book-recommendations

[placid pollen]

exactly why I don't want to post it, it started as a meme but it is evolving to a more serious and potentially misleading essay

[remote sparrow]

idk you can still post it

danimark's lists exist

[placid pollen]

what is a BLL+book?

and the words are chosen so to bait exactly the people who I want to help not get baited by those lists, too

basically it is a guide to redirect people to healthy habits lol

[hasty turret]

Who is your target audience

[remote sparrow]

maa labels certain books as BLL if they think libraries should acquire it. BLL means suggested for library acquisition, BLL* and BLL** are intermediate ratings, and BLL*** are books that in their opinion is a must-have for libraries

baby rudin for example is BLL***

[placid pollen]

Smart undergrads who burn to be in grad school, the kind that gets rudin books by their first year even if their first course at that level is in third year. I just talked to my tutor and he said how most of these kids burn out and stop studying Math, it pains me because I've been so damn close to dropping out just for getting ahead and thinning out too much my knowledge. You feel stupid even though you're reading ahead when you do it wrong. I don't feel ashamed of talking about it, because not only it is common, you're in the minority if you don't burn out

[remote sparrow]

why the reacts to me that's what MAA said not me

[hasty turret]

If it's fine, can you DM me the thing you have rn? I guess polishing and removing the subject parts could take a lot of time

[placid pollen]

it's my face when (mfw) I see Rudin getting mentioned for the billionth time anywhere mathematics is talked about

[fallow cypress]

Rudin isn't even that great a book tbh

[remote sparrow]

well in fairness rudin IS something a lot of places use, and will be used for a long time. and it's a handy reference. which i think would justify the BLL*** rating

since it's not a quality rating

[fallow cypress]

It's a nice reference

[remote sparrow]

it's just something libraries need to have

[dapper root]

MF added another *

[placid pollen]

Yeah bro I'm more of a Ian Stewart guy myself https://en.wikipedia.org/wiki/Evolving_the_Alien

[dapper root]

Oh nvm

[placid pollen]

I guess if I had to review a single book, it has to be Baby Rudin.

"I don't like Baby Rudin" could be anything from:
0. "I don't like Math"

1. "I don't know how to make a proof"
   1'. "I like extremely detailed proofs" (1. But said differently.)
2. "I don't like his lack of generality in the basic topology chapter"
3. "I don't like his lack of generality in theorem 2.41"
4. "I don't like that he didn't name a theorem"
5. "I don't like the lack of motivation"
6. "I don't like the lack of applications"
7. "I don't like the lack of applications to fourier series" (incorrect)

What if I said Rudin books are the most popular example of reverse Mathematics.[?]

[fallow cypress]

How is Rudin reverse mathematics lol

[placid pollen]

What is fourier analysis

[fallow cypress]

oh you mean it in a different sense

Reverse mathematics is the name of a field of mathematics

[placid pollen]

https://www.youtube.com/watch?v=hBcWRZMP6xs

[placid pollen]

Yeah I mean in an analogous sense. If I'd have to think for inspiration, it has to be this Walter Rudin video

[fallow cypress]

Ah okay

fwiw I agree with both 4 and 5

I think there's a lot of books on analysis you could pick up that are just as rigorous as rudin but actually explain things

[placid pollen]

Yes, but still won't replace the need for Baby Rudin in the education of someone. Detailed proofs do end up being dead weight for fast learning and exposition. Students don't learn more because your proof is more correct. Students learn because you exposed the key points, they like to connect point. My bias is towards teaching rather than reading something at a particular point in time. Baby Rudin is written for a specific point in time, when you become a bit more mature.

Some people can be professional mathematicians without ever getting the fact that you can expose things by doing little jumps, and without realizing that this exposition helps students learn to connect dots.

By exhausting all explanation, you steal from the student the capacity to connect dots. More is not better.

[fallow cypress]

Ehhh I dunno, I've read Rudin and compared it with other analysis textbooks, and I didn't feel like I gained something significant by reading Rudin

I'm somewhat fond of William Wade's book

I think it is useful for a textbook to explain the intuition behind concepts

[foggy relic]

Browder is great

does cool topics and explains well

[fallow cypress]

And provide motivation for where the concepts came from

[foggy relic]

problems are very very good

[placid pollen]

I have to ask, did you have a teacher use Baby Rudin?

[fallow cypress]

No

My analysis professor despised it

[placid pollen]

If not then I understand you, oh

[fallow cypress]

It is a good book to go along with a instructor yeah

I can agree with that

You can do all the exposition in class

[placid pollen]

That makes sense then, it was insightful for me to have a professor work through it in class. You learn that you can leave details to memory and get a confidence boost by watching it go in real time

[fallow cypress]

There are certain parts about Rudin that I really like

[placid pollen]

I just did so too in real time and it was like therapy

[fallow cypress]

Such as how he immediately starts with metric spaces

[placid pollen]

"Damn I barely know if I'm going to say the right thing next, but my exposition is working because I don't lose myself in the details"
Magic, I wasn't thinking much, the notion of 'key points' just took my body

It's scary though

[crimson leaf]

I've liked Schroeder so far, I did not like Tao very much though it bored me a lot

[fallow cypress]

I read chapter 1 and it was tedious, I read chapter 2 and it was cool, then I read chapters 3-5 and it was tedious again lol

Should've just read chapter 2 and then quit

[crimson leaf]

Tao?

[fallow cypress]

I've never read Tao

[karmic thorn]

I read 2, a bit of 3, skipped 4, soldiered on from 5 through 11 I think

(Tao's Analysis 1, that is)

It was slow as hell but in retrospect it was nice to have a book that kind of filled in for an instructor when I was self-studying

The book talks a lot but I saw that as a positive

Only downside was a lack of exercises for me

Proving main results and all is fine but it wouldn't have hurt to use some concrete problems or applications as well

[crimson leaf]

That was the negative for me it was nice at first but I got tired of the exposition, though Tao is a good writer. Yeah it is scant on exercises with most of them just being things that were left to the reader

[karmic thorn]

Right

[grand thistle]

4 was my biggest complaint while reading through rudin tbh 💀

i read 1, skipped 2, then did 3-7

for rudin

and imo it was pretty great

but knowing things like the dirichlet convergence test as theorem 3.42 is kinda annoying

[placid pollen]

1-4 7-8 and 11 are the most important chapters

What I omitted is just calculus

[grand thistle]

ive heard that 11 is kinda bad

[remote sparrow]

Sure, you have to encourage students to engage in the learning process too. But students (on average) still need some guidance and scaffolding, someone more experienced to help a student along to get the idea. The best outcome is that the student feels like they independently came up with the idea. Right now inquiry-based approaches are still relatively new, but results are promising. What do you think about IBL?

[grand thistle]

and wouldn't an actual measure theory/real analysis text be better for lebesgue theory? i feel like he just stuck that on at the end for completion and his Real and Complex Analysis would be much better suited for learning the topics

not sure though

[placid pollen]

Everytime you want to learn a topic, aim singlehandedly at that topic and not at an author. I checked Folland, Kolmogorov, Rudin (RCA), Sheldon Axler, etc. But exactly at the same topic

Don't get stuck on one reference

[placid pollen]

I never heard about it. Sounds to me like the way I do learning, and how people write books. When you write a book you saturate the book with references about that chapter. Basically do the same as a student. Get ideas from each and categorize each treatment.
For example there's classical measure theory and modern measure theory.

RCA goes about Lebesgue integration in two chapters, one is general measures, second is more specific measures. Baby Rudin goes into measure theory in the classical way, it's how Kolmogorov did measure theory. Probably how Paul Halmos did too, how Royden does it. Folland is the modern way.

[remote sparrow]

https://www.amazon.com/Introductory-Analysis-Approach-John-Ross/dp/0815371446

well regardless of what you know about IBL, i'm curious what people think of this

[light ether]

what would you say your (books asked about):(books actually read) ratio is, roughly

[remote sparrow]

I'd say 420:69

[vital bane]

[vital bane]

strad

[light ether]

neam #1 top dawg how it move 👑👑

[fierce hedge]

https://www.youtube.com/watch?v=-vaisjq7e34
Thoughts on knapp, Dami kinda likes it? But I remember someone hating it

@restive falcon What do you hate about knapp?

[restive falcon]

i don't hate it

just, the prose isn't amazing

and it doesn't really motivate anything it does in the first chapter or so

[fierce hedge]

My bad, "what do you not like about the book" would be more appropriate

[restive falcon]

like it does a bunch of really boring number theory

[fierce hedge]

So, like the text is boring or unoriginal?

[restive falcon]

without explaining what this has to do with the algebra i downloaded it to learn

[restive falcon]

not unoriginal

just doesn't explain stuff well

[fierce hedge]

Any particular instances you can remember on the top of your head?

[restive falcon]

I didn't get very far

which is telling in and of itself

[fierce hedge]

Also, I believe it is intended as a second pass/graduate level. I might be wrong

[restive falcon]

it is not

i mean

it doesn't say so at least

if it was meant as a second pass idk if it'd have a huge block of linear algebra at the front

[fierce hedge]

similar to jacobson

[quartz edge]

Book recommendation for ultimate level calculus and god level coordinate geometry

(USEFUL FOR OLYMPIADS)

[quartz edge]

anyone just pinged me

[plush arrow]

What are some books every math teacher should read?

[remote sparrow]

I've seen the series Elementary Mathematics from a Higher Standpoint by Felix Klein garner favorable reviews. Be sure to get the Springer edition, not the Dover, as the former corrects some translation errors.

I suppose Lockhart's lament is an interesting polemic, but I've seen people say it unnecessarily puts down pedagogical research, saying good teaching can't be learned. Also, they criticize Lockhart for not really providing alternatives to current math education, even if they agree that math education is deeply flawed.

[slender cargo]

almost done with ch. 1 of Abbott. Cardinality section was tricky!

[remote sparrow]

emily riehl has remarked that publishers often ask authors to understate a book's prerequisites in order to reach a wider market, as was the case for her Category Theory in Context. ofc authors make an effort to make the book self-contained at a formal level, but it may be missing a lot of motivation.

[restive falcon]

her book requires like some algebra and AT right

[fluid bay]

only to understand some examples/motivation i think

[lean pagoda]

the plethora of examples are kind of the main selling point of the book though (at least compared to, say, Mac Lane)

[mossy flume]

^^^

I tried to work through that text (had to stop cause I ran out of time)

and I know 0 AT or AG

so when I was reading through the text, alot of the examples were useless to me

but the explanations themselves required none of that stuff

and enough examples didn't need AT or AG (at least in the 2 intro chapters) that it was fine

[quartz edge]

anyone

[rigid barn]

Idk what @restive falcon was on about, Knapp's 2 books are in the pantheon of algebra textbooks imo. He covers a LOT of ground in a very clear, digestible, and THOROUGHLY motivated way (e.g. look at chapter 8 where he explains how commutative ring theory sprouted from considerations in number theory and algebraic geometry) and is similar to Jacobson in that way.

[fallow cypress]

btw thank you so much for this again!! I'm looking through it now and it looks exactly what I wanted

[solemn forge]

That’s great — glad it helped

[turbid pasture]

:))

[remote sparrow]

hubbard and hubbard could be right for you

[slender cargo]

I've heard people recommend Shifrin as an alternative to Hubbard and Hubbard

[fierce hedge]

Nice, I'd use it as supplement with Jacobson then

[brave yew]

basically

i have two math books i want to read, namely, Homotopy Type Theory and Category Theory for the Working Mathematician

I have terrible proof-based mathematics background; I can't remember how to derive the quadratic formula, but I've gotten through Linear Algebra

I dropped out of Real Analysis twice

any suggestions as to how to move forward? I'm using these books right now

https://smile.amazon.com/Proofs-Long-Form-Mathematics-Textbook-Math/dp/B08T8JCVF1/ref=sxin_15_mbs_w_wsirn_d_i?content-id=amzn1.sym.4431d16c-937a-4649-8387-5e44353eeab2%3Aamzn1.sym.4431d16c-937a-4649-8387-5e44353eeab2&crid=3RUE8JTUWSCHO&cv_ct_cx=jech+set+theory&keywords=jech+set+theory&pd_rd_i=B08T8JCVF1&pd_rd_r=1b46fd6e-4bde-4e46-81b4-4d0d694db1a7&pd_rd_w=sWk8g&pd_rd_wg=v8kBE&pf_rd_p=4431d16c-937a-4649-8387-5e44353eeab2&pf_rd_r=JJ0C0YQ51GCJ4S9KN1EN&qid=1670131913&sprefix=jech+set+theory%2Caps%2C108&sr=1-4-217e09be-bd7d-41c4-874a-1bb8ae9f8268

https://smile.amazon.com/dp/0521597188?psc=1&ref=ppx_yo2ov_dt_b_product_details

[sturdy shore]

any intro to proofs/transition textbook is good, they are all roughly the same

if you want to read mac lane, you will have to not-drop out of real analysis eventually

[fluid bay]

isn't maclane like the least friendly introduction to category theory

in general, ur going to have to learn to crawl before u learn to sprint at a Usain Bolt pace

i enjoy the abstract stuff as much as the next guy, but i found it difficult to make sense of until i got a better handle on the motivation from algebra and topology

therefore, i think your time is much better spent learning a subject, say algebra, than trying to make the jump from "how to prove things" to "homotopy type theory" or "categories for the working mathematician"

[golden bear]

did take a proofs class before you took real analysis ?

[hollow shore]

I don't see the point of a proofs class tbh

[golden bear]

okay, ask your calculus students to prove something

[hollow shore]

the concept of a proof isn't that non trivial

[slender cargo]

eh I think it is for a lot of people

what is considered rigorous enough is hard to figure out

[golden bear]

my math maturity isn't good and that is what led to my failure of first semester of my masters program. I didn't have the writing i needed to achieve.

[sturdy shore]

<@&268886789983436800>

[slender cargo]

<@&268886789983436800>

[golden bear]

<@&268886789983436800>

[slender cargo]

thank you!

[fluid bay]

My first exposure to proofs was self-studying Treil's linear algebra, but when I got to college, I had to take a proofs class. I thought the extra pedantry my professor forced on us was good for really honing-in my proof-writing skills. It helped me realize that to prove a mathematical statement is a very formal kind-of process.
There are also things that people should know, but typically wouldn't just learn through osmosis like writing down truth tables and being able to negate complicated statements

with that said, i don't think very much time needs to be spent "learning proofs" before jumping into actual math

[brave yew]

noope

i was told i was probably going to be more of an algebraist than an analyst, though

i'm terrible at geometry

[remote sparrow]

Well, my point of view is that an intro to proofs class is sort of like an English composition class. It could totally be possible that an English composition class is superfluous if school really immersed students in a lot of reading and writing from lots of diverse topics and that way students could learn how to find their voice and write in an organized and coherent fashion. Similarly, if we were exposed to proof-based math much more, starting from very concrete topics, adding in some tips and tricks on how a good proof should read, holding up a model proof, critiquing some weaker proofs, etc. an intro to proofs class wouldn't be necessary. But things are not that way, and so a math composition class is necessary.

[fallow cypress]

I feel like it's good to learn proofs at the same time as you're learning content (for many people, a first course in this would be linear algebra)

Otherwise it feels very out of nowhere

It's also tricky because different fields tend to have different methods of proof

Like analysis has its own tropes ("we will show that x < epsilon for every epsilon > 0..."), and algebra has its own tropes

[crimson leaf]

Intro to proofs is really just naive set theory, basic number theory and the chapter 0 of algebra and analysis books combined in my experience

[fierce hedge]

Do people have a separate intro to proofs class or is it just posed as discrete maths class? I had neither of those at my uni

[hasty turret]

Depends ig

If it's a cs program, probably part of discrete math

If a math program,then a separate class

[fierce hedge]

I see, isn't calc I+II enough as intro to proofs class? again I didn't have any of that so I have no idea

[hasty turret]

That depends on the region. Apparently in the US and such, it's usually just computations

In Europe, apparently it's proof based

[remote sparrow]

Just as some unis mix math and non-math students into calculus, sometimes unis mix math and CS students into discrete math.

[crimson leaf]

Yeah some universities offer the choice between discrete math or intro to proofs

[gray gazelle]

Can anyone solve q1y

16

[crimson leaf]

#❓how-to-get-help

[remote sparrow]

this is not a request for a book recommendation

[crimson leaf]

Can you not read

[indigo frigate]

Hey all, I want to find a book (or really, as many books as possible) that specifically mention the category of sets, the category of rings, and the category of r-algebras, and goes into hom-set adjunctions that might exist between them. I want to understand how free objects in R-alg (the polynomial rings) are transported into the ordinary category of rings (ie, is there a forgetful functor?)

So really I am looking for a simpler but still category based reference for commutative algebra, but I also would like a method to see a spectrum of more complex titles too.

Actual book recommendations are welcome, and if I should go elsewhere to talk about how to perform this kind of search in general, let me know!

[gray gazelle]

what are the prerequisites for kolmogorov's introductory real analysis book?

[placid pollen]

I do not know about that one. I got his theory of functions (closer to the original, real analysis has been retouched by Silverman), which is about one step up above baby Rudin. Like after you read about calculus and some metric space topology you can read from Kolmogorov. But still, baby Rudin is more modern in style. I would rather have worked through Tao analysis than either of these.

[proven junco]

Some curve books to be able to do a project with a not so well known curve.

[agile harness]

Any recommended books/papers on Random Matrix Theory in Statistical Learning?

[willow pecan]

<@&268886789983436800>

[karmic thorn]

RMT isn't that obscene

[gray gazelle]

[runic snow]

Say if someone hypothetically dint have the cash to buy digital books and dint want to get their ip, credit card info, and gov identification leaked where would they go?

Asking for a hypothetical friend

[crimson leaf]

They'd look for a library that would most likely be named after the first book of the bible

[mossy flume]

They used to look for a library named after the last letter in the English alphabet but that one burned down

[runic snow]

Should said hypothetical human/non-human being use any software to prevent any issues even if said hypothetical being is only hypothetically getting old/ discontinued books?

[remote sparrow]

the most secure way to approach downloading anything would be to set up a closed virtual machine sandbox. but it's not practical for a hypothetical site that lives and dies by its reputation.

[hallow oriole]

check out principles of mathematical analysis by rudin

[cosmic bramble]

Nice. I learned it from Dummit and Foote.

[crimson leaf]

Stanley volume 1 is the best way to learn how to count so you should look there first

[foggy relic]

Serre's course in arithmetic

precisely what you need

naw

[past linden]

<@&268886789983436800>

[dense seal]

Hi, unfortunately we can't allow suggestions like that here due to ToS

(at the very least not that explicitly, feel free to take it to DMs tho)

[remote sparrow]

principia mathematica by russell

very rigorous, detailed explanation that will help you understand exactly why, for example, 2+2=4

[vital bane]

[heady ember]

Lmao

[vital bane]

not sure if this is allowed in this channel, if it isnt just lmk

[quick hornet]

we literally have this pinned, so itd be hypocritical not to allow the occasional meme

just dont spam them or interrupt ongoing convos/questions

[vital bane]

Lmao awesome alright

[compact narwhal]

Guys i’m looking for a book about prime numbers/number theory, something that isn’t so crazy. preferably i would like the book to be in french, but english is fine too

please help

[karmic thorn]

A Friendly Introduction to Number Theory by Silverman is a good book

[gray gazelle]

I think there's a lot French number theory books out there, so I'm sure someone can recommend you a French one

[heady ember]

Manan likes books with titles of "A Friendly Introduction"

[karmic thorn]

[compact narwhal]

Any idea about where i should ask ? or should i just wait here

[compact narwhal]

thank you im gonna check it out

[stray veldt]

this book might also just have a french translation

its quite popular

[quartz edge]

is sl loney good for coordinate geometry

[grand thistle]

morton curtis is really good for linalg ngl

using it to review linalg once again

and it's well paced but complete so far

[slim vale]

Does anyone know books that describe the process of writing proofs? I get the concept and the answer intuitively, but always make silly definition and methodical errors in my proofs…

[remote sparrow]

#book-recommendations message

[slim vale]

Thanks a lot. My uni did exactly what you described: directly to linear algebra and real analysis without teaching how to write rigorous proofs. I hope your recs will help!

[smoky zephyr]

based

[remote sparrow]

https://www.maa.org/press/maa-reviews/partial-differential-equations-an-introduction Strauss PDE Partial Differential Equations Review MAA

https://www.maa.org/press/maa-reviews/introduction-to-partial-differential-equations-with-applications Zachmanoglou and Thoe PDE Introduction to Partial Differential Equations with Applications Review MAA

[zealous light]

[stray veldt]

i like how you answer the question by posting the worst book flowchart ever made

however im removing it

[foggy relic]

Why

Mod abuse

[fickle whale]

It started bad and just kept getting worse

[stray veldt]

your "joke" was making fun of or insulting groups of people

[rigid barn]

Hoffman&Kunze>Axler

Seriously, I find H&K ULTRA-underrated. Only standard linalg topic it doesn't cover that well is Jordan canonical form.

[gray jungle]

for a 2nd course, i agree
H&K is based

[rigid barn]

I really don't like this concept of "2nd course", why do US students start off with a baby-version of linalg (something like Strang) only then to through it again "properly"?

Is there any advantage to it whatsoever, besides it being easier? The European/Russian students seem to manage with the "adult" course perfectly well, why shouldn't the US students? I feel like they're being underestimated by their own departments.

[gray jungle]

Considering its one of the first courses you take in undergrad and assuming the average student has no proof background , it makes sense that they are not ready for something at the level of H&K.

most students even learn proofs through lin alg.

[rigid barn]

proof background
Neither do European students, they pick it up as they go along with Analysis and LA.

[gray jungle]

Doesn't have to be a bad thing , usually a 2nd course doesn't need to go through the basics and waste time on them so you get the chance to dive into some advanced topics along the course.

[rigid barn]

The advanced US courses I've seen end up covering the same ground LA1/2 covers here, so I really see no advantages. I suppose you could argue that LA1 here is the 1st course to LA2's 2nd, but the LA1 courses here are just as proof-heavy as anything else in the curriculum.

[gray jungle]

Thats also not a bad thing in a stronger program , it depends on the university and the standard they have for there students.

The LA standards for a program in a competitive uni is likely to be more proof-heavy right off the bat than something in a average university

should we have the standard for all universities be proof-heavy? depends , can the students really keep up ? or will it be a 20% pass rate cause the students weren't ready for it? which happens at my uni due to that

So its down to the uni to decide how to balance it out

[rigid barn]

Anyway, back to H&K superiority, can anyone even compete? Axler's alright, but has those stupid determinant hang-ups.

[gray jungle]

Friedberg, Insel, and Spence is pretty alright and commonly recommended

[rigid barn]

It's alright, but ultimately inferior.

[remote sparrow]

I would love to see the standards for math education be raised so that on average we are capable of appreciating "higher-level" books sooner, but there is nothing wrong with lower-level books and materials that are released to meet the current needs of students. And even with the bar raised, there will still be weaker students that enjoy math, and an effort should be made to help them, too. Ultimately, the weakness and watering down of math curricula is due to structural, political factors that can't be addressed individually, but only through collective organization.

[remote sparrow]

I think it's because some U.S. universities think they can cut costs by lumping in math and non-math majors into the same class. It's probably to satisfy the more applied people that don't really use much of the more complicated ideas. In addition, U.S. schools focus more on breadth, rather than depth, and deciding your major is much more flexible. European students specialize very early, having taken in secondary school all of what would be called "general education" classes in U.S. colleges. So there's probably more time to focus on math there.

[rigid barn]

Long story short: the European education system is superior (not even European myself, per se).

[scarlet pumice]

Hi, does anyone have any math textbook recommendations for relearning math from year 7 onwards?

[sudden kindle]

Any book recomendations for geometry?

Not like riemannian or differential geometry, nor algebraic geometry

I want like pure geometry

Something like Geometry Revealed by Marcel Berger

[analog lava]

there is this textbook that is not 100% solid enough but it is cool

geometric measure theory by frank morgan

p cool stuff

if you want the hardcore version you can read federeer

[acoustic ridge]

A good book on conics...

[misty wyvern]

This image may be a meme but it reminds me of the book From Calculus to Cohomology by Madsen. Same energy.

[remote sparrow]

https://faculty.utrgv.edu/eleftherios.gkioulekas/OGS/Misc/ARUSSIAN.PDF

pretty neat, could be read with lockhart

[solid fog]

does anyone have any introductory books to algebraic geometry that are relatively fast-paced?

would also appreciate if they had a good amount of exercises

[sudden kindle]

Thats not what I was asking for

I don't want geometric measure theory

I want classical/cultural(?) geometry

[sudden kindle]

Yes

A good book on geometry will talk about conics

[remote sparrow]

are you thinking about euclidean geometry?

[sudden kindle]

Yes but not limited to Euclidean

[remote sparrow]

i've heard of old books that teach projective geometry to engineers so they can use those theorems to make better drawings

they're probably obsolete now, but they might interest you

[sudden kindle]

This book by Brannan, Esplan, Gray touches Euclidean, affine, projective, inversive, hyperbolic and spherical geometry

I want more of this stuff

[remote sparrow]

i think coxeter has some advanced material on geometry

[sudden kindle]

Ooh

[remote sparrow]

https://math.stackexchange.com/questions/15857/coxeters-geometry-revisited-vs-introduction-to-geometry

introduction to geometry is probably what you want

https://www.amazon.com/Introduction-Geometry-2e-H-Coxeter/dp/0471504580

https://www.amazon.com/Real-Projective-Plane-H-S-M-Coxeter-dp-1461276470/dp/1461276470/ref=dp_ob_title_bk

https://www.amazon.com/Projective-Geometry-H-S-M-Coxeter/dp/0387406239/ref=pd_bxgy_img_sccl_1/145-1561213-0365747?pd_rd_w=a4AfK&content-id=amzn1.sym.7f0cf323-50c6-49e3-b3f9-63546bb79c92&pf_rd_p=7f0cf323-50c6-49e3-b3f9-63546bb79c92&pf_rd_r=H4T91ZQGPDW04ZQ63W85&pd_rd_wg=TccEI&pd_rd_r=a3ce3a45-d1ac-4487-b25f-9bb0b1e14ad6&pd_rd_i=0387406239&psc=1

https://4chan-science.fandom.com/wiki/Mathematics#Geometry

[dapper root]

/sci/ wiki Jesus Christ

[remote sparrow]

it's a good wiki, in spite of its affiliation with 4chan

[dapper root]

.

[sudden kindle]

Coxeter's books looks good tho thx

[marble solar]

don't knock /sci/

It's a pretty good resource

[dapper root]

I went on it twice and both times the threads were all a buncha cranks, and one dude asking why Thomae’s function was continuous

At rationals

[marble solar]

I got some comfy help on algebraic curves there

[dapper root]

Sorry, irrationals

[marble solar]

and on riemann surfaces

[dapper root]

That’s why I have this discord

Duhhhhh

[spare ridge]

check out the very helpful article titled 'the cohomology of arithmetic'

[vital bane]

chmonkology of arthimetic

what's a good numerical analysis book that does stuff like RK4, symplectic euler, higher order symplectic integrators and stuff like that

like specifically integration schemes

[willow pecan]

Iserles will cover this in the first section on ODEs I think

[gray gazelle]

What is this for?

Will it be useful for high school students?

Or junior high school?

[vital bane]

thanks looks pretty cool

[gray gazelle]

in which book can I read about the construction of C as a quotient ring of the polynoimal ring over R?

[lapis sundial]

probably any algebra textbook that mentions rings right

[gray gazelle]

is C defined as the algebraic closure of R or is it a consequence? I'm confused as different books introduce it differently

is there a book that answers this?

[hasty turret]

I guess depends actually

[rigid barn]

Good book that.

[vital bane]

what a flex (written by me and my son )

[rigid barn]

Don't read me or my son ever again.

[rigid barn]

I've never seen it introduced as literally the alg. closure of R, usually it's derived as a consequence (probably because by the time you learn about alg. closure you definitely know what C is).

[gray gazelle]

I've seen it constructed as a field of pais, a field of 2x2 matrices, and as a quotient ring of the polynomial ring over R. These are all isomorphic, but then the question is: what is C?

if not the algebraic closure of R

bruh someone help me , i have hard time learning new subjects in math

i think i need to work more

with math

[rigid barn]

You mean an "invariant" description of C?

[rigid barn]

Yeah, but what is R then?

I suppose you could define C as "the algebraic closure of the completely ordered field" (afaik there's only one completely ordered field and that's R).

[rigid barn]

The Cartesian plane with a special multiplication

[gray gazelle]

well then it is what it is I guess

one of these fields which are isomorphic anyway

[rigid barn]

If your question is of practical nature, I don't think there's a better way of thinking about C than x+iy.

[gray gazelle]

nah it's just the many different constructions

[spare ridge]

lmao

[gray gazelle]

even though they turn out to be the same thing

[spare ridge]

dick palais

[vital bane]

closure of Q?

[rigid barn]

What is Q then?

It's turtles all the way down, man.

[vital bane]

Z but inverses are allowed :)

[heady ember]

Read Enderton

[rigid barn]

But what is Z!

[rigid barn]

Answer: the work of God

[heady ember]

[vital bane]

that's where axioms come in

[rigid barn]

Proof technique: appeal to higher power.

[vital bane]

proof by worship

[gray gazelle]

is your pfp unique? asking it because I've seen it somewhere else but don't remember where

[vital bane]

unique as in?

[gray gazelle]

did you make it or is it some famous stock image

[hasty turret]

N but you can subtract

[gray gazelle]

I need a book on mathematical logic that is not boring

any options?

also

I want to see how we can use groups, monoids and other algebraic structures in mathematical logic

[hasty turret]

.

[rigid barn]

What's N then?

Self-evident?

[hasty turret]

A social construct

As in the notion of N was useful for society reasons

And people decided to formalize it

[rigid barn]

Try answering like that on a logic exam

[gray gazelle]

off topic

[heady ember]

If you want to know more literally read a set theory book

[rigid barn]

I don't, the questions were tongue-in-cheek

[gray gazelle]

what's the connection between mathematical logic and model theory? is there a book that covers both?

[karmic thorn]

What does mathematical logic mean to you, and why do you think model theory is disjoint from it?

Anyway, for your preceding requests a tangentially relevant recommendation would be Hamkins' Lectures on the Philosophy of Mathematics

The first chapter takes some pains to describe the essence of numbers, number systems, their historical origins and philosophical problems posed by them, along with categoricity theorems

[chilly vortex]

There's more than just integers

How do you explain e or π

[rigid barn]

The work of the Devil, duh.

[runic snow]

If one were to download a book on a library who's name is the first book of the bible what link would they hypothetically use to get the hypothetical book

Or would it not matter

[tawny crater]

Just put the name of it in the search area

[runic snow]

Afterwards. Which mirror is best

[tawny crater]

They're all the same, as far as I know

As long as it works

[gray gazelle]

[foggy relic]

Does Ireland Rosen have any number theory prerequisites

Can you do it without knowing ENT but algebra

[stray veldt]

hm?

its an elementary number theory book

it requires some abstract algebra and complex analysis in later chapters

[fickle phoenix]

Not sure if it's the right channel but I've already bought this book and was wondering what your (plural) thoughts are on it

[hollow peak]

have heard good things about it

jay cummings seems like a cool guy

I used the book of proof by hammack to learn stuff like that

[zealous dust]

Neat introduction to some math concepts often seen in official olympiads (number theory, game theory, combinatorics, induction, etc.), recommended if you wanna get into some math contests but don't know a lot about maths or what they're gonna ask you

Disclaimer: Math Olympiads are pretty hard so don't expect to be fully prepared just with an introduction

[fathom monolith]

What are some of your favorite non-book math resources? A well maintained blog, a journal the public can access, youtube channel, etc.
I loved Dr Peyam's youtube channel about analysis. His love of the subject shines through and he helped me pass RA.

[remote sparrow]

no

[foggy relic]

oh really? thats great then

thanks

i know algebra and CA but just no nt 😂

[gray gazelle]

What's the best Dostoyevski book

[inner token]

Brothers Karamazov though I only read that and Crime and Punishment

Both good

[crimson leaf]

The gambler

[misty wyvern]

What is the worst Tolstoy book

[inner token]

Anna Karenina is the only one I read and I hated it

[alpine mesa]

Any good recommendation for linear algebra textbooks?

[fierce hedge]

Look at the pinned post

[remote sparrow]

#book-recommendations message

[fallow cypress]

Wrong opinion!

[sturdy shore]

idk whatever this is but <@&268886789983436800>

[dense seal]

thanks

[crimson leaf]

insert funny joke about about how that's a crazy response to above message

[remote sparrow]

[vital bane]

smh now mathematicians are generalizing jokes

is this a good book? has anyone here used it like at least went through 2 or 3 chapters?

[tawny copper]

What are good sources for nice probability problems? Im not interested in like "theoretic" problems, but problems like "given x,y in (0,1) with uniform distribution, find probability that the closest integer to x/y is even".

[vital bane]

hmmm sounds like my thing but I want actual mathematical rigor as well

i guess it's a hybrid

[vital bane]

bump

[tawny copper]

?

[remote sparrow]

http://tableschairsandbeermugsmathemagician.blogspot.com/2015/07/normal-0-false-false-false-en-us-x-none.html?m=1
http://tableschairsandbeermugsmathemagician.blogspot.com/2015/08/normal-0-false-false-false-en-us-x-none.html?m=1

Interesting algebra textbook reviews

[remote sparrow]

Bump is an online slang term for the practice of posting filler comments to move a post to the top of a discussion thread, increasing a message or thread's status and visibility.

[tawny copper]

Oh okay. Didnt know. Thanks haha

[fierce hedge]

ah, it's that guy with super comprehensive book reviews. I tried some of his other recommendations like a first course in topology and was not very satisfied

[wild jacinth]

rd sharma

[wooden frost]

whats a good book on trigonometry?
i checked Larson's trigonometry but its exercises are too trivial

[paper ice]

103 trigonometry problems

[gray gazelle]

hey anyone here know a good book on number theory that is available in pdf. The only number theory I know so far is the modular arithmetic taught on Khan Academy

Thanks

[remote sparrow]

consider the books by burton or dudley

[distant spear]

just wondering
what does arithmetic mean
Serre's course in arithmetic seemed like it was full of algebra

[stray veldt]

arithmetic is an old term for "number theory"

[novel obsidian]

serre's book is just arithmetic geo afaik

[willow pecan]

It is not arithmetic geometry

[novel obsidian]

well shit ocw lied to me

idk what it is then

[stray veldt]

number theory

[willow pecan]

It has an algebraic part and an analytic part

And I don't think they actually require that much background

An advanced undergrad could definitely read it

Nowhere close to arithmetic geometry

[stray veldt]

it seems very brief for what it does

[willow pecan]

Serre is very terse

[stray veldt]

but yes, i agree with your assessment

though i dont really know anything about modular forms

[west heath]

In 4th/final year of my undergrad degree and studying a (probably introductory) differential geometry course covering tangent spaces, surfaces, first/second fundamental forms, and Christoffel symbols. Does anyone have any good books or sources covering these things that would be accessible to me? Finding lots of texts that are much more advanced than what we're covering

[sage python]

Do Carmo is the standard, there's also Shifrin's notes

[foggy relic]

Learned from pressley, its alright for what you're asking for and has very minimal prereqs (no analysis or pointset, just calc 3 + introductory linalg)

i heard needham (visual complex anal dude) has a book on it as well (talks about geodesics on vegetables)

dont really know how rigirous it is

[cedar ridge]

why does this never get old #book-recommendations message

[violet shuttle]

Lee's introduction to smooth manifolds and his other book covering the glaring void to the previous book, introduction to riemannian manifolds (can't remember if that's the exactly correct title)

he has very detailed and picture laden explanations, unlike most GTM books (at least, i'm pretty sure those were GTM books).

[remote sparrow]

i heard tapp's Differential Geometry of Curves and Surfaces is good

[sturdy shore]

wow, those illustrations are clean I might give this one a try soon

[remote sparrow]

i bought a "like new" copy from amazon because why not

it was like $30-ish

i will definitely not put off reading the book until i die of old age

it had extremely favorable reviews on amazon and MAA, with reviewers from both considering it an improvement over do Carmo

[heady ember]

time to pirate it when i get home

[west heath]

Thanks guys! I'll have a look into those later

[dapper mauve]

Why is there a raccoon?

[ripe swan]

arithmetic is just numberz

[heady ember]

Laughs in cardinal/ordinal arithmetic

[vital bane]

raccoons are good at cohomolgical arguments

[vital bane]

again has anyone used this? or know anyone who's used this book?

[grand thistle]

i haven’t used it but i have it on my desk rn

it seems pretty ok tbh

wait

it’s actually pretty good i think

[vital bane]

are you gonna use it?

[vital bane]

Niceee

[grand thistle]

i wasn't going to before, but now that i look at it again, it's seems pretty good

i think i might

[vital bane]

im gonna do it this coming summer then

[grand thistle]

ngl it seems very doable

with some good linear algebra background

i was gonna do probability but then might just take a detour to learn a bit about manifolds

since they seem interesting

[vital bane]

diff geo is very cool

[grand thistle]

though i have no idea if ill have time soon bc i have to prepare for sats 😭

i think after i review a bit of linalg and analysis on R^n i wanna dive into either graduate real analysis from folland or schilling or smth or probability or manifolds

dunno which one to choose tbh

[vital bane]

when will you be done with sats?

maybe we can do that book together

[grand thistle]

i have no idea, ive done 0 prep so far

[vital bane]

sat doesnt seem very hard though, like you just gotta get good at test taking lol

[grand thistle]

i've done one practice test just to see where i am, but i think i did pretty well, got around a 1550/1600 i think

[vital bane]

oohh nicee

yea lots of practice tests and you'll be set

[grand thistle]

yeah id love to

[vital bane]

but you gotta give me like 5 months i need to finish analysis and lin alg

[grand thistle]

sounds good, i'll be learning more real analysis by then ig

[vital bane]

alright

[grand thistle]

just curious, where r u rn analysis and linalg wise?

[vital bane]

1st chapter

i mean i know a bunch of stuff

but i dont know how to prove anything

so

gotta get good at actually doing the math

[grand thistle]

of rudin?

[vital bane]

well, im gonna do abbott then transition into apostol

abbott + apostol

for lin alg im doing LADR

wait did the discord text font change- wtf?

[grand thistle]

ah that's a good idea, i just learned from rudin haha

[vital bane]

[grand thistle]

for linalg the text im using rn is really good

[vital bane]

im very bad at proofs so i need easier book lol

[grand thistle]

it's morton-cutis' "Abstract Linear Algebra"

[vital bane]

ya i've been picking up bits and pieces of lin alg for a year, like im familiar with abstract vectors spaces and stuff

not necessarily but it's okay LADR seems managable from the stuff i've done

[grand thistle]

imo learning a bit of group theory is immensely helpful for linear algebra

[vital bane]

Like viewing VS as a group under addition and stuff? is useful for lin alg?

[grand thistle]

texts that approach linalg assuming a bit of familiarity with algebra seem much more natural for me

well, at least from reading bits and pieces of treil's LADW, hoffman-kunze, halmos, and morton cutis

my fav from those are prob the last two

[vital bane]

finite dimensional vector spaces by hamlos?

[grand thistle]

yeah

[vital bane]

oh yea i've done that stuff

[grand thistle]

also the determinant shit is weird i think

[vital bane]

Lol yeah

gonna use another book for dets and related stuff

[grand thistle]

use morton curtis please

[hasty turret]

Doesn't LADR just not cover dets at all

[vital bane]

lol alright

[grand thistle]

the exterior algebra perspective is so cool

[hasty turret]

HK ch 5

[vital bane]

last chapter

[hasty turret]

Well actually Morton Curtis treatment might be better

Haven't read that

[vital bane]

ooohh im definitely gonna use motron curtis then

[grand thistle]

i thought HK chap 5 was kinda too drawn out imo

[vital bane]

wait what exactly do you mean, do they define the determinant as a map from an exterior algebra to the VS's field or smth?

[hasty turret]

Not quite

[vital bane]

then what

[grand thistle]

it wasn't bad, but then why have leibniz's determinant formula when u can have something this simple

[vital bane]

[hasty turret]

Well that's the det of a linear transform yea

But it's cool seeing that det A is "unique" in a sense

[grand thistle]

ye i kinda forgot all of that stuff about the determinant being the unique alternating multilinear map that sends identity to 1

[vital bane]

[pearl escarp]

hi, I don't know if this is the right channel, but does anyone have a good reference on the well-posedness of nonlinear Schrödinger equations?

[gray gazelle]

Opinions on rudin Real and Complex analysis?

[gray gazelle]

I didn't like it

[gray gazelle]

Is there any other book you'd recommend instead of it?

[gray jungle]

It has some nice exercises

[vital bane]

apostol seems pretty good

[gray jungle]

Well it depends , a book for what exactly? RCA covers a lot of topics

[vital bane]

dont PDE people deal with well-posedness of equations rather than physics people?

[willow pecan]

Yes, and the physics server is completely inappropriate for this situation

[gray gazelle]

from what I recall... Rudin is a mix of measure theory on LCH spaces, basic functional analysis and complex analysis

now that I think of it I didn't like Folland either

maybe it's just about it being an analysis book

[vital bane]

mfw you're a topologist

[gray jungle]

Is there any good books with a throughout treatment of differential calculus done on banach spaces ?

[gray gazelle]

isn't there like this one linear algebra book that does it

[karmic thorn]

I saw this idea being discussed/covered in Zorich Volume 2

I have not read the chapter so I cannot vouch for how thorough it is

[gray jungle]

Alright ile check it out thank you, i have also found out henri cartan has a good book on that so that should be enough hopefully.

[gray gazelle]

What book is this?

[gray gazelle]

I was thinking of Roman but I guess it doesn't cover derivatives, other than something called Pincherle derivative that I haven't heard about

[gray jungle]

Thats funny cause when you said that i thought
"ok no one is crazy enough to do it except roman" lol

[mystic orbit]

Manan no longer mod

[mystic orbit]

Haven't read his complex analysis book but his real analysis book is fine

There are better options, ofc

But you can do it if you wanna

The exercises are great however which makes it an excellent resource for review

[fallow cypress]

It's theoretically nice, but it's not clear immediately how to compute it; I think if you compute it out, you get the same as the Leibniz formula

[fallow cypress]

oops, replying to this

[gray gazelle]

yeah sad, I think Manan was an alright mod

[willow pecan]

@karmic thorn hear that

[stray veldt]

what is this server becoming, next they will mod ryc

[remote sparrow]

consider using zorich's two-volume analysis series so that you can be a guinea pig to try a relatively unknown book

[remote sparrow]

#book-recommendations message

fwiw john baez, a mathematical physicist, recommended meckes as a strong, proof-based first course that covers both theory and applications well

[slender cargo]

I don't understand the point of going to Apostal if you're self-studying and already going through Abbott. Just go through Abbott and then do multivariable analysis/lebesgue stuff separately (*take with grain of salt since I'm not far along myself)

[remote sparrow]

rudin's RCA is a graduate book; apostol is undergrad.

rca is supposed to be done after rudin's pma or a comparable book

zorich ties in many physical applications

doesn't mean he isn't rigorous

but i think it could be really interesting for an aspiring mathematical physicist like you neamesis

[mystic orbit]

RCA? PMA?

[remote sparrow]

if nothing else i have the books at home and they seem like good references

[willow pecan]

RCA = Real and complex analysis

[remote sparrow]

Real and Complex Analysis and Principles of Mathematical Analysis

[willow pecan]

PMA = principles of mathematical analysis

[mystic orbit]

Ah, thx

[elfin scarab]

PMA = Pain in My Ass

[sturdy shore]

<@&268886789983436800> this guy too

[vital bane]

ah i see okay

[vital bane]

i wanna do theoretical physics but yes im interested in pure math and math phys as well

alright i'll check out zorich

[gray gazelle]

i think i can help you become a theoretical physicist

[remote sparrow]

whoa are you really sheldon cooper?

😯

[gray gazelle]

yes i am

[vital bane]

[smoky zephyr]

real

[remote sparrow]

bazinga

[rapid lily]

That one is quite good. It's one of the most complete books. A few other options are
Foundations of Modern Analysis by Dieudonné and Analysis II by Amann and Escher. Both have a few other topics not covered by Cartan and each option gives a reasonably complete overview of the subject.

[gray gazelle]

Is this the same Dieudonne in functional analysis

as in Banach-Dieudonne theorem

[rapid lily]

Yes, Jean Dieudonné. I don't know that theorem though.

[gray gazelle]

[grand thistle]

do yall think i should review introductory analysis/learn it in more depth before proceeding to measure theory and other topics?

i've finished rudin's chapters 1-7 but i feel a very large gap in my knowledge of trig/exponential functions and kinda just wanna review

i'll be learning from amann/escher's analysis I and II

[indigo mesa]

amann escher good

[grand thistle]

this time i want to learn it completely and in depth, with all the details like banach spaces and the topology not hidden

[grand thistle]

do you think i could skip some chapters like these because i should be already familiar with the material?

im more trying to fill in the gaps and get a higher level understanding than learn the subject completely from scratch again

don't wanna go through that pain again lol

[indigo mesa]

you should skim them

at least

you don't have to treat them as thorough but yk at least get an overview of how they treat certain things

[gray jungle]

You should review your set theory as well if you're gonna learn measure theory

[grand thistle]

mm yeah

[gray jungle]

Ch0 in folland gives a good overview on what you need

[grand thistle]

cool cool

i was thinking of proceeding to folland right after i finish some topics like multi variable analysis and complex analysis from amann escher vol 2

[sturdy shore]

skip material at your own risk, amann escher is very hardcore

yeah at least skim them

[grand thistle]

right

i want to progress through this as fast as possible tho

600 pages of material is a lot to cover

but not really since around 350 of those i’ve seen before

[hazy elk]

Goddammit do you need to know some alg top for Serre's trees?

Like baby alg top like fundamental groups, homology and stuff, and some category theory too?

[karmic thorn]

[trail kernel]

https://media.discordapp.net/attachments/718456208725377105/1050877365238108200/IMG_5806.jpg?width=275&height=367

opinions on this book?

[gray gazelle]

there's too many calculus books

[trail kernel]

true tbh

[rigid barn]

Cartan's Differential Calculus, but I'm not sure there's an English translation (there is a Russian one, if that helps).

[fluid bay]

maybe an interesting idea would be to read a book like spivak calculus on manifolds but attempt to generalize as many theorems as possible to banach spaces

[vital bane]

easy just replace the euclidean norm with a general norm

[fluid bay]

Yeah I think that would take care of most stuff

Well, idk about most, but a good bit maybe

[gray gazelle]

any good books for college algebra?

[heady ember]

See pinned

[remote sparrow]

College algebra is another name for algebra of the equation solving sort, not abstract algebra

[grand thistle]

can anyone compare henri cartan's differential calculus on banach spaces to Amann/Escher's analysis volume 2?

(and vol 1)

would it be more appropriate to just work through Amann/Escher's first two volumes linearly or should i just learn the differential calculus from cartan?

im not sure how much Amann/Escher emphasizes banach spaces

[silver axle]

Hello, does anyone have a book to learn maths at second / first level in France

[grand thistle]

the biggest reason why im drawn to A/E is that it's more modern and perhaps covers more applications, while im drawn to cartan for his conciseness and treatment on banach spaces

[heady ember]

Oh

[rapid lily]

They somewhat cover different topics. Amann and Escher cover calculus in Banach spaces in Chapter VII of their Analysis II book. There is a lot more content in Analysis II compared to Cartan's book, but Cartan's book has some results not covered in the other book. Either one should be sufficient.

[rapid lily]

Well, there is a lot of content covered in Amann and Escher's books, while Cartan is only looking at differential calculus and differential equations. It depends on how much time you have and the other topics you need to cover.

[grand thistle]

hmm i see

which one do you think is more fun to learn from?

i'm mostly looking to learn measure theory and probability after i finish either A/E or cartan

[grand thistle]

so which one would you think is more suited toward that?

[rapid lily]

I haven't learned much measure theory, but I don't think you need much for measure theory.

[rapid lily]

I enjoyed using Cartan's quite a lot and haven't read much of Amann and Escher's yet. There are not as many concrete examples, but a lot of the concepts are treated in a general and yet simple way. He also introduces topological concepts when required which is quite helpful.

[grand thistle]

yeah i know, i'm just trying to review and solidify my basic analysis as much as possible

also learning all this stuff about banach spaces and hilbert spaces and stuff will probably make it much easier

[grand thistle]

alright sounds great, i think i'll try both and see which one i like better

[rapid lily]

The first of Cartan's book can be good for that. He doesn't cover directional derivatives though and doesn't mention Hilbert spaces if I recall correctly.

I will strongly recommend reading the beginning of Chapter VI for Analysis II if possible though, because Cartan does not say how an integral of a function from a compact nonempty interval into a Banach space is defined, and that section gives a very nice presentation of how to do that.

[grand thistle]

yeah i was gonna relearn/review everything i covered from rudin from Analysis I, then cover all the new content possible (except perhaps the complex analysis) form Analysis II

since i havent been exposed to anything like fourier series and special functions yet

[rapid lily]

Ok. That can work quite well. I haven't actually read too much of Amann and Escher and have planned to do that, but haven't got around to it yet.

[grand thistle]

amann and escher's books are so great

i wished i learned from them for my first exposure to analysis

they're so much more detailed and general than rudin

and actually names theorems

[wide hornet]

Excuse me

Does anyone have a pdf book of complex analysis

[modern crag]

Start with

number theory
algebra

Next move on to
Set theory
Euclidean Geometry in 2D
Euclidean Geometry in 3D

Then tackle
Trigonometry
Series and Sequences
Matrices
Coordinate Geometry in 2D
Vector Mathematics
Complex Numbers
Polar Geometry in 2D

Then tackle
Differential Calculus (It's absolutely essential to understand limits before moving. If you don't get limits forget about it.)
Integral Calculus
Differential Equations
Calculus of 2 or more Dimensions
Then Go on to
Probability Theory
Statistics

This is a lot, so I want to start from the beginning, what would good textbooks be for number theory and algebra?

I guess, any book that combines some of these would be ideal

[gray jungle]

joke^

[orchid mortar]

I don't see how this isn't all just called calculus in a standard school

I'm not sure what 'algebra' refers to, and I don't know of any number theory books at that low a level

[crimson leaf]

Depending on the algebra you're referring you to you will want set theory before both number theory and algebra

[sudden kindle]

Start with number theory, algebra

[crimson leaf]

It's like the list goes backwards almost

[sturdy shore]

start with algebraic geometry to get a broad overview of algebra and euclidean geometry

[vital bane]

start with category theory

[willow pecan]

Do not

[remote sparrow]

Try Mathematics Made Difficult by Carl Linderholm

(linderholm's book is satire)

[gray jungle]

I think its safe to assume that " NT and algebra" means middle school algebra given the progression and i recommend you use khan academy website

[fallow cypress]

yeah I would ignore this list and just follow khan academy's curriculum

this is a nonsensical list

[modern crag]

Yeah I just pulled this from Reddit. I just want a comprehensive overview just to cover anything I may have gaps in. Like I know for sure I struggle in trig so any trig books

I took that to mean high school algebra but I’m studying computer science so set theory would help.

Does spivak’s calculus cover calc 1 2 and 3

[foggy relic]

1 and 2 but I would not recommend that for you

if you do not know high school algebra/precalculus

[remote sparrow]

spivak's calculus only covers single variable calculus

[foggy relic]

what i would recommend is khan academy, Pauls online notes for algebra, Lang's basic matheamtics

[modern crag]

Well I know it, just wanted to do a refresher, but I will def check those out

[foggy relic]

if you want speedrun just do paul

[shut orbit]

no love for top-down enjoyers huh

what's wrong with starting with hott and lang's algebra ?

[sage python]

Some amount of top down-ness makes sense in the right setting but there are two main problems

(a) Resources often assume that you have, either a certain background or a certain... "mathematical maturity" (really just means ability to pick things up quickly, usually at a pace that one only hits after a fair bit of expertise). This is more of a practical concern, so someone sufficiently clever and with a self-contained resource could avoid this problem

(b) For some subjects, you won't "get the point" without some other context, even if the definitions and theorems are self-contained. I'm fairly certain that you can define, say, etale business in algebraic geometry, without reference to ordinary pi_1 and singular (co)homology. But if you don't understand that the point of etale stuff is that varieties/schemes don't respond nicely to singular pi_1 and cohomology the way manifolds do, then... yeah

[shut orbit]

but i mean humans adapt to difficulties presented to them, why torture urself with Basic Mathematics instead of using it just to fill in a few gaps

i tried following math linearly from beginning and all it did is made me hate sets and proof with sets

[crimson leaf]

I mean if we start someone who knows basic pre-calc with no exposure to proofs or set theory and just drop them on Lang's Algebra I would reckon for 99% of people it would not work

[shut orbit]

well obviously u dont try to extract it only from lang algebra book

[remote sparrow]

and how exactly do humans adapt to difficulties presented to them? when math students are thrown into an abstract topic, one of the first things they usually do is make up or latch onto concrete examples. you can just start with less abstract things and have students generalize on their own.

[sage python]

First, this only addresses point (a) above, and point (b) has importance which is not to be underestimated. But in reference to it, sure up to a point but eventually it becomes inefficient. You'll have to deal with some amount of drudgery in math no matter how you go into it

[hasty turret]

Well once you know proofs, you can start at a slightly higher level. I think that would be like intro algebra and intro analysis

Or maybe something at level of munkres topology ig

[toxic bridge]

Hi hi, sorry to interrupt, but I'm looking for post-calculus books for self-study that I can get for the holidays. Is there a tool I can use to filter for my requirements, or any recommendations you might have?

[inner token]

@toxic bridge do you have experience with writing proofs?

[toxic bridge]

A little, but it was over four years ago, in a part of my memory I can't access.

[heady ember]

Loch has a intro to proofs summary pinned in #proofs-and-logic

[remote sparrow]

#book-recommendations message

[inner token]

"A Book of Proof " by Hammack might be good. It's free online. I think "Linear Algebra Done Right" by Axler, "Understanding Analysis " by Abbott, or "A Book of Abstract Algebra" by Pinter would be my personal choices if you want to dive right in to a subject

[remote sparrow]

of those intro-to-proof books, hamkins is the only one that has full solutions with his companion book

[remote sparrow]

*hammack

[heady ember]

LADR's coverage of determinants and characteristic polynomials has some issues, from what I have heard here

[remote sparrow]

#book-recommendations message

you can do calculus-based probability and stats

there are some proofs but you aren't really expected to do much yourself

or ODEs

[inner token]

Its gimmick is that it does determinants last, but I think it's a good book with fun exercises

[toxic bridge]

That sounds like fun!

[sturdy shore]

have you done calc 3

[remote sparrow]

as long as you know multivariable calculus you can do it, but multivariable calc knowledge is only used in a few places for a calc-based probability and stats class i'm pretty sure

[toxic bridge]

My biggest joys have been statistics, calculus, and proofs.

[sturdy shore]

don't do probability/stats without calc 3 background, and don't do ode's without linear algebra background (imo)

[inner token]

DeGroot has a good intro to probability and statistics book, and I know I found it and the solutions as pdf online

[remote sparrow]

i think blitzstein and hwang is much better for self-study

it's possible other books are better in a classroom setting though

[tawny rock]

Dont do what i did. I tried proof by induction as my first proof

[sturdy shore]

only used in a few places? I don't think joint distributions are that uncommon lol

[tawny rock]

For*

[sturdy shore]

proof for what?

[remote sparrow]

when using one of those books, you'll only spend a little bit of time on it i mean

for further progress you will actually need to know calc 3

[inner token]

@toxic bridge a computational linear algebra book might be a good first pass before you start solving proofs on linear algebra

[remote sparrow]

hefferon or meckes are both good linear algebra books

[tawny rock]

If x is an element of the natural numbers, then prove that 1 multiplied by x equals x

[remote sparrow]

both hefferon and meckes are good at showing the computational and theoretical sides of linalg

very appropriate for first courses

[sturdy shore]

are you high idk why you are posting this here

[remote sparrow]

hefferon is free

you can also buy a cheap print copy

[tawny rock]

I already proofed it and turned it in a month ago.

You asked me what was it on so i gave you the statement

[grand thistle]

what’s wrong with a proof by induction?

[tawny rock]

I just found it much harder than a direct proof or proof by contradiction. I did them later. I should say that I walked into this with a precalc 11 background and one uni level math textbook. I did them for a course that required you to deep dive on a topic you were passionate about. I should state that i am in grade 10 and i took pre calc 11 last year

[grand thistle]

okay but i don’t see how that relates to not doing probability without a good calculus background or doing odes without linear algebra

and aren’t induction proofs part of the standard curriculum

[tawny rock]

I was planning to have a cacl 12 background but the class was cancelled and they put me in a different precalc 12 class that hasn’t started yet

[tawny rock]

Not in my country

[grand thistle]

what is precalc 12?

[tawny rock]

The precalculus class that my school has for grade 12 students

[grand thistle]

oh

well good job that ur ahead i guess

try read a discrete math book

if ur struggling w induction proofs

[tawny rock]

Already did. It was fun. I have gotten a lot better at them

I borrowed one from my math teacher

[grand thistle]

nice

what r u learning now?

[tawny rock]

Im taking a small break rn cause im preparing for the exebition where i showcase my proofs that have been done over the last 2 months

[grand thistle]

cool

if u like proofs and wanna get into calculus, try spivak’s book

or apostol’s one

[tawny rock]

Noted

[grand thistle]

i used those last year when i was just getting into pure math and it really showed me what harder math was like

[tawny rock]

Here is the textbook i have

[remote sparrow]

just so you know, if you know how to read and write proofs, you don't have to go to calculus right away (although you MUST know it down the line some time)

you could do enumerative combinatorics, elementary number theory, or linear algebra

[tawny rock]

Ah i see

[grand thistle]

these topics are all really fun to learn

combinatorics is not really my cup of tea but number theory and linear algebra are really interesting

[tawny rock]

Oh my goodness the photo is taking so long to load

Those are my calculus textbooks

[grand thistle]

ehhh those are okay

[remote sparrow]

they're fine

[grand thistle]

i have stewart and used it a bit and it was okay

[crimson leaf]

Stewart or Thomas are what you would find in most colleges

[remote sparrow]

while stewart has proofs for completeness, you aren't really expected to prove anything

[tawny rock]

Figured as much

[remote sparrow]

i've not heard of calculus an applied approach by larson

i've only heard of just calculus by larson

[crimson leaf]

I didn't really like Stewart for some calc 2 and 3 stuff but for all of the stuff in calc 1 I thought it was good enough

[remote sparrow]

you can still open these books for problems

stewart has a lot of problems

[grand thistle]

to be honest, most of these calculus textbooks are very similar and things you find in one you'll find in the other

[remote sparrow]

also spivak doesn't cover applications of calc like related rates and optimization, but i think apostol does

[crimson leaf]

I believe that's mainly used for things like business and social science majors

Probably doesn't have trig or some other topics

[remote sparrow]

yeah, those classes are really watered down

[tawny rock]

Yea the applied approach is for business and economics

I plan to get a masters in mathematics and then a masters in teaching

[remote sparrow]

congrats

[tawny rock]

Surprisingly it does have trig. Looks like it’s watered down tho

[toxic bridge]

I'm looking (more specifically) for Multivariable Calculus, Probability/Statistics, and an introduction to proofs.

[crimson leaf]

Does anyone know if the international edition of D&F is the most recent version of the book?

[remote sparrow]

probably

more important is if there are issues with the printing

like pages out of order, omitted content, ink that fades easily, etc.

[crimson leaf]

Maybe I'll just grab the hardcover then, I wasn't even gonna get d&f but it's for a class and traditionally she lets students have the final open book but it has to be physical

[remote sparrow]

you could check out D&F from your library

typically uni libraries let you borrow books for like a few months

[crimson leaf]

We don't have D&F in the normal library

[remote sparrow]

if it's not fiction

[crimson leaf]

I'd have to get it loaned from somewhere else

We have Lang, Jacobson, and Hungerford though lol

[remote sparrow]

inter-library loans take a few days to process

but i think uni libraries have a system that lets you do it from their website

[remote sparrow]

usually there aren't any severe issues, just lower paper quality and inconsistent inking (but easy enough to tell what's printed from context) though i'd be worried if one review said some content is omitted

probably just applies to intl ed. of old books like rudin and ahlfors though

i have an intl. ed. of stein's fourier analysis and everything was really peachy

great printing quality

no issues as far as i can tell

could be due to different publishers too idk

[crimson leaf]

Yeah I'll make the call closer to when the course starts it's not anything crazy just a $20 difference 40 and 60 so unless they gaps widens in one direction when I actually go to buy the book I'll just run with it

[remote sparrow]

where are you finding D&F for just $60

used?

[crimson leaf]

Yeah

Both versions are used

[remote sparrow]

actually could be a better call to get a used hardcover of D&F

probably less likely to be a crappy gluebound

like the new copies nowadays

could be a sewn binding

[loud cradle]

i think the D&F 3rd edition hardcover had a reputation as being poorly bound as well alas

maybe i'm wrong though

my 2nd edition hardcover has held up well for 20ish years

[grand thistle]

my copy looks like this

so yeah it's pretty shittily bound

[remote sparrow]

pretty hard to tell whether it's a gluebound or a sewn-bound

[grand thistle]

as you can see i gave up in the group theory section

[grand thistle]

it's glued i think

[loud cradle]

hopefully because you moved on to a better book on group theory 😀

[grand thistle]

yes

[remote sparrow]

still on the hunt for a good bookbinding place

tangentially related, i wish lulu's project design process were more straightforward

[grand thistle]

pov you left ur copy of baby rudin in ur bag during a rainy day

[remote sparrow]

apparently it's not as simple as just uploading a PDF and having them print it

[crimson leaf]

Well there's also legal issues with using Lulu no?

[remote sparrow]

i don't think they check

if you're not selling it anyway

[loud cradle]

alas i have several books in a similar state for the same reason... but it could be worse - i have a couple of books that were in a backpack along with a flask of coffee that somehow leaked 😂

[remote sparrow]

i don't take my books to school

[grand thistle]

holy 💀 can u even read those

i don't use physical books anymore since i got an ipad

[remote sparrow]

i read my books, to be sure, but i like to keep my books safe

[grand thistle]

honestly the best investment ive ever made

[loud cradle]

the coffee mostly fucked up the edges of the pages, so it looks like yours except with brown stains at the edges

[remote sparrow]

e-readers are better than ipads

longer battery life, much less eyestrain

still prefer physical books

also ebooks tend to have DRM, and they're also licensed to you, not owned by you

so companies can revoke access to your books any time they like

same idea with steam

you're technically just indefinitely renting games

[loud cradle]

has steam ever actually revoked "ownership" of a game once you bought it? i don't think this ever happened to me but maybe i've been lucky

famously Amazon has revoked ebooks

[remote sparrow]

yeah, but that possibility is always over your head

that's why i'm slowly migrating to gog

[grand thistle]

the thing is you can do stuff like this on ipads which is really convenient

[loud cradle]

yea i like being able to download the full installation package with gog

[heady ember]

I do my notes in latex

[loud cradle]

the only thing that goes wrong with gog is you upgrade to some new version of windows and some of your old shit just doesn't work anymore

[remote sparrow]

https://castel.dev/post/lecture-notes-1/

[grand thistle]

i used to do this but then i found that i usually ended up rewriting the book so i stopped

[remote sparrow]

have you seen this absolutely wild guide to take latex notes live in lecture?

[heady ember]

For me, I copy the statements of theorems/lemmas/corollaries, and add in anything else I find noteworthy.

[grand thistle]

wtf that's actually crazy

[willow pecan]

I used to take latex notes during lecture

[heady ember]

Not yet, I'm looking at it now

[willow pecan]

No vim either

Just typing speed

[grand thistle]

taking notes that fast while thinking at the same time is already hard but drawing diagrams is next level

[remote sparrow]

there's two more parts

[heady ember]

How would you even find and fix compilation errors quickly in a lecture though

[remote sparrow]

get good

[willow pecan]

It isn’t too bad

[heady ember]

[remote sparrow]

i don't take notes

never have, never will

somewhat of an exaggeration tbh

but i find notes are too much effort

with little return for me

just busy work

[sturdy shore]

most compilation errors can be automatically corected so that the pdf can compile

well, "corrected" the resulting pdf might be faulty but those can be corrected after lecture

[modern crag]

so, khan academy and the lang book? I'm mostly doing this so I can plug up any gaps in my understanding before I take a calc 2 class, I am a nontraditional student and it's been years since I've taken a rigorous math class

[foggy relic]

@modern crag i would start with lang if i were you, if it is very very difficult for you switch to khan academy and if you feel like you learned this material before and are just re-learning it, speedrun Paul's Online Algebra Notes

this is my advice at least

[remote sparrow]

https://castel.dev/post/research-workflow/

oh apparently castel has made another guide on how to make some more notes in latex

[modern crag]

Okay I will try this

[gray gazelle]

Autobiography Michael Jackson book Moonwalk

[tardy walrus]

This is not as big of an issue as you may think. Firstly, once you become proficient enough you make fewer compilation errors. Secondly, most of the compilation errors you do make are simple typos. What I do is whenever the lecturer takes a break (to answer questions, or is thinking, or I've finished writing something down before they've finished) I'll compile my document and fix whatever issues I have quickly. Once you get the hang of it it's not a big deal.

[spice stag]

Which book would u recommend for vectors and 3d ?

[heady ember]

Oh you don't compile them regularly? I compile every couple of lines lmao

[sand crescent]

me also compile very often 🙈

[heady ember]

Oh hi determinant!

[sand crescent]

hewwo grassmannian

[heady ember]

lint?

(but also, this is getting offtopic so yeah)

[toxic bridge]

I guess I'll try again. I've tried googling, but I'm not sure what to look for to tell if a book is good, lol.

[subtle mango]

math stackexchange and r/math usually have discussions over books

#books-old is good too

[toxic bridge]

I'm very sorry, but it's very hard for me to parse through those.

[nimble musk]

Any book for number theory

Please

[rigid barn]

Silverman (more modern) or Niven-Zuckerman (more classical) are good intros. Dirichlet's lectures if you were "born in the wrong generation", Disquisitiones Arithmeticae (in Latin ofc) if you're a sigma male.

Is Halmos' "Naive Set Theory" good for quickly learning the basics? By "basics" I mean the basic tools of set theory that show up elsewhere sometimes, stuff like cardinals/ordinals and so on.

[flat cedar]

I need a recommendation for physics book named " A brief history of time " by Stephen Hawking can I read this book I want to read it but the main issue is I am just 14 I love physics even I can solve the questions of higher classes than my own class I like to know about black holes and singularity space time , interstellar space , time travel can I read this book can I understand this book ?

[willow pecan]

Yes it doesn’t have any math

[honest pier]

best book to get into algebra from scratch ? which explains stuff in detail?

[remote sparrow]

simpler books would be those by dudley or burton

[remote sparrow]

of the equation solving sort or abstract algebra?

[honest pier]

equation solving

[remote sparrow]

khan academy and paul's online math notes

[foggy relic]

those are good, another possible source is lang basic mathematics

[scarlet pumice]

Hi, anyone got any book recommendations to brush up my math skills before commencing my engineering degree?

[remote sparrow]

what classes have you already taken?

or what have you already studied

[fluid skiff]

Are you able to make use of snippets etc for faster workflow?

[remote sparrow]

i don't do anything castel does

i don't even take notes to begin with

[storm cloud]

oh the last one is so based i love his website

[short copper]

Hi!
What are some book recommendations as a Christmas gift for somebody interested in the mapping of maths, the history of maths and (not related) cool visualizations and simplified explanations of maths?

[scarlet pumice]

I have taken IB AA HL but that was a few months back because I did a commerce degree before switching to engineer

[remote sparrow]

i haven't read much math history books, but in general i'd avoid books that treat math history (or history in general) with great man analysis. your friend may be interested in mathematics history sourcebooks, such as those by katz or stedall. i've heard stillwell is fairly reputable. boyer and merzbach have written a standard text for math history classes. all history classes should engage with primary sources. that isn't to say you should exclusively rely on primary sources, as that too is dangerous. additionally, avoid books that have a eurocentric view of math history.

https://www.maa.org/press/maa-reviews/browse?field_tags_tid=37088&field_bll_rating_tid=All&field_maa_review_value=All

consider looking through here as a starting point ^

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

this is a good general guide for how to properly research history

[modern crag]

Hey, so I'm getting started in this lang basic mathematics book, and there's a proof for everything, I've never really touched proofs, should I try to do them, if so where can I start learning proofs

[remote sparrow]

lang is supposed to be a way to learn how to do proofs

besides revising precalc math and learn selected topics

but if you like, you can supplement lang with some other books

#book-recommendations message

[modern crag]

Yeah, I'm just not sure how to do it at all, like even something simple like this, like yes I know they are the same from my years of education, but I guess proofs are about taking it one step further

sorry, maybe wrong channel for this kind of discussion

[remote sparrow]

(a + b) + (c + d) = ||(a + b) + (d + c) = a + (b + d) + c = a + (d + b) + c = (a + d) + (b + c)||

[sturdy shore]

there are no magic tricks here, everything relevant to show this is true should have been given beforehand in the book as properties of addition

like associativity and commutativity

[remote sparrow]

you are given commutativity and associativity

^

[dreamy fog]

Hey can you guys recommend me a book or website with loads of questions on probability and random variables( moments, kumulant, inequalities like chebychev, Jensen etc)

[remote sparrow]

check out blitzstein and hwang's website

[dreamy fog]

Do you have a link? I can’t see it on google

[remote sparrow]

i tried posting the link but it keeps getting deleted

[dreamy fog]

What did u type on google

[remote sparrow]

just type in stat110.net

[dreamy fog]

Ok

[shut orbit]

i didn't know about this statistics course it seems pretty good

[remote sparrow]

it's probability not stats

[sturdy shore]

One Thousand Exercises In Probability - Grimmett & Stirzaker

it is a companion to their textbook probability and random processes but it can also be used as a standalone problem book

[short copper]

thanks sour drop

[gray gazelle]

Michael Jackson biography

[modern crag]

Gotcha, and yes I was given those properties, before I just took them for granted and was taught them. How do I learn to formalize the logic?

[remote sparrow]

you just need to unpack what associativity and commutativity of addition mean. associativity just means you can group terms any way you like and you still have the same result. commutativity just means you can swap the order of the terms and you still get the same result.

just apply those properties

all i did was 1. swap c and d, 2. associate b and d, 3. swap b and d, and 4. associate a and d and associate b and c

[slim carbon]

sas book

[spice stag]

Sus

[fierce hedge]

I ordered Basic Algebra by Jacobson and I think I got a fake copy? It is hardcover and the publisher is not Dover. The paper quality seems decent though the printing is a slightly blurred

[sturdy shore]

the original publisher of that book isn't Dover, they rarely are

just an older printing

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

you can see here

Reprint of the W. H. Freeman and Company, San Francisco, 1985 edition.

[fierce hedge]

Ah, I see. I ordered from Amazon and the packaging was from Flipkart so I thought that was fishy
Thanks for the info

[loud cradle]

the paper does look unfortunately thin (can see the text from the other side bleeding through), so maybe it's an international edition? i have an old US hardcover that doesn't look like that

[hidden hazel]

Is there a recommendation for a hefty multivariable calculus book?

As well as linear algebra?

[sturdy shore]

his says w.h. freeman newyork

is yours the same

[sturdy shore]

shifrin and hubbard & hubbard are the standard

[fierce hedge]

It doesn't say international edition anywhere plus all Dover books I have seen have this type of slightly transparent paper

[loud cradle]

i don't have it right here (it's two floors down) but i'll check when i get the chance, honestly can't remember who the publisher was

[sturdy shore]

shifrin has lectures online so get that if you are into that

[loud cradle]

+1 for shifrin's multivariable mathematics

[sturdy shore]

hubbard hubbard actually has some introductory measure theory in it which I found interesting, but I've skimmed the book very fast

but both have roughly the same content otherwise

I'd go with shifrin because his lectures are amazing imo

[loud cradle]

fwiw, here are a few pictures from mine (sorry about the blurring on the title page, that's my bad camera work, not the book)

[remote sparrow]

i don't recall dover selling any hardcover copies. additionally, dover usually reprints everything in full, generally without making corrections.