book-recommendations

[strong rampart]

i guess any thing we read in math will help us in physics no ?

[rigid trail]

multivariable is definitely going to help, considering that it is required

[strong rampart]

thanks, i'll check

[gray gazelle]

not really anything but yeah a bunch of concepts

[signal badge]

Not in the states, at the very least

[rigid trail]

in the states im pretty sure only math majors actually learn how to do proofs

[signal badge]

The most relatable thing to a proof is probably Euclidean geometry that high schoolers take, even that subject itself is a fraud because of the curriculum

[sick minnow]

who / what are alekx and ixl?

[strong rampart]

what do you guys mean by proofs ?

[naive lava]

if you wanna go into mathematical physics, you're gonna need math, a lot of math, most important ones are topology and differential geometry imo

[strong rampart]

like writing proofs for forumla ?

[rigid trail]

proofs for theorems

[keen grail]

oh some math websites I remember doing in school

[strong rampart]

alr

[gray gazelle]

proofs are awesome, they make math like 100x better

[naive lava]

graph theory/combinatorics/set theory/logic won't help you much

[naive lava]

proofs are awesome, until they are left as an excersize

[gray gazelle]

"left as an exercise to the reader" 😭

[keen grail]

it's tough at first but once you get the hang of it

it's like everything

Yep that's what more people have to be like instead of giving up so easly

[naive lava]

also qm and qft is literally functional analysis but no one actually cares in physics so you'll be fine

complex analysis comes up a lot too

[keen grail]

ooh

Yeah

[gray gazelle]

for programming I recommend algebra, combinatorics, ...

those two can be really important

[naive lava]

in terms of groups, solid state folk use discrete groups quite a lot but particle physics folk just rely on lie groups and their rep. so those are also quite helpful

no idea

[gray gazelle]

idk wtf is quantum computing 💀

[keen grail]

oh come on

I have read about this in a book

how do you not know?

[naive lava]

if you wanna go deeper in qft, you're going to need diff top and alg top too

[gray gazelle]

why tf would I know quantum computing

[naive lava]

like the stuff witten has written about

not really

[gray gazelle]

"our water bottle has top notch AI technology"

[keen grail]

Idk I honestly would not know what it was a few weeks ago

[gray gazelle]

im still in hs soooo

[keen grail]

I was reading this interesting sci fi book

[gray gazelle]

fi?

[keen grail]

science fiction

[gray gazelle]

yeah I know what it means

[keen grail]

why question mark then

[naive lava]

but when you add all things up, it comes about to be like 30 math books so most physicsist just read nakahara and nash

[keen grail]

you literlly asked me

[gray gazelle]

my greatest apologies

[keen grail]

sarcasum?

Loveing math doesn't mean I can't read the signs

[stark lion]

Umm

Why the third edition of topics in algebra is published by a different company

Is this edition even real

I can see no mention of the third edition in any of the forums

[stark lion]

It says herstein on the cover

Though it seems like this edition was revised by other ppl

Even the first edition preface is different wtf

There is no mention of this book anywhere in internet I could find

Excluding internet archive and in amazon where it is cancelled

I feel you

[remote sparrow]

@modern ruin bump

[bitter turtle]

https://www.hipcomic.com/listing/tom-and-jerry-comics-132-fair-dell-low-grade-comic-july-1955-soap-sink/12133423

[bitter turtle]

best book ever

[keen grail]

Why is that not a math book?

worst book ever you mean

[signal badge]

Tom and Jerry is goated

[vital bane]

The intro analysis you want to ignore is how you master these inequalities

I would recommend this for single variable calculus and multivariable calculus and ODEs https://tutorial.math.lamar.edu/

https://www.khanacademy.org/math/multivariable-calculus

Khan Academy is great too

Also don't use chatgpt for math advice of any kind

yea without real analysis you wouldn't have the motivation for where the axioms of a topology came from

[heady ember]

Imagine not recommending Arnold ODEs

[tender cobalt]

what about Cauchy Schwarz master class

[timber mesa]

I think it's a fun book if anything, gives some historic overview of how people generalized these inequalities over time

so a good read in that sense

but to get a good feeling of inequalities and how to use them I guess that only happens over the years as you actually use them

[tender cobalt]

right

[vital bane]

yea by actually doing analysis

[vital bane]

I see

I might check it out then

also how's it going derivada?

[timber mesa]

all's good, I'm starting some courses this week

in theory I should be studying stochastic processes

but I've been taking my vacation time too seriously

[timber mesa]

thus far I've been reading Bass, open to more suggestions I guess

I come from an ergodic theory background if that means anything

and am interested in applications involving data, my school has some people doing that kinda thing

[vital bane]

I'm sure you needed a break

[vital bane]

oooh interesting

Data Analysis using Stochastic processes?

is this where you define Ito integrals and stuff? Stochastics analysis innit?

Stochastic PDEs

[timber mesa]

SPDEs are part of that yes

it's more like, fitting processes to data I guess

[stable flicker]

I think you're doing things more theoretical than I have ever done so I can't give anything good.
Maybe Course notes by Shalizi
36-754, Advanced Probability II

I have other hard (Stoc Proc) books, none of which I have read

[vital bane]

derivada maybe you can make progress in stochastic dynamical systems

[timber mesa]

that's definitely a thing

[stable flicker]

My reference would be something like Gallager, which is super much more applied than Bass in comparison

[timber mesa]

I see

[timber mesa]

these look really good though, thanks for the recs

[stable flicker]

Shalizi's actually a statistician so I think that will help in not going too abstract

Definitely the upper limit of what I would like to read

[timber mesa]

I suppose I'm open to reading rigorous stats stuff

[timber mesa]

yeah I like how it reads like casual commentary at some spots, adding intuition for stuff

[sudden bridge]

i want to learn conditional probability and independence. not just the formulas but the insight

which book to read?

[opaque flax]

hey guyz

just suggest me a best book for maths basic concepts

and jee to

[obsidian seal]

has anyone read The Art of Electronics Third Edition

if so how much calculus do i need

if any

idr whether conductivity and allat is in algebra based physics or e&m

it's just a constant so surely i don't need calculus

[fervent marten]

what are some books to learn computer science as a complete beginner?

[molten gulch]

Sipser's Theory of Computation, though this text assumes some basics of set theory, ability to induction proofs, etc,...

[waxen sandal]

If you're a complete beginner in the sense that you are interested in CS but not sure if you want to pursue a degree in it yet, I would recommend starting with one of the MOOC intro to CS courses like CS50 rather than starting with a book.

[fervent marten]

can you elaborate more on that

[waxen sandal]

An intro to CS course like CS50 does a good job exposing you to a bunch of different topics in CS without getting bogged down in theory right away. That's not to say that you can't find CS books similar in style to some of these courses but most of these MOOC courses are project based and are going to give you way more hands on experience IMO

[sick minnow]

thank you!! going through that website - to what level will it get me ?

[near jewel]

You "can" break down CS to hardware, software and application. Depends on what you want to learn first.

[normal crystal]

fyi, there's a new edition of the companion book next month
https://learningtheartofelectronics.com

[obsidian seal]

where the heck was that

anyway thanks

[molten gulch]

The preface probably

[hearty steppe]

Any good book recs on asymptotic approximations/expansions?

[fiery sphinx]

Like taylor series?

[hearty steppe]

Yea but more general

[sleek python]

Maybe Murray's Asymptotic Analysis

[heady ember]

https://research-repository.st-andrews.ac.uk/handle/10023/12643

[fresh skiff]

https://www.amazon.com/Abstract-Algebra-Comprehensive-Treatment-Mathematics-ebook/dp/B00SC8C7UI

i found another interesting algebra book

sour drop do you kow about it

[remote sparrow]

no

[heady ember]

Its alright, don't get sour: you can't possibly know all the books that exist.

[scarlet geyser]

hello guysb

how is going life

guys somone say the best explain mathmatics anlaysis books

[mighty tartan]

What

[scarlet geyser]

A mathematical analysis book where theorems and proofs are presented in an easy-to-understand manner.

[vital bane]

"Understanding Analysis" by Stephen Abbott

best analysis book ever

best undergraduate math text book of all time in fact

(my opinion™️ is fact)

[scarlet geyser]

how i get this/ is this book sell amazon or any site ?

[vital bane]

yes it's available on amazon

should be available on any other site as well

just search for it

[scarlet geyser]

thx my man i forget analysis and i wanna leran again

[scarlet geyser]

thx

[vital bane]

2nd edition is the latest edition btw

[scarlet geyser]

okey thanks again

[vital bane]

All the best Jack

[heady ember]

Just prove the theorems yourself

[scarlet geyser]

when i proof theorem it feel so emotional and i feel so good/ but sometimes it is so hard

[heady ember]

Yeah

I get that

[tranquil breach]

anyone knows a book that focuses solely on limits and derivatives

[fresh skiff]

Neam be like: I have spend my entire life with abbott Believe me it is worthy

[hollow shore]

that's a bit subjective, no?

I appreciate the historical tidbits and the fluidity of exposition in Abbott

The exercises are very good

but it's not devoid of weird pedagogical choices imo

My nitpick would that it's way too tongue and cheek

[tender cobalt]

@vital bane I'm starting shifrin diff geo today

[hollow shore]

there are instances where there are a few things which is supposed to be read between the lines but as a novice I may never grasp it unless given the context

[vital bane]

you should start analysis first

[vital bane]

see: #book-recommendations message

[tender cobalt]

why

[vital bane]

also why not visual differential forms by needham?

[fresh skiff]

why not spivaks collection

[hollow shore]

[grim ore]

Having read that text (not fully), and sitting in a class for diff geo (ug), i dont see why either

You can take diff geo in my uni without analysis

[heady ember]

what

How do you learn rigorous diff geo without knowing stuff like the implicit and inverse function theorems

[grim ore]

Our prof kinda just taught it along the way, hes also a diff geo research guy

[heady ember]

What are you? A Phy*icist?

[grim ore]

lol hell no

[molten gulch]

here you have to take RA to take diff geo

[grim ore]

Damn

[molten gulch]

y'all weird smh

[grim ore]

Which I guess as a explanation of the prereqs, you can proceed with Lin alg, calc III (multivar), and intro proofs

[molten gulch]

here you need real analysis 1 which has a prereq of proofs and calc 3

[grim ore]

Yeah i dont really understand why you would need analysis, but again our prof (cantarella iykyk), taught it during the semester

[molten gulch]

"mathematical maturity" maybe? IDK I haven't done any diff geo yet

[grim ore]

Perhaps

[molten gulch]

also possibly some notions of continuity and other properties of R etc...

[grim ore]

https://www.reddit.com/r/Physics/comments/7lmx36/comment/drnknjn/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

This is something i found on the topic and its pretty applicable to what we did

[molten gulch]

yeah, I guess it's more familiarity with the topological properties

[grim ore]

I guess it just matters about how in depth you go into

[grim ore]

We do have diff top, and that does have a ra prereq lol

diff top isnt really taught often tho, it is on the grad lvl tho

[molten gulch]

here diff top has a pstop, alg, and RA prereq

[grim ore]

gotcha

[vital bane]

because the starting point of diff geo is being able to do analysis on manifolds, and how you do analysis on manifolds is you just do analysis on R^n and translate it to patches of your manifold

without analysis on R^n how would you do it on a manifold

[grim ore]

Gotcha, makes sense tbh

[hearty steppe]

Thanks for the Murray rec on asymptotic analysis. Nobody has other recommendations? This might work. Skimmed the beginning a bit. I don’t think it will be the most rigorous text I approached but I might be able to handle it quite well given my experience so far with math books. I’m making a habit to try to work through more text book problems as necessary and work out things given my struggle with rigor and formalism based expression as opposed to comprehension but if there are easier texts with more broken down wording I’m all ears

I like how Murray starts off so far… not too terse, middle of the road which could work well for me throughout the course of the chapters

Doesn’t seem to handle itself like a Representation theory book that kicks your ass like Harris and Fulton with rigor thrown all over the place

Seems like a lot of people are used to a lot of rigor and not so much explanation of the rigor but hey I guess that’s taste 😆

[stable flicker]

Not much. Won't need more than differential equations

[graceful moon]

You need it for proper diffgeo, but you can avoid it entirely for curves and surfaces

My unis curves and surfaces course doesn’t require or use any analysis

[floral lantern]

Do you want a rep theory book?

[tender cobalt]

really nice book

[tender cobalt]

but shifrin diff geo is just analysis on R^3 not manifolds

i mean learning diff geo of curves and surfaces

[tender cobalt]

Thats based on shifrin diff geo notes right?

[hearty steppe]

I do definitely. One that isn’t just for mathematicians or mathematical physicists 😂

or one that isn’t too mathematically contrived through tons of rigor but not much explanation about it

I’m largely in the cognitive science arena tbh but math is pretty important in terms of exploring different concepts and structures

[sick minnow]

what's the best way to learn mathematics in an enjoyable and engaging manner, with concepts that can be leveraged/appleid in business and finance (price optimization, resource allocation, maximizing profit, etc etc) - would applied mathematics be a good fit?

[floral lantern]

Try Patel etingof’s book

You need to know linear and abstract algebra

But it is very accessible

[hearty steppe]

Yea I spent a bit of time with linear algebra. I might need to spend more time in abstract algebra land

But I found texts for abstract algebra that match my reading comprehension style

[floral lantern]

Yeah try etingof’s book

[hearty steppe]

Thanks mate I’ve tried so many books 😂

Well about half a dozen.. slightly more maybe

But my maturity built up a bit since then

[grim ore]

yeah, since i go to uga, most of the courses funny enough were modelled by him

Its also the reason why we do rings and fields first instead of groups

(Thats the explanation i got from word of mouth, idk how true this is, but his related textbooks are similar to the order of what we learn)

[molten gulch]

I'm sorry WHAT

[hollow shore]

I think Aluffi takes a similar approach in his UG algebra book?

he starts with rings iirc

[molten gulch]

he does rings, then groups

[hollow shore]

would that be considered bad pedagogy?

I honestly went through fine with the Groups -> Rings -> Field approach

I followed Pinter

[molten gulch]

I don't know, I'm only familar with the groups -> rings -> fields approach

[hollow shore]

Although the first algebraic structure I saw was that of a vector space

[molten gulch]

yeah same

[hollow shore]

At this point, I'd just pick up a grad text like Rotman/Aluffi and wing it

They are mostly self-contained anyways

[molten gulch]

Oh this reminds me, Rotman also does Rings before groups in his grad book

[hollow shore]

yes

[slow roost]

it's an approach with some good reasons behind it. Hungerford's undergrad algebra book also does this

[molten gulch]

what are those reasons?

[slow roost]

arguably the most basic and important algebraic structures that so much has been generalized from are Z and Q, and rings more specifically abstractify their features than groups

groups in some sense are really "about" symmetries of things, which is arguably a less elementary idea than basic arithmetic

(Aluffi’s reasoning)

[grim ore]

I used hungerford in my class fyi, but my class was apparently an exception bc all the other profs use shifrin lol

but still, same pedagogy

[slow roost]

I learned groups first from Herstein but I think this approach makes a lot of sense

[grim ore]

hotter take :

Maybe we should move to #math-discussion

[spiral sky]

Also learned groups first but I find constructivism more appealing imo i.e. N/~ to get Z is like a miracle! or group actions but not so formal or rigurous as in most texts though, but just the geometric intuition behind it (similarly for quotient groups) in fact they coincide in many things, I would even say it's the same thing (non trivially)

[torn blade]

any pure learning PDEs books that are good? i find alot of stuff on PDEs too applied for my liking and sweeping alot of things under the rug like issues of convergence

[floral lantern]

Is this like…cad?

It’s not standard

[floral lantern]

Evans

[remote sparrow]

rustum choksi seems best for undergrads

[dim sierra]

Anyone know a differential equations book where I can quickly learn about convergence theorems? Just stuff like when we can say a sequence converges in C^1 (or however you’d say this)

[foggy quest]

what is a specific example of such a theorem?

[foggy quest]

books by Folland, Taylor, Evans are standard

[dim sierra]

f_n -> f, f_n’ -> g (both of these pointwise), then f’ = g

or uniform boundedness of derivatives implying the limit is C^1 (or something along those lines)

[torn blade]

i rmb this being in Abbott

i cant rmb if ive seen the other one before

[obsidian seal]

yeah but ik nothing so that means finishing precalc on my own

but i'm not complaining this will do nothing but good

[glad prairie]

this is not quite true, consider 1/n sin(nx) for |x| < pi/(2n), 1/n for x >= pi/(2n), -1/n for x <= pi/(2n)

the functions converge to 0 uniformly, the derivatives are cos(nx) on |x| < pi/(2n) and 0 otherwise, and so converge pointwise to the function that's 1 at 0 and 0 otherwise

[dim sierra]

Ok the thing I was reading it from assumed C^infty

Does that make a difference

[glad prairie]

for f' to be g you need fn' converging to g uniformly

i dont think so

[dim sierra]

oh wait it literally doesn’t here I’m stupid

I can’t read

[glad prairie]

i think you can smoothen this example out, its just annoying to write down

[dim sierra]

https://math.stackexchange.com/questions/4250457/smooth-sequence-of-functions-converging-pointwise-to-a-smooth-function-and-limit wtf is this just nonsense then

[dim sierra]

nvm i can read but also you’re probably right

Anyway do you know a source where I can refer to a lot of these theorems

[glad prairie]

not off the top of my head but i will think

[dim sierra]

this one assumes the limits are C^infty

I can’t read rip

[dim sierra]

this is true tho right

if the convergence is uniform

Sorry I meant to write that you get C^1 convergence or something

[heavy vault]

Do you think Rotman or Hatcher is a better intro for someone who's read part 1 of munkres and a basic algebra book (undergrad hungerford)

[dim sierra]

Rotman is probably more friendly. Hatcher has really nice pictures and intuition tho. Sometimes he’s a bit less rigorous and it can get confusing.

[heavy vault]

Do u think there'd be any benefit to reading both simultaneously

Or one after the other

I'm kinda of the belief u need to read abt a subject twice before u understand it (or at least I do lmao but things are always much clearer on the second time through for me)

[dim sierra]

What you said is very true but I don’t know about reading them both. I think Rotman has a bunch of weird notation and it might get a bit confusing (this is a minor thing ofc). I think just reading Hatcher and re-reading it or consulting other books like Bredon (or Rotman) and whatnot is good

[heavy vault]

Hm ok

So prolly start with Hatcher?

[dim sierra]

Yeah that’s what I’d recommend but a few things: don’t be discouraged if chapter 0 is very hard, it’s harder than the remaining chapters

And also don’t feel stupid if you feel very challenged (which will definitely happen with Hatcher): algebraic topology is just a hard subject and your first pass on it won’t be smooth

[heavy vault]

I have a friend who's a lot smarter than me who says Hatcher is like insanely hard for him so im thinking maybe like something a little more gentle first

[dim sierra]

Go for Rotman then yeah

Just personally speaking tho I haven’t found Hatcher too much harder than the other stuff I’ve tried learning from and his pictures are very beautiful

[heavy vault]

Rotman it is 👍

I might read topological manifolds by Lee for a second time of the point set stuff

[dim sierra]

That book is also quite good, the later chapters are on algebraic topology too

And he does the classification of surfaces

[heavy vault]

Oo Alr I'll read that then Rotman ig

[dim pendant]

Most important thing to do is to keep in mind a few different sources and to move between them as desired

You generally don't want to read a book from cover to cover once you get through undergraduate

[urban heron]

Anyone here finds out the Allen Hatcher's "Vector Bundle and K-theory" is almost unreadable?

[spring epoch]

hey guys

[urban heron]

I know this is typical Hatcher's writing style, wordy description without a diagram... but in in "Algebraic Topology", he assumes the readers have the minimum point-set topology and group theory only

However, in VB, he assumes you're already completely familiar with everything about vector bundles and algebraic topology. It seems like he's deliberately making the content more difficult to understand, and his explanations are often jumpy.

[royal scaffold]

how is life

[vital bane]

I'm doing this section right now in Abbott!

[torn blade]

i dont remember what the exact theorem is is that bad lol

[vital bane]

6.3.3

for the general version

and 6.3.1 is the first version of the theorem

"Differentiable Limit Theorem"

[vital bane]

as ryc said this is not true, but what is true is that is f_n --> f pointwise and f_n' --> g uniformly then f' = g

in fact assuming pointwise convergence for f_n is too strong of a condition, all you need to assume is f_n converges at a single point in the domain x_0, then you can prove f_n converges uniformly due to the uniform convergence of the sequence of derivatives of f_n i.e (f_n')

[spiral spear]

Is there any books like basic mathematics or algebra by serge lang

[dim sierra]

ye I’d just read the stack exchange post totally wrong

But jeez we need so many hypotheses lol

[dim sierra]

yo what’s up

Let’s talk in DMs

[vital bane]

it's just two

1. uniform convergence of f_n'
2. f_n should converge at at least a single point in the domain

[dim sierra]

uniform convergence of f_n’ is a lot

[vital bane]

perhaps

[heavy vault]

Can anybody comment on proof theory by takeuti

In terms of quality and prerequisites and such

[rigid trail]

Extremely good

[rigid trail]

No prerequisites needed strictly speaking. Just some mathematical maturity

It isn't an easy book, at least for me

but I think it has at least some insights for everyone

[heavy vault]

Do you think it's at a level where like an average undergrad with basic topology and algebra would benefit from it

[remote sparrow]

is there a reason why you want to start with proof theory when you haven't mentioned any other logic background?

[heavy vault]

Idk it sounded fun

It might help me to read a logic textbook first

[fresh skiff]

Is it true, D&F and Hungerford algebra are of the same level?

Like both have almost the same material

[gray gazelle]

Hey I want to touch Evans PDEs

Ive taken a course on ODEs mostly thru Strogatz nonlinear book, also took standard ug classes like analysis

Is that enough background?

Im assuming that it is because appendix covers a lot

[remote sparrow]

you might be able to read the chapters on linear pdes but that's about it

i think multivariable analysis is also required for those initial chapters

you need to know functional analysis later

try this book instead: https://bookstore.ams.org/amstext-54/

[gray gazelle]

I mean I have that i think

But its iffy

Did stuff like ift and thats all I remember tbh its been a long while

Ill give this a read

[slow roost]

they're pretty similar overall. The first four parts of D&F (on groups, rings, modules, and fields+galois theory) all have similar coverage in Hungerford. The fifth part, on commutative algebra and algebraic geometry, has some overlap with Hungerford and some of its own stuff (mainly ch.17 on homological algebra and group cohomology is only in D&F). The final section (representation theory of finite groups) is only in D&F.

Hungerford has a more thorough introductory chapter (logic, sets, axiom of choice & zorn's lemma, cardinal numbers, etc.), and some things about the structure of rings toward the end of the book that aren't covered in D&F.

I think they're at a similar challenge level, but D&F is almost twice as long (932 pages vs. Hungerford's 502), and the main reason for that is it's wordier, which some people like about it and some don't

[heavy vault]

wait can you expand on this do u think not knowing logic well will make this book unfun

i mean i only know like super basic stuff but from the amazon preview it didnt look like takeuti assumed a bunch of previous logic knowledge

will i fall into like a "high school category theorist" adjacent type pitfall

[remote sparrow]

proof theory, by nature, necessitates pedantry and very close attention to detail, moreso than typical mathematics fields. it'd be hard to appreciate all the technical considerations made without situating the material in a broader context, especially the interplay of syntax (roughly corresponding to proofs) and semantics (roughly corresponding to model theory) in logic.

[heavy vault]

ive just been looking for something on methods to tell us that proofs are actually correct in formal logic cause i think that sounds rly cool and important but do u think ill get too bogged down by the level of detail rn

or just like the study of proofs as their own mathematical objects

[remote sparrow]

#book-recommendations message

https://www.logicmatters.net/tyl/

[heavy vault]

will these actually tell me like whats happening with lambda calculus proof verifiers or is it like truth table hell

[remote sparrow]

#book-recommendations message

[heavy vault]

this looks helpful ty

[remote sparrow]

if you're curious, you can read about type theory and its relationship to proofs. usually those are a bit more accessible. people seem to like nederpelt/geuvers around here.

https://www.amazon.com/Type-Theory-Formal-Proof-Introduction/dp/110703650X

[heavy vault]

hmm ok

[remote sparrow]

https://softwarefoundations.cis.upenn.edu/

you can also look here

[heavy vault]

i would say im more interested in this on like a pure mathematical / philosophical level and not as much in terms of comp sci or proof verifiers but i understand the two r like inseparable at some point

thoughts on proofs and types girard

[remote sparrow]

one of the original inspirations for proof theory is the idea that proofs are something that can be mechanically checked or reduced to pure calculation, without regard to the meaning of the words used in them. a computer is a natural way to realize this (vague) dream.

[remote sparrow]

truth tables are semantic objects, not syntactic ones

[remote sparrow]

there aren't many exercises, but people here seem to like it. it seems like a pretty good general overview that's not too difficult to follow.

[heavy vault]

hm ok ig i'll start there

[remote sparrow]

https://www.amazon.com/Introduction-Proof-Theory-Normalization-Cut-Elimination/dp/019289594X

[heavy vault]

it's always hard when you get into a new topic and there's no like industry standard textbook (i.e. rudin for analysis)

[remote sparrow]

if you're still curious, this book is more detailed (perhaps too detailed in some parts as the authors assume very little to no mathematical background)

and there's more philosophical motivation

[heavy vault]

what does mathematical background mean in this context

i mean ig the more mathematics you do the more proofs youve seen but like presumably knowing how to diagonalize a matrix is useless in this context

sour drop how did u first get into logic and all this cause by ur roles id guess thats like the focus of ur postgrad stuff?

[remote sparrow]

it's very much written for the philosophy student that has minimal mathematical experience. they might have had an intro to proofs class at best, although they've probably had a class in symbolic logic and first-order logic with some natural deduction system.

it goes out of its way to explain what proofs by induction are

[remote sparrow]

i'm just in a masters program that doesn't offer logic

i just thought logic was cool so i started reading about it, and i eventually did a directed study with a professor who himself has done some work in logic

[heavy vault]

nice nice

im kinda worried that i end up finding a professor i like and pursuing their field and then 10 years later i realize i actually hate it yk

so im tryna get like a little tasting of what most things are

but i do think it's much easier to stay motivated in a field if it you think it's philosophically valuable / the questions and methods are important and elegant

I'll read the mancosu book having a textbook be too a little below your level isnt the worst thing in the world

ok im off to sleep farewell ty for advice 🙏

ok sorry to bother you further but could you expand a bit on the pros and cons of these books?

[night granite]

Anyone know any useful textbooks for introduction to mathematical Methods and Models

[fresh skiff]

holy yeah
so wouldn't it be good if i use hungerford as reference along with D&F

[heady ember]

Yes, it quenches your algebraic hunger

Why read the introductory chapter of Hungerford when you can read Jech's third millenium edition

[dusky finch]

A good precalc book is A Graphical Approach to Algebra and Trigonometry. It gives you all the tools you need to get start with Calculus.

[fresh skiff]

Hell NO
Big jech is massive heavy book

[odd sentinel]

I just graduated with a bachelor’s in math, and I’m kinda regretting not taking differential equations. Does anyone have any recommendations on rigorous differential equations books for ppl who wanna self-study?

[hollow shore]

https://link.springer.com/book/10.1007/978-3-319-45261-6

[odd sentinel]

Thank you groundbreaking electronic DJ Aphex Twin!

[heady ember]

Arnold ODEs is a common rec

For PDEs, I have heard Evans' and Taylor's books thrown around here.

[fresh skiff]

Evans' book need MT

[heady ember]

Yeah

PDEs tend to have many prereqs

Taylor's books also assume DG and other stuff

[fresh skiff]

DG?

[merry sphinx]

It does fa and dg in the appendix

[fresh skiff]

Hell

[remote sparrow]

differential geometry

deez gonads

[fresh skiff]

yea, but i was wondering why DG in pdes

[remote sparrow]

probably because you can interpret solutions geometrically

[fresh skiff]

oh

makes sense

[naive lava]

all classical mechancs pde's are actually provide more insight when looked at from a symplectic manifold pov

[fresh skiff]

i see

[vital bane]

apparently for the first 5 chapters you don't need more than some basic analysis and vector calculus

[vital bane]

Differential equations on manifolds (I bet)

[vital bane]

Jet bundles when? (for lagrangian mech)

[foggy quest]

https://mtaylor.web.unc.edu/notes/math-524-second-semester-ode/ is good.

[naive lava]

hear me out

we use alg top to categorize mechanical models

then find general properties of unrelated systems

i should ask to my friend about this

he studies dynamical systems

[vital bane]

alg top friend?

oh nice

everyone should have a dynamical systems friend

[naive lava]

for when you just don't want to solve that DE

[hollow peak]

Have you heard of the Arnol'd conjecture?

That's a fun dynamical statement in terms of the algebraic topology of your symplectic manifold

[naive lava]

no, but i checked it out rn

seems cool asf

[wispy moss]

good book for graph theory and discrete mathematics ?

[molten gulch]

rosen's discrete maths

[elder stratus]

Bollobas - Modern Graph Theory

[wispy moss]

thx again

[wispy moss]

you sure ? I am getting a variety of books for graph theory , dont know which to chose .
options include : Introduction to Graph Theory – Douglas B. West & "Graph Theory" by Reinhard Diestelor just graph section of CLRS is enough ??

[molten gulch]

Diestel is good, assumes a little bit of linear algebra at points as it uses adjacency matrices in places, assumes some mathematical maturity and ability to do proofs, goes in-depth, whereas the graphs section of CLRS probably contains graph algos and most discrete maths books only contain a short chapter on graphs. Bollobas is also quite good and AFAIK in a similar regard in the sense that it covers graph theory

However both texts are written with very different goals so the text you eventuall should settle on depends on what you want to do in graph theory

[wispy moss]

hmm I will probably go with Diestel then as I am familiar with linear algebra , thanks a lot mate

[molten gulch]

one sec, lemme get the prefaces and contents of all of them

Diestel

bollobas

[elder stratus]

Diestel and Bollobas focus on very different topics although they are apparently have similar titles. Bollobas is written towards a view with extremal graph theory (think Erdos), whereas Diestel is biased towards classification type problems (like the graph minor problem or the strong perfect graph theorem)

I personally like extremal graph theory so that’s why I recommend Bollobas

admittedly there are parts of Bollobas you might want to skip on a first reading like ch 2

but he mentions this in the preface

[molten gulch]

yep, CLRS is just algos

as is to be expected

[wispy moss]

I have to do CLRS anyways for my course but i think i personally more interested topics covered in Diestel , but perhaps i may read Bollobas second .

[elder stratus]

if you are looking for a more approachable book I reccomend Bona - A walk through combinatorics

it might be my favorite combinatorics book of all time

[dim pendant]

Definitely grab a copy of 2 or 3 of these options and just bounce between them as necessary

[molten gulch]

Is your course, perchance, a course on algorithm analysis?

If so, you don't particularly need a full graph theory text

[wispy moss]

DSA and DAA

[wispy moss]

learning for interest not particularly for course

[molten gulch]

I see

[wispy moss]

@elder stratus thx for the help

[elder stratus]

np

[heavy vault]

Can i get some recs for an intro to logic at like a mid undergrad level

Preferably with some cool stuff and not just the and not or stuff that's everywhere

And good exercises

[heavy vault]

specifically can i hear comparisons of enderton vs mendelson

if im js tryna get into this stuff do you think i'd be best off starting with a set theory book like halmos or a logic book

i think i have all the basic knowledge in books like "how to prove it"

or can i jump straight into something like proofs and types by girard

[remote sparrow]

#book-recommendations message

[remote sparrow]

set theory by halmos isn't set theory as practiced by set theorists

[heavy vault]

Ty

I think I'll read the friendly introduction

[grim ore]

set theory by halmos isn't set theory as practiced by set theorists but set theory as practiced by halmos

[heavy vault]

Damn

[real stratus]

can you go from stewart calculus to rudin?

assuming you know how to prove things & do proofs?

[grim ore]

Yeah

[north summit]

Why is munkres so widely used? I just started reading it from the second chapter and i can say is poorly written

[grim ore]

yeah tbh cant lie i agree

[naive lava]

Prolly cos there is no better alternative with similar exposure

Maybe except Willard but that's harder

[foggy gorge]

I'd like some recommendations on trigonometry for calculus. I want a book that explain how stuff there works and such, like what is a secant line, what is a tangent line etc

[grim ore]

You would have to look for precalculus books, which contain such topics, cant recommend any myself, but helps narrow your search

Maybe OpenStax has a precalc text as well?

[molten gulch]

out of the books you've read, have you found a topology book you enjoyed?

[grim ore]

I forgot who it was that recommended me around a month or two ago, either neamsis or spamakin, but they put me onto Topology and Groupoids and its been my favourite so far

It doesnt have exposition tho until the AT section tbf

@gray gazelle

Thats who, and thank you so much for introducing this text

[foggy gorge]

I've read that one along side to Stewart's precalculus

But I didn't grasp well

[grim ore]

What did you not grasp about trignometric concepts

Maybe there is a foundation that isnt met, and if thats the case we can look backwards

[foggy gorge]

Like when using the trigonometric functions to find some angle, how do they help to find that angle? When inputting some angle for Sin, let's say 2pi, how does it output 1

Things like that

[grim ore]

Idk, the unit circle does seem like a normal precalc concept iirc, maybe someone can recommend something I am not aware of, if not have you looked into algebra texts?

[foggy gorge]

Sin is like the y axis while cos is the x axis, what lines are Tangent, Secant, Cosecant in the trigonometric circle?

This is another doubt I have

Maybe I skipped them on these books but I don't remember about it teaching this stuff

[grim ore]

The tangent line is defined as sin/cos, and so we are purely defining these points accordingly?

The trig circle is used to associate the angles with these values

We can get trig functions and their mappings based on the way we look at a trig circle, which is the intuition if that is what you are asking?

Im going to let someone else recommend a precalc text, but lets move to #math-discussion if you want to continue talking about it

[grim ore]

https://openstax.org/books/precalculus-2e/pages/1-introduction-to-functions

@foggy gorge

[foggy gorge]

I have it already yk

I've said I read Stewart's and that one

[gray gazelle]

Want to learn about stats computing

Any book recommendations?

Assuming wasserman stats background

[real stratus]

read chapter 5 of stewart precalculus again

it's clearly explained

[gray gazelle]

You need help w precalc?

I have some time so I am willing to explain some concepts so feel free to dm me questions

[gray gazelle]

You’re welcome!

[remote sparrow]

https://discord.gg/QkpCHSUZ

you can ask here too, might be better off

[fervent shore]

Hi who knows basic mathematics by serge lang?

I was wondering if this playlist is good enough like if I only watch this would i be ready for calculus?: https://youtube.com/playlist?list=PLMcpDl1Pr-viA25VUkHNmcUkWx9usPgyb&si=M6VXyBaOA9NnhQwo

[mortal ore]

<@&268886789983436800>

[cunning elk]

least obvious scam

[naive lava]

sure, but make sure to find some excersizes and do them

[fervent shore]

?

[fervent shore]

Its a YouTube link

[fervent shore]

Okok

So u think’ it’s good idea to follow this playlist? @naive lava

[mortal ore]

someone else posted a scam, dont worry

[cunning elk]

my message was in reference to a now deleted message

you’re ok

[fervent shore]

Okok

[fervent shore]

Oh alr

[naive lava]

idk, i haven't read much of lang's books

they are known for being terse but good

[remote sparrow]

@vital bane

[brittle citrus]

Is anyone into AI/ML? If yes, what mathematics do you think is most relevant for it? I've heard of linear algebra, probability & statistics, calculus, and discrete mathematics. Book recommendations?

Also, any book recommendations for actual AI/ML books?

I'm a freshman btw.

[remote sparrow]

https://discord.gg/QkpCHSUZ

you may also have more luck specifically for AI/ML books here

[near jewel]

Calculus, linear algebra and statistics are usually what you need. You can also find the prerequisites in a ML book.

[torn blade]

holy fuck lets fucking gooooo

[south scarab]

not really a book reccomendstion but anyone know a video that covers mvc in depth

couldn't find anything

[vital bane]

https://tenor.com/view/charlie-woooo-yeah-baby-gif-24480925

[karmic wave]

is there any source i can use to learn set theory and logic from a 9.th grade level to basicly university level, im feeling bored

[merry sphinx]

holy shit

[vital bane]

ikr

[foggy gorge]

It has shown for some specific angles, like pi/3. pi/4, pi/6. But for other angles like 2.2, 0.98, it told us to use a calculator.

[timber holly]

How to prove it: A structured approach by Daniel J Velleman is my favorite book

[foggy gorge]

Im reading that one

Alongside the Discrete Mathematics with Applications by Susan

[gray gazelle]

what book you recomend i (finisched primary school and i going to high school)

?

[vagrant cipher]

bro's skipping middle school

[molten gulch]

We've completed courses in single and multivariable calculus and computational linear algebra (up to diagoanlization and SVD but I am not very good at those two especially), slowly working through abbott's real analysis (mid way through chapter 2 now), friedberg's linear alg (skipped some exercises I need to redo but material wise I read up to and took notes up to chapter 5), and artin's algebra (barely started this yet)

We want to learn ODE's; we've heard that the actual proofs for a lot of why ODE theory works requires a solid foundation in analysis, which we don't have much of yet; so I wonder, should we hold off a bit or just go read something like a standard ODE's text?

I doubt we'll have a chance to take an ODE's course at uni just due to scheduling conflicts

[grim ore]

in my uni we don’t need analysis for ODEs and use Strogatz textbook

If you were to go into ODEs or PDEs at a grad level for more intuition and understanding then analysis is required

[grim ore]

i’ve also heard this is a standard text

[foggy quest]

read a good ODE text, like https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2020/10/diffeq.pdf, or do intro analysis and you'll study ode in a several variable analysis course.

[molten gulch]

tysm

[molten gulch]

ty I'll look into it :)

both your suggestions seem like things I should look into

[remote sparrow]

most universities don't have an ODE class that's proof-based

they do generally have a problem-solving course based mostly on boyce and diprima or some similar text

usually not rigorous

these are very standard topics

thankfully i never had to learn sturm-liouville and my second semester was based on strogatz

there's a lot i guess

generally only the first semester is required

[trim tapir]

What book should I get for calculus

[tranquil breach]

I second that!

[near jewel]

Thomas or Adams (or Stewart). Choose from one of those, and you're ready to go.

[tranquil breach]

who do you think is best?

[timber holly]

Such a great book to get proofing started

[fresh skiff]

Cool i did first 3 chapters

[waxen sandal]

Stewart is probably the most used Calculus book in the US and Canada if that counts for anything

I've heard Thomas is used a lot in India and other parts of the eastern world

I've also heard that older editions of Thomas are harder than the newer ones so keep that in mind if you go with Thomas

[vital bane]

absolutely criminal review of Abbott @torn blade look at this madness

that fits perfectly for Abbott

fake Abbott review...

[torn blade]

definitely does not do it justice, maybe they haven’t read it 😭

[fast portal]

The review very clearly vibes that they have only skimmed it

[random estuary]

Which book would someone who wants to learn linear algebra get?

[jovial parrot]

Wait why?

Isn’t there calc assumed? I remember the discussion sections and stuff they always had calc

[fast portal]

I would recommend friedberg for someone in engineering, lay is also equally good. People who are in mathematics seem to favor the duo of "Linear Algebra done right" and "Linear algebra done wrong", get the 4th edition of former one.

[random estuary]

I'll check it out thank you!

[vital bane]

sure

but that's like reviewing Shakespeare by saying "It has english words "

or reviewing Mozart by saying "there are musical notes in it "

[timber holly]

I use steward to tutor others imo its better but pick your pick

[merry sphinx]

ngl didnt know about schroeder analysis

seems to cover a ton of stuff

[jovial parrot]

I don’t understand

I’m not reviewing Abbott but also I do not think it is a good idea to try and do Abbott without any calc at all

Like atleast a little

[vital bane]

calculus was not the point

I'm saying it's a disingeniuous review

which overlooks all the good points of Abbott

an analysis book needing calculus is the norm...

except for a few exceptions

[sage python]

I mean I did preface by saying "People seem to like Abbott"

It's as much a guide as a review

Don't start here if you don't know what a derivative is, but otherwise it's one of the more gentle books. And people seem to like it

The alternative is to not include it at all lol

And only suggest the books I've read personally

In which case I'm telling everyone to read Spivak if they're absolute beginners, or either Rudin, Kolmogorov-Fomin, or Sally

[vital bane]

This fits for Abbott as well imo

[sage python]

I didn't wanna restrict to that so I looked over other books + compiled the thoughts I got from people

[vital bane]

that's fine

[torn blade]

the 2 most commonly recommended are Friedberg and Axler, of which i prefer Axler, but either is fine

[sage python]

If it's fine, why'd you call it disingenuous

[vital bane]

Then you might want to consider Bartle as well, that's also pretty good

[sage python]

You're acting like I just shat on it even though the overarching tone was positive

[vital bane]

I was only half serious, I didn't mean it in any negative way towards you, I apologize if you were offended

but anyway

[sage python]

It did not sound half serious lmao

[vital bane]

I used an emoji 😔

[sage python]

Don't take a shot unless you understand what I'm saying

[vital bane]

my main problem is that you've missed out all the selling points of the book

[torn blade]

i think its a decent review. sounds like u just went off what other people said

[merry sphinx]

neam is upset you didnt glaze abbott enough

[vital bane]

it's amazing for beginners, if you don't know any proofs it's the perfect place to stars

and much more

[sage python]

I mean I literally said "People seem to like it" which is approximately all I can say about a book I haven't read lmfao

[vital bane]

I actually have only one problem with the book

[vital bane]

Yea i now realize you haven't read it

[torn blade]

yeah i mean why would you praise a book highly if u havent even read it

[vital bane]

and that's fair

[vital bane]

it doesn't talk much (or at all) about the derivative as a local linear approximation

this one

maybe I should email Abbott asking him to include it in the 3rd edition

[jovial parrot]

Yeah idk what was up with that

I’m glad darq and Zorn and Eric were doing the Rudin reading group or

[merry sphinx]

left as an exercise for the reader to figure out

[stark lion]

Is it still going on

The reading group

[foggy quest]

are you sure? Abbott cover's Taylor's theorem, for which this is a special case

[vital bane]

That's true but I'm saying he should've talked more about the general idea of the derivative of a local linear approximation, that idea is crucial when you want to generalize the idea of a derivative to higher dimensional spaces or even more general spaces

[foggy quest]

His book doesn't cover higher dimensional spaces

[vital bane]

I know but I wasn't talking about higher dimensional spaces, I was elaborating the importance of that view of the derivative

[jovial parrot]

It’s over unfortunately

[stark lion]

I see

Thank you for replying

[dapper root]

It lives on

In your heart

❤️

[vital bane]

sotrue

[jovial parrot]

Fr

[pine quiver]

Happy pi day

[steep lance]

I'm probably taking graduate numerical analysis next semester and I want to read up on it beforehand, anyone have any good recommendations?

[gray jungle]

do you have a syllabus ?

graduate numerical analysis can mean a bunch of things

[steep lance]

Unfortunately not yet, though the course description notes topics about numerical approximations and algorithms, solutions to nonlinear equations and systems, differentiation/integration, initial value problems

I'm assuming that doesn't narrow it down 😔

[near jewel]

What about previous years?

[fresh skiff]

Does apostols calculus 1 and 2 good enough for multivariable calculus?

[barren lantern]

hello, math ppl i need some book references for differential geometry for both Riemannian and non-Riemannian manifolds..regarding GTR
i saw the links above but as i m not familiar with the terminologies used by math ppl so plz help me with these..(i hope a physics prsn will not be treated as a trojan horse in this server{joke}) . i have the basic ideas..i just want to be more rigorous

[tribal crow]

almost certainly

some linear algebra wouldn't be a bad idea too, but I know you already have that so

:p

[vital bane]

No, I wouldn't recommend any analysis book without prior calc knowledge

[vital bane]

You want a rigorous differential geometry book? for reference? For Smooth Manifolds and Riemannian Geometry the books by John M. Lee is pretty good

And by "Non-Riemannian Manifolds" do you mean Pseudo-Riemannian Manifolds? (also called Semi-Riemannian Manifolds). I haven't gone through this book but you can check it out it's "Semi-Riemannian Geometry With Applications To Relativity" by Barrett O'Neill

Usually the mathematically rigorous study of abstract differential geometry (the kind that's used in GR) requires knowledge of Real Analysis, Abstract Linear Algebra and some Point Set Topology, you should make sure you're good at those before seriously studying rigorous DG.

[foggy quest]

check out https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/analmv.pdf and https://link.springer.com/book/10.1007/978-3-031-33859-5\

[vital bane]

ooh Taylor's multivariable analysis notes are nice

thanks

[foggy quest]

the diff geo parts kinda leave out some technical details some places. Lee's book is good to compensate for Taylor's omissions.

[barren lantern]

thanks, guys..i saw the books... precisely what i was kinda looking for🤝

[vital bane]

ye ye it's a nice intro to the subject, after this you can use a more technical book like Lee or Spivak

[remote ginkgo]

have u seen browder

[fresh skiff]

Got it
Thank you Higher !

[sharp brook]

haii does anyone know of a good book to act as a supplement to d&f? my algebra class uses d&f but i have a hard time following it since its so wordy

the class covers all of the first 2 parts on group and ring theory (ch1-9)

[vital bane]

I like the fact that it's so wordy, it's nicer to read

[sharp brook]

i know everyone loves it 😭 its just not working for me for whatever reason

[vital bane]

perhaps it's a problem with prerequisties?

[sharp brook]

it could be, i dont feel very comfortable with the number theory stuff since i havent had any exposure to it before this semester

[vital bane]

regardless you can check out Artin or Gallian for a supplement

Also see: #book-recommendations message Algebra book recommendations

[vital bane]

same

I mean I had a course on Number Theory but I didn't pay attention

[fresh skiff]

Well I am using it as well
Idk but it's fun to work with D&F
(That's another issue i am stuck on some problem of section 1.3 lol)

[sharp brook]

its working fine for me some of the time, but there are a few problem points that are kinda killing me

[sharp brook]

ill check out these tho tytyty

it also might not be entirely about the book being too hard (i dont have a hard time with the math, it just kinda puts me to sleep when i read it 😭)

[fresh skiff]

I think it's fine to not do all exercise problems. I skip some problems (that I can't solve) in the hope that i will cover these later

[tender cobalt]

What's the bare minimum prerequisite for V.I Arnold Mathematical Methods of Classical Mechanics?

In this book we construct the mathematical apparatus of classical
mechanics from the very beginning; thus, the reader is not assumed to have
any previous knowledge beyond standard courses in analysis (differential
and integral calculus, differential equations), geometry (vector spaces,
vectors) and linear algebra (linear operators, quadratic forms).
oh nvm i think i can read it, except idk DEs

[vital bane]

you can check out Simmons for DEs

[tender cobalt]

George F Simmons "Differential Equations with Applications and Historical Notes" ?

@vital bane whoa it has calculus of variations too

[slender cargo]

D&F is great but that first chapter is dense if you have no prior exposure to algebra

[fresh skiff]

I know group like upto some of permutation stuff from Gallian

[slender cargo]

Oh then you'll be perfectly fine

[fresh skiff]

Yay

Idk why i find permutation stuff harder

[slender cargo]

I mean, it is tricky stuff

[fresh skiff]

True

[novel hound]

KConrad's blurbs are a nice supplement to D&F. https://kconrad.math.uconn.edu/blurbs/ I also found Nathan Kaplan's (from UCI) youtube videos on D&F very useful. He also references KConrad's notes where he finds them most useful, so you can go by him for selecting the blurbs as well. https://www.math.uci.edu/~nckaplan/graduate_algebra.html

[vital bane]

oh yea I forgot about Keith Conrads expository articles they're nice

I also forgot they're mostly about algebra

[vital bane]

I wouldn't say it's necessarily dense, but D&F does require some mathemtaical maturity

[remote sparrow]

https://www.youtube.com/watch?v=JzId_0-lA4M

[tender cobalt]

I love this channel!

[remote sparrow]

@mystic orbit how's your journey with billingsley so far?

[stark lion]

Ohh I love this guy

I always watch his video

[mystic orbit]

oh I actually haven't touched that book in a bit

there are a few sections I still wanna do but I did the majority of what I was interested in

loved it. the exposition is very clear, the exercises are super satisfying to do

would recommend

[static nova]

Could anyone recommend book for NMTC which is good for a class 10 child?

[static nova]

National Mathematics Talent Contest

[lost arch]

what's the best book on proofs (and some basic logic)?

and the best book on real analysis to complement the three books of Analysis by Amann and Escher? I've been reading it for some time and i feel that occasionally i better have something else to read on the same topic, so that i have better knowledge

[remote sparrow]

<@&268886789983436800>

[mellow wren]

<@&268886789983436800>

[sage python]

Damn derivada won

[viral gorge]

At an introductory level both The Book of Proof and How to prove it are okay but might be too "hand-holdy"

The one I recommend is A Transition to Advanced Mathematics by Smith, Eggen, and St. Andre

[trail hemlock]

unc is reading abt probability

wowzers

[lost arch]

thanks

[lost arch]

but what about the analysis request? i am russian, so promarily used to look at Zorich I, II, still skimming through the book on occasion. Also, for some reason there is no translation of Laurent Schwartz's book in two tomes called Analysis I, II. This book is of pure excellence, unmatched in terms of completeness of material coverage. Was trying to find something like that.

You may ask why i dont stick with the books mentioned above. Zorich sometimes doesn't encompass some of the topics covered in Amann-Escher, and Schwartz one feels like a professional mathematique encyclopaedia, sometimes too rigorous to understand a concept.

Heard some things on Pugh and Rudin, deduced they got some unclarity. Still searching for the perfect match for A-E 3 tomes.

Also, i have a book of Gorodentsev Algebra, which was translated and afterwards printed in Springer. Amazing book, written on a high level, perfectly modern. But the vibe is that of Schwartz's Analysis, encyclopaedia kind. Is there any comparable books on algebra of this level? I mean, i have Ernest Vinberg's Algebra and Kostrikin's three books, but they all are of differeng material coverage. Wanted something as big as Gorodentsev, but more detailed. Don't know of any books in english on algebra, unfortunately.

[viral gorge]

I cannot comment at all on the algebra books you mentioned, but if I remember correctly (since I didn't read everything so take this with a grain of salt) Amann and Escher did a good job covering the basics of analysis. Topics that are related but aren't key for basic understanding (say manifolds in book 2) are moreso there to gain some familiarity and if you are interested there are books that delve deeper into those topics.

Amann and Escher, while very thorough, simply can't cover everything. Beyond this I can't comment much.

Although, I will say that I thought that despite being skinner than the A&E series, Zorich's books do a good job.

[naive lava]

my friends all tell me that it's a dry book

[foggy quest]

https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/ for analysis

[static nova]

Could anyone recommend book for NMTC (National Mathematics Talent Contest).

[sick minnow]

what's a good resource for multivariate calculus

[jovial parrot]

I’m use Fleming

[brisk rapids]

I found it painfully slow. Like I'm sure there are other books which build the same amount of intuition or more without going on about the same thing for a whole chapter.

[trail hemlock]

folland has a good mvc book

[remote sparrow]

have you printed any books from lulu lately?

also you should send a screenshot of your book(s)

[trail hemlock]

i have not sadly

the last book i bought was either rotman's alg topo from springer (there was a deal) or bass's RA for grad students, both of which were cheaper retail

[trail hemlock]

wdym

[remote sparrow]

oh i thought you had printed lee's ITM

[remote sparrow]

bass stopped uploading the latest edition for print several years ago

[trail hemlock]

i do

[remote sparrow]

three versions have elapsed since

[trail hemlock]

silly bass 💔

[remote sparrow]

did you ever share a picture of it in, say, #point-set-topology

[remote sparrow]

well i printed a 2022 version last year (there's a 2024 version now)

[trail hemlock]

i think? cant remember so ill post it again

[remote sparrow]

turned out pretty well

[trail hemlock]

mine jus says "second edition" lol

[remote sparrow]

lol

[trail hemlock]

but man bass is an amazing book he does a whole section on pst and then probability , harmonic functions, sobolev space, spectral theory

like damn

[remote sparrow]

waiting on blackbeard probability arc

[trail hemlock]

i’m a few chapters until probability in cohn

i’m waiting on the geometric measure theory arc tbh

[remote sparrow]

maybe durrett arc

it's free online

although that's technically a draft

i noticed some differences between the final print version and the online draft

though they're mostly the same

[trail hemlock]

oh this looks nice

[remote sparrow]

billingsley is nice too

as are ash and gut

but not free

[trail hemlock]

i also wanna do this book abt sobolev space after cohn

ion think anything after that is feasible before uni tho tbh

[static nova]

please telllllll anyone

[naive lava]

andressicu has nice problem solving books

i'd reccomend

[lost arch]

thank you

[covert mauve]

this sounds kind of silly, but are there any books that build geometry from a set theory perspective? (ie: using pure set theory to build all of geometry or atleast something close to it)

[tender cobalt]

if one finishes artin algebra do they still need to read a linear algebra book ?

[tender cobalt]

Ohh

[foggy gorge]

Id try Axiomatic geometry

[fresh skiff]

do you mean Euclidean geometry?

[gray jungle]

yes

[brisk rapids]

I mean some people like it, I personally found it to be that way.

I mean just know the material and do the exercises I guess.

[foggy gorge]

There is a book called Axiomatic Geometry, which approaches both Euclidean and non Euclidean geometry. I haven't read it yet though, because it seems to use calculus notions for some parts

[fresh skiff]

oh dont you know caluclus?

[surreal bay]

hello : )
i’ve been looking for algebra 2 book recommendations for a while now but haven’t seem to found any
what do you all recommend?

[vital bane]

Bro is eating GOOD tonight!

[naive lava]

<@&268886789983436800>

[molten gulch]

<@&268886789983436800>

[covert mauve]

axiomatic geometry is an branch though, what author?

[foggy gorge]

John M Lee

[lost arch]

is it only used for studying how to write proofs? or is it an introduction to real analysis and abstract algebra?

[viral gorge]

They devote the first chapter to logic and proofs where they cover the most common types of proofs. The rest of the book is dedicated to other topics (set theory, relations, functions, cardinality and the very basics of analysis and groups) where they showcase standard ways of tackling problems with plentiful examples and exercises. If you are looking for more variety in proofs I heard that Conjecture and Proof by Laczkovich is good. Check your DMs.

@lost arch

[pale scarab]

I'm looking for any good books to help prepare for the math subject gre. Are the schaum's books decent for this?

I have been out of college for a bit but I figure it should come back quick with reps.

[jagged zealot]

Hello friends. I took two weeks off between jobs and promptly fell ill. My plans to do some Serious Self Study are thus right out. Can anyone suggest something easy and interesting in pop math history? I liked Fermat's Enigma eh

[pale scarab]

Infinite powers by Steven strogatz is a great pop history math book

[slow roost]

Donal O'Shea - The Poincaré Conjecture is very good

[lost arch]

hey guys, another question. I'm looking for a good, informative, clear and covering all the main topics of the subject course in linear algebra. Heard good things about 'Linear Algebra' by Friedberg, but people seem to be having a hard time going through it. Any other books of this level? Preferably, again, clear

[weary sable]

I'm looking for analysis of zero-sum-utility auctions, but auction theory texts I've looked at don't cover zero-sum anything and game theory texts don't explore auction-like zero-sum games.

I'm especially curious about dominant and equilibrium bidding strategies for sealed bid 1st & 2nd price actions of single items, but would still like anything on zero-sum auctions.

It seems strangely under explored. Auctions in zero-sum situations exist, like board games.

[slow roost]

FIS is clear and well regarded

[lost arch]

i do not doubt it, though some find it to be not that clear

that's why i asked for a book similar to this

gonna use Friedberg's anyway but wanted to have a complement to the book so whenever i get lost i can look up the thing in another one

[slow roost]

gotcha, that’s a good plan

[still panther]

I like greub

[lost arch]

for a first reading?

well, i already know something of groups, rings, fields and polynomials from the Amann-Escher books, but only in context of analysis

i guess it still counts a first reading then

[still panther]

¯_(ツ)_/¯

i like to put things into a wider mathematical context right away and greub does a better job at that than FIS or Hoffman&Kunze (which is understandable given the respective target audiences)

[lost arch]

that seems the book would fit my needs

thank you!

[last cipher]

thoughts on david c lay's linear algebra with applications?

Speaking at an elementary level

[molten gulch]

It's a book on computational linear algebra, we thought it was fine but far prefer treatments with more theory such as that by friedberg or axler; though lay should be fine if you want to learn the basics of matrix algebra and such

[last cipher]

I see

[last cipher]

yeah I just want a beginner book with applications then later on move into theory

so i think i'll get it then get a book with more theory

[keen orbit]

anyone has some good recommendations for books on multivariable real analysis ?

[foggy quest]

The book here: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/. Also "Advanced Calculus" by G. Folland.

[naive lava]

https://tenor.com/view/fire-writing-gif-2088247993237804628

folland writing a book about literally anything

that mf has books ranging from advanced calc to qft

[upper plover]

Any recommendation to learn Number Theory alone, shit ton of exercises and all that good stuff?

You know, knock your hair off kind of stuff but still an introduction.

[keen orbit]

what is the difference between this book of folland and his "real analysis"

[keen orbit]

is this for undergraduate real analysis and the one i am talking about for functional analysis or something like that ?

[pliant stream]

they dont cover the same topics

[keen orbit]

i see tysm

[keen orbit]

tysm for the recommendations

have a great time

[sage python]

Real analysis is much more fancy, does stuff like measure theory etc

[keen orbit]

but isnt measured theory usually done in real analysis for multivariable functions because of lebesgue integration ?

[sage python]

It depends. A lot of these multivariable analysis books happen before measure theory

So they just stick to Riemann integration on R^n etc

For the measure theory books you don't necessarily need that much background in multi (you'll prove Fubini for measures differently than for Riemann)

But yeah the advanced calculus book is basically honors multivariable calculus for second year undergrad students (or first years who did calculus in high school)

While "Real Analysis" is a first year grad school qualifying exam type of book

[keen orbit]

but is there a difference between the assumed background for measure theory books and the ones without it ?

to my knowledge , i need single variable analysis and linear algebra for multivariable analysis

are there more prerequisites if the book deals with measure theory ?

or is this same background sufficient

[dapper root]

Folland?

[sage python]

Yeah

[dapper root]

Nah dude advanced calculus is straight up analysis

[sage python]

When I looked at it it seemed like the kind of material you'd have in "honors multi/with proofs"

[dapper root]

Hell no

The first chapter is like straight up analysis point set topology

That book ran me my hands freshman year

Like 20 hours of hw a week

[sage python]

@dapper root I mean my point is that the honors multi feels like it has that flow

[jagged zealot]

"Zero sun" means the utility adds to 0? Or something else? I am not super knowledgable here, but if I can understand what you mean, I'll forward the question to my finance friends, seems like they might know

[weary sable]

Yes. Losers experience the winner's utility divided by 1-n such that total utility across all players sums to zero.

[weary sable]

In a 3 bidder scenario, say the winner values the item at v and ends up paying p. Winner gets v-p utility and each of the 2 losers get (v-p)/-2 utility.

[weary sable]

And thanks!

[remote basin]

A Tour of the Calculus by David Berlinski is quite intuitive, very descriptive, and highly informational

[abstract copper]

Any recs for computability with register machines?

[glacial mica]

what would you recomend for a first abstract algevra textbook

for someone who has done stwart calc and linear algebra done right

[mortal ore]

i enjoyed Gallian, though it was weak with group actions

[glacial mica]

thanks

for follow up what would you recomend because ive seen a lot of people you included saying it has some holes

[mortal ore]

you could switch to dummit and foote once ur satisfied with gallian i suppose

[glacial mica]

should I finish gallian then go to dummit or is their a good switching spot

[mortal ore]

you could read up to being finished with fields

the extra topics are cool but unnecessary

so after that u can switch

[glacial mica]

thanks for the help

[floral lantern]

If you have already read linear algebra d&f is fine (but dry)

Artin would be a little redundant since you’ve Alr done Linalg

[vague granite]

gyatt

[floral lantern]

Maybe aluffi’s undergrad book?

[floral lantern]

Bro

💀

Primescord is so done for

[vague granite]

im getting kicked out dont sweat it

icl ts pmo

[floral lantern]

Watch me get kicked w you

💀

[vague granite]

lmao

😭

[floral lantern]

I’m fried

[vague granite]

its wtv i tried hard

[floral lantern]

You’ll be fine bro

Dotted got “this paper is unsatisfactory as is”

Or some shit

[vague granite]

too late to worry now ¯_(ツ)_/¯

[remote sparrow]

https://www.amazon.com/Computability-Introduction-Recursive-Function-Theory/dp/0521294657

[abstract copper]

Neat! Thanks

[hasty sluice]

Should I try to proof theorems myself when reading math books?

[wispy bison]

Yes

[remote sparrow]

<@&268886789983436800>

[tender cobalt]

Shifrin's "Multivariable Mathematics"

[vital bane]

you used folland's "advanced calculus"?

[dapper root]

Yup

[vital bane]

during 1st year of undergrad? based

[gray jungle]

Follands advanced calculus is really good for MVC, thats along my freshman course in it

right choice for math students

I would have linked my profs lectures if they werent in arabic, i had a really good experience in MVC

altho i wonder if he kept them on youtube

our department is really strong in these courses, my banach space differentiability course was also one of the best classes i had.

the profs clearly enjoy teaching them

so yeah if you had a professor that cant be fkd ouf, gotta find some stuff online

i think MIT had a good course iirc

some french professor

[vital bane]

wait James didn't you have a different account?

or is this the same account?

[gray jungle]

https://www.youtube.com/watch?v=PxCxlsl_YwY&list=PL4C4C8A7D06566F38 oh here it is

[gray jungle]

this is the same account, unless you somehow noticed my very first account i used here which is now deleted.

i dont even remember its name, but i had to delete it after a melddown i had (unrelated to this server)

[vital bane]

hmmm

[gray jungle]

been using this one ever since

like it was when i was in freshman so thats 5 years ago

[vital bane]

wait wth Folland doesn't cover calculus on R^n

the stokes theorem is presented only in R^3

oh wait there is a section on differential forms

Generalized Stokes' Theorem my beloved

it's there guys, we can relax

[gray jungle]

integration by parts my beloved

[vital bane]

these days all integration by parts reminds me of is weak derivatives and self-adjoint operators

[gray jungle]

its kinda funny how the funny integration by parts technique is to me one of the most important concepts in analysis

[vital bane]

yea it's surprisingly very useful

[jagged frigate]

hey there , can you reccomend some good books for permutation and combinations

[brisk rapids]

There's Miklos Bona's book.

[molten gulch]

What have you studied so far? Do you have experience with mathematical proofwriting?

[uncut salmon]

Book solely on Galois Theory (with excercises)?

I already studied a bit of it in an algebra course, e.g. we covered the main theorem, so if the book is more advanced it's better.

Plz🤓

[tender cobalt]

Folland based

[tender cobalt]

@vital bane yo bro do yk whats the best book to learn about differential forms and generalised stokes

[jagged frigate]

no not as such cengage and all

in my country they dont teach permutation combination and probability in that detail

[molten gulch]

Cengage is a company, this tells me nothing about your mathematical maturity

[jagged frigate]

you can consider me a beginner

[gray gazelle]

Start from Calculus 1-3 and Linear Algebra

I guess?

[molten gulch]

I'd recommend possibly checking out a book on discrete mathematics

[jagged frigate]

nah i have studied calculus 1-3 linear algebra ,matrices and set theory was just asking for the permutations part

[jagged frigate]

okay

[tender river]

bonas walk through combinatorics

[jagged frigate]

thank you

[next ocean]

I like Abstract Algebra by Dummit and Foot's treatment of linear algebra through an abstract algebra perspective. Unfortunately, it stops short before inner product spaces 😢 . Can I please get some recommendations for relearning about inner product spaces with an abstract algebra approach?

[dim sierra]

Not sure about being from an abstract algebra approach (tho it might be since it contains material about modules) but Roman’s Linear Algebra might be worth looking into

[next ocean]

I'll check it out, ty!

Are these bad things focused on a specific set of topics (for example, do they dislike the field theory section)?

[graceful dawn]

Need some math book covering some interesting questions upto undergraduate level to keep my math knowledge fresh.

[next ocean]

I just took a look, and it's not really what I want. The inner product chapter is an incredibly well written, but standard treatment of inner product spaces

[dim sierra]

alr, good luck finding something else then

[next ocean]

ty

[surreal heart]

What are standard recs in rep theory? A link to another post if there is one would be fine

[next ocean]

I took a look at Shilov's linear algebra. While it's not really using abstract algebra, it does make use of more abstract ideas in linear algebra to talk about inner product spaces

In contrast to repeatedly applying axioms

"A guide to advance linear algebra" by Steven Weintraub is like Shilov's book, but much more comprehensive

"Comprehensive Introduction to Linear Algebra" by Broida and Williamson is less abstract but also looks nice. Available for free here
https://cseweb.ucsd.edu/~gill/CILASite/

[floral lantern]

I recommend Artin if you haven't already done linear algebra

or even if you have?

[heavy vault]

Any opinions on munkres for alg top compared to like Hatcher or Rotman

I'm enjoying it for general but I don't really hear people talk about the second part of the book

Based on the pins I think I'd prefer Rotman over Hatcher but idk if munkres is good for alg top

[still panther]

its just an introduction though, not really comparable

[heavy vault]

Do you think reading munkres for alg top then Rotman might help or is that just wasting time

I wanna read like one gentle book and then one more deep book

[still panther]

yeah, its a reasonable plan

[remote sparrow]

@still panther what's the dummit and foote of algebraic topology, since you mentioned D&F was the hatcher of algebra?

[still panther]

ive read a total of one AT book

so no comment

[remote sparrow]

and i suppose that was hatcher? i assume you rather disliked it

[still panther]

no it was rotman

hatcher i just couldnt

its gibberish

[lost arch]

Courant, Robbins, 'What is mathmatics?'

or you can try Jay Cummings, Proofs. He explains what maths is essentialy about (making and statement and finding its proof/finding the proof of its negation) in quite an intriguing way, using lots of examples, stimulating readers to think themselves.

and besides, there are a lot of, i believe, brochures serving the purpose of introducing some key mathematical concepts to those who are new to math. You could find something written on sets, functions, relations, some basic logic and stuff. It could help you get to real math

[lost arch]

how decent?

idk

try then Amann-Escher and see if it's too difficult.

it's pretty self contained and clear

why not then proceed reading it?

he builds the intuition you're talking about in those very 6 first chapters

[foggy quest]

https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[next ocean]

I highly recommend translated Soviet textbooks/books designed for a general audience. I read (part of) a Soviet combinatorics book in high school, and it was incredible

[north summit]

can i get some probability theory book recommendations for self study. Measure theoretic ones

[remote sparrow]

billingsley, ash, and gut are good

rather helpfully, billingsley and ash has some hints or solutions in the back

[keen orbit]

is this analysis or calculus

[remote sparrow]

gut has a solutions manual for the first edition, but the majority of the problems are the same in the second edition

[north summit]

billingsley has 3.3 on amazon

[remote sparrow]

kinda both

[remote sparrow]

the anniversary edition is bad yeah

lots of typos

third edition if u can get it

[keen orbit]

what does that mean

[north summit]

school library only has that one and for ash first edition

[keen orbit]

so like it focuses a bit on calculation and a bit on proofs ?

[north summit]

gut has 3.8 on amazon why i so hard to find a probability theory book with good rating

2005 version at least

[remote sparrow]

the proofs are pretty complete, but there are also some routine calculations

and plenty of problems with proofs

[keen orbit]

ohh ok tysm