book-recommendations

[marble solar]

wrong

[sage python]

So I was 3 and had the speaking level of a 6 month old

[tight crag]

How many languages do you know?

[tulip blade]

Too many examples

[marble solar]

have you read a dictionary? they have example uses of words

[tulip blade]

@marble solar how

My friends enjoyed it

Im not an algeber person so i dont really care

[marble solar]

Algebra is just a mistake

[tulip blade]

Im not anti algeber tho just not an aspiring algebraist

[tight crag]

Algeberist

[tulip blade]

This^

[sage python]

Eventually when they realized I wasn't deaf or had... developmental problems

They said okay stick to one language, English, don't let him hear anything else

[velvet briar]

Algebrist

[tight crag]

That's wild

Algebro

[sage python]

(Apparently the doctor who figured out what my parents were doing were like omg wtf is wrong with you guys)

[velvet briar]

Algae

[willow pecan]

[sage python]

Anyway so now they know the strat but I'm super behind

[tulip blade]

My parents didnt even acknowledge me

[willow pecan]

I did fine hearing English and Chinese growing up

[sage python]

And to get me caught up they taught me how to read and speak simultaneously

[tulip blade]

Locked me in a room w rudin and d&f

[sage python]

That way I can just read a dictionary and figure out the words I don't know

[glossy grove]

But most people should be able to grow up bilingual, shouldn't they?

[tulip blade]

Eventually i managed to open them and start reading

[sage python]

By this point I already spent a few years getting confused

[tulip blade]

And here i am

[sage python]

Like if my parents did the multiple languages thing correct from the beginning it could've worked

Like if they chose just 2 instead of 4 and if one person spoke each language instead of all of them mixing

[tight crag]

Lol unfortunately it seems like a hard strat to implement

[sage python]

My dad would speak English and Berber mixed

My mom would speak Arabic and French mixed

[glossy grove]

and have you learnt speaking multiple languages by now, or did you become uninterested after that failed attempt 0.0?

[sage python]

My aunt same

When my grandmother was around she would speak Arabic and Berber

[tulip blade]

What is berber?

[sage python]

So yeah that just confused me and I completely closed up

Indigenous language of Morocco \subset North Africa

[tulip blade]

Woah

[sage python]

And yeah once I basically closed up and didn't learn the doctor was like

Sugandese mf nuts

Well you had a window to teach him multiple languages but at this point you missed it

So don't even talk to each other in another language while he can hear you

[broken meadow]

dami is too good at this

[sage python]

I never miss

[broken meadow]

i will find a way\

[sage python]

You will try

[broken meadow]

if it takes years i will do it

[sage python]

But yeah so I have learned sketchy Arabic and I can kinda understand some Berber

I used to know a bit of French but it's deteriorated

[broken meadow]

...

[sage python]

Yes

Especially wendyz nutz etc

[broken meadow]

L

Fail

[sage python]

I am invincible

Anyway point being I had this huuuuge dictionary as a kid

And basically my way of catching up was, if I ever encountered a word I didn't know I'd look it up

So yes

That said I feel there are more fun ways to learn algebra lol

Herstein like I said was good esp with Keith Conrad's notes

But the problem is

I got every cycle notation problem wrong for a while

Because he would mess with right to left vs left to right

Slim wtf

I was on board but using complex analysis to learn algebra?

Like Riemann surfaces or smth?

Oh I mean you don't need complex analysis for that but sure

I think like

Combinatorics/S_n works

Group theory is what we have in mind and I think you should basically focus on linear algebra, geometry, and combinatorics

Algebraic topology is mad fun

[flint forge]

Hatcher is the canonical book

and you absolutely should learn alg top if you plan to go to graduate school

[sage python]

Rotman is the good easy book, Bredon if you like manifolds, Hatcher if you like visuals

[flint forge]

I disagree

Hatcher if you aren't incompetent with visuals

you dont need to like them

[marble solar]

I've only read chapter 1 of Hatcher - I think he does a decent job at bringing up to speed on what things mean visually

[flint forge]

house with two rooms is unironically not hard to picture and I will die on this hill

[marble solar]

Without getting bogged down in too much rigor

[sage python]

Lol so I think some people are just built as visual thinkers to use a meme

[flint forge]

i mean its def a skill and also a talent

[sage python]

And if you're a visual person you find Hatcher to be smooth otherwise you just don't

[flint forge]

you have to practice to be good either way

and if you just get frustrated and give up like dami here

[sage python]

You can force it but it's very difficult if you're not predisposed

[flint forge]

you'll never get any better

(admittedly some people are neurologically incapable of visualization)

but thats a real medical conditio

[hearty steppe]

errr, its just harder

[flint forge]

no

i mean literally incapable

[hearty steppe]

well it is not my place to argue about that in this channel, but depends on how you define "visualization" criteria

[flint forge]

use hatcher

[sage python]

So the reason I say Hatcher if you like visuals as opposed to just capable of understanding the visuals is

[flint forge]

hatcher uses visuals like

4 times

[sage python]

He has other disadvantages

[flint forge]

when discussing homotopy and building intuition for it

[sage python]

Like he waits wayyyyyyy too long to do category theory

[flint forge]

you literally cannot avoid visuals

and you don't need category theory in a first class on alg top

[sage python]

You don't need it but I feel that's where you should learn it

[flint forge]

alg top is already loaded with first-time things

but yes its not a bad idea

hatcher is a good book that introduces the material without frontloading a bunch of machinery

and stresses the visual intuition that is essential for early computaitons

there are like 2 places where i think the visuals are ridiculous (i.e. they took me more than 20min to properly picture)

but i think otherwise hatcher does a good job

I think the thing to keep more seriously in mind for alg top is like

which proofs you actually need to read/understand (on a first pass)

and what stuff you can just sorta look at and say "neat"

[gray gazelle]

What kind of stuff would this be?

[flint forge]

Uh, for example I still can't write down the construction of generic universal covers

i know the vibe

and how it works more or less

but its not something you need to really kill yourself over

and hatcher presents it in a kind of lengthy way

[sage python]

Anyway yeah my take on Hatcher in detail is:
Chapter 0 is okay, though I don't like how he explained genus g surface and I don't get house with 2 rooms
Chapter 1 is okay but the Van Kampen bit was trash
Chapter 2 is good
Chapter 3 is bad
Idk chapter 4 it's probably fine

[flint forge]

Honestly

you probably don't really need to know how to prove the snake lemma

but its a good exercise in diagram chasing

so you might as well for practice

[sage python]

Anyway my thing is, Bredon's topic selection is best. Like he presents things "correctly"

[flint forge]

Basically my opinion is like, if a proof doesn't help you do computations, you don't need to understand it the first time through

NO

what

thats just not true

bredon does a bunch of weird stuff

i dont recall much about topic selection but like

iirc he starts with like the category of pairs and stuff

its just like

alg top isn't supposed to be hard or confusing in a first introduction

and it doesn't need a lot of machinery

i think that doing things with an eye toward generality and even future development is good but not helpful, and that hatcher's more geometric perspective can be really helpful for a first timer

bc you can just rely on your mind's eye a lot more

I should write an alg top book for undergrads

like explicitly with them in mind, taking minimal algebra pre-reqs etc

do all my (co)homology over Q

[sage python]

That's Rotman lol

[flint forge]

or R

Rotman introduces the fundamental groupoid before the fundamental group

[sage python]

Does he?

[flint forge]

i was just looking at the contents earlier

[sage python]

Either way he very slowly introduces the category stuff

[flint forge]

i would not introduce it at all

[sage python]

Like it's slow

[flint forge]

other than the word "functorial"

i think slowness is not what I am thinking

I think just focusing on the details that provide key insights

rather than developing all the details but slowly

is my point

[sudden kindle]

i did a directed reading project with a grad student on homology using hatcher chapter 2 and we mostly just skipped the technical proofs

[sage python]

Yeah I guess it's a disagreement of pedagogy lol, I mostly don't believe in that choice

[flint forge]

i learned alg top over R the first time and it was great

obvi the homotopy groups were not rationalized but like everything else was

A lot of the harder pre-reqs in alg top come from generic coefficients for your (co)homology

like the universal coefficient theorems and stuff

[sage python]

That's unfortunate

Uh oh

[willow pecan]

[marble solar]

the university I work for isn't even teaching algebra in the fall

[sage python]

F tier

[marble solar]

We don't have complex analysis

Real analysis was taught for the first time in over 5 years this spring

[sacred swan]

5 years????

[marble solar]

I work for a small Historically Black college

Where we don't have the student demand, resources, or faculty that can handle it

There's no physics major

There are no engineering courses

etc.

I don't know if it's sad - it's more of a function of what population are you serving, and how can you best serve them

But I was brought on specifically to bring a math perspective to the center

thanks - Although I'm not actually a frog

[sudden kindle]

🐸

[flint forge]

uchicago also has no engineering hahaha

[quick hornet]

but uchic econ students fill the role that engineering students usually take up

tis the natural balance

[flint forge]

no

[gray gazelle]

this happened to my school too, they removed the physics major, we still have engineering though lol that's weird.

neverrrr

[obsidian valley]

one makes money, one doesn't

[gray gazelle]

I'm saying it's weird that they removed engineering

also people can make money with physics degrees lol

there are jobs that you can get with any degree

I always thought that was stupid. Because if I "need any degree" to get it, then what's the point of getting the degree?

[quick hornet]

its typically easier to get a job if your degree is literally the title of the job

you have a much higher burden of convincing the employer "no, no, i actually am qualified despite my degree only being tangentially related)

and if an employer has 50 applicants

theyre not gonna listen to you explain all the intricacies

theyll pick another applicant

[flint forge]

Also performing well in a difficult major is a good signal to your strengths and level of general education and problem solving

so even if your major is unrelated theres a reason college grads are prefered

(even if that reason is a little sketchy)

[quick hornet]

though honestly

speaking from a position of pie in the sky idealism

[obsidian valley]

I'm saying the school makes money off of engineering majors

[quick hornet]

i hate that degrees are valued by how they perform on the job market

i dont necessarily disagree with this system of valuation

its certainly utilitarian

but it still sucks

and it extra sucks that more fancy/frilly/less employable degrees are, as a result, often pursued by the privileged

since they dont need to get a degree that enters the workforce in 4 years guaranteed on the dot

but this is a complete side tangent away from #book-recommendations at this point

so ill stop my rant

[static crest]

no keep it going

I like the rant

[obsidian valley]

no poros, we must obey the rules

🙂

[static crest]

no

🙂

actually jk, I love following the rules

I am a very honorable server member

[agile moth]

I don't know if this is the right place to go for this, but I'm looking for some resources to help me learn calculus. I've been working on it over the past few summers as a challenge to myself, but I want to try something new this time. I actually take the AP Calc class next year in school, so any knowledge I have coming into the class would be a big help. For reference, I got 20% through the Khan Academy "AP®︎/College Calculus AB" course last summer, but found it wasn't moving at a good pace. After that, I used Barron's "Calculus the Easy Way" textbook. This summer, I'm hoping to find something better. I tried to get this answered in the #calculus section, but didn't have any luck. If anyone has a book recommendation, I'd love to hear it.

Thank you!

[lofty sluice]

@agile moth no need to thank me
Have u heard of james stewarts calculus?From what I have heard it is basically the bible of beginners calculus.

[agile moth]

I have not. I'll certainly look into it though. I'm looking partly to keep myself mathematically active, and partly to prep for AP Calc next year. It's supposed to be a killer course, so anything I already know going in is going to help.

[lofty sluice]

@agile moth oh i see... in that case you can do a book search on google and you can download it from pdfdrive and zlibrary, they have a plethora of books

[agile moth]

I had never heard of pdfdrive before tonight. It seems to be quite the resource. I'm very intrigued by the possibilities it brings.

[loud trail]

i found paul's online math notes to be quite helpful when i was learning calculus

[quick hornet]

just fyi, our server doesnt allow links to piracy resources like pdfdrive

this isnt our decision, it's Discord's.

[tame coyote]

To kill a mockingbird audiobook

[broken meadow]

i remember that quote

forgot where it was from

[tame coyote]

What’s up metal

[agile moth]

I was a little curious when I tried the link if it was a piracy site. I couldn't find out either way.

[quick hornet]

technically its just a pdf repository, but if you can only find a pdf there and nowhere else, its probably pirated

since they dont take down pdfs for that

[agile moth]

Okay. Thank you for the information.

[agile moth]

Thank you Jennifer. That looks like an excellent resource.

[lofty sluice]

@quick hornet oh ok...i will remember that..srry for the inconviniance

[quick hornet]

no worries

[gray gazelle]

What is the best book for discrete mathematics?

[quick hornet]

what sort of discrete math course? is it targeted at CS students?

[gray gazelle]

Just discrete math in general

[quick hornet]

(in general, the material of discrete math will vary heavily from course to course because its kind of a hodgepodge of topics from more specific fields, so its hard to give great recommendations)

[gray gazelle]

An elementary discrete math book

that is well written

[quick hornet]

again recommendations are hard

[hasty turret]

Rosen?

[willow pecan]

Rosen I guess

[quick hornet]

i know a lot of people recommend rosen

and a lot of people hate rosen

so

[hasty turret]

But,then discrete math is just a bunch of random topics

[quick hornet]

Scheinerman comes up a lot

but if you wanna learn discrete math like a mathematician would, learn proofs and intro groups/rings, then pick up diestel graph theory and ireland-rosen number theory

[broken meadow]

i hate rosen

[hasty turret]

Too verbose?

[quick hornet]

usually i hear people complain about rosens exercises being bad

purely algorithmic, not insightful, etc

Scheinerman isnt as famous but ive only heard good thingss

[sage python]

Sample size = 1

[quick hornet]

and it has a chapter on intro groups and rings

[gray gazelle]

I've heard Scheinerman is good too

[quick hornet]

which IMO any proper discrete math text should cover

[gray gazelle]

For an intro discrete math book

[hasty turret]

Alternatively you could do algebra and learn NT while doing it

[quick hornet]

as i said:

if you wanna learn discrete math like a mathematician would, learn proofs and intro groups/rings, then pick up diestel graph theory and ireland-rosen number theory

[gray gazelle]

What's the difference in the one targeted at CS students?

[quick hornet]

most math students dont take a "discrete math" course unless thats their intro to proofs

[quick hornet]

more focus on building up necessary material to learn algorithms and stuff

CS treatment of discrete math often uses RSA to motivate its number theory stuff, for example

or data structures for its graphs

it generally only considers digraphs for example

[broken meadow]

i didnt like the manner in which many of the subjects were explained they never seemed to do them too deeply which i guess is like to be expected?

[quick hornet]

whereas the mathematical approach typically considers mainly undirected graphs

or covers both

[broken meadow]

but idk it never felt like i was totally learning things

[gray gazelle]

How long do you think this would ake?

[quick hornet]

2 semesters if you speedrun it lmao, but more realistically a couple years

(obviously depending how much time you dedicate)

[gray gazelle]

By speedrun you mean spend all day on it?

[quick hornet]

(im assuming youre treating these like a proper course)

no thats unhelpful after a point

i mean like

you can skip the proofs stuff and try and learn proofs as you learn algebra

[hasty turret]

Do you have any prior exposure to math(like Olympiads,etc.)?

[quick hornet]

for some students it clicks

and this works

for others it doesnt

and you can skip a lot of the prereq algebra, you really just need the basics

[gray gazelle]

Nothing other than school

[quick hornet]

so you can spend like

2-3 weeks on groups and 2-3 on rings

and thatll be more than enough for ireland-rosen

and then read ireland-rosen and diestel simultaneously

ireland-rosen is meant for a 2-semester course and i think youd stress yourself out trying to cram it into 1

but it might be possible

diestel is typically done in 1 semester

[gray gazelle]

Those require knowing how to write proofs?

I don't know how to write proofs yet

[quick hornet]

yes.

again, as i mentioned

some students are able to pick up proofs as they learn abstract algebra

others need more time dedicated to proofs specifically

[gray gazelle]

What's the book for abstract algebra?

[hearty steppe]

Shouldn’t you do analysis before abstract algebra tho at least a little bit of analysis

[quick hornet]

see #book-recommendations message

analysis is both completely unnecessary and mostly unrelated

and also IMO a harder environment to learn proofs in

[gray gazelle]

I thought discrete math didn't require any prerequisites

[quick hornet]

it doesnt

again, im giving you the way a mathematics student typically picks up on the materail

NOT the way a usual "discrete math" course works

[gray gazelle]

I see

[quick hornet]

the point of discrete math courses are to give more surface-level treatments approachable for students without the mathsy prereqs

usually CS students

or, sometimes, to teach math students how to do proofs in a setting with simple, well-behaved objects

[gray gazelle]

I think I'll go learn calculus first, then abstract algebra, and then the graph theory and number theory

[quick hornet]

(as opposed to limits and/or groups)

[gray gazelle]

Where do you learn groups and rings?

Or is that part of abstract algebra?

[hasty turret]

I didn't do analysis until like after one year of doing LA and AA

[quick hornet]

but if you ask them whether they know the material covered in discrete math, probably all 30 would say "yes"

wtf

my first message didnt send

one second

[hearty steppe]

Why is that?

[hasty turret]

I didn't care

[quick hornet]

i meant to say:

if you ask 30 mathematics graduate students whether theyve taken a discrete math course, probably at least 25 would say "no"
but if you ask them whether they know the material covered in discrete math, probably all 30 would say "yes"

[hasty turret]

I did LA only because I wanted to solve differential equations,which is only because I wanted to solve reccurences

AA was a natural continuation

[quick hornet]

yes

[gray gazelle]

Do you have a list of the topics that are in discrete math?

[hasty turret]

.

[dense pewter]

sshhhh! we're not supposed to be talking about discrete math out loud!!!

oh wait nvm, that's discreet math

[hasty turret]

Sir,This is creet math

[quick hornet]

• proofs, induction, pigeonhole principle
• basic set notation, maybe cardinality of countable/uncountable sets but usually not (since uncountable quickly becomes nondiscrete)
• maybe some sequences and series, but no limits or anything
• basic graph theory
• a bit of elementary number theory (divisibility, modular arithmetic, chinese remainder theorem, etc)
• a dash of combinatorics (combinations, permutations, inclusion-exclusion)
• mayyyybe the definition of a group, ring, or field (if your course is SUPER fancy, finite fields are covered in the number theory part)
• relations (equivalence and order relations, properties like symmetric/transitive/etc)

thats basically everything except for the CS-focused stuff

[gray gazelle]

Okay thank you

[quick hornet]

like an intro to algos, O(f(n)) proofs, RSA, boolean algebras, finite state machines

basic data structures

which are covered as CS "applications" of the prior material

[gray gazelle]

Alright, thank you

Have a nice night

[quick hornet]

look at like

the Rosen table of contents

if you want

you can preview it on amazon https://www.amazon.ca/Discrete-Mathematics-Applications-Kenneth-Rosen-dp-125967651X/dp/125967651X/ref=dp_ob_image_bk

(dont actually buy the book on amazon its overpriced)

dont buy the book in general if you can help it

[gray gazelle]

Okay thank you Namington

Hopefully I'll actually be able to get through with this

[gray gazelle]

Any books with harder problems about arithmetic/geo sequences for highschoolers?

[hasty turret]

Generatingfunctionology

For sequences in general

[gray gazelle]

Hmm too advanced, need something more highschoolish

[sudden kindle]

This good book

[hasty turret]

Just get good

gfology is not difficult to read

[gray gazelle]

I'm tutoring a kid and I know his level

[karmic thorn]

Perhaps something by AoPS?

[gray gazelle]

Yeah I was trying to find something but it seems AoPS doesn't really cover that much of them, or at least couldnt find a fitting book

[gray gazelle]

rudin talks about geo sequences

[gray gazelle]

Thanks I'll tell him to read rudin

[quick hornet]

rudin is not high schoolish lmao

generatingfunctionology is an easier text

[gray gazelle]

If carla recommends rudin, then rudin is the correct choice.

[quick hornet]

[gray gazelle]

Carla any book recommendations for Basic Number Theory?

[prisma snow]

||carla, reccomend a course in arithmetic||

[quick hornet]

luna i think you missed the joke

[prisma snow]

No

I refuse to accept it

[gray gazelle]

as someone said before, rudin is written for babies

Maybe Rudin's Real and Complex analysis is for high schoolers then

[granite vine]

a math book for a highschooler which is advanced yet doable?

which covers most concepts

[whole rain]

"most concepts" gonna be hard lol

[granite vine]

uf

[whole rain]

do you have anything specific that you like ?

[granite vine]

i wanna learn calculus but i have a very vague idea..

[whole rain]

Sry I don't know much beginner calc textbook, I'll let someone else answer

[karmic thorn]

Tfw Shika read straight out of Bourbaki

Anyway Spivak's Calculus is one of the standard recs on the topic

[whole rain]

I thought of Spivak

but like Spivak may be a bit hard for a complete beginner no ?

[karmic thorn]

Maybe, but it's worth checking out in any case.

As an aside, has anyone used Axler's Measure, Integration and Real Analysis before? Is the text suitable for a course on measure theory?

[stray veldt]

judging from the first page its a great book

[karmic thorn]

[stray veldt]

i haven't read it but Axler has good writing style

[karmic thorn]

Does the measure theory bit seem comprehensive enough?

I'd basically like something covering this much

Possibly in a similar order as well, going back and forth is a bit of a pain.

[stray veldt]

looks good

no Carathéodory though

at least i didnt find it in the index

[karmic thorn]

Ah, okay

[stray veldt]

which you do in week 3

i actually have no idea how to do measure theory without it

[karmic thorn]

I see. Where exactly does one see stuff like L^p spaces?

Would a class on functional analysis cover that stuff?

[stray veldt]

you need it for functional analysis yes

[karmic thorn]

[stray veldt]

it's first (and most important?) examples of banach spaces

[karmic thorn]

I see

[stray veldt]

doesn't tao have a book in measure theory as well 🤔

(i used https://www.springer.com/de/book/9788876423857)

(even have a physical copy)

[prisma snow]

DONT TELL MANAN THAT

he needs a tao detox

[karmic thorn]

Yeah, that's what I've been considering too but the physical copy is a tad expensive

Smh Luna you think I didn't know about it already

[stray veldt]

use the book i suggested to realize that europeans do math too

[karmic thorn]

[stray veldt]

luigi ambrosio is one of the biggest researchers in measure theory

[karmic thorn]

[prisma snow]

Oh

That's the book I was going to suggest

[karmic thorn]

Yeah you'd suggest anything but Tao

[prisma snow]

Lol, but that one specifically because I started reading too

[stray veldt]

its obviously the correct choice

since i used it

[prisma snow]

Indeed

[frank root]

My measure theory course used Axler and I liked it

[karmic thorn]

Thanks!

Will get a copy of Axler since it is open access anyway. I'll take a look at Heil as well.

[karmic thorn]

Thanks a bunch!

[willow pecan]

[sour briar]

damn... so I'm a pure math major, and reading Stewart somehow still makes my calculus journey feel empty imho. I guess I'd probably be happier reading another textbook hmm

[broken meadow]

spivak

[sour briar]

spivak does look very promising, and I'm willing to read it to complete my single-variable experience.

Any book I can use to read in lieu of Stewart for multivariable calc though?

something that treats multivar more rigorously

[willow pecan]

Spivak Calculus on Manifolds is a common recommendation for multi

[sour briar]

interesting

[halcyon hornet]

Hello people.
I have a question.

So which books from Openstax or some other site should I use for Algebra 1, Algebra 2, Trigonometry and PreCalculus?

I think it should be the "Algebra and Trigonometry" book from OpenStax, or what else?

[gray gazelle]

You can try Apostol or Courant

Apostol has a kind of honest to goodness pure math flavor.

[sour briar]

alright. Thank you all for the recommendations so far.

[gray gazelle]

The book by Susanna Epp is what I am doing. And in terms of pedalogy it's actually pretty good.
PS. I like it more than Rosen.

[frail jungle]

Hey guys
did anyone read hitchhiker's guide to galaxy
if so, How is it?

[stray veldt]

its great

[frail jungle]

without any spoilers can u tell what it talks abt

[stray veldt]

earth is about to be destroyed so some guy hitches a ride into space

[frail jungle]

thanks 🙂

[gray gazelle]

Yo do you guys have any books that explains all types of math?

French or English

[stray veldt]

this will be a very long book

[karmic thorn]

Napkin/Princeton Companion, maybe?

[stray veldt]

i was going to suggest napkin for an overview of lots of modern math

[karmic thorn]

Stillwell's Mathematics and Its History might be good for a fairly comprehensive historical account of development of math.

[flint forge]

Hatcher's Algebraic Topology covers all of the most interesting fields of math

[stray veldt]

there is this german book called "4000 years of mathematics"

well, its 2 books

that seriously covers the history of all of mathematics

[karmic thorn]

[flint forge]

including this moment right now

its in the book

[stray veldt]

indeed

he wrote another book titled 4000 years of algebra

which is another 600 pages just on the history of algebra

the author should learn english

[karmic thorn]

[stray veldt]

the 4000 years of mathematics series is so in depth i had to pause it in undergrad

because my schooling was too bad

and it's quite technical

[karmic thorn]

What is the exact title of the book?

Or name of the author

[stray veldt]

its actually called 6000 years of mathematics

author is Hans Wussing

i think he wrote some english stuff as well

pretty well known math historian

https://www.springer.com/de/book/9783642313486 and https://www.springer.com/de/book/9783642319983

first book is up to euler, second from euler until now

wait the author died in 2011

big sad

[karmic thorn]

I see, thanks for sharing!

[marble solar]

it's very good

just ignore the exercises that say "don't use a coordinate system for this"

[karmic thorn]

[marble solar]

I used this text as part of a class

Math 106 at UCLA

The class had 2 grading systems 10% hw, 20% exam 1, 20% exam 2, 60% final

OR

100% Final

I took the first test, got a 39/40

After that I was like "Ok I can do 100% final"

Ended up w/ a 94% on the Final, prof told me "You played a dangerous game for no reason"

I said "Honors Algebra and Grad Complex are taking up all of my time - I just can't think about anything else rn"

He still let me into grad Riemannian Geometry

what a bro

[hasty turret]

If it's dangerous,why even have it?

[still jay]

For people who want to be dangerous

[marble solar]

Always runnin' for the thrill of it, thrill of it...

[hasty turret]

https://tenor.com/view/dark-wing-duck-letsgetdangerous-daffyduck-gif-8875670

[crude gulch]

Some one have a good book in english or french of advcend maths

The next years i will be in my first years in university

Or a book of probality

[willow pecan]

@slim peak will know

[slim peak]

What kind of field

what ever the field I recommend Xavier Goudon's books

Les Maths en Tête, Analyse
Les Maths en Tête, Algèbre

Also Mathématiques MPSI-PCSI Pearson, Mathématiques MP-MP* Pearson

(what ever the edition they are all good, just the old ones contains more technicals results in Analysis and no probability, the last one does iirc)

(i have the books but i'm not at home)

[crude gulch]

You have all ?

[slim peak]

yes

but not all editions of all books, just one edition of each book

[crude gulch]

It's normal you are in prepa

?

[slim peak]

I was

Now I'm a PhD Student

But I kept them since they are really good books

useful for general non trivial basic results

Especially Xavier Gourdon's

[crude gulch]

In the first , i was think you talk aboutir the mother Xavier who has the collection "méthode X"

[slim peak]

they contain results even higher than the one you could learn in Prepa/Undergraduated Classes

the Analysis one contains an appendice on Hilbert Spaces and Baire Theorem

(but not only)

[crude gulch]

I will note that ... and you haven't a book of probality... i am not good enought in probality but i am so interresed by it

[slim peak]

All I know is High End books

since I really looked into propbability after having a measure class

[clever fox]

ohh les maths en tete are good!!

[crude gulch]

Yes the next year i will be in mpsi a Neuilly a pasteur if you know paris

[clever fox]

Oooh good luck!!!

[slim peak]

Good luck

Buy the four I recommended to you, but be aware of the fact that the class content have changed for a year now

(it is closer to the very old program (2009) with an additional chapter of probability)

[crude gulch]

The four: mathématique mpsi -pcsi pearson

[slim peak]

not the fourth

all the books

four of them

buy them

buy them all

If you have only one choice

[crude gulch]

The programme have change un 2012 of prépa et the programme of terminale have change this years

[slim peak]

then Xavier Gourdon

[crude gulch]

Yes i will buy all of them

[slim peak]

right the B.O. was published this year for the next one, my bad

I did my prepa in 2014-2016, I didn't use enough books at this time I regret

Use them until each page of them falls on the floor

[crude gulch]

What is your only choise

I think i will buy Many books of prepa

[slim peak]

For the first year, Gourdon's book seems quite hard to me

[crude gulch]

I think also

[slim peak]

You won't have the the time the use more than 3 books including other subjects like Physics, Chemistry or Computer science

[crude gulch]

You think the max book that i would buy is 3 for all first years or for maths only

[valid orchid]

Please book recommend me

I'll have a nice shelf hopefully soon

If I don't fuck up my studies

I always wanted to have a copy of euclids elements

[pale scarab]

Could you switch at anytime? I have only ever had Finals prevent a A rather the get me a A. That's a interesting grading idea I might adopt even at high school level for the smart kids who just can't be bothered to do work.

[marble solar]

You get whatever gives you the best grade

[alpine wedge]

Guys

What book you should read before you die ?

[gray gazelle]

Bible

[hasty turret]

Which one

[willow pecan]

Omniscient Reader's Viewpoint by Sing-Shong

[sharp latch]

The Brothers Karamazov by Fyodor Dostoevsky

[karmic thorn]

Analysis 1 by Terence Tao

[narrow echo]

the hungry caterpillar Metamagical Themas

[tulip blade]

1984

[hearty steppe]

You like Hofstadter as well?

[flint forge]

ORV isn't even my favorite webtoon currently updating

[willow pecan]

Ok but it's a novel

[zinc walrus]

Any book recommendations for iit??

[willow pecan]

IIT?

Indian institute of technology?

[zinc walrus]

Yup

[willow pecan]

Shame that there isn't an Indian ping

@karmic thorn

[zinc walrus]

Means

[worldly basalt]

Try Objective RD Sharma

It's a bit dated nowadays but good for learning concepts

[zinc walrus]

That's for boards

Rd Sharma is only good for boards

[worldly basalt]

There is a different one for boards

I'm talking about objective RD Sharma

[zinc walrus]

Sorry

Yup I'll see and try

[worldly basalt]

You could always go for cengage and arihant

[zinc walrus]

Ya I have those books at my home

[worldly basalt]

Then why do you need more???

[zinc walrus]

For more marks??

[worldly basalt]

Cengage and arihant are more than enough

I suppose you also have books from your coaching as well???

[zinc walrus]

Ya allen

[worldly basalt]

And you still need more???

[zinc walrus]

Nah

[worldly basalt]

[zinc walrus]

[hasty turret]

tfw the indian representative doesn't do JEE

[broken meadow]

L

[hasty turret]

You don't need to know any concepts at all for JEE. Just grind papers. You will learn all you need to know

JEE is literally a hack exam

[willow pecan]

Oh Manan didn't do JEE?

[hasty turret]

Ye,He made the correct life decisions

[willow pecan]

[karmic thorn]

[molten wave]

bet his parents are disappointed

which must be effecting poorly on his mental health

[hasty turret]

Bold of you to assume his parents are not based

[karmic thorn]

Yeah, fortunately pulling "I'll do research in math" card worked out just fine.

[valid orchid]

How to not die by Chris P. Bacon

I kinda wanna live forever but that's just me

I never finished the first 10 pages of any book, but I have a feeling I'll kinda have to grow a new pair of reading testicles if I want to actually finish my masters and do a thesis

[halcyon hornet]

No replies?
Okay.

[alpine wedge]

lmao new testicles might be a fun thing

[wicked nymph]

for what subject do u want?

[wicked nymph]

objective rd sharma is one of the best books for maths in jee

[gray gazelle]

[deft hare]

Hey can someone recommend me good books for algebra for olympiad preparation?

[frosty girder]

well a very basic one i would recommend is "Thrills and challenges of Pre college mathematics"

this is a very nice book

so u can try and use it

[frosty girder]

ok i liked that book

[hasty turret]

I haven't really used it. You can ask xi if you want to hear more

[frosty girder]

Dont think i would want that

[narrow talon]

Anyone know a good modern book on harmonic analysis, barring Grafakos?

[marble solar]

https://www.amazon.com/Fourier-Analysis-Graduate-Studies-Mathematics/dp/0821821725

People recommend this one a lot @narrow talon

[marble solar]

https://www.math.ucla.edu/~josephbreen/Lectures_in_Harmonic_Analysis.pdf

Here's a free version of some lectures from Visan's class

[narrow talon]

This seems really nice, but very brief

[marble solar]

and finally

https://terrytao.wordpress.com/category/teaching/247b-classical-fourier-analysis/

[narrow talon]

The first one seems quite nice though!

[marble solar]

https://secure.math.ubc.ca/~ilaba/wolff/notes_march2002.pdf

This is pretty brief however

There are more texts by Stein which are much older

[narrow talon]

I could easily be convinced to read Stein's trilogy. They're pretty much exactly what I'd want topics wise but admittedly I find them quite challenging without background in Harmonic

But all of these look great as that needed background to read Stein. Thanks!

[marble solar]

I've read through Terry's notes, they're pretty good

but I found it not to be as useful to what I was doing at the time so I didn't pay as much attention as I should have

[hearty steppe]

I remember reading Terry's essay https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/

I liked it but I agree, its not really helping you immediately learn more math in a more intuitive way but at least the essay helps you not feel completely lost in the experience of trying to learn.

[sage python]

Cat man that's not what they were discussing

Moonbears was saying that Terry has notes on Fourier/harmonic analysis

But he didn't pay as much attention because it wasn't covering the stuff in harmonic analysis that's useful to his math

[hearty steppe]

I just figured I'd bring up that particular essay I liked by Terry cuz I just remembered it and I recommend it as well.

[sage python]

Moonbears is probably at the level where "more than rigor and proofs" essay already very firmly applies

[hearty steppe]

I feel like its one of those things that are easier said than done.

[flint forge]

lmao rigor and proofs are for children. real mathematicians read vibes

[marble solar]

I'm so fucking lost, I was just thrown in the deep end and now I do discrete harmonic analysis, martingale, probability stuff

I haven't taken a class on any of it

[sage python]

I mean hey do you get weekends off from work? Maybe this is the time to learn it while your main math endeavors are slightly on pause

[marble solar]

Most weekends, but now I'm spending time on the subject GRE

[hearty steppe]

I thought you took the subject GRE?

[marble solar]

It got cancelled twice in a row

in my area

But I basically got to get a lot of PDE experience, Harmonic Analysis, and Probability w/ Martingales

I spent the past few months doing PDE stuff as it was more related to the work that I could do

[quick hornet]

rigour: boring
proofs: irrelevant
pencil sketches made on figures from munkres: the future of mathematics

[next anchor]

thoughts on How to Prove It

Daniel Velleman

[obsidian valley]

people like it

[hearty steppe]

try not to spend too much time on it. Stop after chapter 4. Don't worry about being stuck with some of the exercises toward the end of each section.

[next anchor]

i was going to do up to chapter 6: induction

[hearty steppe]

not necessary

[next anchor]

as preparation for real analysis

[hearty steppe]

youll cover chapters 5-7 in Analysis

in better depth and first impressions

[next anchor]

would the functions chapter not help a bit?

[hearty steppe]

no it won't

that stuff is introduced in beginning chapters in an analysis text

[obsidian valley]

real analysis??

[hearty steppe]

yea

[obsidian valley]

does this mean different things to different people

this is a third year course to me

[hearty steppe]

spending too much time on Velleman is not going to save you for Analysis. It won't make starting analysis easier

[obsidian valley]

you shouldn't need HTPI once you're doing RA

[next anchor]

i haven't really had much exposure to math proofs

[obsidian valley]

are you an econ student or something?

[hearty steppe]

yea well trust me you'll feel like stopping Velleman after chapter 4. It is really set theoretic heavy after that chapter anyway and you aren't missing much

[next anchor]

nah from europe. we do real analysis in first year

[obsidian valley]

ohh okay

that is "analysis" here

that makes sense

[next anchor]

ah ok

[hearty steppe]

its better to be exposed to functions in an analysis text

and induction is pretty straight forward after you learn the basics of proofs

[next anchor]

yeah i guess. chapter 3, which im doing right now seems to be the most important

[hearty steppe]

you won't be using induction too much. And when you do, its really trivial process

chapter 3 and 4 are good for Velleman

[next anchor]

i'll move on to understanding analysis by abott afterwards

[hearty steppe]

but don't be too worried about the last few exercises after section 3.3

well by that time, just go thru a standard analysis text and find other analysis texts as supplements to break the standardization down

[next anchor]

ok will do

[hearty steppe]

most people go with baby Rudin or Apostol

[next anchor]

thanks

[hearty steppe]

as the standard

[next anchor]

yeah have rudin as well

[hearty steppe]

Getting back to actually learning analysis (as an example to my discourse I am about to provide)... It would be nice if we had some channel or means in this server to help people strategize understanding the mathematics they're trying to learn. Like what way should people take notes to retain important information? What ways do people interact with the resources they're using? Etc

I know we have a pedagogy channel, but I don't know if there is anything pinned in it that would be useful for people trying to learn rather than trying to teach. Maybe a separate channel altogether would be best for this.

Cuz it would be amazing to pin a bunch of learning strategies somewhere

[sage python]

I feel like beyond a certain point there isn't a lot

Like there isn't much advice that applies uniformly (or even close to uniformly, I'd wager) beyond that which is common sense

Read, make sure you understand what's up, and solve problems

[flat lantern]

Step 1) watch lecture
Step 2) try questions
Step 3) baby rage at the question
Step 4) of step 3 no longer occurs you have learnt the content

[sage python]

But how you write notes/whether to write notes at all? Strikes me as a personal decision

[hearty steppe]

Personally I don't find it that intuitive from the get go. There is the "decoding" step that I think is essential.

[flat lantern]

I don’t take notes at all i learn from mark schemes more than anything

[sage python]

Well you don't find what intuitive? When I said this what I meant was like

There's some very small set of things which are obvious

Basically don't be passive

Beyond that there's not much I can say that's general

I don't write notes much, but if I'm reading out of a book I do scratch work

[hearty steppe]

It's an interesting dynamic though. Maybe if some people are interested they can share their strategy to learn math effectively. I'm trying a whole new strategy on note taking at the moment, but I feel that it is also easy to stagnate, so how do we help people avoid stagnating and feeling lost?

[hasty turret]

Why take notes when all the material is in the book

And if you are gonna make notes, better Tex them

[sage python]

Yeah see that's the thing lol, there's basically a finite set of sensible strategies and I'd wager their effectiveness is not very far from being equidistributed

[hasty turret]

You will be losing physical notes

[worldly basalt]

I like to take notes especially if I'm following a lecture even though the material is provided.

[sage python]

For some people the process of writing while they're lecturing helps remember

For me it's distracting

[hearty steppe]

So @hasty turret is there a way you interact with the material other than doing the exercises?

[sage python]

Some people handwrite notes but don't tex

[hasty turret]

I think of why the person motivated a particular definition/theorem/lemma in that particular order

As in why is it natural

[hearty steppe]

yea im trying to do that as well, but do you make diagrams or something?

[hasty turret]

No

Physically drawing diagrams is kind of distracting

[hearty steppe]

like you know like trying to bridge ideas sort of thing? That's what im talking about

[hasty turret]

For all things that require a diagram, I just visualise in my head

[flat lantern]

I bridge ideas together by doing problems

Also trying to prove results from the notes before reading the proof of them is useful

But that’s basically just “make up more questions to do”

[gray gazelle]

Any LoTR-esque books that you recommend? (LoTR was pretty short tbh)

[hearty steppe]

So ironically, this is where I've been trying to better strategize and figure out how to do so appropriately. Thanks for pointing that out

its not always obvious when you need to spend time to work out the reasoning of a proof. Sometimes maybe I deceive myself into thinking I get it when I don't really get it enough.

[rose dragon]

Anybody got any recommendations for an introduction to topology. 4th year maths student year. I haven't taken real analysis yet, but I've had some decent experience with proofs and a tid bit of analysis with that.

[hasty turret]

Munkres

[quick hornet]

popsci for nerds*

[flat lantern]

I use the metric "if I can come back in a week and prove it without looking at the notes I understand the proof"

it works pretty well in my experience but obvs "a week" is very arbitrary

[hearty steppe]

ahhh ok

so i guess im doing ok

im starting to really enjoy the adventure of analysis thru Rudin. I see why this book has the praise it has. It is an interesting book filled with interactive riddles.

[sage kelp]

The title is very explicit. Overall it’s a smooth book to go through

[gray gazelle]

Bad take

[stray veldt]

read #book-recommendations message instead

[quick hornet]

sorry loch, your sections are 0-indexed but your subsections are 1-indexed

so your text is bad

[stray veldt]

its because 0 can be skipped

[quick hornet]

excuses

[stray veldt]

it must be deliberate

since default tex doesnt do this

i had to google how to 0 index my toc

[willow pecan]

[gray gazelle]

Knuth confirmed to be actually not that computer scientific

[stray veldt]

i looked into this a bit more and noticed that if i don't start a subsection after a section immediately, the theorems etc are still 0 indexed

[willow pecan]

[stray veldt]

this is somewhat weird numbering

i might have to fix

[timber mesa]

a hackish fix would be to use \setcounter

[stray veldt]

i might just remove the 0 indexing

nami is right, its so greatly written that you should read everything

[hearty steppe]

Bad take?

[solar patrol]

One of the books I would recommend would be One Hundred Years of Solitude. But if you're into really complex and realistic science, the Three Body Trilogy is an outstanding read.

[bitter plaza]

does anyone have any recs for romance/thrillers?

[willow pecan]

For romance I am currently reading The E-Sports Circle's Toxic Assembly Camp

[obsidian valley]

youre only going to get weeb shit here

[willow pecan]

For a thriller, I would recommend Omniscient Reader's Viewpoint

[bitter plaza]

where do u read this😭 it sounds good

[willow pecan]

https://www.lightnovelworld.com/novel/omniscient-readers-viewpoint-lightnovel-10051457

This is where I read it

There are some other sources floating around the internet

The ORV subreddit has an epub file

[bitter plaza]

thank you so so much

[willow pecan]

[bitter plaza]

wait and this one?

[willow pecan]

https://chrysanthemumgarden.com/novel-tl/camp/

[karmic thorn]

[willow pecan]

What

What if I pin the orv link

Will a mod unpin it

[broken meadow]

yes

[willow pecan]

Why

[broken meadow]

j

you could probably pin it and no one would notice

[willow pecan]

j?

[broken meadow]

im kidding around

plenty of the pins here are not on topic anyways so w/e

[quick hornet]

are you implying that math makes sense 5: a cohomological approach is not a good prealgebra textbook recommendation

[golden bear]

This is true, but sometimes students tend to take a little longer to understanding the concept and approach of induction. So it does make sense that @next anchor should go up to chapter 6 induction. Is better to see the material first then learn what you didn't understand the second time around

[gray gazelle]

Has anyone read G Polya's How to solve it?

[marble solar]

I think G Poyla has

[gray gazelle]

[gray gazelle]

After Abbott's book, which book do you recommend for Analysis?

Tao's or Rudin's?

(for self-learning).

[worldly basalt]

Tao is certainly better than Rudin for newcomers

[quick hornet]

both will tread over a lot of territory abbott already covered

that im not sure you need a second treatment of

in light of that, rudin insisting on doing things in more generality might actually make it preferable here

as rare as that is.

[river bear]

Can someone confirm this? I'm about to take a full course on Analysis and I'm a bit confused

[karmic thorn]

Probably go along with the recommended text for your course. I've been using Tao for studying by myself and have found it very comfortable, but it may be a "slow" text to go along with a course.

Other than that I really like Tao's pedagogy.

[river bear]

The prescribed one is Bartle and Sherbert, with some sections from Rudin

[quick hornet]

rudin is famous for being... demanding

in terms of mathematical maturity

or to be more vulgar, "fucking hard" relative to its peers

i used to agree with the rudin approach of doing everything in arbitrary metric spaces at first but

now i think that makes it needlessly difficult

all the obvious theorems extend to metric spaces anyway, studying R^n is really enough for students still getting their feet wet

i digress

rudins proofs are very terse; he often goes for succinct/clever/cute arguments over ones that demonstrate a widely applicable technique or really strike at the heart of whats going on

his expositing is not particularly good either

but its a very very good collection of results in elementary analysis

(hence it being by far the most commonly cited textbook)

and its not like, unapproachable

hell, as harsh on it as i was, i still think its difficulty is often overstated to perpetuate a "big boy math so hard, im so smart for being able to do it" mentality

its perfectly readable... it just doesnt do anything to make reading it particularly easy or pleasent

as a supplementary text its perfectly fine IMO

so if your course is using select sections

probably okay

[river bear]

This is supposed to be covered in next sem, so based on that anything?

[steel viper]

the problem is more that a lot of the content feels incredibly fucking boring and not at all motivated imo

Like

its just not very fun to read a lot of the time

[karmic thorn]

Read Tao 😌

[primal island]

does anyone have any recommendations for a textbook (or any other resource) for learning linear algebra

im just using khan academy right now and watching the videos

but i noticed there are no questions i can do

[karmic thorn]

Friedberg/Insel/Spence's Linear Algebra is a frequent recommendation

Or you could look into Strang's Introduction to Linear Algebra

[primal island]

does this start with basics? or do i need some background knowledge first

like vectors and simple operations and stuff

like dot products

[tulip blade]

those are completely different books

use strang

[karmic thorn]

Some familiarity with proofs might be fine

[primal island]

ah okay ill look into it then

thanks!

[karmic thorn]

[livid ermine]

is hoffman & kunze better than friedberg, are they much different?

if one has gone thru the first 6 chapters of friedberg, is it worth it going thru and doing most of the exercises in h&k? a lot of people cirlcejerk it as the best linalg book

[tulip blade]

I think friedberg is sufficient

[hexed scroll]

So after googling, searching here on discord and coming up with only one result (How to Write a Master's Thesis - Yvonne N. Bui). I was wondering if anyone have any** book **recommendations on writing your master thesis? Not these 1-40 pages but proper, with styling, referencing, word, sentence and paragraph building, and all the nitty gritty stuff. I will take even if it only takes one of those. Even the best PDF you think encapsulates the writing experience.

[sage python]

I like Hoffman-Kunze quite a lot but I will say it's very old school

Friedberg probably cuts it fine

[marble solar]

H&K is solid

[hearty steppe]

H&K is definitely a step up. Not sure by how much but essentially it’s definitely more abstraction and depth for LA

[dire comet]

Any good books regarding category theory. I've seen a few ones, but I don't see any solutions to exercises. Sometimes it's apparently "online", but I don't know where to look that up

e.g. https://www.researchgate.net/publication/265489971_An_introduction_to_category_theory

[willow pecan]

Riehl seems to be the standard text

[velvet briar]

Answers to exercises are not common haha. I'm enjoying Lienster which is not a common rec

[pale scarab]

What are some books I should cover before trying to learn mirror symmetry?

[quick hornet]

what do you mean by "mirror symmetry"?

there are 2 very very different ways i can interpret that phrase

do you mean mirror symmetry of calabi-yau manifolds?

[pale scarab]

Yes

[quick hornet]

relevant mathoverflow question: https://mathoverflow.net/questions/40062/roadmap-for-mirror-symmetry

might be worth reading through the answers

you want some symplectic geometry at least going in

[pale scarab]

Thanks that link is what I was looking for

[sleek spear]

HAH IMAGINE READING BOOKS

[willow pecan]

[ripe granite]

mirror symmetry

[sudden kindle]

i only watch videos

i dont read books

[ripe granite]

Auroux's notes are good to start learning fukaya cats

[willow pecan]

Auroux was at Berkeley

Before Harvard stole him

And Lauren Williams

[ripe granite]

There were some notes on fukaya cats and hochschild homology online

[willow pecan]

Of course, Berkeley had just stolen him from MIT two years prior I think

[ripe granite]

I cant find them anymore

[willow pecan]

And Lauren Williams

[ripe granite]

but if you do find them, those are good too

[willow pecan]

Very cut throat

[ripe granite]

and then the Polishchuk-Zaslow paper should get you started on mirror symmetry for elliptic curves

you dont need to much simp geometry to start learning this stuff, but you probably do if you want to work in it

[gray gazelle]

fukaya? well fuk ya too buddy!

[sick plover]

I thoroughly enjoyed Hefferon's exposition

It's free (in both senses), but you can get a paid hard copy

He starts from the very basics

[primal island]

oh okay ill check that out as well then

thanks

[gray gazelle]

anyone know a website that has a listing of linear algebra problems with their solutions? i need to go over some problems and i havent thought about it in a decade

[slim peak]

MyCopy Springer link is awesome, you should try it every time, every day

[karmic thorn]

[slim peak]

Springer Mycopy link, each book for 25$/25€

[karmic thorn]

Yeah, unfortunately available in select countries, and that too only when your uni has subscriptions. 😔

[slim peak]

Not that comfortable to work

[karmic thorn]

^^^

Physical copies are definitely nicer

Paperbacks tend to be a bit annoying to work with sometimes

Like the books Anatole sent above are paperbacks, you can fold their covers only with little more force than you'd need for paper. Hardcovers have cardboard like covers.

[slim peak]

Hardcovers are really goods, but very expensive

[karmic thorn]

Yeah lol

[karmic thorn]

Strangely, a lot of Springer titles have harcovers and paperbacks for the same price, and sometimes the latter is even more expensive!

[slim peak]

HardCovers are Grimoire-like books

and Hardcovers talking about Category Theory/Algebraic Geometry are real Grimoire about Black Magic

[karmic thorn]

Also, hardcovers tend to have binding which is long lasting compared to paperbacks, which tend to go out of shape more quickly.

I'm not sure how much are book prices justified

Like I agree graduate math texts aren't some bestsellers

And hence they're going to incur storage costs for longer

But they still seem to be a tad too expensive

Like, Hindustan Book Agency here did a joint collab with Springer to publish "Texts and Readings in Mathematics" series(a part of which is Tao's Analysis 1/2), and I got the hardcover for both at ~$10 in all

Springer and Elsevier do make a lot of bucks Although I feel the greater share comes from uni subscriptions

Yeah, that's a sad state

But honestly

This is starting to see its demise

As more and more authors are moving to hosting free copies of their books

Some even try to get physical copies published cheaper(like Hatcher's AT has a very cheap paperback)

True, but I doubt if most authors wanted the money anyway haha

I just think they want their works to be read and appreciated

[pale scarab]

As a teacher I get luxury of unliminted printing so I just print a book and bind it at kinkos for 5$ and it works nice as a paperback. I can't stand staring at a screen all day to read. I am jealous of those nice hardbacks. I would prefer only hardbacks for the aesthetics

[karmic thorn]

Fair enough haha

I've been considering printing out some of the freely available books too

[broken meadow]

i like the hard back aesthetic

easier to transport too

less rippage and creasing

[stray veldt]

if your books arent partly ripped and coffee stained, have you really read them

[pale scarab]

You can sometimes find good deals for used hardbacks on amazon and ebay. Those are great deals for hardback though nice collection.

[karmic thorn]

Tea stained Tao 😌

[stray veldt]

[quick hornet]

could you not

[willow pecan]

[glossy grove]

[hearty steppe]

I won’t be able to unread that

But it doesn’t bother me either

[glossy grove]

[stray veldt]

now my sully is out of context

[quick hornet]

stop giving them what they want

god damn

[lofty sluice]

did my comment got removed? I was joking. Pls dont ban me

[glossy grove]

(just remove his second comment, too. for the memes)

[lofty sluice]

wut?

[karmic thorn]

Wow I just felt like my remark got bombed

[timber mesa]

I'm too OCD for that shit

[karmic thorn]

[lofty sluice]

i am too broke to have a book in the first place

[broken meadow]

having access to logs is a burden

not a privilege

[lofty sluice]

btw does anyone how can i get used books

[broken meadow]

amazon usually has an option

[lofty sluice]

I live in southern asia and shit costs very fucking high

[broken meadow]

o

[timber mesa]

https://www.bookfinder.com/ is a great page too

international shipping can be a bother sometimes though, as someone living in south america

maybe try looking into printing services, printing a .pdf yourself can be a ton cheaper and serve the same purpose

[lofty sluice]

Thats what I do honestly. Put on my pirate cap , download the pirated books from the dark depth of the ocean and bind it with spell after rolling a nat20.

[gray gazelle]

hungerford or lang?

[sage python]

Yes it is

[sage python]

Oh I had missed this, Hungerford's a lot shorter and I've heard easier

Corollary Lang does more stuff

[golden veldt]

What do people think about the gunning analysis text?

https://web.math.princeton.edu/~gunning/bk.pdf

[tulip blade]

Looks fine

Looks pretty good tbf

[sage python]

Idk this one

And it's not loading lmfao

When it loads I'll look at it

[quick hornet]

great start

huh, weird text

doesnt seem like its meant for a first course but it defines union and intersection?

ah reading the intro clarifies its target audience, nvm

it makes sense for that target audience and approximately no one else

IMO

jumped to random sections and checkedd out the exercises and they seem good too

but not that many of them

relative to the sheer amount of materail

so youll probably want to do ALL the exercises, and maybe more

but honestly it just seems wayyyy harder than most students can handle

on a skim i actually prefer its exposition to rudins though

but thats just based on a quick skim

of a few random pages

idk, seems like a great text for the 0.1% of students its actually appropriate for

[tulip blade]

It is for princeton students

[quick hornet]

yea

the most advanced princeton students even

and in that context it seems good

might be a good source for interesting exercises though, even if you cant handle all the material

they all seem pset-like and fairly insightful

all the ones i read, at least

[rough hawk]

Would Elementary Topology by Gemignani serve as a good introduction to Topology by Hocking and Young?
I know nothing about topology but looking at the Table of Contents it looks like Gemignani covers the first couple chapters of Hocking and Young with much greater depth\

[rough hawk]

Also, what prerequisites would I need before tackling topology?

[quick hornet]

cant answer your first question, but as for prerequisites:

on paper, all you need is comfort with proofs + mathematical maturity, and indeed some people have learned topology just with this. But it's typically recommended you also know some real analysis or else everything is gonna seem unmotivated and youll lack intuition for metric spaces and limits