1007/978-3-642-21298-7 ?

Why is it better

[rugged seal]

this book is very new but the content is very fitting are there perhaps older ones, with similar content

which 3 germans books, i am from germany so there is a high chance my university has them

yeah but i cant get my hands on them very easily and for free

thank you very much

[woven forge]

has anybody had experience with either rotman's algebraic topology or advanced modern algebra

[rotund flint]

Book.

[woven forge]

found a great book in real analysis

https://www.amazon.com/Real-Analysis-Theory-Measure-Integration/dp/9814578541

it even has full solution manual availabe

the downside is it is hard as f**k

[hallow oriole]

and expensive as fuck

[woven forge]

tbh using l/i/b/g/e/n is one way

[hallow oriole]

yeah but the issue is that i prefer physical books :/

[woven forge]

just go to print store

[woven forge]

oh i prefer physical books too

but damn college loan

[hallow oriole]

do you happen to live in the US?

[modern stone]

What are some good resources for getting an intuition for the definitions in topology?

[timber mesa]

visualize everything in R^2

things like bases generalize how open balls generate e.g. the euclidean topology or that of a given metric space, the definitions of things like closure and compactness generalize properties in R^n etc.

always think of examples

[gray gazelle]

When in doubt, think geometrically

[modern stone]

What about the definition of a topology?

I can’t see how it captures the notion of “closeness”

[stray veldt]

just like in a metric space, two points are close if both of them are in "many" open sets

[gray gazelle]

In what sense

Closure of a set kind of does

$x\in \overline{A}\iff $ for any neighbourhood $U$ of $x$ we have $U\cap A\neq \emptyset$

So x is "close" to A

If you expand it even a little, it crosses A

[lapis heart]

Uhh I can't unravel this, wut

[stray veldt]

its incomplete

[hasty eagle]

Blitz

[gray gazelle]

Here

This is not completely obvious at first sight if you defined the closure of A to be intersection of all closed sets containing A

So an exercise

Other than this there's not much surprises in early general topology course imo

It's all set algebra

[small socket]

@rugged seal Try Klenke's Probability Theory book

@gray gazelle Try Abbott's book and https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/anal1v.pdf Taylor is notorious for terse writing, but this book is readable.

[gray gazelle]

Book suggestions to learn all functions types, limits, derivatives and integrals?

[fervent lava]

Hmm, do you want to learn it rigorous?

If yes we have spivak calculus if not, any calculus book will do.

Stewart calculus is a common recommendation. Paul's online math notes work as well.

[gray gazelle]

U can study with these books without teacher?

[fervent lava]

Definitely.

[gray gazelle]

How?

[fervent lava]

Read, do problems then repeat. Ask questions.

[gray gazelle]

I never read a textbook before

Ill give it a shot

[fervent lava]

I feel you, my favorite recommendation for learning calculus is paul's online math notes.

https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

[gray gazelle]

Alright ill check that out thx

[fervent lava]

It's easier to self study using that.

[gray gazelle]

Can I do calculus 1 without having seen logarithms?

And trig?

As in Pauls review is good enough?

Or do I need more in depth

[subtle mango]

logs and trig are fairly important for calculus

[gray gazelle]

So I should spent a lot more time than just a couple exercises on a review?

[fervent lava]

You need to have a good understanding of trig.

log too.

Try khan academy for those.

[gray gazelle]

Alright ill get started on that

How long would it take to finish that

And calculus I

[fervent lava]

It depends on how much work you put in.

So I can't tell.

[gray gazelle]

Doable in a month or three?

If say spend a 2 hour a day

[fervent lava]

Calculus 1 is usually a semester course. As I said, I can't tell you how long it would take.

Just get started and go through it slowly.

Sooner or later you will finish it.

[fervent lava]

Paul's online math notes has a college algebra course that has a section that covers logs.

Also paul's online math notes has a review for logs and trig in the calculus 1 course.

So you should be fine.

[timber mesa]

honestly, even this might be good but make sure you really understand logarithms and trig

logarithms and trig aren't exactly rocket science, there isn't a ton to know about them within the context of a freshman college course

you may want to review them on the fly while studying calc

trig is important for trig substitution on integrals, which sometimes is part of Calc 2

[half sentinel]

Are "algebra" and "analysis" separate things at the undergraduate level? Can I learn the em stein series1-4 if I only know "linear algebra done right"

[hallow oriole]

algebra usually refers to abstract algebra at undergrad level, think rings, fields, galois theory, etc, while analysis is like real and complex analysis

i don't know the answer to your second question, sry

there's a good amount of overlap tho

[subtle mango]

Good books/courses for learning MATLAB?

[hasty eagle]

No selfroles matching deying.
See ,selfroles --list for the list of valid selfroles.

Apr 1, 2022, 6:43 AM

[rugged seal]

thank you it looks great aswell

[solemn mantle]

is there any book for linear algebra that is mostly theory rather than computational

[sage python]

Sooooo

Giving a longer answer

[frosty girder]

why dont u recc ur pin here

@solemn mantle

[sage python]

That's algebra, abs is asking linear algebra

[gusty smelt]

That’s not la

[frosty girder]

oh

keep going, sorry for interrupting

[blazing canopy]

Linear Algebra by Friedberg, Insel, Spence

To elaborate: I think the book is the most clean and modern presentation of the subject at the introductory but fully rigorous level.

It does not try to be too complete

[solemn mantle]

It's enough for something like Jacobson, right?

thank you btw

[blazing canopy]

Not sure what you mean by "enough", but F.I.S. (my abbreviation) is not like Jacobson at all

Jacobson seems more like a complete reference

[solemn mantle]

Dami said for Jacobson (abstract algebra) you'd want some LA going in

[blazing canopy]

I suppose it's helpful to get some familiarity, but technically not necessary. You could develop the theory of rings and modules first, before specializing to vector spaces

[solemn mantle]

yeah but aren't modules generalizations of vector spaces? lol

[frosty girder]

modules from my knowledge are just vector spaces over rings instead of fields

[blazing canopy]

You can say that, sure. But sometimes more general things are actually cleaner because fewer properties means fewer theorems

[solemn mantle]

true, but from a learning point of view, I may not understand the motivation behind some choices

not sure if that's true or not here but sometimes that's happened when I learn the abstract thing before the specific thing

[blazing canopy]

This is true. That being said I don't believe that a standard text on linear algebra really prepares you in any meaningful way for a broad study of algebra, unless you're only studying modules, or only studying matrix groups

Other than perhaps preparing you via mathematical maturity

It's true that the connections run deep (eg with representation theory) but an actual course in linear algebra is focused on very different things

[solemn mantle]

what is a linear algebra course focused on?

[blazing canopy]

At the level of a 1st course, I'd call it a study of the linear maps and matrices

In particular how to decompose them and characterize them

There are several key topics that don't figure very heavily into abstract algebra

One is eigenvalue problems

Another is matrix factorizations from the standpoint of inner product spaces (eg orthogonal decompositions)

These end up being more like geometric study of linear spaces

Rather than algebraic

[sage python]

Linear Algebra Book Review

Traditionally, people do a first LA course focusing on computation at the expense of theory, then a theoretical course assuming you know computations. This is mostly because of inertia + first course is service course. I'm targeting this list for math majors, so I ignore books like Strang, and I comment when "second courses" are actually viable first courses

I think it's best to work over general fields whenever possible in linear algebra, since there's cool content over eg finite fields, and it's good to know whether you need the ordering on R (say for inner products), char 0, the field structure, etc. That said, ymmv. All these books cover some content that necessitates restricting attention, but I comment when books make that assumption right away.

• Lang: First book is computational, second is theoretical (self-contained, but fewer computations). Organization feels screwy, and it's probably boring to read because Lang. Works over subfields of C
• Linear Algebra Done Right: Calls itself a second course (meaning theory at the expense of computations), but it's self-contained and has rather gentle prose. Works over R and C. Anti-determinant, which in previous editions led to stupid choices. 4th edition is much better (I'd still change some stuff, but it's no longer unhinged), and now it's one of the few books that does multilinear algebra properly rather than just doing the minimum needed to define determinants.
• Linear Algebra Done Wrong: Works over R and C, balances theory and computation (prefers to prove theorems using row-reduction). Mixed reviews: some say it's great, but there are complaints about treatment of diagonalization and undefined terms in problems
• Halmos: Goal is to present linear algebra as finite-dimensional functional analysis, so it prefers the coordinate-free approach. Works over general fields (though a large portion of the book is on inner products and analysis). More theory than computation. Old-school typesetting and notation/terminology
• Hoffman and Kunze: Does matrices first which is fair but awkward. Extremely detailed, slightly abstract/tricky at times but not unreasonably so. Assumes fields are subfields of C in examples/exercises unless otherwise noted. Contains both theory and computations
• Friedberg, Insel, and Spence: Basically a modern Hoffman-Kunze. Somewhat easier (at the expense of some topics that are honestly cool), better organized (should canonical forms have come before inner products? Jury's out). Assumes fields are char 0 in examples/exercises unless otherwise noted. Contains both theory and computations
• Charles Curtis: Feels like a shorter FIS. Friends who used the book in a course didn't like it, and at a glance its organization feels screwy. Balances theory and computations.
• Morton Curtis: Very abstract and efficient, finishes off by classifying normed algebras over R. Works over general fields, and uses multilinear algebra for determinants. Prioritizes theory, and in fact omits stuff like SVD which are imo important (though it's surprisingly complete for what it does cover, given the length)
• Shilov: People here seem to like it. Very hard hitter, works over a general field, and covers more advanced topics. Starting with determinants feels like a meme

There are books I'm less familiar with (never referenced, TAd from, or had friends comment on) which seem interesting. Katznelson-Katznelson looks quite efficient, though it does many details such as Vandermonde matrices and SVD that eg Morton Curtis misses. Greub feels like The Reference™️ and quite a hard hitter. Roman is on crack: does module theory and Hilbert space stuff, also "Umbral Calculus" (?)

Some algebra books, such as Knapp and Artin, develop linear algebra from the ground up. If you're clever and want to move fast, those are worth considering (Knapp seems harder than Artin).

This is my take @solemn mantle

[frosty girder]

Probably the correct answer tbh.
Based as fuck

[heady ember]

Yeah I saw quantum complaining about LADW diagonalization yesterday

[blazing canopy]

My only exposure to LADR and LADW was in choosing which book I wanted to teach from

I felt that both were extremely idiosyncratic, for no particular reason really

[heady ember]

[blazing canopy]

Given the future interest in learning algebra I agree Artin is a decent choice, though it's not a complete coverage of linear algebra

[heady ember]

I see.

Interesting.

[sage python]

Ah you're a faculty member, nice!

Seem to be interested in analysis/applied math?

[blazing canopy]

I was formerly teaching while I was a postdoc, no longer, at least for now. And yes my area is applied math

[runic hatch]

Is roman bad? Or is it significantly harder than the other texts

[sage python]

Roman is very niche. It's explicitly not a first book, but usually by the time you're ready for Roman you're reading algebra and functional analysis books rather than linear algebra 2

Good stuff Mipchunk

[runic hatch]

ah I see

[dense wren]

Anyone here ever read Altman and kleimans commutative algebra book? If so what’s your opinion on it

[sage python]

Seems like a more modern Atiyah-Macdonald but somehow he exposits in a way that pisses me off and I'm not sure why

(Haven't read much of it tbf, just that what I've read turned me off for reasons I cannot put my finger on, so ymmv)

[dense wren]

@sage python funny you say that, I was thinking the same thing reading the first few sections

I think for me it’s just too terse

Maybe that’s the wrong word, I guess barely any exposition in addition to the math itself

[blazing canopy]

I've not, but I've heard it's really good, at least as far as rigorous calculus texts go

I personally feel that there's enough calculus resources online and floating around that the concept of using a specific book is not necessary

[sage python]

Mipchunk is this blasphemy against our lord and savior Spivak?

[heady ember]

[solemn mantle]

Spivak is goat

[sage python]

(To be fair I do think some things could probably be improved upon in Spivak I just find it funny to be like :0)

[solemn mantle]

I used the Ron Larson books for ap calc

[sage python]

Lucy: honestly if you already know computational calc you can probably do an analysis book rather than Spivak

[heady ember]

[sage python]

I found this one book lately by Browder which tbh might just be superior to Rudin

Jury's out

[solemn mantle]

Is rudin generally more in-depth than spivak

[sage python]

More general

[heady ember]

What's the full name of the book? Just curious. (im a billion light years away from analysis but just curious)

[sage python]

Like

Spivak does things in the "calculus way" rather than the "analysis way" so to speak

[solemn mantle]

By the way thank you very much for this, shouldn’t you pin it?

[sage python]

For instance, his proof of intermediate and extreme value theorem avoids topology in favor of working directly with suprema

[blazing canopy]

Ha. It's more that I object to the idea of tying studying math to studying specific books. Too much emphasis on trying to do things the "right" way

[sage python]

If you guys think it's good sure. Mipchunk any objections with that linear algebra review?

[blazing canopy]

I don't have any skin in the game, it's up to you 🙂

[sage python]

Fair, I guess just since you taught linear algebra do you think it's a fair assessment 😛

[blazing canopy]

I've only taught from FIS, Axler, and Lay

But also, teaching from is very different from learning from

When selecting a book to teach from, you pay attention to things like good exercises to steal HW out of, familiar notation, and good ordering of topics

But maybe less attention paid to exposition

[frosty girder]

do apostol

apostol the best

(apostols analysis, not calc)

[frosty girder]

allyc will be happy

u can kind of try to wing proofs

like doing basic ones ur self, and getting an idea of how they work

[mystic orbit]

you haven't said anything about hubberd's

[sage python]

Hubbard and Hubbard?

[mystic orbit]

ye

[frosty girder]

(i dont happen to know of any specific proof teaching series, but i think some youtubers like michael penn and prof leonard might have something for u)

[sage python]

I'll check it out

[frosty girder]

Hubbard feels a bit off to me for some reason

idk why

true

well u can ask for help here, to verify proofs and stuff

i dont think they are much cons

i really like apostols book

i havent completed it by far

but its got everything u would need

examples, proofs, theorems (these should be there, obviously)

and exercises, a ton of exercises

[sage python]

From the table of contents... I'll be honest this feels like a "the linear algebra you need to introduce to teach something resembling a correct multivariable calculus class without explicitly requiring students saw it before opening this book"

[frosty girder]

really nice ones as well

[sage python]

Defers a lot of proofs toward the end which is bizarre

Honestly this book is just incredibly strange

[frosty girder]

yeah exactly dami

[sage python]

I feel like Shifrin's probably just better tbh

[frosty girder]

whats shifrin?

[sage python]

Multivariable Mathematics by Ted Shifrin

It's this but with less of a wtf organization

[mystic orbit]

only the particularly hard ones or the ones it deemed less important

[coral narwhal]

not trying to say anything about apostol but these are just things present in most math books ?( I mean like undergrad books and above )

[frosty girder]

yeah as i said, these should be there in a good ug book

but its that apostols problems are pretty damn good

[sage python]

Yeah ofc not all the proofs are being deferred lol

[frosty girder]

like, the topology chapter has 50, limits and continuity has 70+

[sage python]

Just that like

[normal sandal]

Fwiw a large number of problems isn't a comment on their quality

[solemn mantle]

Wait artin … I want to learn linear algebra and abstract algebra, is this both in one? I was going to try Jacobson later on at some point but now artin seems like a better choice. Is there any downside?

[sage python]

Idk it feels like it's trying to achieve some weird balance between being good for calc 3 students who care less about proofs and for honors math students that wanna do things right? That aside though... idk it mixes shit up in such a bizarre way

[frosty girder]

i said good problems bruh

[sage python]

I haven't read much of Artin myself tbf abs_0, but at a glance it seems good

[mystic orbit]

it is quite unorthodox

I picked it up mostly because 3b1b highly recommends it

[sage python]

Yeah idk how much I like it. I could see it appealing to a certain niche

In any event it doesn't include enough linear algebra to be a contender on this list

[blazing canopy]

Artin is a great survey of algebra and is thus very suitable for learning, especially as a first time through

[normal sandal]

I like how LADR is the first one on the list lmao

[mystic orbit]

I'm planning on doing artin later on, so maybe it'll be enough to fill the gaps

[gray gazelle]

@sage python did you check Tao's linear algebra notes? It uses FIS as a supplement and is pretty short(almost 300pages)

[sage python]

Idk Tao's notes

My own path through linear algebra was basically

I did an REU summer after first year which had a class that was a week of graph theory, 3ish weeks of linear algebra, and a week of spectral graph theory

[solemn mantle]

That’s awesome, wdym survey?

[sage python]

(It was 2 and a half hours/day, 5 days/week, so we did cover a fair bit)

[blazing canopy]

Artin covers many topics, but not in too much detail

[solemn mantle]

Wow that’s perfect

[sage python]

I had LADR on hand going in but honestly the lecturer was extremely good, and did things in a different way than LADR anyway, so I never really used it much

[blazing canopy]

Surely you know that question can't really be answered!

[sage python]

Then I took an analysis class and... basically up until that year we didn't have a linear algebra class. You did a few weeks at the end of calculus, some stuff in analysis as needed, and mostly during the ring/module theory quarter of algebra

But then the department was like nah we need to have a straight up linear algebra class, and we'll make it a prereq for second quarter analysis (where they start multivariable differentiation)

[solemn mantle]

Easy to unfathomably difficult

I don’t know rudin but if it’s proof based they will not be computational at all

[sage python]

Except honors analysis taught the multivariable calculus already during first quarter, and profs just taught the linear algebra they needed

[solemn mantle]

Well the goal isn’t to do every single exercise

[sage python]

So the department said alright if you do first quarter honors analysis you're exempt from linear algebra

Corollary the prof now had to cover a full course in linear algebra along with the analysis. Which our prof didn't want to

So he just gave us the book that the linear algebra class was gonna use (Hoffman-Kunze), each week had us read the chapter and do an extra pset from it

[solemn mantle]

@gray gazelle https://www.reddit.com/r/math/comments/fug6z8/a_short_guide_on_how_to_use_rudin_to_learn_real/?utm_source=share&utm_medium=ios_app&utm_name=iossmf

[blazing canopy]

Time estimates will be difficult because the problems vary so much in difficulty. There are probably some that could take over an hour if you get stuck

[solemn mantle]

lmao

[sage python]

My friends who took linear algebra told me they used "Abstract Linear Algebra" by Morton Curtis instead since Hoffman-Kunze was out of print. Ended up being a bit much. Switched to a book written by a different Curtis which idk well. Eventually settled on LADW which seemed to be good from what I've heard/checked out. And I graded psets from a class using FIS

Plus I tried Artin a bit when I started learning algebra before I switched to D&F and eventually to Herstein

So that's pretty much where the list I'm reviewing comes from

[heady ember]

This reminds me of spending one whole day on 3 basic set theory qns

[solemn mantle]

@gray gazelle to understand set theory and logic I have a book I really like, it completely babies you but it’s perfectly rigorous and understandable

Those are the most fun ones

Oh nice ok you’re set with that

Wait do you already understand set theory and formal proof

Oh that’s rly cool

https://opentext.uleth.ca/PDF/proofs+concepts.pdf

It’s fun yeah

The exercises are hilariously easy, but it gives you a very solid basic instinct about logic

[frosty girder]

u need some logic and idea about how things work for analysis yeah

[solemn mantle]

No you definitely need all of it

It’s also fun because it makes it very easy

But yeah I recommend it

[mystic orbit]

I find books with easy exercises kinda meh ngl

that's why I dropped velleman

[blazing crane]

Rs Aggarwal grade 10 has tough math questions and if you want even though ones then try ML Aggarwal

[sage python]

Updated the review slightly to go into more detail on Morton Curtis

Also threw in a lol for Greub

Because lol

[frosty girder]

the people currently talking werent looking for 10th grade problems

lmao

[frosty girder]

can you do a few more of these book review thingies? for like say functional analysis, or diff geo

or comm alg

stuff like that

[sage python]

I prob will at some point yeah

Let's move to chill rq

[frosty girder]

[gray gazelle]

What's a good beginner book on ODE

[woven forge]

i found book of proof by hammack to be better

[smoky zephyr]

same

[woven forge]

it has more solutions

and its explanation is just better

[woven forge]

just read boyce

tbh ode shoudn't be that hard on undergraduate level

if you didn't totally screw up your calculus course

[gray gazelle]

K

Thx

[woven forge]

are there any good books for referencing trig , exponential and equations

I threw away my high school and middle school textbooks

and am regretting it

[frosty girder]

why are you regretting it?

[hearty steppe]

Don’t regret it, those books were probably garbage in comparison to what you’ll find in pins

[runic hatch]

Honestly wikipedia is a good reference for those things

I constantly hop on to wiki to find the identities I need

[wintry quartz]

I tried linear algebra done wrong and I found that to be a little difficult, not because of proofs but my lack of knowledge in linear algebra, such as matrix multiplication, etc. could anyone recommend a book that if rigorous but also introduced those topics?

[marble solar]

Schaum's outline to linear algebra

will give you lots & lots of examples

[blazing canopy]

I don't suggest trying an "all-in-one" approach for this. There are lots of free materials online on just the calculation elements of linear algebra that can supplement a more rigorous book.

[marble solar]

There isn't any, Boyce & DiPrima is alright. Better if you can get an older edition (before 5th?)

Schaum's outline to ODEs is decent too

but I wouldn't call it "good" by any stretch

[wintry quartz]

what online recourse would you recommend then?

[blazing canopy]

MITs OCW for linear algebra is decent, I used that course many years ago. I think some people use Khan academy as a simple intro as well.

[gray gazelle]

Whats the best textbook for commutative algebra......?

[gray gazelle]

bible?

eisenbud

good, matsamurua or atiyah macdonald

[gray gazelle]

@gray gazelle is good a name

[gray gazelle]

i like your name also

[smoky zephyr]

[gray gazelle]

I mean is good a name

[terse moth]

Not a book but https://youtube.com/playlist?list=PLVFUQ1rop3OmnHHxIZnHMKweObkqjXfbR

[gray gazelle]

@gray gazelle

[gray gazelle]

Differential Geometry Books & PreReqs?

[gray gazelle]

?

[gray gazelle]

.

[blazing canopy]

Have you already studied the basic concepts, e.g. basics of topology, smooth manifolds?

Lee's "Introduction to Smooth Manifolds" gives a decent survey of some of the main topics concerning smooth manifolds and a few topics in geometry

For strictly differential geometry, there's Do Carmo's "Differential Geometry of Curves and Surfaces" as well as his other book "Riemannian Geometry"

You should know vector calculus and linear algebra at the very least. Real analysis is also valuable.

[sage kelp]

You can try A Course in Game Theory by Rubinstein and Osborne, Game Theory by Gibbons. Even Microeconomic Theory by Mas-acólelo and Advanced Microeconomic Theory by Jehle & Reny have some chapters devoted to game theory

[gray gazelle]

Oh ok thanks

[marble solar]

Schaum's outline to ODEs is great because it solves a million problems

which is honestly what you need in ODE

Don't forget to brush up on Calc 2

[gray gazelle]

Ok thanks so much

[marble solar]

yUh no problem

[gray gazelle]

And for PDE what would you recommend I use?

[marble solar]

Ok

So have you learned real & complex analysis?

That'd be like Fourier (S&S volume 1), Rudin chapters 1-8, Spivak Calculus on Manifolds, and pick your favorite complex text

If you've learned that stuff I'd go for Evans PDEs

If you're still in undergrad material pre-analysis Walter Strauss' book is alright

But honestly going into Stein and Shakarchi's Fourier, then complex would probably be the best

Since to do PDEs "right" you need a lot of real/complex analysis, and ODEs

And several variable calculus a la spivak calc on manifolds

@gray gazelle Hope this helps, but if I had to pick an order, it'd probably be like S&S Fourier, then Rudin, then Spivak, and you can do complex at the same time if you feel you have time

[gray gazelle]

Ah ok

[marble solar]

If you wanna get straight to PDEs without mumbling around

Strauss' Book

[gray gazelle]

Rudin's "Principles of mathematical analysis"?

[marble solar]

Yeah, baby Rudin chapters 1-8. If you intend to go further in PDEs

You need to know real & complex pretty well, like the back of your hand

(Even functional, but I haven't learned functional so I can't gripe)

[sage python]

Does complex appear a ton in PDE?

[marble solar]

If you go a harmonic flavor it does

[sage python]

I see

That's like dispersive stuff right?

[marble solar]

But also thinking about things geometrically

[marble solar]

Yeah

[sage python]

Iirc dispersive PDE is fairly big on the harmonic analysis

Elliptic PDE with calc of variations?

[marble solar]

Elliptic PDE you wanna know your complex for sure

Maximum principle

etc.

A lot of complex is PDE theory in disguise

Geometryhards will try and tell you otherwise

[sage python]

I do agree but I thought it was gonna be the opposite flow then

Like oh it's good to have some idea how elliptic PDE work before complex since you'll mirror properties of harmonic functions 😛

[marble solar]

lol

"Just do elliptic PDEs before complex"

[sage python]

Honestly Souganidis prob just believes that

[marble solar]

In other news I got my teaching schedule for next year??

[marble solar]

Mooney told me that Elliptic PDEs takes 2 years to go from beginner to research

If you've done the analysis thingies

Ofcourse time may vary by maturity level

[sage python]

Yeah I think Soug doesn't give a shit about complex analysis is the thing haha

[marble solar]

I can see this: from a current perspective, a lot of it is dated and not useful

If you wanna do relevant research

Complex will hardly show up, but you know what I had to do in my fucking research on day 1

Multivariate taylor series expansion and integrating factors

So when I teach calc 3, everyone's gonna learn about multivariable taylor series

[sage python]

Lmfao

Just don't do PDE simple

[marble solar]

Yeah, but one of the most employable fields in math

[sage python]

One variable is enough

[marble solar]

Don't like academia? Bee-line for industry right there

Do like academia? half your competition went to industry for better salary

If I could do anything I'd probably choose topology

[sage python]

Just gaslight industry into thinking that multiple variables is just one variable

[marble solar]

But y'know a man's gotta wife and what not

I'm teaching trig next year

Should I just teach fourier instead

[sage python]

Gross

[marble solar]

I got 2 pre-calcs, some algebra, pre-algebra, geometry, & trig

[sage python]

Lol not very accessible but tbh more useful

Like

[marble solar]

(Classes meet once per week)

[sage python]

With trig at the end of it all just use complex exponentials anyway

[marble solar]

I taught inverse trig derivatives last week

Using inverse function theorem

In the pre-calc class, even tho it wasn't in the curriculum

[sage python]

That feels a bit odd lol

[marble solar]

And my company has the audacity to try & say Stewart will be the calc book for our curriculum

[sage python]

Spivak bruh

[marble solar]

They don't even cover the inverse function theorem!

[marble solar]

Honestly, I might just bring my copy of spivak and say

Do this instead

I don't think there's a canonical one here, just do as many problems as you can

If you get stuck for longer than 15 minutes, look at a solution

[sage python]

Khan Academy is good for most things iirc

[marble solar]

Then write down what your mistake was and reflect why you made that mistake

Try to find something every week or 3 weeks to "test" yourself honestly

Be as mean as you can to yourself

When you grade, don't give any pity or "Oh I almost got it"

None of that

[tame plaza]

I've heard that Spivak's Calculus isn't for beginners

[marble solar]

Ok that's wrong

It literally starts with 1 + 1

[sage python]

Spivak Calculus starts from scratch, it's a difficult book but it's not undoable

[marble solar]

You have to be dedicated to make it work if it's your first frolick in calculus

[sage python]

I went into it barely knowing any calculus (I placed out of one quarter of calc in college, so not even the integration class), and the only proof I knew of was induction

[tame plaza]

hmmm

[sage python]

And I found it quite doable

[tame plaza]

what about Stewart's?

[sage python]

Stewart and Spivak have different use cases

[marble solar]

I went into it with failing most of HS math, and it was a combined class (calc 1 & 2) so we did derivatives and integrals at the same time

And I came out of the spivak class just fine

[sage python]

A lot of non-mathematicians need to know calculus

e.g. natural science, engineering, economics

[tame plaza]

oh well, you guys didn't self teach

[marble solar]

Stewart is like the McDonald's of Calculus, it'll get the job done ~ just without any nutrients

[sage python]

Those guys don't really need to think very hard about how you prove the intermediate value theorem using suprema

Like

Just know how to use what comes in your stuff

[tame plaza]

hmmm

[marble solar]

Thomas' University Calculus is a superior text to Stewart's in many ways

[sage python]

Stewart has a bit of delta epsilon proofs and all floating around but its emphasis is on not shoving unnecessary stuff in the face of people who don't need it

[marble solar]

Many of stewart's "proofs" are infinitesimal hand-wavy arguments

Also in the multivariate section, Stewart just straight up doesn't give enough examples

Spaced repetition. Put something down for a week or two, go do something else

[sage python]

Within its category I'll say that there are probably options that are approximately as good but much cheaper

[marble solar]

Come back to it every now and then

[sage python]

Probably Thomas as Moonbears mentions

Spivak is more meant for students who are actually gonna be math majors

[marble solar]

I straight up wouldn't use Stewart for Multivariable

[sage python]

So the theoretical development is important

[marble solar]

Just do like a 1/3 of the problems

go to next section

[sage python]

Noneuclidean when there are a lot of duplicates once it's super clear you get the point move on

[marble solar]

Wait a few weeks, do some more problems you haven't done

The worst thing you can do is open up 1 chapter, and try every problem

In one week

You want longer term memory

[sage python]

But yeah that's the whole Spivak vs Stewart thing imo

If you're self studying and not on too much of a clock

[tame plaza]

so, having some knowledge of proof writing before taking Spivak's would help

[marble solar]

There are other issues I have with Stewart's calculus text (Lack of Inverse Function theorem, atrocious proof of quotient rule, lack of good examples, too many exercises require a calculator, etc.)

[sage python]

I mean like I said I knew how to prove that 1+...+n = n(n+1)/2 and shit by induction

Spivak can simultaneously be an intro to proofs and an intro to calculus

[tame plaza]

hmmm

[sage python]

As long as you're not in a rush

[marble solar]

It'd be hard to learn spivak on your own, usually you need a mentor that can guide you through the forest when you get stuck

[sage python]

It's not entirely trivial to pull this off, since calculus proofs have sneakier logic than discrete math proofs

[marble solar]

I guess this discord can act as a proxy

[sage python]

But it's doable

[marble solar]

I'd say it's only worth it if you really like Math for Math's sake

It might be easier to just do fast-food calc

and come back to rigor later

If it interests you

[ionic torrent]

why is it sneakier? is it usually because it deals with uncountable infinity?

[sage python]

I mean, real numbers are uncountable but I don't think you're referencing that a ton

It's the nested quantifiers

[ionic torrent]

so introductory discrete math courses use less FOL?

[sage python]

FOL?

[ionic torrent]

first order logic? cuz most idscrete math usually sticks with propositional logic?

[tame plaza]

well that's what this server is for

[marble solar]

You get a feel for what a solution should look like

[sage python]

Honestly I don't think too hard about what type of logic is what lol

I just mean like

[tame plaza]

how long do you think it'd be to study the entire book?

how long did it take you in college to learn it? @sage python

[sage python]

When people hear for all epsilon there's a delta such that blah blah

[ionic torrent]

idk i think discrete math, most things are countable
while in analysis, its more open balls, and shrinking infinitely, in uncountable ways

[sage python]

They get confused

They're like oh wait for all delta there's an epsilon

Or like accidentlaly make the delta depend on both x and epsilon

etc etc

So I'm not sure about formally what's propositional or anything

[ionic torrent]

never mind me

i personally feel proofs on Z are easier to visualise than R, and I was blaming that on it being countable or not

but i don't think thats the only reason why calculus proofs are sneakier

it might be a factor, who knows

[timber mesa]

it's probably best to do it right after each exercise since you'll remember what you did, so if there's anything wrong so you can trace back and find the mistake

this doesn't sound like it'd be useful at all

[neat crypt]

Apologies if I've missed any general pins that answer this question. Can anyone suggest some books that would be a great start for differential geometry?

or Lecture notes

[gray gazelle]

You want to learn manifolds?

Pollack and Guillemin or Lee

Also there's Hirsch

I think people consider Milnor to be a cute introduction

[neat crypt]

You're so sexy man I appreciate you

[gray gazelle]

Thanks

[neat crypt]

Would Riemannian geometry be a good place to move onto after the Manifold stuff?

I'm just a tad confused on the progression of things

[gray gazelle]

Yeah, I think so

[neat crypt]

cool bean appreciate it

@gray gazelle Are you canadian?

[gray gazelle]

No

[pale scarab]

I wonder what approach you take for more theory classes? Like in general how long should you attempt a proof before realizing your not making progress and look for the solution. That is a tricky thing for me when self studying and I can't check with other students in the class.

[hearty steppe]

What book are you using

I think after what I went thru to learn basic concepts/proofs, the best route is probably Chartrand and Zhang

[gray gazelle]

I need a book! I need a book to understand differential equations.... like "differential equations for dummies 101 basics for slow people" >__<

tag me or dm me >__< thanks

[gray jungle]

_<

[gray gazelle]

Any mathematical reasoning/mathematical logic books \

[empty mortar]

teschl

[marble gulch]

Is there a comprehensive book on formal logic that covers classical, intuitionistic, linear, modal, temporal and fuzzy logic?

[gray gazelle]

need a book comprehensive on basic geometry that doesnt require anything more than algebra & has lots of problems

[hearty steppe]

Good luck

You can try an introductory topology book but you probably still need to go through some kind of analysis based text at some point I would imagine, to get very far in something like algebraic geometry or differential geometry

[gray gazelle]

no i dont mean anything advanced but like comprehensive on the basics with lots of problems

[hearty steppe]

Oh

[gray gazelle]

my bad i will rephrase the question

[tranquil orbit]

best books for claculus

?

[gray gazelle]

Topology isn't geometry

He edited his question though

Maybe it was a good advice for the previous question, we'll never know

Nevermind

[cursive orbit]

I believe they were asking for a euclidean geometry book

[gray gazelle]

Stewart, early transcendentals

[pale scarab]

The geometry book by AOPS is my favorite for a first book. The geometry books by kiselev are also really good.

[hearty steppe]

It’s not but it’s not totally unrelated either

Originally AFAIK topology was considered a subfield of geometry but too many debates happened I guess

I would say geometry really mostly is how we abstract spatial concepts in mathematics

So those concepts are not mutually exclusive to being geometry but part of other fields for instance that pertain to algebraic structures*

[solemn mantle]

AoPS geometry for sure. Great explanations and over 900 problems with written solutions for everything. https://artofproblemsolving.com/store/book/intro-geometry

[solemn mantle]

Why is topology not geometry? Topology feels like if you took geometry, forgot what measurements were, and made a whole field out of it

[gray gazelle]

thats what it is

[marble gulch]

Topology studies limits and continuity. That's all.

[gray gazelle]

For someone good at algebra 1, geometry, algebra 2 what books to master them?

You can try higher algebra by Hall and Knight

That’s good for practicing and learning algebra

1 or 2

Or both

Both

But better if ur 2

Oh no i just wanted to perfect it for SATs im in diff eq

Ok so u want a calculus book?

No I use spivaks

Ok

It’s great

You should try it

Ok, im doing Apostle rn

Apostol is really good

That’s pretty good too

Yeah

Ye

Anyways, if you want to master algebra, Hall and Knight’s Higher Algebra is my recommendation

Yep reading rn

After which I guess I’ll do AOPS geometry

Yeah that’s good

[gray gazelle]

Can someone recommend books to learn basics of calculus, algebra, trigonometry etc?

[hasty turret]

.

[grand thistle]

u mean apostol?

or is that a different book

[gray gazelle]

What's a good college/university level book for starting with proofs? Should I begin with something geometry based, or go right into something specific to proofs?

[stray veldt]

if you want to learn actual mathematics, you should not read a highschool geometry "proof" book

[radiant coyote]

Hard this. No one uses that style and it disgusts me that they're taught that way

[stray veldt]

overall i dont think an intro proof books is that useful, for a short introduction you can check my text pinned in #proofs-and-logic
if you want a longer book, people like velleman (which i dislike) or hammack (which i dont know), alternatively i like aluffis notes http://www.math.hawaii.edu/~pavel/Aluffi_notes.pdf

[gray gazelle]

I don't understand, and bare in mind I'm coming into this as an outsider.

What about studying Euclid's Elements itself? I realize many of the proofs and assumptions have been questioned over the years, but his approach is proof + geometry based. Is this not the basis for proofs in modern mathematics?

[stray veldt]

it is not

euclid is only relevant as a historical perspective

[gray gazelle]

Hmm. Well, of course I want to optimize my study time with the most relevant books possible... Let me see if I can find your note. @stray veldt

[heady ember]

#proofs-and-logic message

The link to the msg if you cant find it ^

[stray veldt]

more precisely: euclid did what is known as synthetic geometry, which doesnt have a very big place in modern mathematics
similar style of math was employed in the 19th century and is still done today to some extent, but its not a big theme in modern mathematics

besides, euclidean geometry itself is 'solved' and not studied anymore

the big appeal in the past was deriving theorems only from axioms, but today that is just all of math and other math is just "better"

[gray gazelle]

Got it. Interesting intro, thanks for writing this @stray veldt .

What do you guys think of books like An Introduction to Abstract Mathematics by Bond or Mathematical Proofs A Transition to Advanced Mathematics by Chartrand, Polimeni & Zhang? I'd like to develop my ability to do and evaluate proofs

I should mention I'm not necessarily looking for research topics right now, just skill building 🙂

[woven forge]

I've loved book of proof by hammack

it has a lot of solutions and its free

tbh you can just pick any of the book and it will be fine

though it might be good idea to read amazon or maa reviews first

[green blaze]

Can I recommend non math books?

[woven forge]

yes at least to me

[gray gazelle]

Really high reviews on Book of Proof. It looks like it's more revolving around Discrete math?

[woven forge]

hmm

more like mixture of discrete+set theory+logic

teaching you essentials of proofs basically

[gray gazelle]

Ah nice. I shall check it out then.

[gray gazelle]

Ye apostol sorry

[shell geyser]

Yeah, it is mostly discrete math. Most of the examples the book uses come from elementary number theory, I guess presumably because that requires next to no prerequisites beyond high school math. There is a dedicated calculus chapter, but the rest of the book doesn't assume any prior knowledge to my understanding. I too would recommend Hammack. Really well-written and understandable.

[hearty steppe]

If you think about it too, geometers also deal with lots of limits and continuity don’t they? Haha

I like to think they are different lenses of approach to certain concepts

[night prism]

Hello, everyone! I’m working on my own through the beginning of Friedberg to give myself a chance at a full run-through of linear algebra. I have familiarity in abstract math, but much of it came from cherry picking topics or learning with an application in mind.
With that said, Friedberg seems just a touch slow to me, and the exercises a hair easy (not all, but again, most)

Would Artin instead be a good alternative, or am I just too early in the book? (Only Chapter 1 finished so far)

[gray jungle]

this list was made recently and artin seems to fit your bill @night prism

[night prism]

Thank you!

[smoky zephyr]

i see my diagonalization comment was acknowledged

[blazing canopy]

Too early in the book imo. Artin is a broader survey of abstract algebra and it also doesn't cover linear algebra in as much detail

At chapter 1 you've basically just defined vector spaces.

Friedberg is just a more complete book (on linear algebra specifically), even if perhaps the first chapter is too slow

[night prism]

Ok, understood; would Morton/Curtis be a good book to concurrently read for added perspective and approaches to overlapping topics, or better relegated as a second treatment after finishing Friedberg? Thanks so much for everyone’s insights!

[blazing canopy]

I don't know the book unfortunately. By the way I think that Artin is a great book and develops a lot of the foundational concepts of algebra quite well. As such it has a largely algebraic slant, whereas I think to fully be an expert on linear algebra one should also have a geometric perspective (esp since a lot of "useful" linear algebra is done over R and C). For example I do not remember Artin covering SVD or really saying that much about eigenvalue problems at all other than the basic definitions.

[gray gazelle]

need a friendly trigonometry book

[night prism]

Ok i understand, will stick with Friedberg then and maybe browse through interesting sections of Artin. Thanks much for your help

[tender cedar]

hey guys, I want to start studying Group Theory for hobby because I think it seems pretty interesting and fun. Any books you recommend? Bare in mind that I'm a sophomore CS student, so my mathematics isn't that advanced (but I'm able to read somewhat complex math texts because I've been doing a research on discrete dynamics) and I'd prefer a more introductory language.

[cursive orbit]

visual group theory?

[sudden kindle]

Abstract Algebra with Applications by Audrey Terras

[tender cedar]

Group Theory but I guess the right term is abstract algebra

[cursive orbit]

oh I mean that's my recommendation

[tender cedar]

oh

[cursive orbit]

the book "visual group theory"

[tender cedar]

ok I'll take a look at those two!

do you guys think there are any prerequisites before I get started with group theory?

[stray veldt]

have you seen proofs before?

[tender cedar]

yeah

matter of fact, I'm taking discrete mathematics this trimester

[hearty steppe]

Terras? I think Pinter has been fine so far and im working through that currently

[stray veldt]

then you're good to go

[sudden kindle]

I recently found this book and it introduces abstract algebra with applications so I think that's pretty cool

[hearty steppe]

Yea I’m actually noticing my improvements in maths

I am going thru Knuth and Matousek to approach Bona’s combo + graph theory book

Yea Pinter is a fun one and there’s some fun problem sets in there that aren’t overwhelming

[tender cedar]

I guess I'll take a look into Relations a bit better because I feel like I'm a bit weaker on that end

set theory I could say I've learned so well I don't even wanna talk about it anymore

[hearty steppe]

Relations is where you start learning about functions

[tender cedar]

yeah exactly, I hate functions

lmao

Just never got them right

[hearty steppe]

It’s the other half of math other than algebras

[tender cedar]

alright, guess I'll revisit functions and relations then before getting into abstract algebra

cuz I really suck at it

[hearty steppe]

Well actually go thru Pinter and Chartrand and Zhang? Try that route

The chartrand and zhangs abstract math transition text

Shouldn’t take you long

[tender cedar]

oh ok

I'll check it out

[hearty steppe]

You basically can go thru the relations part. Then you may be ok to go thru a book like Abott’s understanding analysis for more abstraction

If your already good with the rest of basic concepts

[tender cedar]

"A Book of Abstract Algebra" this one?

[hearty steppe]

Yea

So functions are just about assigning some relational meaning between sets, usually it’s some computation involving fields in R or C

[tender cedar]

sometimes I just get the concepts of things like bijections confused

[hearty steppe]

Injection means you have elements uniquely map from one set to another

Surjection is you have all the elements of one set map to another set (maybe not all the elements of another set though)

Bijection is both

[tender cedar]

so like

hm

yeah alright

I think I got it

I'll do some exercises to review though

I think injection is the hardest for me to understand

injection is like, every element is mapped uniquely to another element

right?

[potent plinth]

Hi I wanted to recommend this book to anyone that is in last years of highschool and knows some italian

It is the "plus" edition so it has some additional things about integration, derivatives and probability density.

However, if you don't want the "Plus" version the standard one is quite good as well

Note: this book is in Italian Language

https://acrobat.adobe.com/link/track?uri=urn:aaid:scds:US:ef1ceb35-8544-31db-8187-69a390c2b417

It's called "La Matematica A Colori 5 PLUS"

[solemn mantle]

I was checking out reviews of Artin’s algebra text and some were saying it’s written very concisely and is not good for self-study. Is this true?

[tulip blade]

it isnt objectively true. Plenty of people really like the book. Try reading it yourself and seeing if you like it or not.

[solemn mantle]

Ok thanks

[atomic stag]

I'm asking for a book a becouse last one didn't include all topics
I'm looking for a integral book that contains.

1/integration using trig identities
2/partial fractions
3/same standard int formula based
4/definite integrals using properties
5/integration by parts
I'm currently in grade 12 India
||my current book i.e (RS Aggrawal) has missing pages from integration chapter)||

[timber mesa]

Stewart's Calculus has all that

any engineering calc textbook should, really

I own a calc book by Dennis Zill (found it cheap when I was a freshman) which also has all that

[timber mesa]

and by "engineering calc" I mean any textbook that focuses on calculations, visual intuition and applications rather than proofs

[gray gazelle]

Thomas' Calculus or it's variant: Thomas' Calculus in Si Units by George Thomas

[warm glen]

if you do find artin too difficult for self study you can try pinter's abstract algebra book, which is much easier but still rigorous

[blazing canopy]

I don't have an opinion either way for Artin, but a book could be not suitable for self-study without being difficult. It could simply not be thorough or detailed enough, or have extensive enough exercises to give the reader good practice.

[solemn mantle]

Ah good point

[solemn mantle]

I just read the preface of Pinter and wow I really love that

Seems like he put a lot of effort into good pedagogy

[trim solstice]

Good book for abstract algebra?

[night prism]

First course or graduate level?

[sage python]

Check pinned messages for my review of algebra books. In a nutshell, Artin's the correct answer for absolute beginner (as in, you don't even really know linear algebra well). Jacobson is my favorite, D&F is a more standard, drawn out, imo less interesting alternative. Lang if you're a masochist

[trim solstice]

I know linear algebra but otherwise first course

[trim solstice]

By jacoboson u meant basic algebra 1 right?

[sage python]

Yea

[glad heart]

is Higher Algebra a good book for national olympiads?

[stray veldt]

higher algebra by lurie? no

[woven forge]

an extremely intimidating looking book

[karmic thorn]

Which author(s)?

I'm aware of a book by Hall and Knight, and it may or may not be very helpful other than the bare minimum I guess.

The other one is by Lurie as pointed out and I'm not aware of any research mathematician tier olympiad where it would be useful.

[night prism]

When I had to learn select topics in algebra, Fraleigh never made me feel left behind. @sage python advice is probably more sound, however.

[restive falcon]

what's a good book for general banach space analysis

[gray gazelle]

I've tried Yoshida once and it was pretty good tbh. But I haven't read a lot

But not sure if it's what you're looking for

[gusty smelt]

try pederson's analysis now ch2

pretty good imo

[humble folio]

Any book recommendation for me??

@anyone?

[subtle mango]

The Subtle Art of Not Giving a F*ck is a good book

[humble folio]

Bruh

[subtle mango]

wdym “bruh”

[humble folio]

I read tht

[subtle mango]

isnt it good

[humble folio]

ImoPov no!

It's the first book I've ever read

Try sapiens in case u didn't

It's great

Ofc

[subtle mango]

added to my list

[gray gazelle]

Symbolic Integration by Bronstein

[humble folio]

Is it a math

Book

Bruh I'm not into calc yet

Or any serious math nw

[gray gazelle]

Yes, it's about algorithms for calculating indefinite integrals

[subtle mango]

oh that sounds cool actually

[humble folio]

Can recommend anything regarding pshyc..

[subtle mango]

Taylor Classical Mechanics

[humble folio]

Bruh I said phsyc

[subtle mango]

psych?

[humble folio]

Yeah!

[subtle mango]

the deepest well

[gray gazelle]

It is, but it's more for a computer tbh

[subtle mango]

it’s about the connections between mental health (esp. trauma) and physical health complications

[gray gazelle]

A lot of cool algebra there though

[humble folio]

Any other?

[subtle mango]

the empire of depression

[humble folio]

Sounds cool

How abt behave??

[subtle mango]

behavioral psych?

[gray gazelle]

So called differential field theory

[humble folio]

Is it good?

Nope

The book behave

[subtle mango]

never read a book called behave

[humble folio]

Thinking fast n slow??

[gray gazelle]

I only read math books, sadly can't recommend anything

[humble folio]

Oh thts fine

[humble folio]

Are u in uni??

[gray gazelle]

Yes

[humble folio]

Masters ig

[gray gazelle]

Doesn't matter

[humble folio]

Are u into topology?

Set theory?

[gray gazelle]

I'm not into set theory but I did consider learning it more as it's useful for deeper understanding of some things in topology

So called set theoretical topology

[humble folio]

Does ur course contains game theory??

I found tht to be interesting!

[humble folio]

Woah great

[gray gazelle]

I did a course from game theory but I don't remember much

[humble folio]

Awesome

I probably heard something like prisoners dilemma

[gray gazelle]

But I recently learned about von Neumanns minimax theorem which has some cool applications I guess

[humble folio]

I think it's a jargon

😅.

[gray gazelle]

Huh

[humble folio]

I jus know some some random stuff in math

Which is hella useless btw

😅.

[gray gazelle]

It's a theorem in functional analysis that has applications to Nash equilibria

[humble folio]

Yeah

I heard tht too

I think I got tht from scishow

Hank

Do u watch those hank chnls??

[gray gazelle]

But there's also an application to fixed point theorem for affine maps

So called Markov-Kakutani fixed point theorem

[humble folio]

It's a perfect tie situation where it's the perfect situation for everyone

Am I right?

*nash equilibria

[gray gazelle]

I wouldn't say that tbh

[humble folio]

U r throwing sharp jargons at me😔.

[gray gazelle]

But I'm not advanced in game theory at all

[humble folio]

It's my rough estimate 😅.

[gray gazelle]

You can prove that under some assumptions they have a common fixed point

[humble folio]

Probably I want to do math in uni

[gray gazelle]

I think it's nice but I haven't seen it applied yet

[humble folio]

Integrared math with data analytics

U r my insp if I did so

Lol..

[gray gazelle]

Thank you? Lol

[tame plaza]

is precalculus just algebra +trigonometry?

[humble folio]

Yeah

[tender cedar]

guys

I need a good book to get good at linear systems and matrices

currently using College Algebra by stewart but idk I think I could use something more advanced

[tacit abyss]

does anyone have any recommendations for good measure theory books? Not looking for learning content, just challenging but not impossible exercises

[woven forge]

found a good book on multivariable analysis

https://www.amazon.com/Multidimensional-Real-Analysis-Differentiation-Mathematics/dp/0521551145

[woven forge]

https://www.amazon.com/Real-Analysis-Theory-Measure-Integration/dp/9814578541

this even has solutions

[grand thistle]

isn't munkres also good?

[woven forge]

i've heard that munkres was good too

tho i haven't used it

we use rudin for our college and I detest it so much

[grand thistle]

hmmm

do you guys like studying with solutions?

[tacit abyss]

had a look at this and it looks perfect, thanks

[tacit abyss]

yes

[grand thistle]

i like it bc i know when im doing stuff right, but i also feel like i learn better when i dont have them

bc

if there aren't solutions, i'm more motivated

to actually

solve the problem

instead of giving up after 10 minutes

[tacit abyss]

yeah it's a balancing act

I do feel like peeking at solutions can still enable learning

as long as you pick up the idea and flesh out the details yourself rather than just copying the solution without thinking

[woven forge]

to be honest i don't really look at solutions

before 3 failed attempts at solving a problem

even then I try to look only parts of it

maybe cuz im stubborn

[tacit abyss]

tbqh right now I do look at solutions more often than I should

more because I'm revising for exams

[woven forge]

I don't print solutions

and I study without computers and smartphones

[tacit abyss]

so I'm more concerned about being able to answer exam qs than learning the maths xd I'll try to catch up on being actually good in the summer

[tacit abyss]

I do most things on my computer, I only handwrite to practice for handwriting in the exam

[woven forge]

maybe thats of preference

but looking at solution manual isn't really a recommended thing tbh

unless you have exam tomorrow

and you haven't studied

online book club?

seems interesting

[tacit abyss]

on my list I have distributions, fourier analysis and more functional analysis

i also want to learn basic algebra like galois theory kind of stuff

even though i prefer analysis

but that's for the summer after i've done celebrating end of exams

[woven forge]

I have manifold theory and complex analysis

maybe a bit of algebraic topology if possible

[grand thistle]

im thinking of going through real analysis, abstract algebra and point set topology over the summer

[tacit abyss]

oh im doing both this year and both have the potential to be quite nasty exams for me

[woven forge]

my goal is to at least understand proof of stokes theorm on all manifolds

[tacit abyss]

ive done not enough pdes

[tacit abyss]

oh thats actually not too bad

[woven forge]

you mean manifold and complex?

[tacit abyss]

yeah

[woven forge]

which book do you use for complex?

[woven forge]

you mean pde using analytic methods?

[tacit abyss]

doing that + 2x functional analysis, probability, pdes, measure and set theory

[woven forge]

thats brutal

how do you even bear with it

[tacit abyss]

well i've mainly done my lecturer's exercises but I think I'm going to pick Ahlfors and Ablowitz and Fokas

[woven forge]

is ablowitz and fokas rigorous?

[tacit abyss]

i'm not sure I haven't looked at it for a while, I learnt complex for a while prior to taking the course formally but the lecturer puts more of a geometric spin on it all, so I don't think something applied-ish will be too bad

also he's not very tight on a lot of details

[tacit abyss]

idk I like all those courses but PDEs was my least favourite

even though I should like it - it was just a bit dry playing around with integrals

the coolest thing was finding out that harmonic functions are to real analysis as holomorphic functions are to complex and they're extremely similar

[woven forge]

dunno about graduate pdes

[tacit abyss]

that's about it xd

[woven forge]

do you have thoughts on doing linear algebra btw?

its just suggestion

[cursive orbit]

sounds like a lot

[gray gazelle]

Are you talking to me

[woven forge]

yes

[tacit abyss]

i did linear algebra last year but not a lot of it was relevant to what I want to do

[gray gazelle]

I'm gonna do tao's course

[woven forge]

theoretical one

[tacit abyss]

the linear algebra you need for analysis is pretty basic

[grand thistle]

whats CLRS and FIS?

[woven forge]

or ones focuse on matrix?

[tacit abyss]

the one i did in first/second year was basically just finite-dimensional stuff with matrices ye

so not very relevant to me

[woven forge]

oh

didn't realize it

[grand thistle]

oh

[woven forge]

lol

thought it was abbreviation for some computer related stuff

my bad

mine is tu's introduction to manifolds and conway's complex analysis

[tender cedar]

anyone?

[woven forge]

can you specify

if you only need to know how to calculate matrices strang's linear algebra should be fine

[tender cedar]

I'm gonna take linear algebra next trimester but I don't wanna get stuck with the linear systems and matrices stuff, I know linear algebra is made specifically to solve those but I wanna get a head start you know

[woven forge]

strang's linear algebra or lang's linear algebra introduction is what you might be looking for

I don't recommend anton's book btw

[tender cedar]

apostol?

[tender cedar]

ok i'll take a look

[woven forge]

haven't read apostol linear algebra tho

[tender cedar]

my school recommends apostol

but idk

I read a few pages of it and it seems confusing to me

[woven forge]

apostol isn't the most friendly author btw

[tender cedar]

alright

thanks for the help man

btw is this the one from strang? Introduction to Linear Algebra, 3rd Edition
Textbook by Gilbert Strang

[woven forge]

yes

[tender cedar]

ok

thanks

[gray jungle]

what are the prerequisites for chaos theory and dynamics in general? and what are the sorta standard books for both

[frosty girder]

for dynamics, i know you need a ton of diff eqs

idk anything more than this, sorry

[regal wasp]

Pretty sure strogatz is the standard undergraduate textbook

[jagged quartz]

can anyone recommend an introductory book about bio-informatics (or anything biology-related from a mathematical point of view)

[gray gazelle]

any book recommendations to enhance math writings and to get better at putting thoughts into words

[forest sleet]

I don't know if any book is dedicated to that, but there are a number of notes that people have written about how to write mathematics