book-recommendations

[molten gulch]

dw most ppl here can't

[restive nexus]

Counting isn't math

That includes combinatorics

Jk

[molten gulch]

[gray gazelle]

Can anyone offer any high school algebra and calculus textbooks? I'd appreciate the most rigorous possible - I'm searching for proofs and derivations of things, always!

[molten gulch]

spivak's calculus; abbott's analysis

for algebra? there's not much on the side of derivations

[fervent merlin]

Anyone got tips on learning math for competition

Any indo?

[remote sparrow]

i'm not aware of a complex analysis book written by spivak

#book-recommendations message

[gilded shuttle]

normal for who? when i was 14 i played fortnite all day

[spark jay]

Same lol now I'm 15 and now I study math all day

[restive nexus]

Relatable

[bleak pebble]

dear all I have some basis on category theory I would like to understand better what topos are and possibily some practical application as I SA

saw this presentation from caramello's https://aroundtoposes.com/relative-toposes-and-meta-learning/ where she claims that some trading systems have been developed using meta-model

[torpid stump]

Thanks

[trail hemlock]

"we have dami's book reviews at home"

[analog pollen]

me fr fr

[trail hemlock]

erm ... ur a nerd

[analog pollen]

What?? no really????

[trail hemlock]

@jovial parrot point and laugh

[jovial parrot]

lol

Math at 14 is normal.

Algebra 1, that is

[trail hemlock]

abstract algebra?

[analog pollen]

stole my joke

was about to say that lol

[trail hemlock]

jacobson thinking hes funny naming his book "Basic Algebra I" 😭

[jovial parrot]

LOL

[mossy flume]

https://link.springer.com/book/10.1007/978-1-4684-9884-4

[trail hemlock]

😭

[mossy flume]

Number theory sounds fancy enough compared to arithmetic and algebra

[normal crystal]

they should call it Basic Numbers
for similar effect

[trail hemlock]

"a simple introduction to numbers, and their properties"

i would much rather read "advanced BLANK" than "a simle, gentle, and somewhat reductive glance over BLANK"

[copper glacier]

Hey guys

@trail hemlock Dude, can you answer my questions, I'm from another country and I was thinking about taking an online math course, I ended up really liking math, especially after the recommendations, is it a good one, if so, which one would be good to do?

[trail hemlock]

sorry i have a lot of hw rn

but if u post ur questions in the approproate channels im sure someone will answer you

[copper glacier]

sorry thanks for help

[heady ember]

It is basic

[fresh skiff]

What about knapp's books?
Basic analysis
Basic algebra
And all are graduate level

[opaque light]

Any recommendations for some good calculus books?

For a 9th grader?

[sage hill]

Thomas calculus is pretty good

Does anyone knows a good book to start with functional equations?

[low gazelle]

Hi guys

I bought this book called, how to solve it by George polya

Has anyone read it before

Is the book worth reading while doing my a levels

I want to improve my skills

[dusty gazelle]

somebody know a book about mathematical logic?

[molten gulch]

enderton

[dusty gazelle]

thanks

that was fast haha

[stoic sage]

Intro? or something more advanced?

[dusty gazelle]

i understand a litlle

[stoic sage]

For some historical context, it's a lite read, John Stillwell, "The Story of Proof". Not just logic though.

[dusty gazelle]

thanks

this is interesting too

[wind osprey]

Rudin or foland grad analysis?

[molten gulch]

we lurk book recs 😈

[dusty gazelle]

Hhahah

[remote sparrow]

#book-recommendations message

[remote sparrow]

folland

[remote vortex]

I mean, both, they don't cover the same things.

Folland's Real Analysis assumes you're more or less up to the Riemann-Stjelties integral in Rudin's PMA

Unless you mean measure theory/functional analysis, in which case I recommend Folland over Papa/Grandpa Rudin, at least to begin with

[bold kite]

ill start computer engineering tomorrow , james stewart calculus 9th edition is a great book to start with ? i asked a similar quetsion before and you helped me btw thanks

[hallow oriole]

it will do

[gray gazelle]

How is intro to statistical learning for refreshing knowledge? I'll probably choose the python version since I'm more experienced with the R libs

[dreamy vault]

What's a good book for algebra 2

?

[flat ermine]

We got a Canadian in the chat

[bold kite]

what? im from spain

[molten gulch]

dude wtf is your username, that is...so not appropriate for this server

<@&268886789983436800>

thanks doot

[stuck zephyr]

oh canada 🗣️

[night prism]

I’m looking for a resource- preferably a book- that specializes in construction proofs, or at least has many exercises which require constructions. Does any such thing exist?

[normal crystal]

if you think Stewart Calculus is only used in Canada, I have news for ya

[remote sparrow]

what is a "construction" proof

like in plane geometry?

or are you looking for proofs that adhere to constructivist philosophy?

[solid lake]

I guess he means proofs where you have to construct some structure/assume it exists to do the proof?

[remote sparrow]

could be

[solid lake]

Don't we like do that all the time.

[remote sparrow]

but they want a compilation of those kinds of problems

also there are many results where a constructive proof exists, but the usual proof given is nonconstructive

[night prism]

No, a couple examples would be:

A proof of the iteration theorem using n-admissible functions

Constructing the reals from the rationals

Etc.,

Essentially, they are proofs in which you demonstrate the existence of a mathematical object by providing a method for creating it

[lone ferry]

any good mathematics book for a 9th grader

[raven jungle]

yeah 8th grade books too

[gray gazelle]

Pearson.

[gray gazelle]

Pearson x2.

[broken pecan]

any one can recommand a finite element methods book?

[molten gulch]

Like this?

If so, Atkinson and Han - Theoretical Numerical Analysis is the book with that ToC; it's theoretical tho so idk how many listed applications it'd have

[brave glacier]

Are skandalis books any good? Anyone have read his books?

[plush coyote]

Hey guys, i havent learned anything in math for 3 months now, im wondering what lessons/branches in math i need to learn to regain my knowledge for this senior high school

do ya'll have something?

[broken pecan]

hehe it's not going to be a book chapter, it's a subject itself deserves a book

[molten gulch]

Oh yeah fair we don't have any dedicated books on it

[wispy moss]

which edition to go for ? will differenteditions have any change ?

[molten gulch]

Nope, you should buy an older edition

The problems might be a bit different but these books are not worth $100+

[wispy moss]

so the content is the same , but problems are different is what you are saying

[molten gulch]

Yeah, if even that

[wispy moss]

tysm

[molten gulch]

Yw

[wispy moss]

I hope i am not troubling you but i just saw there is a precalculus book by the same author , should i read it before the actual calculus book ?

[molten gulch]

Do you know trigonometry and algebra?

[wispy moss]

yes, the basics

[molten gulch]

If your foundations are strong you shouldn't need too much of precalc but there are also much cheaper and easier options (such as watching khan academy or using paul's online math notes) for trig and precalc

[wispy moss]

got it ,then i will dive directly into calculus book

[naive lava]

so, i'm going to start physics graduate school next semester and throughout there i will need to learn some math, i was hoping to get some recommendations regarding this, so here are the topics:
complex analysis(i know the basics but would prefer to learn more)
group theory
differential geometry(lie theory too)
topology(emphasis on differential topology and algebraic topology) and lastly
Algebraic geometry
can you guys recommend me some books in these topics that'd teach me these topics at a "physicist" level, i wouldn't mind too much rigor, i've also checked out the link above but couldn't really decide on it

im also kinda making this post because i don't really know what covers what, like i know abstract algebra covers group theory but i don't know how anything's relationship looks like with topology

[modern crater]

Stein Shakarachi is good for compelx analyis Alfhors is a classic and I really like it but it might be a bit dated you can give it a try though

Algebra Chp 0 is great for group theory with a categorical viewpoint if you find that uncomfortable though Dummit and Foote is safe (learning basic cats is useful if you want to make progress with alg top though so its probably worth the sludge through aluffis book even if its a bit new)

Idk about diff geo or lie theory.

The standard reference for basic alg top is Hatcher (which I really like) but since youre doing it for physics and you need a diff geo flavour then Bott and Tu's "Differential Forms in Algebraic Topology" ive heard is very good

For alg geometry ravi vakils notes are probably the best i would avoid hartshorne like the plague unless you have 5 years of free time its awful

[crimson leaf]

1. Conway's first compelx analysis book is very easy to follow and read with good coverage, also a good starting point depending on your background i.e. if your analysis is weak (like me lol)
2. I'm partial to Hungerford's Algebra or Robert B. Ash's Basic Abstract Algebra
3. Diff Geo I'm not too wise to but for lie theory after diff geo I've heard wonderful things about Duistermaat and Kolk's Lie Groups and love Lie Algebras and representation by Humphrey's so far
4. I really like Bredon's Topology and Geometry it's so good and clean
5. I haven't read much beyond undergraduate stuff here Fulton's book was very good though if you want a little look at some basic stuff in that direction

[naive lava]

thank you, i also don't know regular topology, i suppose i need to read a book on that before, is that correct? and if so, i was thinking about reading munkres, would that suffice?

[crimson leaf]

Bredon starts with basic topology

It's quick but a good crash course

Also Hatcher has some good notes, Munkres is too slow and tedious imo

[modern crater]

Yes! You will not understand a word of any alg top/diff top book without that.

[modern crater]

Yup Simmons book is nice plus it has a analysis brained approach and gets through the (mostly) same material as munkres much faster

[gray gazelle]

Hmm, I also want to know that. How is Willard or Dugundji?

[modern crater]

No clue I only ever read Simmons an Munkres imo book choices really dont matterthat much (at least with basic point set topology) you should be more comfortable with ditching books and switching around if its not what you need

Admittedly thats not obvious to do alone so its better to ask a prof who knows you and the material youve covered

[gray gazelle]

Aha, that's the skill I gotta work on. Thanks!

[naive lava]

so, from this conversation, i'm understanding that i need to learn about abstract algebra first, for that i will use algebra chapter 0 or dummit and foote, than i will probably read brendon's topology and move on to bott and tu, than learn about diff geo and lie theory and after that i will learn alg geo using ravi vakil's notes, would this be a good path?

[modern crater]

Step 0 is ask your professors what you need lol but yea that is a reasonable path

[crimson leaf]

The only problem you might run into is you'll need more than group theory for algebraic geometry, ring theory and field theory would be best

[naive lava]

my prof just gave me a list of stuff to learn and said learn this

[naive lava]

i was planning on reading the entire book on abstract algebra, not just the group theory parts

[modern crater]

alg chp 0 does this and plus introduces some homological algebra

[crimson leaf]

Yeah I just wasn't sure if they were planning to read the whole book or not

[modern crater]

if youre starting from pure scratch algebra up to geomtry will take you quite a long time you should check if there are grad math classes in your uni that you can just sit and audit

[crimson leaf]

Usually a load like this even self studying I would expect to take a year or two depending on how deep you're going maybe even more

[naive lava]

well i probably do not need all of these straight away, at least thats what everyone else told me, especially the alg geo and topology stuff won't be needed at all for another year or so

so until than i will most likely learn about abstract algebra differential geomerty and lie theory and after that i will start the topology and alg geo

and if all else fails, these will be thought to me in my physics classes just in a way more sloppy and hand wavy forms

[nova lotus]

Would you guys recommend Algebraic topology by Tom dieck as an introductory book for AT

And yes I know about Hatcher but I was looking for alternatives

[remote sparrow]

there's an AT book review post pinned in threads

[covert mauve]

i have only ever had a "rough" (although not completely constructive, not too deep either) treatment of set theory till now, any books (preferably with motivation) that build set theory from scratch?

[nova lotus]

There seems to be no threads for this channel?

Oh nvm i found it

Sorry for the ping I am blind sometimes lol

[molten gulch]

Jech

[still panther]

depends on your goals

my go to recommendation is levy

[covert mauve]

Well, i dont have any hard goals, just find set theory cool and would like to learn more about it.

[modern crater]

What have you read so far?

I usually recommend Halmos' book to beginners but I would classify it under the rough and not too deep category have you already read that or something similar?

[gray gazelle]

any thoughts on steve warner's topology for beginners book?

[remote gorge]

Just curious, are you not interested in basic algebra? Group theory/ring theory/Galois theory?

[torpid stump]

I am. I am currently learning it. I meant to put it there but I forgot

[boreal herald]

anyone know some like algebra 1 books that arent textbooks but are more like neil degrasse tyson type of writing?

[spiral sky]

Is basic ANT by weil a good book, the table contents seems good for me

[gray gazelle]

can anyone suggest me books or yt videos for diff and integration? I have almost 0% knowledge about them or maybe you can say I only know some formulas but not how to implement all of those in a question

[abstract copper]

Professor leonard is a safe bet

Blackpenredpen gives a lot of examples

[molten gulch]

stewart's calculus
thomas' calculus
spivak's calculus
strang's calculus (free)

for books

[gray gazelle]

thanks would definitely try and let you know whether I got it ir not (hopefully I start getting it)

[remote sparrow]

@mossy flume

[mossy flume]

lol more than enough

[remote sparrow]

have you already learned logic?

[mossy flume]

if you can set up a computer algebra system (SageMath!) then that'll help alot

since some of the examples are nasty to compute and not worth doing by hand (and the book even says this)

but yes IMO the text is a very good idea as an introduction to algebraic geometry

if you want a less computational approach then I recommend Fulton's Algebraic Curves

but that does require more algebra background

[gray gazelle]

what's the book reference for the foundations channel?
(in other words what do I have to learn for understanding that channel?)

[remote sparrow]

bare minimum is basic mathematical logic (which is moreso about metalogic than actually using logic)

[gray gazelle]

like any GTM in logic?

[remote sparrow]

undergraduate texts are okay too, e.g. enderton

[gray gazelle]

thanks , thanks a lot
what are the advanced books used there?

I only know about set theory (jech) and model theory (marker)

[remote sparrow]

well, after basic mathematical logic, you can branch out into set theory, model theory, computability theory, and proof theory. there's more subfields, but the first three are the most widespread at places with logic programs. proof theory is big but doesn't get as much attention from the mathematical community. however, i think computer scientists are doing a lot of work there

@solemn rover feel free to correct me

[remote sparrow]

you can look at diligentclerk's pinned logic reading list in this channel

you can also look at https://logicmatters.net/tyl/

[gray gazelle]

thanks a lot , again , I thinking about the intersection of computer science and logic

[gray gazelle]

I checked that 2 years ago, but is a little philosophical

[gray gazelle]

where is that?

[remote sparrow]

some things you can google are automated theorem proving and formal verification

[gray gazelle]

like type theory stuff?

[remote sparrow]

there are plenty of books geared to mathematics students. check again

[gray gazelle]

ok

[gray gazelle]

where is the pinned logic list?

[remote sparrow]

if you're on desktop, at the top there's a thumbtack icon you can click

[gray gazelle]

oooooooooh I see it, I didn't knew that

[gray gazelle]

thanks a lot , this was really useful , I thank you like 100 times

[gray gazelle]

you saved me, now I am free.


thanks a lot again

and also thanks to diligentclerk for existing, the GOAT 🐐

[covert mauve]

Some basic real/complex analysis

[covert mauve]

I can do most proofs i have encountered, but never really did "logic" formally, if thats what you are asking.

[trim skiff]

Would I be able to start reading Evan Chen's napkin even with math experience that is basically just high school algebra and geometry?

[remote sparrow]

you should probably learn some basic mathematical logic. would you care to mention which set theory book you read?

#book-recommendations message

here are some introductory books on logic you can consider reading

[covert mauve]

Havent read a book specific to set theory till now, most of the stuff i have learnt from Velleman's books and tao's Analysis I.

Thanks, will check that out

[remote sparrow]

#book-recommendations message

here's some set theory recommendations. they don't assume prior background with logic, but they're more rigorous than what you've done so far

[covert mauve]

thanks

[shy silo]

What is a good path to go to Langlands, without a background of algebraic number theory or representations of algebraic groups?

I'm currently taking a class in algebraic geometry but since it's only one semester I don't think it's enough

[solemn rover]

You're right. Although there are more mathematicians working on proof theory in Europe than in the United States.

[gray gazelle]

need a good book for coordinate geometry

[slate gull]

There is one by arihant publication

[gray gazelle]

pink book?

[slate gull]

I don't remember its name

[gray gazelle]

or the sk goyal skills in maths: coord geo

[slate gull]

Don't know tbh

[gray gazelle]

alright

[viral oracle]

hey, i need recomendetation for ode’s in range of maximum 200pages, do you have any?

[tender cobalt]

im kinda finding james stewart or thomas calculus boring to read

[marble solar]

It's a math book not disneyland

Spivaks Calculus can be a better read, but it's still a math book

[gray gazelle]

just gaslight yourself into enjoying it

[rigid pagoda]

Can someone recommend a good material for learning probability and advanced probability?

Thanks in advance.

[molten gulch]

blitzstein and hwang (stat110 book) for basic probability and statistics

Klenke or Billingsley for advanced probability (you'll want some real analysis and measure theory for this)

[cunning ingot]

Hey guys, has anyone read "A Mathematical Primer on Computability" ?

[rigid pagoda]

Thanks! That means I should learn real analysis and measure theory first? And then get to the advanced probability?

[molten gulch]

yes, you can do normal probability with just calculus

[rigid pagoda]

Thank you!

[remote sparrow]

it's good to have an intuitive understanding of probability before diving into measure-theoretic probability

[rigid pagoda]

Gotcha!

[plain belfry]

can i ask for non math book recs here? was looking for an intro to stat mech book. currently taking a second course in thermodynamics, and mostly have all the required math background i think (stats and prob, calc iii, currently taking ode). have studied some quantum mechanics in the past.

[gilded shuttle]

https://discord.gg/physics

[signal mountain]

https://www.susanrigetti.com/physics

[gritty gale]

ye that's fine to ask about

i dont' have an answer 4 u off the top of my head, mostly bc im really tired, but ur free to ask

[stoic hearth]

Looking for Geometry books. I'm not really sure where my knowledge currently lies on the subject; I'm well out of High School but have only recently picked math back up (as a hobby, mostly).

[stone axle]

What’s a PDE’s book that’s good for a first course in the subject?

[gentle arrow]

evans

[gray gazelle]

Any books that focuses on proofs?

And is easy to understand

[molten gulch]

velleman's how to prove it

[marble solar]

Walter Strauss Intro to PDEs

Evans requires a lot of background, not really a good recommendation. Also for general undergrad ODEs, Boyce & DiPrima is very good

[leaden citrus]

Anyone know some good trigonemtry books to read through?

[karmic thorn]

I liked Olver's PDEs

[rose raven]

I want to study calculus of variations,does anyone know which book to read?

[tender cobalt]

thats true i dont expect that "entertainment" from a math book but its kinda boring i dont see much theoritical stuff

it just shows some definition

some examples

then goes to exercises

[tender cobalt]

yeah I like that better somehwo

[gray gazelle]

Thank you!

[frozen minnow]

Any books for introductory statistics for scientific research? Like https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10324782/ but in detail

[gray gazelle]

Some good number theory books.

With loads of theory

And proofs

[molten gulch]

Ireland and rosen

[gray gazelle]

I might have seen that a library, does it have a orangish binding?

[molten gulch]

I think so

Google it online for images of the cover

[gray gazelle]

I'll fs check it out the next time I'm there

[molten gulch]

Also if that's a bit tough, there's Hardy's book and Silverman's a friendly intro to number theory book

[gray gazelle]

GH HARDY?

[molten gulch]

Yes that hardy

[gray gazelle]

Yea I wanna start from scratch

So does Hardy's book work?

[molten gulch]

Hardy and silverman both might be good ideas

[gray gazelle]

Alr

Thanks man

[tender cobalt]

any good introductory physics book with calculus

[molten gulch]

Halliday and resnick

[tender cobalt]

not rlly available here, any alternative

[old belfry]

See:

“An Introduction to Probability and Statistics” by V.K. Rohatgi and A.K. Md. Ehsanes Saleh, Third Edition, 2015, John Wiley & Sons

[remote sparrow]

#book-recommendations message

try niven

[winged dome]

Hello there,
Despite not being in the curriculum our math teacher quickly talked about how the sin and cos function are constructed with the sum of the series $\frac{x^n}{n!}$ which define the exponential function first. Does someone have a book recommendation on that subject ? (Building math in general)

[hasty eagle]

Lilly (NasaExploration)

[molten gulch]

Well this is just real analysis

So any real.analysis textbook or even calculus textbook should cover sequences and series

[hallow oriole]

give abbott's understanding analysis a try

[rigid pagoda]

Thank you!

[gritty gale]

had another think abt it and: mandl's statistical physics and Nordling/Oesterman's Physics handbook might be helpful

or at least a good starting point

[broken pecan]

Pathria's stat mech book is the one. Yes it is grad level but you had two courses in thermodynamics, should be ready. You math level needs to improve tho

[torpid stump]

Hello! Do you have any advice and book recommendations for a high school freshman interested in mathematics? I know single and multivariable calculus and I want to learn some more.

[hallow oriole]

abbott analysis

[gray jungle]

I would recommend tao analysis and hoffman kunze linear algebra.

[hallow oriole]

if you want an easier alternative to hk use friedberg insel spence

[torpid stump]

Any supplementary texts for abbot?

Bartle and sherbert maybe

[hallow oriole]

no need

[torpid stump]

I would prefer one

I like books

[hallow oriole]

mm sure then, whatever you like

[torpid stump]

Thanks! I will look at them.

[remote sparrow]

abbott was inspired by bartle and sherbert

he taught out of bartle many times before writing his own book

[hallow oriole]

the specific books you use won't matter too much

you just need to stay within the rough archetype of "gentle intro proof based textbook"

[torpid stump]

I see. Maybe Baby Rudin?

I also don't know proofs

[hallow oriole]

i am hesitant to recommend baby rudin as someone's first intro to proofs

[torpid stump]

Is Pugh good?

[hallow oriole]

it's fine

[torpid stump]

I saw it on stack exchange a lot

[hallow oriole]

tao, abbott, pugh, etc will cover mostly the same content

you can try all three and find whatever is easiest for you to read

[gray jungle]

If you are not familiar with proofs then i definitely recommend tao over abott

despite it being a good book

[hallow oriole]

tao is very hand holdy even as an intro to proofs imo but maybe it'll mesh w ur learning style better 🤷‍♂️

just skim all of them

see what you like

the best book to read is the one that you can learn from

[torpid stump]

Yeah

[gray jungle]

you wont need to worry about analysis 2 for a while

but no they are seperate volumes

[torpid stump]

Oh

Alright

[gray jungle]

But as mentioned its a rather friendly book that takes it times building the foundation

abott is more efficient but more difficult without proof background

[hallow oriole]

if you're a high school freshman you might want to try competition math too

im a heavy advocate of learning as you go

[torpid stump]

I am not interested in that

[hallow oriole]

intro to proof books certainly have a place but i dont think most people need them

[torpid stump]

I do want to become a mathematics researcher

[hallow oriole]

competition math can really only help you

but, it's not necessary

and learning more proof based math will probably help you more

but doing advanced math in grade school without other people who are doing similar things (competition math) can be lonely

[torpid stump]

Alright

But I don't care

[gilded shuttle]

why not?

[hallow oriole]

well, if you're set on it

then skim tao and abbott and figure out which you prefer, and read it

do all the exercises

[torpid stump]

I am much much more interested in advanced mathematics.

[gray jungle]

i think tao does a good job teaching you proofs before he reaches the actual analysis, you should be fine

[torpid stump]

Alright! Thanks so much james and valley!

[hallow oriole]

mhm!

good luck, remember to ask questions in the server when you have them

[torpid stump]

Yes

[gilded shuttle]

if you’re interested in getting into elite universities it isn’t exactly a bad idea

[hallow oriole]

use everything you have available and remember to connect with your peers

[hallow oriole]

if you're advanced enough in regular math comp math is unnecessary

[torpid stump]

My dream university is Princeton or MIT.

[gilded shuttle]

great for the resume though

[torpid stump]

I am in a vocational school

[gilded shuttle]

for the application

[torpid stump]

Im a smart boi

[hallow oriole]

sure, but going into undergrad at a grad level also looks pretty good

plus he is not interested in comp math, there is no need to do it, so it is ok

[torpid stump]

I am mostly interested in the super advanced stuff like homological algebra algebraic geometry differential topology that kinda stuff but I have to learn the basics first

[gilded shuttle]

saying you’ve self studied it is much less reliable

for the person reviewing your application

[hallow oriole]

if he is in a vocational school he should have phd level teachers who will be able to vouch for him

huh, i got very active back

hm

[torpid stump]

valley

You got active

[hallow oriole]

i was emeritus so it isn't that impressive

now my pfp, name, and pronouns match again

[torpid stump]

When will i get active 😭

I have been waiting

So long

[gilded shuttle]

just send more messages

[hallow oriole]

don't rush it

[torpid stump]

I have 524 messages

525 now

[hallow oriole]

a solid foundation is much more important than anything else

[torpid stump]

Yup.

[hallow oriole]

anyways, no time like the present

go read tao or abbott or something

[torpid stump]

Yes sir 🫡

[old belfry]

Some of these you can learn within a year after learning Calculus to be fair, homological algebra and differential topology are undergraduate topics

[hallow oriole]

it will go quicker

than that

[old belfry]

Well at the end of Abstract Algebra is Homological Algebra. A year to finish basic real analysis is insane unless you purposefully are going through every exercise in Rudin or something

[gray jungle]

[torpid stump]

I agree

[old belfry]

Reading 500 pages of Aluffi within a year is ?

[gray jungle]

brother im at my 5th year and i dont know shit about differential topology

[hallow oriole]

i think rein's take is wrong but i also think a year for analysis and alg is long

[torpid stump]

I am probably going to be spending about 1-2 hours a day

Not a lot

[torpid stump]

You a metal fan?

[gray jungle]

rudin is a semester course, abstract algebra is two since the subject is kinda massive

[torpid stump]

I saw your spotify profile

[gray jungle]

yes sir

[torpid stump]

I stalk peoples profiles whenever I see them lmao

[gray jungle]

you and me brother

[hallow oriole]

that's fine, i think took me about two months at the same rate for analysis and alg each

[torpid stump]

Lets go! Fav band?

[torpid stump]

Nice

[old belfry]

I agree with you, am I misunderstanding what they mean by differential topology then? If they mean like milnor it's right after analysis and topology, no?

[hallow oriole]

you'll def be able to do it in under half a school year

[gray jungle]

but like i dont think its realistic to go from real analysis -> diff topology

neither AA-> homological

[hallow oriole]

even if you can't it probably just means you are learning

[gray jungle]

parkway drive

[hallow oriole]

so it's not that big a deal

[torpid stump]

[hallow oriole]

if you want a supplemental real analysis book actually maybe check out the cauchy-swartz masterclass

i just remembered it

[torpid stump]

I like Cannibal corpse and tombstoner

[torpid stump]

Ok

I might do abbot and tao

Tao gonna teach me proofs

Gotta go will be back in 20-25 mins

[hallow oriole]

i think people should also learn linalg and ra concurrently

but that's just an opinion

honestly i think people should learn linalg whenever they cover R^3

[old belfry]

Well next term I have a Differential Geometry & Diff Topology class and I learned Calculus 3 last term, I don't really think the gap is too big but I'm taking 5 pure math classes this term to be fair

[gray jungle]

you need at least analysis on R^n , diff geometry of manifolds (assuming they skip curves and surfaces), and general topology (general topology itself needs some background and maturity, as does differential geometry which assumes linear algebra and multivar analysis)

and assuming someone wants to speedrun there way to diff topology for some reason

unless its a incredible bright student

1 year wont be enough

[molten gulch]

Even if you're super bright, 1yr is incredibly slim

[old belfry]

My class assumes analaysis in R^n and Topology, it covers curves and surfaces in like 4 weeks before moving on to manifold theory

[molten gulch]

Manifold theory seems like diff geo rather than diff top

[hallow oriole]

i think 1 year assuming you know linalg and multivar anal should be enough

[old belfry]

Covers both it is taught by a topologist, but it is meant to be a diff geo class

[gray jungle]

i would recommend people explore more topics before diving into specific topics like diff topology either way

first two years should be spent exploring

[hallow oriole]

but i think people should learn combinatorics

and algebra

and everything really

[old belfry]

I need to learn combinatorics some day

[hallow oriole]

you should learn it today

[old belfry]

D:

[hallow oriole]

combinatorics is my first love

it's the best

there is nothing else like it

[gray jungle]

probability , discrete math, complex/numerical/fourier analysis, linear algebra, analysis on R^n, intro FA, metric spaces and topology , combinatorics, abstract algebra, intro number theory

life has given you so many good options to discover

[hallow oriole]

add more alg things to that fr

[gray jungle]

no need to rush

[hallow oriole]

there's literally a billion things i think everyone should no

the saddest thing in the world is that it's impossible to learn all the things you want

[molten gulch]

We can't sleep at night knowing this

[gray jungle]

indeed

[remote sparrow]

everyone MUST learn mathematical logic and axiomatic set theory, you will use it all the time outside of foundations, trust!

[old belfry]

Read until your brain falls asleep

[molten gulch]

The thought's making our insomnia unbearable

[gray jungle]

but you can absolutely explore a wide variety of math topics

[hallow oriole]

yep

[gray jungle]

specializing is important after that

[hallow oriole]

i specialized super early (first sem of college, ug) and the last year i've been learning other things and going super wide

[old belfry]

Even though I'm relatively sure I want to go to Algebra grad-school I still want to reach atleast Harmonic Analysis in the Analysis route

[remote sparrow]

try to think about topics that interest you rather than what's "hard" or "hot"

[old belfry]

you're hot math-rassment

[gray jungle]

classical harmonic analysis?

thats basically just post rudin

if you know rudin you can pickup steins book right now

if we are talking harmonic analysis on topological groups then that will take a lot more time

[old belfry]

This basically https://link.springer.com/book/10.1007/978-1-4757-3085-2

I need atleast Measure Theory from what I can see

[hallow oriole]

this reminded me of that time i tried to read enderton

[old belfry]

I will learn Measure Theory after my fall term

[winged dome]

Okay so this book is really pertinent but it's not really what I as looking for. I am looking for books that build math from the grounds up. Like that's just real analysis when the results I have are for any normed vectors spaces which are wider result

[hallow oriole]

axiomatic set theory is probably the worst of all time

[gray jungle]

you need measure theory, functional analysis and spectral theory

[hallow oriole]

ohh

[remote sparrow]

for me, i only want to know measure theory for probability, since probability is one way we can reason about the world in addition to logic. not sure if i care about functional analysis per se. i like physics, but i'm also very much a person that feels very comfortable reasoning like a physicist. i don't feel particularly compelled to do mathematical physics.

[gray jungle]

and thats a tall order in itself

but you also need to know some lie theory and analytic number theory if you wanna explore that route of harmonic analysis

[hallow oriole]

generally the way you do this is by reading real analysis and then generalizing it later

[gray jungle]

abstract algebra goes without a saying

[hallow oriole]

functional analysis is so cool

[gray jungle]

something like rudin functional analysis ch1-4 + 10-12 is probably needed

[old belfry]

Lots of Math to read

[hallow oriole]

it also has lots of connections to ergodic theory

which is also one of the coolest branches of math

[gray jungle]

knowing diff geometry helps too with motivating examples

[hallow oriole]

plus it contains operator theory

which is also one of the coolest branches of math

[winged dome]

Okay so I guess I will just wait and see what my teacher impresses me with. Though I wish we see something interesting soon cuz boredom is extremely present right now in class

[hallow oriole]

i think every branch of math is 'one of the coolest branches of math' with the possible singular exception of basic set theory

so maybe im biased

operator theory really is super cool though

[old belfry]

Basically,

*Measure Theory
*Functional Analysis (incl. Spectral)
*Lie Groups, Reps, et. Al
*Analytic Number Theory

[hallow oriole]

because it involves super neat things like vertex operator algebras

[torpid stump]

Im back

Oh the discussion ended lmao

[gray jungle]

yeah, but make sure the functional analysis is over topological vector spaces

thats usually the more common type of arguments you'll see

problem is idk how well you'll digest that if you didnt do FA over normed spaces

but godspeed brother

[torpid stump]

Can I learn measure theory right after real analysis?

[remote sparrow]

my understanding is that functional analysis is useful for mathematical QM and PDEs. are there other mathematical applications of FA?

[gray jungle]

yes you can

[old belfry]

Understandable, thanks

[torpid stump]

Cool

[hallow oriole]

yep

[gray jungle]

operator algebras and abstract harmonic analysis ofcourse

[torpid stump]

Though

[hallow oriole]

focus on real analysis and linalg

[torpid stump]

👍

[hallow oriole]

linalg is the most important math thing you will ever learn

there is not a single math field in the world that does not make heavy use of linear algebra

[torpid stump]

https://www.youtube.com/watch?v=PvXp4Ru-6OQ Does anyone know this dude? Good channel.

[remote sparrow]

unfortunately i'm not drawn to any of those directions, except maybe mathematical physics (for which operator algebras has applications in mathematical quantum statistical physics). but i'm okay with my physics education coming purely from physics textbooks

[torpid stump]

I see

[remote sparrow]

yeah i know who struggling grad student is

[torpid stump]

Is he on here?

[remote sparrow]

idk

[hallow oriole]

doubtful

[torpid stump]

😢

[hallow oriole]

it's possible tho!

[gray jungle]

i used to listen to cannibal corpse for a while but didnt stay in death metal too long, went more towards doom and black shit

off topic but do recommend me any stuff you find interesting in #1207416531303014461

[torpid stump]

I find that stuff sad honestly lmao

I like the fast and energetic stuff

[torpid stump]

Will do

[gray jungle]

sometimes its just a lie down and feel sad days yknow haha

but i feel you

[torpid stump]

Black metal is just about killing yourself lmao

And how transylvania is scary

[gray jungle]

lets move to music

[torpid stump]

Ok

[torn crypt]

Cts logic sorta?

[remote sparrow]

https://en.wikipedia.org/wiki/Descriptive_set_theory

maybe cool but still thinking about it

[torn crypt]

Not quite what I meant by cts logic but sure

[remote sparrow]

no i was on a different train of thought

[modern ruin]

YOOO really? i’ve looked at some of his videos in the past, idk what he’s up to these days

[remote sparrow]

no, as in i know the channel

[modern ruin]

oh

[tribal crow]

even stuff like logic?

[hallow oriole]

maybe not that!

butttt

https://arxiv.org/pdf/1407.2650

[remote sparrow]

do people here feel grimmett and stirzaker's One Thousand Exercises in Probability make a helpful supplement, insofar as it is a source of "applied" problems and exercises that are a little more on the problem-solving side, to measure-theoretic references like billingsley and durrett? i don't feel like picking up grimmett and stirzaker's main text, Probability and Random Processes.

@orchid mortar @misty wyvern

[misty wyvern]

Er what's your goal

I definitely did not do Grimmett and Stirzaker's One Thousand Exercises and here I am publishing probability in top journals

on the flip side I might be slower at probability problems on a quant test

[remote sparrow]

i have basic problem-solving skills from calculus-based probability, but i also feel compelled to be able to reason about more complex applied situations.

[misty wyvern]

Grimmet and Stirzaker would be helpful to build confidence in solving probability problems, but you can skip straight to measure-theoretic probability, which builds a very different kind of reasoning ability, closer to functional analysis than undergrad probability.

[remote sparrow]

of course, i don't plan to work through grimmett and stirzaker's main textbook. i just want to be able to solve probability problems after or at the same time i'm learning measure-theoretic probability

[misty wyvern]

You can try the One Thousand Exercises. Wouldn't hurt but I don't think an academic career would suffer too badly.

My general take is undergrad probability problems are mostly trivial once you're a grad student, so the real benefit you get from practicing them is speed.

Which is important on technical interviews.

If industry research is something you're after.

But if you want to stay in academia, do it for fun, not mandatory.

[signal zenith]

(& the math gre if you’re planning on taking it)

I am not sure I would say go ahead and do literally 1000 problems but as someone currently struggling with the gre I do wish I did some more probability practice

[remote sparrow]

nah, i don't need to take the GRE for my masters lol

it's not even something you can submit

i just feel like i should

[fickle belfry]

does anyone know any calculus oreiented books on mechanics

[molten gulch]

classical mechanics? taylor
electrodynamics? griffiths
quantum mech: sakurai (or griffiths again)

[fickle belfry]

not classical

[molten gulch]

well for qm there's sakurai, shankar, conen-tannodji (or however you spell it), etc...

tons of books

[fickle belfry]

im trying to get into physics and you seem to be knowledgeable, do you have a starting book reccommendation

[molten gulch]

Halliday and Resnick
Taylor
Griffiths
Griffiths (or Sakurai)

For Thermo there's Blundell and Blundell
for Stat Mech there's Pathria
Schutz for GR
Carroll for GR
Carroll and Ostlie for Astrophysics

Frankly I'm FAR more knowledgable in maths than physics, I actually flunked p. bad in secondary school that I'm now self studying through halliday on my class off-days from uni (CS major)

[fickle belfry]

ok thanks

[stray niche]

Any recommendations that cover the philosophy of science perhaps?

[steel cloud]

Problem book for group theory for an undergraduate

[remote sparrow]

you can look up past qualifying exams if you want

oh wait undergraduate

well, undergraduate can encompass books between gallian to something that has been used as a graduate text like dummit and foote

[remote sparrow]

@blissful shore

[steel cloud]

What are the problem books for an undergraduate?

[remote sparrow]

can you state specifically which book you are learning algebra from?

[steel cloud]

Lang, Herstein

I need a book like the Berkeley problem book

[fierce hedge]

Herstein already has a lot of good problems, if DnF is not enough you can look at "Problems in abstract algebra" although it has some problems at much harder level

I think there's also - Exercises in Algebra: A Collection of Exercises, in Algebra, Linear Algebra and Geometry

[steel cloud]

Okay thank you

[granite olive]

You can check The Science of Mechanics by Ernst Mach.

[ebon lance]

Any recommendations for Multivariable Calculus.....

[blissful shore]

No problem! Here's the information about the Mercedes CLR GTR:

• https://www.jstor.org/stable/20114958
• https://www.marxists.org/archive/lenin/works/1908/mec/index.htm
• https://academic.oup.com/book/7116
• https://books.google.co.uk/books/about/Against_Method.html?id=8y-FVtrKeSYC
• https://global.oup.com/academic/product/philosophy-of-social-science-9780199645107
• https://www.google.co.uk/books/edition/Philosophical_Papers_Volume_1_Mathematic/yHQZHdZ1NQIC

[rose hazel]

Whats the golden standard of complex analysis books? (something in the same category as tao's is to real analysis)

[signal zenith]

Stein and Shakarchi probably

[remote vortex]

Mercedes CLR GTR?

[blissful shore]

The Mercedes CLR GTR is a remarkable racing car celebrated for its outstanding performance and sleek design. Powder by a potent 6.0-liter V12 engine, it delivers over 600 horsepower.🔧

Acceleration from 0 to 100km/h takes approximately 3.7 seconds, with a remarkable top speed surpassing 320km/h. 🥇

Incorporation advanced aerodynamic features and cutting-edge stability technologies, the ClR GTR ensures exceptional stability and control, particularly during high-speed maneuvers. 💨

Originally priced around $1.5 million, the Mercedes CLR GTR is considered one of the most exclusive and prestigious racing cars ever produced. 💰

It's limited production run of just five units adds to its rarity, making it highly sought after by racing enthusiasts and collectors worldwide. 🌎

[abstract copper]

Holy brainrot

[remote vortex]

!nogpt

[hybrid sparrow]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[blissful shore]

yea thats not a mathematical task or a help question so im chillin

[marsh ingot]

For that you have #chill

[upbeat vine]

Ahlfors but it's very terse

[modern sphinx]

Definitely not the standard “gold standard” but my program used a new book by Zakeri, and if you already know some complex analysis (say at the level of Churchill and Brown), it’s really good for a second course. Only complaint is it has no analytic number theory the way Stein and Shakarchi does, but I’m biased. I should add: Zakeri does complex dynamics, so there’s a heavy slant towards dynamics and a dose of hyperbolic geometry, in case those are of interest to you.

[vital bane]

QM: Shankar

the other recs are on point though

[molten gulch]

mentioned shankar in the message after

[hollow drum]

Can anybody recommend a book to learn Schubert calculus or enumerative geometry.

There is 3264 by Harris. Should I really just go through that book? Or is there some alternative

[modest prairie]

anyone has some good recommendations for basic calculus other than AOPS and spivak?

[molten gulch]

Stewart, thomas

[modest prairie]

thanks

i'll check them out

[remote sparrow]

#book-recommendations message

not the "gold standard" but i like these

much more approachable than ahlfors or stein/shakarchi

[south elbow]

is non euclidean geometry by wolfe good?

[gray gazelle]

where do i find more problems in each sections?

[reef granite]

any math book recommendation which would wake my conciousness and make me fall in love with mathematics again

[toxic willow]

https://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192

[cyan epoch]

Any book recommendations or resources for transitioning to undergraduate maths from a levels.

Im interested in any and all recommendations to bridge that gap. But a particular interest of mine is learning the basics of number theory, i touched on it very lightly in a levels. Basic modular arithmetic, gcd, fermats little theorem, divisibility tests, euclidean algorithm, congruence equations, and some combinatorics. (All of this was in very minimal depth) But i wanna take it a bit further, but idk where to start without being completely in over my head

[open merlin]

Algebra Notes from the Underground uses what you described as a starting point for teaching abstract algebra.
But probably some intro to proofs / set theory makes sense first?

[slender wasp]

niven, zuckerman supplemented with borcherds berkeley math 115 lectures on youtube. And perhaps 18.781 in mit ocw. One may feel the need to supplement it with other books like burton/silverman/davenport for selective topics but i think NZM is great as the main reference.

if nzm feels a bit hard, then burton and silverman are better and nore popular for pre-undergraduate first course with the aim of doing nzm as second course.

[oak tendon]

Books for all levels of calculus. From limits - pde’s basically

[golden whale]

any recommended books on linear algebra?

ive been tryna look for some but all i find are books that dont go as conceptually in depth as id like

[molten gulch]

lay lay mcdonald for computational
Friedberg insel spece for a bit more proof-based intro

some people also like axler but AFAIK he has determinant-phobia and doesn't introduce determinants until very late and the book has a lot less computations

[candid creek]

any problem books for real analysis?

some "spammy" like schaum's series for calculus

[hallow oriole]

rudin has a lot of high quality problems

if you're talking about grad analysis there are lots of qual books

[remote sparrow]

you can't really find drill-type problems in real analysis

you may find routine ones

[hallow oriole]

oh, if you meant 'drill' problems there aren't many

[candid creek]

but like, there are common themes and tricks right?

this is for a first course undergrad in analysis

I don't think they will be giving us the hardest putnam/competition style questions in the exam

[hallow oriole]

if you do the problems in rudin i guarantee you will be fine for a first undergrad course

[candid creek]

are they not like. ... too hard?

[hallow oriole]

i'm not saying to learn from rudin; i actually discourage that

uhh

not in my opinion

[candid creek]

ok

[hallow oriole]

use another book to read and use rudin for problems

[candid creek]

yeah I'm reading abotts

[hallow oriole]

and you'll be fine

abbott is good, very gentle

[candid creek]

can i just skip straught to the questions in rudins?

idk if I will have time to read both properly

[hallow oriole]

yeah

maybe read a few pages to get a sense for notation

[candid creek]

ok yeah

[candid creek]

what about complex analysis?

only insofar as contour integrals, laurent expansions, residues

[hallow oriole]

for that?

[candid creek]

the full course is "real and complex analysis"

[hallow oriole]

try ron gordon's complex integration for an intuitive treatment

it won't cover any other complex analysis but it will do those

[candid creek]

thankx

[hallow oriole]

mhm

alternatively you can flip through to the relvant sections in stein and shakarchi

this is actually what i recommend

you'll have to learn complex analysis one day anyways so you might as well find a book in advance

[candid creek]

what about serge lang complex aalyasis

[hallow oriole]

i dont like lang books as anything outside of references

maybe if u only use the problems you'll be fine

[languid cipher]

What's up

Any calculus recommendations?

For beginners

[warped barn]

Hi, i learnt all my derivatives and integral rules/concepts. But now I wanna get really good at difficult/tricky questions. Does anybody have a good workbook for someone that knows all the concepts, but wants to get technically proficient?

[remote sparrow]

https://www.amazon.com/Essential-Calculus-Practice-Workbook-Solutions/dp/1941691242

[warped barn]

Ty! Does this one have questions leaning on the harder side?

I'm about to tutor a highschooler that goes to a private school. And I'm sure the questions they assign for homework/tests are harder than what I learned in my classes

So im a little nervous

[remote sparrow]

they're mostly standard, but is there a reason why you're expecting you need anything beyond routine problems?

[warped barn]

Mostly this

[remote sparrow]

do you know what textbook they use?

[warped barn]

Not yet

But I should find out...

Good idea Lolll

[remote sparrow]

you can look at bartle and sherbert. there are hints for many of the problems in the back

[remote sparrow]

idk about the quality of the text per se, but i'm aware this has a full solutions manual associated with it

#book-recommendations message

i like the complex analysis books listed here

[remote sparrow]

stewart

you can save money by buying an old edition

[marble solar]

It depends on the level you're looking for. At the undergraduate level I think Stein & Shakarchi is the best

If you've done a decent amount of analysis, and prefer technical precision then Conways Complex functions of one variable is very good

If you did some amount of analysis, but prefer geometry, then Ahlfors is the book

[remote sparrow]

#book-recommendations message

[marble solar]

There's also Rudin's Real & Complex Analysis which is good, but difficult. I'm personally a big fan of Marshalls text, but it tends to be a little non-standard

[candid creek]

is it normal for a maths + cs double major to be perma studying

otherwise, how do you guys have so much time to go through so mabny textbooks

I can barely get through one in a semester

am i just using them wrong?

[hallow oriole]

im a math & cs student and i only spend 2-3 hrs studying

maybe you are trying to do everything in a textbook

which is a mistake

[candid creek]

are you american?

at my current university (australia), I do not know of a single math,cs major who can survive on only 3hrs a day

[hallow oriole]

im american yes

i'm also pretty talented and was doing coding and math in hs

[candid creek]

maybe that's why

[remote sparrow]

in college, there is an unspoken expectation that you cannot necessarily know the subject completely (at least within the context of the course)

[hallow oriole]

i don't study for my classes but i still get through multiple textbooks over the course of the semester so one textbook a semester is still a little slow, but if you learn best, then that's what really matters

talent < hard work

[candid creek]

do you like

ignore the proofs to theorems

[hallow oriole]

no

[candid creek]

and just focus on using them

do you do all the excercises?

[hallow oriole]

three hours a day is the maximum time i let myself spend a day like

sitting at my desk and doing math

but i think about math like

[candid creek]

three hours a day per subject?

[hallow oriole]

6-7 hrs of the day

[candid creek]

or overall

[hallow oriole]

no i dont bother studying for cs over 20 min a day

[remote sparrow]

the exercises assigned to you will help you decide whether a proof given in the text is simply "technical" or whether it uses ideas that you will apply to your exercises

[hallow oriole]

no, doing all the exercises is a waste of time

you should do the exercises that are instructive

[remote sparrow]

there is not enough time in the day to do everything. especially for graduate studies

sometimes you will black-box things, and that's okay

[hallow oriole]

^

it

it's something you'll learn

[candid creek]

it seems to me that I need to black box everything given the pace

especially for a first course

and since the proofs aren't really examined

[remote sparrow]

if you feel like you need to black-box too many things, go to office hours

[hallow oriole]

what books and courses are you taking?

also, yeah, office hours are great

[candid creek]

analysis

our uni crams real + complex into a single first course

[hallow oriole]

nobody ever seems to go to them, and the professor will just be able to tailor what you want specifically for you

[remote sparrow]

your university may also employ tutors at their in-house tutoring center

[hallow oriole]

and it helps you build rapport with them which can only help

[remote sparrow]

you can also form study groups with peers

[hallow oriole]

learning to read and do a textbook properly is a skill that you will develop with time

invest the effort and you'll get the results

[candid creek]

also, I don't really get why I need to understand all the proofs

especially since they're not examined at all for us

it's mainly learning how to use the main theorems to prove new things

[hallow oriole]

hm

[remote sparrow]

there could be a lot of reasons why graders don't look at all your solutions. maybe you're in a big class?

[candid creek]

huh?

I meant like

legit, no proof recall type questions in the exam

[hallow oriole]

do you have to prove new things in the exam?

[candid creek]

do you guys get examined on the proofs?

[candid creek]

yeah

[remote sparrow]

why would an exam necessarily be about regurgitating proofs from the book?

[hallow oriole]

doing proofs helps you do proofs

[candid creek]

there are 5 questions in total in the final

all of them are using results from the lectures to prove new things

[marble solar]

Slightly off topic from books, but reading one book in Math deeply can take over a year

[remote sparrow]

that seems normal

[hallow oriole]

are you reading the proofs in the book or are you proving them yourself

[candid creek]

it would take me like 3x longer if I were doing this

[marble solar]

If you're just skim reading or looking at things, but not solving problems, then you will read faster. Yet it won't stick

[hallow oriole]

"math is not a spectator sport"

you can't learn how to do proofs without doing proofs

[candid creek]

well, I'm not exactly spectating if I'm doing the end of chapter excercises lol

[marble solar]

You don't have to read everything in detail. It's good to get a wide exposure to many things, then you can pick & choose what you need to learn more about

[hallow oriole]

analysis is something you really should know in detail

[candid creek]

I'm not bothering to prove the theorems myself, but I am taking the time to end of chapter excercises

if, in some cases, the question says "model the proof to theorem __", then yes, I will go back and try to understand and prove it myself

[remote sparrow]

your professor deemed exercises are sufficient for your purposes. try not to worry too hard

[candid creek]

otherwise, I don't really see the point

[marble solar]

If it's for recreation, then that's totally fine. You don't have to prove the theorem yourself, but there's no reason to reinvent the wheel every time

As you read & do more, you'll get more efficient at it

[candid creek]

you mean like, reading the proofs to the theorems?

[remote sparrow]

math is also a social activity. very few people lock themselves in a room and work completely isolated from other people. if you have gaps, there are other people to assist you.

[marble solar]

Yeah, there's little details that can be very difficult to see at first

[candid creek]

this aint my first proof-based course btw

[marble solar]

But if someone said "Oh ok, can you show me how this detail pans out?"

Then you should be able to fill a board with a direct calculation

I have my quals in Real & Complex next week. We're reading Conways Complex & Follands Real. Often times, they skip a lot of steps. I've been able to fill in most steps to a reasonable degree during my prep for myself or my classmates

[candid creek]

So, should I take the time to try memorize the main ideas behind the main theorems?

[hallow oriole]

yes

[candid creek]

yes, i can mostly do that

[marble solar]

If it's recreation, then no

If it's for your class, then yes

[candid creek]

what do you mean recreation

like, for fun?

[marble solar]

Are you required to read these for your class

[candid creek]

no

our class doesn't follow any specific textbook

[marble solar]

Then there's no point in trying to memorize the theorems. Just try to broadly think about them

[oak tendon]

Math for fun is lit bro

[marble solar]

Your classes should give you enough to think about, that you don't want to take up extra resources by filling it with something that you don't need to know

[remote sparrow]

it just depends. there are some "technical" results that have unenlightening proofs and which you're really just supposed to understand the nuances of applying them.

[oak tendon]

I’m learning calc on my own because I’m bored of my current math class and they wouldn’t let me move up

[hallow oriole]

i dont think he should memorize the theorems

but memorizing the main idea behind them?

[candid creek]

yeah memorising the main ideas and tricks

[hallow oriole]

that is important

the tricks and the specifics arent that important but you should know, morally, why something is true

[marble solar]

That's just thinking about the big picture

[candid creek]

often, a proof to a theorem in analysis seems like just two pages of inequality tricks and manipulaitions

that does not seem particularly "enlightening" as to why the theorem statement is inherently true

[hallow oriole]

sure, but you can break that down into bigger steps

[remote sparrow]

yeah, i feel that way, too. but like learning techniques of integration, there are some very common and routine techniques that thankfully someone else figured out and now we just think about whether they can be applied to the problem at hand

[hallow oriole]

like "oh, they used cauchy swartz here to bound it by a known result" blah blah blah instead of focusing on the particular inequality

[remote sparrow]

also, try writing down "scratch work" if you aren't already doing that

work backwards from the result and try to guess from that what an appropriate choice of delta might be, for example

[candid creek]

what I mean is, often, the proofs to the results only have 1-2 key parts that are worth taking note of, and really understanding the motivations behind

the rest is like standard / non-enlightening

and occasionally, some proofs are indeed novel and englihtening

mainly the constructive existence ones (or all the existence ones in general)

[hallow oriole]

then you don't have to know the standard parts

you'll learn those eventually anyways via osmosis

[remote sparrow]

not every proof will make you feel like you've gained deeper insight. sometimes, it's just there to let you know a result is true. proof =/= psychologically convincing

[candid creek]

So how do you guys take notes while reading a textbook?

If only the results? The excercises?

Only the questions? Or your working too?

Then how do you return to revise for exams when it comes along later?

[remote sparrow]

i don't take notes

[hallow oriole]

i write down definitions, theorems that seem useful or important, proofs that seem useful or important, and exercises i decide to do

to revise i usually pick a couple exercises from the section and see if i can still do them, if i can't, i skim over my notes until i can

[candid creek]

Pretty similar to what I do

[gilded shuttle]

i take notes of things that feel important and for exercises i do the ones that i don’t immediately know the answer to or know how to do just in my head

the ones that require thinking

and a bit of work

[candid creek]

I only take note of the ones that were hard when I first did them, and a few bullet points summary of the solution

And all those I didn’t get / got wrong ofc

[gilded shuttle]

if you don’t know how to solve something you should probably do it

[candid creek]

or maybe some with cool / novel solutions.

[candid creek]

I do

It’s mainly for revising / making sure I still remember it when I come back some time later

[remote sparrow]

from an early age, teachers try to make you take notes because it's a tangible and replicable method for getting students to reflect on their work. it helps many students, but the important part is that you're actually thinking about your work. there are many people who just copy what the lecturer says without thinking about the material. take notes if it helps you, especially if you're more forgetful, but the key part is that you're actually thinking about what you're writing down

[hallow oriole]

fair enough!

[gilded shuttle]

yea lol definitely don’t just write things down and continue on thinking you’re accomplishing something by writing it down

you have to understand it too

a 5 year old can write down schrödingers equation but that doesn’t mean they’ll understand any of it

[remote sparrow]

https://www.ams.org/journals/notices/202409/noti3032/noti3032.html

@gray gazelle

[remote sparrow]

@fierce hedge have you ever looked at Basic Abstract Algebra by bhattacharya, jain, and nagpaul? it has solutions to odd exercises in the back

i think it's useful as a reference and as a source of solved problems

[fierce hedge]

I have looked at it and it's pretty popular here in India but haven't really used it for anything. Maybe I'll have a look at the exercises today

[remote sparrow]

i looked through and it's pretty much definition, theorem, proof, so it's really terse

there's zero chitchat

but as a supplement it looks pretty good

[fierce hedge]

Sounds like a expanded version of Herstein

[remote sparrow]

nah, herstein gives a little motivation

[fierce hedge]

Fair enough

[fresh hull]

so you know how Lee topo manifolds has excercises interspersed in the theory

what are some other good undergrad/grad level books that have this aswell?

because I find myself absorbing and enjoying the subject way more when I am doing a book that has excercises throughout like Lee

I know Jones's measure has this and Carothers real analysis, although I'd like to find more

[karmic thorn]

Sharpe's Differential Geometry, Tao's Introduction to Measure Theory as well iirc

Bona's A Walk Through Combinatorics

[molten gulch]

Undergrad real analysis: Abbott, Tao I and II

Measure theory: Folland, Cohn, Tao, Axler

I'll let someone else answer that I need to run to class rn

[covert mauve]

I have only done Tao, but I can somewhat offer a superficial comparison. tao starts from the very basic, building off natural numbers with peano axioms, the operations on them, and then later moving onto set theory and functions.

then he later builds the rest (rationals, integers, reals, etc) of the number systems. finally moving onto sequences, series, and the rest of the usual topics. (Riemann integral, differentation, etc), he also has a chapter on infinite sets.

tao's book has no solutions in the back but offers hints about problems. (which makes them much more fun to solve!)

tao's appendix also introduces proofs and logic (which I found rather complete at least for solving the book itself)

I could not find any high-quality lectures based on Tao's book, but the material itself is quite easy to read tbh.

tao's analysis 2 (which I haven't completed yet) covers more analysis stuff (metrics spaces, Fourier/power series, multi-variable calculus, Lebesgue integration) . also, buying hardcovers of Tao's book is much cheaper than Abbott's. (at least here, i bought from Hindustan Book agency, and the quality is okayish)

abbot does not cover natural and set theory axioms, but is shorter and has great lectures based on it. it's not comparable with analysis 2.

the solutions for abbott can be found here

(there are third party solutions for tao's book, but i dont think any of them are updated to the fourth edition)

[molten gulch]

We cannot distribute those, if your uni has springerlink, it may be available through there

(For both abbott and tao)

:(

[fresh hull]

Thanks so much this is perfect

I would love to find more

[fresh skiff]

Same issue ugh

[molten gulch]

<@&268886789983436800> this message has the link to a piracy website in it

[primal summit]

Discussing piracy is against discord ToS

(i.e. could get the server deleted)

[stable flicker]

There are free analysis books. And they will probably work if you are under very strict rules

[open merlin]

[left as an exercise for the reader]

[vital bane]

you can just google it and find it

[reef granite]

any good book recommedation that can be covered in a month

preff geometry and probability

[tranquil tide]

Does anyone know what book I can read to deepen my knowledge in algebra?

[glad rampart]

i like the AoPS algebra books

[tranquil tide]

Sounds interesting, I will look for more on this

[molten gulch]

Don't discuss piracy

[tranquil tide]

Why not?

[molten gulch]

It's against Discord TOS and can get the server deleted

[tranquil tide]

Oops

[trail hemlock]

because big rich publishing companies who overcharge for books to the point where most of the target audience cant even afford them have feelings too 🥺

[pliant wadi]

Can someone recommend some references to read up on Elliptic curves as topological tori?

Books, papers, anything.

[rigid pagoda]

What is a good real analysis material? I'm looking for something like video lectures and books

[molten gulch]

for books, abbot, tao, rudin, etc...

unsure of videos

maybe MIT OCW stuff

[rigid pagoda]

Oh I see, thanks!

[remote sparrow]

#book-recommendations message

[rigid pagoda]

Wow this is a lot, thank you!

[trail hemlock]

also consider using this along with any of this boos:
https://www.youtube.com/playlist?list=PL0E754696F72137EC

[slim nacelle]

god if only

[molten gulch]

[grim delta]

Hey, im looking for a book that explains the common "formulas" for example, why the volume of a sphere is 3/4piR^3 and all the stuff that seems basic as we use it as "mechanism" but atleast for me, I don't really understand it

thanks in advance

[molten gulch]

Well for volume of circle or sphere, you need some calculus to rigourously justify it

[grim delta]

It was an example but yeah, a book that really explains why the formulas we use all the time makes sense, as I feel I just memorize the formula but I really don't understand why it works

[grim delta]

I'm with precalc :/

But i can maybe handle it

[molten gulch]

Well you'll need to wait a bit then

[molten gulch]

I can't think of any book that makes rigorous some large list of formulas, the closest I can think of is the 2 integral proofs books we have but that won't be of use to you for..a WHILE

[grim delta]

Okay, thanks anyways

[gray jungle]

Any good books on semi-group theory (C_0 semi groups, Hille-Yosida, Lumer–Phillips etc) and evolution problems?

[upbeat vine]

one parameter semigroup for linear evolution equations

Hits all of your buzzwords

[near jewel]

When it comes to linear algebra, which one is more "comprehensive"

Introduction to linear algebra, by Gilbert Strang

Linear algebra and its applications, by Lay David

[near jewel]

And also, speaking of the second book, are there any differences between 5th edition and global 6th edition?

[molten gulch]

global editions of books generally have some small changes from NA editions, such as being printed in cheaper paper and binding; but they can also have different problems and omitted chapters sometimes

[near jewel]

But the thing is, the local one is on its 5th edition, while the global edition came to 6th edition.

It’s a bit awkward to say that the global one has newer stuff than the local one.

[molten gulch]

Esp. with these books, new editions don't normally have a lot of new material

[normal crystal]

wrong
there is a US 6th edition
it's just Pearson is becoming obnoxious with how they make the print versions available
they basically want you to rent or sign up for one of their digital subscriptions

[hallow oriole]

you can find the pdf copy of any edition online!

[near jewel]

Alright, thanks for the information:)

[molten gulch]

<@&268886789983436800> Discussion of piracy (again)

[hallow oriole]

piracy is a strong word for it; the books listed are available everywhere on university websites

[timber mesa]

yes it's common to find .pdf of copyrighted books in e.g. personal webpages or uni professors' pages, that doesn't make it not technically piracy

best to avoid directly linking media like this specifically

[hallow oriole]

🫡

[flint rune]

what's a good intro to sheaf theory?

[red marlin]

hey guys i am doing pure maths edescel pearson igcse o levels any book recomendations for me?

[fierce hedge]

In algebra books, so far I have only seen this in Vinberg

(I am assuming you mean proper exercises in between instead of in the end. If you instead mean question in the text itself such as Tao then I don't remember any algebra book having that)

[smoky wing]

anybody got a recommendation for a statistics book? my Applied stats course "textbook" (if you can call it that) really sucks.

[open merlin]

very silly question: if I'm buying a springer textbook, which is less likely to fall apart, softcover or hardcover?
I've heard they're a bit fragile these days

[mellow wren]

they're both pretty sturdy

I have some soft cover books that are holding together very well

and I've used them a lot

but in general hard cover books will hold out for longer

[open merlin]

neat, good to know 😊

[latent pelican]

is goldberg's book on real analysis good for undergrads?

[full cairn]

I don't know why Aluffi's Notes from the Underground isn't more recommended here. I love how he keeps including teasers of algebraic geometry

He also wrote a paragraph about Krull dimension, and how algebraic geometers think about fields as 0-dimensional points, and PIDs that are not fields (like Z) as 1-dimensional curves

[tender zephyr]

The fuck

Im in 10th grade

[molten gulch]

Then this book isn't relevant to your mathematical studies at this stage

[fresh skiff]

Is it his undergraduate algebra book?

[tender zephyr]

Ic

[molten gulch]

Elementary Algebra (the stuff you normally learn in HS) is not what Aluffi covers. Notes from the Underground is AFAIK an undergraduate abstract algebra book, and his other book Algebra: Chapter 0; is a grad level abstract algebra book that also uses category theory a lot

[vital bane]

@coarse frost have you read these seems interesting

[tender zephyr]

Wow

Im not really pursuing maths i dont even know why im here

Im pursing astro physics is there a server for that?

[vital bane]

check #old-network for a physics server

[full cairn]

Yep, slightly easier than Chapter 0

[fresh skiff]

I see. I tried to study categories from chapter 0 but it was quite hard haha

[full cairn]

Yeah, same 😅 For a more gentle approach to category theory I think Seven Sketches in Compositionality is pretty decent

And Topology: A Categorical Approach is nice. I think knowing some specific examples of categorical constructions from e.g. topology is useful before learning category theory in its full generality

[foggy quest]

It depends on your level. "A Course in Large Sample Theory" by T. Ferguson is good.

[fresh skiff]

oh I will check these books Thank You!

[flint rune]

what's a good undergrad book for stone spaces?

[remote sparrow]

it's kind of a new book

[remote sparrow]

i'm not aware of undergraduate books for stone spaces. the only reference i've heard of is by johnstone

[flint rune]

ty!

[indigo blade]

howdy
what branches of mathematics or mathematical books in general are related to relational databases such as SQL?
at first i thought it should be linear algebra then i noticed matrix multiplication doesn't make any sense in relation to SQL databases lol

[molten gulch]

https://en.wikipedia.org/wiki/Relational_algebra

[frail kiln]

my favorite book is icebreak

er

[subtle ocean]

Mine is facebook

[frail kiln]

i dont understand

[subtle ocean]

Face "book "

[frail kiln]

put face on book

[limpid bear]

if you're interested in the history, you could read that first paper by Ted Codd from 1970 where he laid out the relational model https://doi.org/10.1145%2F362384.362685
if you want more afterwards, there's that book from Abiteboul et al "Foundations of Databases", I've read it very sparsely but it sounds like it really fits your bill (accessible freely here http://webdam.inria.fr/Alice/)

[sage kelp]

Can anyone recommend me a book on Convex Geometry in Rn?

[remote sparrow]

as far as cover wear, the hardcover obviously wins. however, i'm not so confident about how well the cover stays on with a hardcover compared to a paperback.

this is of course assuming you're buying a new book

[hallow oriole]

you can also buy the pdf and get it printed and bound

[hallow oriole]

nope

yes, abbott, tao, etc

it'll suffice!

i prefer abbott btw but if you don't know proofs very well tao is maybe better

[modern sphinx]

I got a lot out of the first couple of chapters of Vakil's Foundations of Algebaric Geometry. I don't know about recommendations that would go more in depth, though.

[flint rune]

ty!

[kind thunder]

anyone have some favorite algebraic number theory books?

[hallow oriole]

marcus number fields is probably good for intro

[nimble kayak]

does someone know a good book that is introductory to basic number theory?

[hallow oriole]

weil's book

in seriousness; silverman's if you want it easier and ireland/rosen if you want it harder

[molten gulch]

I read weil as weibel and was about to ask why you were suggesting k theory

[gray gazelle]

hey, i wanted to ask about the linear algebra done right book. Is it fine for a senior in hs to read it or is it too advanced?

so far im in chapter 2 and ive managed

[tribal crow]

your current level of education isn't a good metric to decide whether or not a book is "too advanced" for you

given by the fact that it seems like you've gotten to chapter 2 without any issues, I'd say you'd be fine

[gray gazelle]

figured

thanks still

[tribal crow]

don't be deterred from picking up books that people say are "for" advanced undergraduates or graduate students, etc

the labels mean nothing

if you're able to understand the material and do the problems, you'll be fine

[hallow oriole]

to be fair i don't think ladr is the best first intro to linalg

but otherwise you seem fine

hi higher!!

[tribal crow]

I get the feeling that this may not be their first time doing LA

I think LADR can be okay for a first course, but you'll need to supplement it with something that will teach you how to compute

or else you're losing a lot

[tribal crow]

hi valley!!

[hallow oriole]

agreed!

how are youu

[gray gazelle]

i see, will remember that

[tribal crow]

I'm okay

[hallow oriole]

yayy!

[tribal crow]

I hope you're doing well too

[hallow oriole]

phenomenallll

[pseudo forge]

book on control theory wrt estimation tracking?

[quasi sonnet]

https://imgur.com/hXvVMmP what book would have more theory, examples on these kind of limit questions? I was reading tao but it doesnt seem to have a lot on this

[remote sparrow]

a multivariable calculus textbook?

[quasi sonnet]

yes