book-recommendations

[prime oak]

idk never seen that outside the internet tbh everyone i know including profs worship it

[crimson leaf]

I think one of the main issues is also that they were making money off piracy which is a big no no

[sage python]

But yeah it was kinda like

[misty wyvern]

Well people have different opinions on each of the Rudin books.

For instance a lot of complex analysts don't like RCA.

[prime oak]

thats the only one ive seen negative opinions about
though i am not at any stage to be able to read it so i cant comment lol

[misty wyvern]

And not that many people use Rudin's FA.

For courses.

But these are the books I return to so

[regal wasp]

If you can read words you can go through an analysis textbook tbh

[gray gazelle]

i do, and seems like theres an anti rudin(PMA) cult in my uni

[regal wasp]

Itll be difficult but thats really the only prereq

[prime oak]

start a pro rudin cult

[sage python]

I guess it was a weird snake between Rudin and Sally but we mostly did multivariable calculus from Sally chapter 5 which was a dumpster fire

[dapper root]

Rudin is for babies

[sage python]

To be fair we did LA from Hoffman-Kunze which doesn't get to inner products until fairly late

[dapper root]

If ur a grown-up you use mathisfun.com

[prime oak]

sacrifice apostol every second sunday as a ritual

[regal wasp]

Umich uses analysis on manifolds by munkres which was pretty sick

[prime oak]

TRRRRRRUE

[willow pecan]

Does it

[gray gazelle]

baby powder is also for babies

[sage python]

So many of us were confused about why Sally's doing this nonsense about taking gradient dot product f

[willow pecan]

Do you go to u mich

[regal wasp]

Yeah

[willow pecan]

[sage python]

Like hold up why are we dotting a linear map with a vector wtf

[dapper root]

Creep

[sage python]

We only realized next quarter after we did Riesz rep what that was all about lol

[willow pecan]

Maybe I've walked by you in one of these hallways

[sage python]

But still Sally had... more mistakes than is reasonable in a problem-heavy book

[gray gazelle]

no im one of them

[crimson leaf]

My profs I've asked do not like Rudin

[misty wyvern]

Your profs are cringe.

Make sure they know that.

[sage python]

Rudin's mostly fine

[regal wasp]

Like pedagogical mistakes or content

[sage python]

Content

Like

[misty wyvern]

I mean where else am I going to review results in analysis I already know? Stein and Shakarchi? Too wordy. Pugh? Basic bitch shit.

[sage python]

There was one point where he gave this one function and said

Prove directional derivatives exist but the function isn't continuous at 0

[regal wasp]

Doubt it i skip most of my classes

[sage python]

And we're struggling to prove this

Until someone glances at Rudin 9

[regal wasp]

Stein and Sakarchi is too wordy?

[sage python]

And it has a problem involving the same function but says "prove it's continuous at 0, but not differentiable"

[misty wyvern]

Yes? There are literal blocks of text.

[sage python]

And while thankfully I hadn't even started that part of the pset yet a lot of people were like fuck this shit wasted so much time

[misty wyvern]

Rudin spends very little time outside direct lemma, theorem, proof statements.

[sage python]

Also a lot of smaller typos

[misty wyvern]

Stein's singular integral book is probably worth mentioning but I've only referenced in like twice.

[regal wasp]

That does suck. Happens to me in all my physics courses though

[crimson leaf]

He likes the princeton lectures series minus the fourier analysis but he thinks it is "fine" for those who don't know measure

[regal wasp]

Steins complex and fourier analysis are incredible

[sage python]

But yeah Rudin is near optimal as a reference, my main issue with it is that chapter 10 is so bad that I genuinely think the man Walter Rudin himself did not understand differential forms at all

[winged gust]

This is definitely something I worry about as someone trying to learn mathematics on my own...

[misty wyvern]

If I ever teach analysis I will do the funny thing and teach it out of the appendix of Taylor's PDEs vol 1.

[sage python]

And also I don't like that in chapter 2 he presents compactness as a property of a subset of a metric space and sorta roundabout says oh it doesn't depend on what space you're in

[regal wasp]

Thats kinda sick tbh

[sage python]

In general he could make the whole subspace topology shtick a bit more clear

Also Rudin 8 is just a random hodgepodge of stuff lol. I don't see the point in the Fourier analysis in particular

[misty wyvern]

Oh I just didn't read Rudin on differential forms.

[cinder trellis]

I really don’t get the hype about PoMA to be honest

[sage python]

(Though it has the best elementary proof of FTA)

Rudin 9 is okay but doesn't do enough

[regal wasp]

What is Poma

[misty wyvern]

I actually learned differential forms first from a math phys text lol. Because for some reason math doesn't have multilinear algebra classes in ugrad the way physics likes to.

[cinder trellis]

Baby Rudin

[sage python]

Rudin 10 is legendarily fucking stupid

Rudin 11 is kinda pointless

But otherwise Rudin's great

[regal wasp]

Learning differential forms from algebraic topology is the play

[misty wyvern]

Learning from Wikipedia is what the Alpha Mathematician does.

[cinder trellis]

Does anyone know of a good book that covers Newton polygons in depth?

[cedar ridge]

armold?

who is ryc, that the name of the Chalk youtuber?

[gray gazelle]

@glad prairie this is ryc

[cedar ridge]

oh

[marble solar]

So the thing is Rudin isn't meant to be a book you read alone

It's meant to be a set of lecture notes for professors to fill in details depending on their students ability

When Rudin's Principles, Real & Complex, or Fcnl is used as a "litmus test" for "math ability" it can create a lot of problems and induce many a student's imposter syndrome

[hallow oriole]

'math ability' is bs until a certain level anyways

[grand thistle]

rudin pma's kinda fun imo

i enjoy learning from it

though i feel like it's one of those books you really only appreciate after like 5-6 chapters or so

[loud cradle]

or after you've already learned some/most of the material before.. in that case rudin is a nice clean reference that's better than most

[forest sleet]

I just use stackexchange

if I forget something from real analysis

I never used Rudin PMA but it looks fairly dry, especially with all the tedious results about R

[loud cradle]

you could always just skip ch 1 and refer back to it as needed (particularly its appendix, which is the only really tedious part, construction of the reals via dedekind cuts)

[cinder trellis]

Bumping this

[sudden kindle]

💯

[gray gazelle]

I do not know you, but this is not very professional behavior. Do some self-reflection, it is subjective anyway.

I would rather be wrong than some loser who tells people they’re wrong without any basis.

Never seen his Calculus book, but the other two are terrible for exposition. Unless you’ve read them yourself, please don’t talk about them.

[fierce hedge]

Isn't lang algebra decent for a second course on abstract algebra? What else would you recommend instead for a second pass on algebra

[gray gazelle]

It is great for a second course.

I specifically said exposition.

It is concise and gets definitions quickly. I appreciate that.

[fierce hedge]

Ah, makes sense. I thought it is obvious that it is not intended for first exposure to algebra

[gray gazelle]

I’ve seen some terrible recommendations by people who have no credentials to give those recommendations. This is a rather pedestrian discord for pedestrian mathematicians it seems.

[cursive orbit]

ah yes very professional

[misty wyvern]

Believe it or not Rudin was my first introduction to proof-based math. I started undergrad as an English/Bio major.

I took Bioinformatics, got recommended Rudin by the prof (lol), and swapped majors.

It took me a long time to work through it, it was incredibly dense to mathlet me.

It's amusing how trivial it is to me now.

[sturdy shore]

savior prof

[misty wyvern]

It took me the better part of a year to get through PMA, IIRC

But it's absolutely possible without assistance, Rudin is comprehensive. He's just terse.

[hazy elk]

(real)

[cedar ridge]

looks to be the same content as spivak calc on manifolds

im guessing shitter tho since it's 40 pages

[gray gazelle]

I was not talking to you, and this adds no argument, so do not reply.

[cursive orbit]

https://tenor.com/view/lizard-dancing-lizard-cry-about-it-gecko-dance-gif-20175430

[gray gazelle]

Sure

Ill get back to being productive

[hazy elk]

What recommendations annoy you particularly?

[gray gazelle]

Terse books that no one uses. I did some snooping around and found a website that shows a complete lack of knowledge by people who I assume are highschoolers.

[hazy elk]

Lots of people use Rudin tho? It works for a few ppl

[gray gazelle]

Rudin is fine.

[cursive orbit]

how about lang

[forest sleet]

lang has a lot of different books

[cursive orbit]

algebra

[gray gazelle]

Bad for exposition.

[hazy elk]

Are you talking about gristles website aka "sheafification"

[gray gazelle]

Might be called that.

Not sure. Don’t care.

[forest sleet]

Lang Algebra is more a reference

[hazy elk]

Ok

I've got some decent recommendations here, just saying

Some quality content in pins btw

[crimson leaf]

You are very upset about something

And very rude as well

[gray gazelle]

I’m not.

[crimson leaf]

Clearly are lol

[gray gazelle]

I know my current feelings lol.

[cursive orbit]

idk man lang is a standard text for grad courses

[gray gazelle]

The problems in Lang are boring and terrible.

The actual text itself is okay.

[hazy elk]

Oh btw, are the problems in the ring theory section of DF nice?

[gray gazelle]

Yes

[cursive orbit]

well they're good enough for the graduate algebra course at my university, which is taught by a professor who is far from a "pedestrian mathematician"

[gray gazelle]

Dummit & Foote exercises are the golden standard for Abstract Algebra exercises

Anyway, practice makes perfect

Abstract Algebra is not something you should spend too much time on, whatever resource you use just master the content.

[fierce hedge]

I thought Herstein had that title. I kinda like the book even though it has some weird notations

[grand thistle]

any opinion on hungerford?

some situation arose where i have to review a lot of algebra i learned last summer (a lot of which i forgot)

and i’m looking for a good review book that starts from the basics but is concise

[gray gazelle]

Yeah, I get a similar feeling about this person. Unfortunately people learning math come from a wide spectrum so it's not uncommon for people to be rude

[vocal panther]

Shout out to Gallian for making abstract algebra not suck 😭 😭

[fluid bay]

its okay. i think that in some places (like the rings and modules chapter) the generality is a bit annoyingly excessive for anything the average person cares about.

[grand thistle]

cool, this is hungerford's "Algebra" and not his "Abstract Algebra" right?

[fluid bay]

yeah, im talking about the graduate text

i liked the field theory chapter alright

[grand thistle]

great, do you have any recommendations over hungerford you would suggest, or do you think it's fine?

i was kinda drawn to it by how concise it was (seems to be laid out almost identically to lang), but seems to be much more manageable to an average person than lang at the same time

[fluid bay]

hmm if it looks good to you then i say go for it. The main reason I'm familiar with the book is that my class used it. From the times i have dipped into lang, I didn't find it much less readable than hungerford personally tho

other than hungerford or lang, there's also jacobson. I'm even less familiar with jacobson, but i've heard good things

[grand thistle]

alright i guess ill try all and see which one looks best

thanks

[sage python]

They're both on differential forms but Rudin's treatment of differential forms makes me almost want to say that he doesn't understand differential forms

[quick hornet]

to be frank, im not sure spivak's treatment is much better.

i mean, anything's an improvement over rudin ofc

but i would not want to learn forms from either of them

[rich sun]

What's your suggestion?

[fluid bay]

an actual differential geometry text maybe

[heady ember]

Lee?

[fluid bay]

lee hard imo

i kinda like warner personally

[median fossil]

Opinions on Barry Simon's Comprehensive Course in Analysis (especially the 1st 2 vols)?

[hearty steppe]

Oh boy… this looks like a can of worms I just found https://www.researchgate.net/publication/318786308_Eigenforms_interfaces_and_holographic_encoding_Toward_an_evolutionary_account_of_objects_and_spacetime

So much learn

[hazy elk]

Klaus Janich, Vector analysis

I haven't read it tho😅

[rich sun]

This is indeed what I started with

[hazy elk]

Just putting it out there

[rich sun]

The first chapters are fine

[hazy elk]

Oh how did it go

[rich sun]

But when it comes to integration and stokes, I prefer a more to the point exposition

[placid pollen]

What about Cartan's forms

[tropic thorn]

Hi guys,
I want to learn about LMI to apply in in control theory

Do you know any ressources that can help me

Im just starting out on this.

I went through calculus multivariate calculus some abstract algebra and linear algebra and numerical analysis in prep school.

[vast obsidian]

Of course they are bad for exposition they're not supposed to be a first course are you dumb or some shit?

Are you the type of guy who picks up research papers and GTM books then complain they're not made for first year undergrad? Like stfu lol

[cinder trellis]

Still curious…

[vast obsidian]

this guy is absolute cancer

[gray gazelle]

This is one of the funniest messages I've read on this server.

[grand thistle]

bruh why does hungerford use $\varepsilon$ instead of $\in$ tho 🤨

[hasty eagle]

sean

[grand thistle]

i've never seen this type of notation before

[spare ridge]

silence, aops pfp

[tropic thorn]

Hi guys,
I want to learn about LMI to apply in in control theory

Do you know any ressources that can help me

I went through calculus multivariate calculus some abstract algebra and linear algebra and numerical analysis in prep school.

[cinder trellis]

There are not enough sully emotes in the world for this post.

[gray gazelle]

The funny thing is that they're not even wrong. They just phrased it in the worst possible way.

[fluid bay]

oh yeah AHAHA i forgot

[vast obsidian]

[U+1F928]

[median fossil]

Bump

[remote ginkgo]

cope

the back-handed insults are unpleasant, please refrain

i know you are not being honest

it seems that, to you, professionalism is passive aggression and covert politicking

to me, professionalism is working very hard and trying to create things

[gray gazelle]

I guess roasting someone is societies way of correcting abnormalities.

[viral roost]

feedback is important

feedback can come from other people or the real effects of your own work

but the number of people who can just do work that is immediately impactful is small, it is very difficult

[deft bloom]

are there any books that can help me do functional equations from basic to advance

[tawny copper]

Evan Chen notes or Varderlind are nice

If you mean elementary functional equations

There's not so much content to learn for this type of equations, its just training

The book by small is also nice

[wanton pier]

Anyone here read A Mind for Numbers? I binge-read half of it a few years back, but I’m looking for someone to discuss it with

[viral roost]

Functional equations generalize in a bunch of different ways

Kernels of integral operators usually obey a certain kind of functional equation

Sum formulae like for trig go to coalgebras and representation theory

So it's not clear to me if functional equations as a concept are studied generally

[cinder trellis]

I’ve tried looking around online, but have only found short handouts.

[gray jungle]

Are these 2 books any good as a introduction to differential geometry?

"Differential Geometry:A First Course in Curves and Surfaces by Shifrin"
"Elementary differential geometry by Andrew Pressley"

My professors recommends both as a reference so i'm just getting some feedback , and which one would you prefare over the other?

[hearty steppe]

Oh boy another RG article and I just found it

https://www.researchgate.net/publication/331368433_Consciousness_and_Topologically_Structured_Phenomenal_Spaces

[grand thistle]

asked this once before but didn't really get any answers so asking again, any books on interesting series/integration techniques that cover stuff like generating functions, recurrences and recursion, special integration techniques like leibniz's formula, differentiation under the integral sign, series expansion, special functions, etc.?

kinda looking for a book that teaches all those techniques used in the youtube integral videos by michael penn, flammable math, and other similar youtubers

looking for a singular book that covers these subjects together and how they can be used together, rather than i.e. a specific book on generating functions, a specific book on integration, etc.

[steep badger]

There are various integral books if you search on google. They should contain all the technique solving integrals that has been solved before.

[foggy relic]

I’ve read the latter and it’s pretty good, only prereq is calc 3

[gray gazelle]

https://isabelle.in.tum.de/index.html

[placid pollen]

will there be a second print of Allen Hatcher's book?

[quick hornet]

its available freely online, you can print it yourself if you have a local printing service https://pi.math.cornell.edu/~hatcher/AT/AT.pdf

no clue whether theres plans for a second print run but i doubt it, hard for a publisher to justify it when its available freely for personal use

[silk axle]

Anyone have any insightful math/ML related books I can add to the collection? This is what I already have so far, but looking for some new recommendations.

- Infinite Dimensional Analysis: A Hitchhiker's Guide
- Applied Predictive Modeling, Kuhn, Johnson
- Deep Learning Architectures - A Mathematical Approach, Calin
- Mathematics for Machine Learning
- Probabilistic Numerics - Computation as Machine Learning, Hennig et al.
- High-Dimensional Probability, Vershynin
- Probabilistic Graphical Models Principles and Techniques, Koller, Friedman
- Probability Theory; The Logic of Science
- Advanced Linear Algebra, Loehr
- High-Dimensional Statistics - A non-asymptotic viewpoint
- Statistical Inference, Casella, Berger
- ESL 
- Bayesian Data Analysis, Gelman et al.
- Large-Scale Inference; Empirical Bayes Methods for Estimation, Testing, and Prediction
- Convex Optimization, Boyd
```Thanks!

[hearty steppe]

I just found another crazy paper on RG

Well… I officially take back what I say about RG being crap

https://www.researchgate.net/publication/328672126_Quantum_probability_in_decision_making_from_quantum_information_representation_of_neuronal_states

[gray gazelle]

What does RG stand for here?

This doesn't look anything like the RG I know (Riemannian Geometry), so I'm wondering if there's another common use for the acronym.

[hallow oriole]

the name of the website, if i had to guess

you know, in the url

[gray gazelle]

Makes sense.

I had assumed it was mathematical.

[hallow oriole]

in clash royale rg usually stands for royal giant 👍

@surreal phoenix @tardy walrus

you guys should know that

[tardy walrus]

Wtf

[heady ember]

Lmao

[whole wedge]

of course

[loud cradle]

i'm surprised not to see these already in your list:

- Bishop, Pattern Recognition and Machine Learning
- Murphy, Probabilistic Machine Learning: An Introduction
- Goodfellow et al, Deep Learning

[crude sage]

Does anyone have any thoughts on Poole's intro lin alg book?

[orchid mortar]

No Shalev-Shwartz & Ben-David?

[devout hollow]

Hello, I have a question. Currently, I am up to page 130 of Linear Algebra by Serge Lang. Thus far, I solved around 90% of the exercises (except repetitive or easy, computational ones) and have managed to reproduce the proof of almost every theorem in the book before looking at the proof. And yet, I am still in great doubt of my intuitive understanding of what the book has covered so far; for example, although I can prove that a finite dimensional vector space with a non-degenerate scalar product is isomorphic to its dual space, it feels like I still don't have an intuitive idea of what that statement is about. Is my self doubt reasonable? Or is it merely the imposter syndrome at play? I would appreciate an answer. Thank you.

[stray veldt]

Is my self doubt reasonable?
no

i dont know what else to tell you

[orchid mortar]

Maybe you can hang out in #linear-algebra and see if you can help us. That sounds like a good yardstick for if you can do it

[blazing canopy]

This is very impressive and being able to produce proofs of everything in the book is far more than most good students achieve. But you may be correct that you lack some intuitive understanding, and typically the reason is simple: you just need to see more examples of where many of these results are used (for example, the result you mention can be visualized in terms of geometry). This sort of intuition will come in time and you should not expect to attain it immediately.

[loud cradle]

An intuitive idea that may help: the dual space is the set of linear functionals from V to the underlying field. When V is finite dimensional, a linear functional has a matrix representation as a row vector. (Note that row vector times column vector = 1x1 matrix, which is identifiable with a scalar, so that checks out.) It is hopefully clear that the set of column vectors is isomorphic to the set of row vectors, and that can guide your intuition for the more abstract but basically equivalent isomorphism between vectors and linear functionals.

[blazing canopy]

The result he's describing is slightly different since there is a "natural" isomorphism arising from using the scalar product. As you said, every finite-dimensional vector space is already isomorphic to its dual by choosing a basis representation (column vectors) and then choosing the corresponding dual basis (row vectors), without needing any scalar product structure.

[gray gazelle]

In a finite-dimensional space, and more generally in a Banach space, you have the concept of orthogonal system.
It consists of a sequence of pairs of vectors ${(e_i^, e_i): i\in\mathbb{N}}$ and it has to satisfy $\langle e_i^, e_j\rangle = \delta_{i, j}$. Here $e_i\in E, e_i^\in E^$ where $E^*$ is a space of dual vectors of $E$, that is (continuous) linear functionals. What are you concered with is the concept of dual pair - given two spaces $E, F$ we have some way of telling the "scalar product" of $E$ and $F$. This gives us a natural isomorphism between $F$ and the dual space of $E$, for $f\in F$, $e\mapsto \langle e, f\rangle$ is a (continuous) linear functional on $E$.

[hasty eagle]

Blitz

[gray gazelle]

in general there is no way of obtaining an isomorphism of E and E* without some arbitrary choices - the spaces are isomorphic because their dimensions agree (they aren't (algebraically) isomorphic for infinite-dimensional spaces)
But the scalar product already imposes some way of constructing such an isomorphism

alright, and why did I talk about orthogonal systems
Because it's the most natural way of constructing a so called dual basis

[surreal phoenix]

this is royal information 👑 Always count on valley to keep ya in the loop

[clear mist]

Hey guys, do you guys have a recommendation of euclid geometry book with proof?

[acoustic ridge]

Is this book good for senior high school students? Note that I am a 12th grade student and I only have 5 months before the final exam starts but I studied almost nothing so shall I start reading this book for better understanding or read smaller books than it?

[tawny copper]

Probability book that touches on measure theory since the begining but not too sophisticated?

[gray gazelle]

Written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year. The main prerequisite is a working knowledge of calculus.

I think a high school student shouldn't have a problem

[silk axle]

I do have bishop & murphey, but not goodfellow. Was looking for more grad level books

[orchid mortar]

Not all of your list is really grad-level

Having strong foundations is essential however

So you don't need a pure grad-level list

[silk axle]

Yes if there exists a topic im not well versed in then id be interested. But basic undergrad books are something which wont help me

unless someone has an upper level undergrad book that grants some novel insight

[gray gazelle]

Does anyone have any recommendations for a supplementary book/reference for a course in probability theory with prerequisites assumed to be basic probability theory and measure theory to accompany the book "Probability Essentials" by Jacod and Protter?

(P.s. by basic probability theory I mean that we've done a sort of 'introductory course to probability theory and statistics in our first year' - now I'm in my second year)

[solar mural]

hi, i was wondering whats a good book to get for someone who likes mathematical physics and functional analysis?

or anything that has to do with string theory, representation theory, random matrix theory, combinatorics, homological algebra, etc

[sage python]

@gray gazelle People seem to like Durrett, also check out http://www.math.uchicago.edu/~lawler/probnotes.pdf and from these two courses:
http://galton.uchicago.edu/~lalley/Courses/381/index.html
http://galton.uchicago.edu/~lalley/Courses/383/index.html

[sturdy shore]

speaking of probability course notes, I know of this absolutely massive one

https://mathweb.ucsd.edu/~tkemp/280A/Driver-Probability-Lecture-Notes.pdf

also has yt vids accompanying it, by "todd kemp"

[grand thistle]

any opinions on schilling’s ‘measures, integrals, and martingales’?

the only complaint i’ve seen online is the abundance of misprints but that’s been largely corrected in the second edition

do y’all think it’s fine for someone who wants to learn probability but doesn’t know measure theory yet?

[acoustic ridge]

What will be the best book for giving a fresh start to learn calculus then?

[gray gazelle]

Thanks a bunch @sage python and @sturdy shore.

[sage python]

@grand thistle it covers the measure theory from scratch

We should ask a probabilist if it's good for that

[grave thorn]

I like it, but I prefer Jacod and Protter

[sage python]

Meaning is it "a book for real analysts with a side of probability" or is it "a book that's also good for future probabilists"

@forest sleet thoughts?

VMM: Jacod and Protter feels like it gets to Radon-Nikodym wayyyyyy too late

[forest widget]

Hi i was wondering if anyone have anyone has recommendations for calculus books, i already completed 2 calc courses but i would like to "relearn" it and plan on spending winter break and possible more if needed on it, any help would be appreciated ^^

[sage python]

Eleanor do you want to learn calculus with or without proofs?

[forest widget]

i think i would like to learn with proofs, do you feel like it would help with better understanding the concepts?

If proofs arent really needed for a greater understanding i feel like i wouldnt need it though

[gray jungle]

If you intend to do more mathematics post calculus you should do it with proofs, if you just want the machinery for something else you could go without them.

[sage python]

What is your aim in math overall?

Like if you're thinking more engineering and the point in understanding calc is toward the end of engineering

Then proof-based isn't a good idea

[forest widget]

i want to learn more math and i am studying physics and really like the subject and generally just want to learn

[sage python]

If you wanna do more theoretical math

[grave thorn]

Yeah that's one of my complaints with the book

[sage python]

Then that's where proofs come in

[grave thorn]

(and w/out radon nikodym their introduction of conditional expectation is just bad)

[forest widget]

Okay so do you have any good calc books with proofs in mind?

[sage python]

Maybe try either Spivak Calculus, Tao Analysis, or Schroder Analysis

[forest widget]

Thank ill look into those ^^❤️

[grand thistle]

sorry i should have clarified, i’m using this primarily for learning measure theory and real analysis for just the sake of them, probability is just something i wanna do in the future, it doesn’t have to be completely probability based or could just be a normal analysis text liek folland

[sage python]

Then Schilling is pretty good yeah

[grand thistle]

that’s why i’m trying to avoid learning measure theory first from a probability text like jacod protter, since it would be my first time learning the subject and i want to have as many viewpoints as posssible

[sage python]

I think it's one that's good both for future probabilists and analysts, though perhaps one could argue as a corollary that it isn't optimized toward either

[grand thistle]

ah okay

well i guess schilling is fine then

thanks

[forest sleet]

Hmm I don't have much experience with reading the measure theory parts of different probability texts, but for just general measure theory I like Teschl real analysis (free on author's website)

[brave yew]

what's the best book for someone who wants to get into mathematics?

I've gotten As and A-s in the standard calculus track, but I've had to drop Real Analysis twice

my fundamentals are shaky as all hell

I'd like a book, or maybe books, to start mathematics over again from the very beginning

[hasty turret]

Spivak calculus is goof

Well the problems are challenging but the writing is good

[brave yew]

no, but fundamentals, like number theory, proving theorems, basics of mathematics

[orchid mortar]

I think calculus is a good 'start from scratch'

[brave yew]

i don't have mathematical maturity, i can't prove stuff

okay, so maybe spivak could work

[gray gazelle]

Schilling is not that much of a probability text

[civic python]

Maybe “How to prove it” by velleman

[fierce hedge]

I am thinking of speedrunning UG maths from MIT OCW, just doing some readings and then jumping onto problem sets. Anyone having experience with ocw maths courses? In particular ug courses

[placid moon]

lotr

duh

best recommendation 10/10

[foggy relic]

@fierce hedge what do you mean learning math from ocw

i used ocw solely for finding which problems to do (i self studied so i didnt know which problems were the most worth and didnt have the patience to do all)

and ocw was very very good for that

[fierce hedge]

Not learning, I meant revising. Like doing problems and such

[foggy relic]

idk about the readings but the problem sets are generally well-chosen

imo

[fierce hedge]

noice

[fickle whale]

So I've been asking around for Complex Analysis recommendations, they seem to boil down to Needham, Ahlfors, or Stein and Shakarchi

Is there anything anyone would add or remove to that list?

[spare ridge]

i love schlag

[sage python]

I have a list in recommendations where I talk in detail

(Tbh even that's missing stuff that I've heard about recently maybe I should update)

But the gist to me is: Gamelin is good if you don't have much background in real analysis. Freitag-Busam is a better alternative to those you mention. Narasimhan, Marshall, or Schlag if you're cracked at everything other than complex analysis before going into complex analysis

[hazy elk]

Whyd you say Alhfors has been surpassed, in what respects ?

[sage python]

Honestly I don't think the book is that special. It has a good amount of material yes, maybe good problems? But its exposition is mediocre imo, he doesn't really section off theorems super well

Rather he chit chats and oh we proved a theorem! Which is fine for flow's sake but less so as a reference. And his chit chat isn't some masterful prose in any event

Wouldn't be surprised if most of its appeal is nostalgia lmfao

[quick hornet]

My hottest take is that this server cares way too much about prose and not enough about exercise quality

Admittedly the former is easier to judge than the latter

[foggy relic]

@sage python what does everything other than CA mean lol

[remote sparrow]

presumably real analysis, point-set topology, algebra, etc.

[sage python]

Narasimhan you want some measure theory going in

Schlag you want algebraic topology/differential geometry

But yeah re exercise quality: I guess I am rarely wowed by books in that regard. Tbh I find most complex analysis exercises to be highly obnoxious anyway lol

But even e.g. Rudin doesn't compare to exercises written by profs

So that's why I'd say just teach out of a book that reads moderately well, most importantly is well-organized and good as a reference

Then just write the psets

[foggy relic]

sure but what about someone who is self studying

then you need to consider ex quality

[sage python]

Fair I guess I tend to focus primarily on classes rather than self-studying

Though you can still follow online courses

[foggy relic]

hm tru but it can be hard to find old courses with psets (where the links arent broken) besides whatever is on mit ocw

[sage python]

For undergrad it's pretty often there. And honestly I prefer class setting 100x over sitting with a book lmfao

[lapis sundial]

Fr

[gray gazelle]

I am reading Velleman currently, it's very good, but I've read Chartrand/Zhang as well and I have to say it's a lot harder than Velleman's and is written more formal

So far at least, Velleman is a lot gentler

Chartrand/Zhang feels like its a lot faster paced, there is little text to explain + some example + solution then straight to exercises

Velleman does a lot more explaining

This is my experience so far

Oh and also, Velleman does not include any Combinatorics which C/Z has (C/Z also has proofs in LA, Topology, RA, GT, RT but that's a bit too advanced and can be ignored)

[icy knot]

You could try some coding books. Python for Data Science and Math for Data Science by Oreilly. Also Introduction to Statistical Learning.

[cedar ridge]

why is this pinned lol

[dapper root]

Cuz it’s funny af

[quick hornet]

because this is a pedestrian discord for pedestrian mathematicians

[forest sleet]

yeah no cars allowed

but I do like Stein Shakarchi for a first complex analysis course

it has a few annoying parts/inefficient proofs but overall it is nice to read

[tough zealot]

agreed
the class setting also helps you set up your own pace, even if it is adjusted by yourself. with a book about something you dont know, it gets kinda complicated

[acoustic ridge]

Suggest me 5 best books for learning calculus for 11-12th grade students

[quick hornet]

i doubt there are that many people in the world who are familiar with enough high-school-appropriate calculus textbooks that they would be able to pick out 5 of them to recommend

even lecturers who have been teaching it for their entire lifetime probably only change textbook every decade or so at most, and that's because they think the old one isn't worth using anymore lmfao

and if you do get any such recommendations, i would caution against trusting them — anyone who claims to be that familiar with so many intro books is probably just parroting whatever hot takes they saw on Quora.

[hallow oriole]

just use stewart bro

pirate it or buy a used old edition for cheap

[acoustic ridge]

Ok

[acoustic ridge]

How many versions does this book has?

[lime sapphire]

Many

[mighty marsh]

Cengage - Calculus for JEE (Advanced)

[acoustic ridge]

Which version should I read first?

[lime sapphire]

Doesn't matter which

Maybe go for early transcendentals

[acoustic ridge]

Ok

[regal wasp]

Nuclear spaces and stuff of that nature

[stiff sentinel]

Any book recommendations for cellular automata?

[vital bane]

not on topic but-

[rose geyser]

Hi, any book for Lie Groups similar to Postnikov?

What I don't like in Postnikov is maybe lack of details

[whole wedge]

i wanna study like group theory? what prereq shld i know first?

ive only done some calc, and complex analysis

[dapper root]

Honestly not really anything

Most algebra books start with a tiny bit of set theory which you need to know to do it

[whole wedge]

what book shld i start with

[dapper root]

And then it helps to know basic basic number theory

Like bezout’s lemma will be used a few times

[whole wedge]

idk i was jumping into abstract alg and infinite dim analysis

[dapper root]

But you can just look that one result up and you’re probably pretty fine

[whole wedge]

they seem to assume a lot of group theory stuff or sets stuff idk

[dapper root]

Any book on abstract algebra probably starts with groups

[whole wedge]

i shld start on algebra? or what then

[dapper root]

you can debate what’s the best forever

But honestly I’d just get whatever you can get your hands on and then try a different one if you don’t vibe with it that much

[whole wedge]

when they got to axiom of choice i was so lost

[dapper root]

At least early on it doesn’t really matter that much I think

[whole wedge]

any recommendation on which topic to start with

idk im scared i get into 1 thats too hard and i get demoralised

[sturdy shore]

I think there are some that start with rings, tho it is rare

[sturdy shore]

...if a book on abstract algebra assumes group theory it is a graduate level book

[whole wedge]

idk if it does that T.T idk group theory. i just felt it seems like it mayb

anyways any book recommendations?

[sturdy shore]

a book on abstract algebra is literally where you'd learn group theory, it is a part of abstract algebra?

I think artin is good

but there are many books

[whole wedge]

ehh so i shld start with group theory?

[sturdy shore]

what

[whole wedge]

im so confused

so i can just jump into abstract algebra with no prior knowledge?

or would i need some prerequisite

[sturdy shore]

if you know what a proof is you can jump in

[whole wedge]

hm oki thanks

[remote sparrow]

group theory is a concept covered in abstract algebra. the two are not separate.

[whole wedge]

hm oki ty

[spare ridge]

nice about me

[sturdy shore]

credit: Hofstadter - Metamagical Themas

I guess it is also a book recommendation

[turbid surge]

is there anything on non-convex optimization?

i have a problem modelled by a bivariate cubic function with 2 unknown coefficients that i want to optimize but can't find closed form solutions for the coefficients, substituting values for 1 of the coefficients yields solutions just fine and it's pissing me off

[orchid mortar]

for multivariate cubic doesn't differentiation solve it? Even if you go through all the candidates in a combinatorial manner I don't see how it will be a problem

Unless you need to do this by hand

But you shouldn't be doing anything >degree 2 univariate by hand (i.e., anything with degree >2, any variate should be automatic)

[turbid surge]

lemme see if i can dig up my notes

i might be misremembering and there might be fractions of polynomials involved but i was banging my head against it and didn't get very far

[orchid mortar]

I would still do automatic differentiation on rational functions

[spare ridge]

i love hofstadter

i really liked his discussion on superrationality in metamagival themas

[sturdy shore]

nice, I haven't read that one yet

[cedar ridge]

where does lang/marsden and hoffman fit

[gray gazelle]

Discrete math books?

can anyone give me some recommendations

[gray gazelle]

for what level?

[gray gazelle]

Im a beginner

University or school?

if University you can start with Differential and integral calculus and analytical geometry of Thomas

[gray gazelle]

hmm... well I guess they do use some basic stuff like that in combinatorics

I wanted to complain that it's a different thing but maybe it's adequate

[surreal ravine]

"winning ways for your mathematical plays". Its a fun read that covers nearly everything about combinatorial game theory, from the ground up

[little rapids]

Hay anyone have a good calculus book recommendation?

[crimson leaf]

Proofs or no proofs

[gray gazelle]

Differential and integral calculus and analytical geometry of Thomas

[little rapids]

Thanks man I go get those! Appreciate it!

[gray gazelle]

William Boyce's differential equations and boundary value problems can help you for differential problem

[little rapids]

I’ll add that too thank you!

This is relatively introductory right?

Because I’m gonna take calculus next year.

So I’m not starting from a whole lot

[gray gazelle]

it's basic book that learned in university for beginner , are you school or university student?

[next thicket]

Personally found Openstax Textbooks (Calc1 and 2) very helpful, lots of exercises and they're free:
https://openstax.org/subjects/math

[tulip blade]

that isnt a discrete math book lol

[gray gazelle]

Hii

Can I get suggestions for real analysis

And functional analysis

Bcz I'm gonna begin analysis in a few days

[sleek hawk]

For real analysis I recommend Tao's book

For functional I think Rudins functional analysis is still quite good

[gray jungle]

bruh ,DO NOT use rudin if you're new to analysis

Introductory functional analysis with applications by kreyszig is quite good and a friendly read.

I approve of tao if you're new to formal math , you might need to switch for something else for real analysis over metric spaces.

[gusty smelt]

hmm my prof says that rudins func anal is a bit outdated so to speak

but for basic analysis id say baby rudin is still as good as ever, ofc depending on tastes

For functional analysis pedersons "analysis now"

Its my fav book, and im an operator algebraist so i have a bais to it.

[crimson leaf]

You could try Stein Princeton lecture series

You need ug analysis but it covers real and functional

[gray gazelle]

Redirect me if this isn't the best place but are there any apps you guys would recommend for getting more confident with fundamentals and pre uni stuff (powers, algebra, etc.). I'm not doing mathematics as a major but it has a big part and I get really confused looking at equations, any recommendations?

I use brilliant but I'd like something more like a test to really put my nose to the grindstone

[willow pecan]

Khan academy

[grand thistle]

tbh rudin is pretty fine and fun once you survive chapter 2 or so

[grand thistle]

if you're feeling confident and have experience with proofs, rudin is honestly a great option

[gray jungle]

I was commenting on rudin functional analysis.

[fierce hedge]

For metric spaces I'd recommend Topology of Metric Spaces by S. Kumaresan

[marble solar]

Open stax has lots of teepos

[gray gazelle]

Dami says Tao's books are ass

[gray gazelle]

I'm using Lang for Complex

Once I'm done with Complex, I'll begin Functional or sth

I also need one for Fourier analysis if I were to be honest

[loud cradle]

stein and shakarchi vol 1 is very nice for elementary (non-lebesgue) fourier analysis

[grand thistle]

ah okay my mistake

[remote sparrow]

Just curious, has anyone designed a course around Zorich's two analysis volumes as the main text? They're pretty long, but I'd be curious to see some syllabi.

[cedar ridge]

i doubt it

[upper notch]

hiya!!

sorry for this being my first message in this discord U_U

I've enrolled in a math degree, and the set theory course is probing to be complex, furthermore, class materials don't help much

anybody know of a good book for practicing exercises in set theory? no need for much theory, just lots of goods exercises, with a gentle learning curve, and preferably with solutions

[heady ember]

Axiomatic or naive?

People normally recommend Halmos for naive set theory

As for Axiomatic set theory, it depends on what level you're studying it at

[upper notch]

math degree

I don't know the difference between axiomatic or naive

but we're asked to provide proofs in many exercises

so I gues it's axiomatic?

[hollow shore]

naive shouldn't require any solid pre-recs right?

[upper notch]

btw, thanks for helping, guys, I'll make sure to return the favor ❤️

from WIKIPEDIA: Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language.

[heady ember]

For an introduction to axiomatic set theory

1. Enderton's Elements of Set Theory -- Great for beginners, less mathematical maturity required compared to Jech. In my experience of nearly 100 pages into it I think its pretty good
2. Jech's undergrad set theory book -- Excellent if you have some mathematical maturity / familiarity with proofs. Covers some more stuff than Enderton. (Disclaimer: I haven't read this book but I have heard good things about it)

[upper notch]

yeah, we're doing axiomatic set theory @heady ember

[heady ember]

If you're doing more advanced axiomatic set theory, like grad level stuff, then look at Clerks recs in pinned

[upper notch]

whoa

thank you so much!!!

[heady ember]

Np! : )

[upper notch]

I'll make sure to return the favor to the community whenever I have the capacity to do so 😂

[hasty turret]

<@&268886789983436800>

[fierce hedge]

Second this, although I don't think Zorich is that popular

[golden moat]

Hi

[lime sapphire]

would someone really be new to analysis if they were doing functional analysis

[trail kernel]

Are these books:

1. Topics in Algebra - Herstein
2. Abstract Algebra - Dummit & Foote
   good books to teach myself abstract algebra? (starting off as an undergrad)

[willow pecan]

D&F is a good book

[lean pagoda]

Best books on lattice and order theory?

[orchid mortar]

If anyone suggests anything mind pinging me too? I need them for reference, I think.

[gray gazelle]

I was also looking for one, and what I found was book by Birkhoff is one of the recommended ones though it's a bit old

I also browsed through another such book but at some points it felt unclear to me so I stopped reading it

Probably any good book about universal algebra should contain an intro to lattice theory

of course no one recommended me those in person, I just saw a recommendation in another book iirc

@orchid mortar

the other book was Lattice theory: foundation by Grätzer

this was still in the time when I was interested in weird algebra stuff

I suggest to just experiment. Birkhoff is probably nice and kind of diverse

so maybe I'd start with that

[orchid mortar]

1948

thanks though

I'll look into them later

[gray gazelle]

Birkhoff was the one who "birthed" lattice theory

and the theory is fairly old

maybe there are better books, we'd probably have to look up some professor that specializes in lattice theory and bug them about it

[gray gazelle]

1967 actually

1948 is second edition

also see https://en.wikipedia.org/wiki/Lattice_(order)#References

there are some texts I already mentioned

recommended, and sorted with your level of advancement even/specific topic (!)

I wish I knew about this when I was trying to read about lattice theory. I could have just picked myself something instead of looking it up

[orchid mortar]

Elementary texts recommended for those with limited mathematical maturity:
UWU

[gray gazelle]

Difference between JS Calc and JS Calc: Early transcendentals?

[grand thistle]

et introduces trig and exponential/logarithmic functions early

[gray gazelle]

So the non-ET assumes you already know trig and logs?

[cursive orbit]

no, non-ET will present and define the transcedental functions using calculus

[gray gazelle]

And ET version will how?

[cursive orbit]

they'll present it in a more elementary fashion, but not as rigorously

[remote sparrow]

has anyone used jay cummings' real analysis book and liked it? i would look for myself but a copy is not lying out there on the internet

https://www.youtube.com/watch?v=oE3Q7EoYT4U

[gray gazelle]

you really like checking out books, huh

[remote sparrow]

i'm already using another book

[heady ember]

I have a catalogue of like more than 100 books in a folder

[remote sparrow]

but i think it's enormously helpful to look around for books and post about them

it will help future users with the same question

and i think it's interesting how different people teach the same topic in different ways

tangentially, i think there's a bit of a spurious conflation between making things "easier to learn" and "lowering standards." the former should be something we should strive for without lowering standards as well.

it's always a good idea to try to figure out how to transmit and receive knowledge more effectively

these new, more friendly and conversational books have yet to prove their worth i'm sure, but i'm particularly biased to them since i enjoy engaging with material in a sort of personal dialogue

[worn oasis]

oh I have this book

[remote sparrow]

would you like to give a review?

[worn oasis]

I haven't gone through it, I am taking analysis in the spring and I bought it as a second resource

The sections I have read were good

its a lot of discussion on the how tos of proofs

[gray gazelle]

Anyone done C. Pinter's book on AbstractAlgebra?

[lean pagoda]

Thank you for all the suggestions, the book by Grätzer doesn't look too bad but I'll double check with some of the suggestions on the Wikipedia pages

[smoky zephyr]

i only read like 100 pages of it but i liked what i saw

[gray gazelle]

Would you say it's good for introduction to the topic?

[karmic thorn]

Yes

[smoky zephyr]

definitely

it’s pretty easy from what i saw

[gray gazelle]

I am considering between Pinter and Artin, Pinter seems easier

[smoky zephyr]

pinter just looked nicer to me as well

[lean pagoda]

Also, and this might also be of interest for @orchid mortar, I came across an introductory Lattice theory text by Steven Roman and it looks pretty good I think (he's a good writer tbh). Unfortunately the typesetting is pretty rough in some spots (no idea why that is, his category theory text also has some horrible formatting in some places)

[karmic thorn]

The diagrams in his category theory book

Such a pretty book otherwise

[lean pagoda]

Yes omg, surely someone from Springer could've told him that they look really bad and that doing them in Tikz would be much better

[karmic thorn]

Right

[cinder trellis]

Advanced linear algebra by roman has the worst diagrams

his entire book is in LaTeX but his diagrams are garbage

somebody please teach roman tikz

[dapper root]

[loud cradle]

roman seems to have squandered an inordinate amount of time and energy on other dubious computer software:

[willow pecan]

Oh no

[remote sparrow]

he seems like he has a cool book on folding knives

[grave thorn]

On his website there is this video (though I added the text)

He just seems like a Chad

[cinder trellis]

LOL

[remote sparrow]

gigaboomer roman

[left cloud]

i don't understand memes

[remote sparrow]

https://www.youtube.com/@mathsorcererespanol/videos

math sorcerer has a spanish channel

[cinder trellis]

His Spanish is pretty good, what on earth

[manic cape]

what are the standard texts on distribution theory?

[remote sparrow]

he's of cuban background apparently

lives in florida where there's a lot of cuban americans

[grave thorn]

gelfand generalized functions

[grand thistle]

prerequisites to and books for p-adic analysis?

[slender rain]

can someone pls reccomend me a book that explains laurent series well

[gray gazelle]

Analytic functions book?

[gray gazelle]

I think you want to look for a complex analysis book?

Unless you mean things like real analytic

Yeah

I think real analytic

[gray gazelle]

Basically real analysis extended to multivariable calc

S. Krantz, H. R. Parks, "A Primer of Real Analytic Functions" maybe?

I just found it

https://link.springer.com/chapter/10.1007/978-0-8176-8134-0_2

They have this chapter for example

It advertises itself as "the only existing monograph devoted to real-analytic functions"

So I guess, it might be your only option

[median fossil]

I think they're looking for a book on real analysis and multivar calculus, not analytic functions...

[median fossil]

Given this

[gray gazelle]

why don't you ask them then

[median fossil]

I thought they'd tell us when they come here

@gray gazelle

[solar lake]

has anyone ordered books off springer website directly recently?

specifically the hardcovers, do they still have the shitty binding as you would get from amazon

(they're doing a 55% off all books rn)

[icy knot]

I bought Stillwell’s Real Numbers when they had a sale, has held up well.

[solar lake]

aight thank you good to know

hope they're not like this

[icy knot]

I wish you didn’t share this. I’m torn between a PDE book, Axler’s Measure Theory, that well known Cryptography book, and Statistics and Data Analysis for Financial Engineering

[bold knoll]

Hi, I want to learn general relativity but I lack background tensor calculus and differential geometry.
Does anyone here have books to recommend on these subjects?

[gray gazelle]

Nah. Analytic functions is what I’m looking for

[vital bane]

Barrett O'Neil "semi-riemannian geometry with applications to relativity" would be good for that

he says all you need is "multivariable calc and some odes"

I assume by that he means analysis in R^n

[sage python]

Wald's GR book I think is self-contained relative to manifolds/diffgeo/tensors, and I would wager approaches it from a physicists' angle in case that's a positive

[bold knoll]

Thanks!

[forest sleet]

yeah Wald and O'Neill were both books I heard recommended for GR for mathematicians

[remote sparrow]

afaik most springer books are currently print-on-demand glorified paperbacks like the hardcover you showed

[solar lake]

I bought Eisenbud
If it comes like that again then I’ll just order used books from now on

[fluid bay]

Always buy springer used

Anything 15+ years old is better quality

They went downhill when they were bought by venture capital firm in 2004

[forest sleet]

^ yeah the new springer books I've received are glue bound

which is fine if you're getting a mycopy paperback for cheap but kinda sucks if you think you're getting a nice hardcover and it's basically a mycopy paperback glued into a hard cover

[remote sparrow]

strange, i bought zorich's first analysis volume new as a hardcover and it was a crappy gluebound

for his second volume, i got it used and it shipped from the netherlands

but it had much better binding

think it's a sewn binding

btw, these books were published in 2015

axler's LADR also came in new and it had good binding too

[forest sleet]

the AMS books like Graduate Studies in Mathematics have sewn binding

[remote sparrow]

it's got some hits and misses for sure though

conway's complex analysis volume was a gluebound

[icy knot]

As much as I wanted to take advantage of this promotion, I’m just hoarding math books now.

[remote sparrow]

ugh i also heard dummit and foote is a crappy gluebound now based on amazon reviews

at the very least i've heard of companies that will rebind your books

i think lulu does that?

[forest sleet]

if it's gluebound they can't really make it sewn though

since you need double size sheets for sewn binding

(if the gluebound is single sheets)

[remote sparrow]

I HATE CAPITALISM I HATE CAPITALISM

mfw most gluebounds can't even be rebound into better books

[forest sleet]

maybe they can still do it better than the original binding though

hm maybe there are sewn bindings that can work with single sheets, II'm not sure

normally I think it's double sheets, e.g. on the AMS books if you open to the right pages you can see the stitching and see it's a double size sheet

[fluid bay]

Solution is to just learn to like pdfs

Instead of wasting money on consumable books

[remote sparrow]

[foggy relic]

both of the GTM books i have are dogshit gluebound but one of my books is UTM and its nicely swen

sewn*

so could depend on series

[rancid bone]

What is a great beginner level proof book?

[remote sparrow]

#book-recommendations message

[rancid bone]

Thanks bro

I’m looking at the hammack one rn

[next storm]

Good book

Has anyone read Serge Lang Algebra?

[gray gazelle]

just first chapter but yeah

[next storm]

Okay then I will read it tell you how it is.😁

[gray gazelle]

sure

I kind of gave out at rings (second chapter), too much definitions

[next storm]

Aight

I am reading another book but wanted to read something like lang

[gray gazelle]

I don't think contents of Lang are supposed to be hard

just the exercises

but maybe I'm wrong about that

[next storm]

Looks pretty cool

[analog lava]

rec textbooks for differential geometry

pref one that teaches some algebraic topology too if that exists

[fathom monolith]

I’d also be interested in some geometry textbooks. I don’t know anything about geometry, but every textbook I find is for high school.

[cinder trellis]

Does anyone have any thoughts on Shafarevich’s algebraic geometry books?

I’m thinking of getting copies but I wanted to know of other options, or some honest reviews of it.

[grave thorn]

I have the russian version of one of his books, they seem pretty good

though I cant comment on his algebraic geometry book specifically

[cinder trellis]

I was looking for a gentler introduction than, say, Hartshorne’s book

[sudden kindle]

i like Geometry by Brannan, Esplen and Gray

nice introductory book on various kinds of geometries, like Euclidean, Affine, Projective, Inversive, Hyperbolic, and Spherical

Emphasises the Kleinian pov of geometry, which is that a geometry consists of a space together with its group of symmetries

some familiarity with groups is helpful but not necessary

I believe any high schooler could pick up this book and benefit from it.

[fathom monolith]

Yea this looks cool. Its going on the christmas list. Thanks

[gray gazelle]

Hey does anyone have recommendations for books on algebraic geometry for beginners ?

It could be in both English or French

[dapper root]

EGA

Just kidding, this is kinda hard to answer to be honest

Common recommendations are like, Shafarevich

Milne’s algebraic curves

And I’ve heard stuff about a book called like “royal road to algebraic geometry” or something like that

[gray gazelle]

Ok will look up thanks mate

[dapper root]

For scheme theory, I recommend “Algebraic Geometry and Commutative Algebra” by Bosch

At some point you’ll probably have to work through most of Hartshorne or Vakil, but I like the book above because I think it’s the most detailed in the rudiments of scheme theory

It works out some of the really insanely tedious stuff the other books make you do, but these are some of the most difficult things to do when you’re starting out because you have no ide what to do

Also Mumford’s Red Book seems really nice from what little parts of it I skimmed

[gray gazelle]

Ok good to know thanks a lot man

[dapper root]

Good luck

[gray gazelle]

It’s mostly for my vacation because at the moment I’m wayyyy too busy 😭

So I’ll preserve the luck for my upcoming exam

😂

[gray gazelle]

https://books.google.pl/books/about/Topology_from_the_Differentiable_Viewpoi.html?id=ORCnDwAAQBAJ&source=kp_book_description&redir_esc=y

[devout sphinx]

someone un-ironically recommended this to me

they said it's easier to understand than hartsthorne

[dapper root]

I mean…

In some sense?

But it’s a very meme answer

Also hope you are willing to read French lol

[devout sphinx]

haha no

[gray gazelle]

Lmao i am tho 😂😂

Still it is painful to me not being able to access books physically so math books get pretty complicated for me 😭

So I try to get them at libraries but I mean it doesn’t feel the same as having your own and being able to highlight and all 😭

[remote sparrow]

https://www.amazon.com/gp/product/157586598X/ref=ox_sc_saved_title_3?smid=ATVPDKIKX0DER&psc=1

anyone know if this is a good intro to modal logic?

[heady ember]

The one's I have heard reccomended here before are Lee and Toring Lu

Also, John has shared his notes here before

[cursive orbit]

Loring Tu*

[heady ember]

https://drive.google.com/drive/folders/13QqswmY7gHF39_YnmV6blcilm3ZZ_tSd?usp=sharing (John's notes)

[heady ember]

Oops sorry

[devout hollow]

Will Linear Algebra by Serge Lang prepare me enough for more advanced books such as Finite Dimensional Vector Spaces by Halmos? Or will I benefit more from other texts such as LADR by Axler?

[willow pecan]

You will benefit from a good linear algebra book like Friedberg

LADR is controversial at best

Lang is controversial at best

[sturdy shore]

LADR is like halmos but worse idk why you'd read it if you want to progress to Halmos

[loud cradle]

imo, those three books are at more or less the same level

[devout hollow]

Thank you all for your reply. I hereby apologise for my ignorance; as I am relatively new to the subject, I don't know much about books, yet.

[willow pecan]

No need to apologize

[loud cradle]

hoffman and kunze is also worth a look

[sturdy shore]

h&k is even more difficult than halmos though, I think FIS is the best recommendation if you aren't so confident on your math

[loud cradle]

agree, FIS->H&K is probably what i would recommend to most people, although I do like the exposition of the first 2/3 or so of axler

[sturdy shore]

but you can read all the other greats later, there is genuine worth in reading more than one LA book imo

[devout hollow]

Okay. Based on the feedback received, I will be sure to check out FIS. Currently, I am halfway through Lang Linear Algebra; should I finish Lang then move on to FIS?

[loud cradle]

imo if you're enjoying lang and it's not at too high or too low a level, why not continue reading it?

[sturdy shore]

I've never read lang but if you want to finish it you can then probably jump to halmos/h&k instead, up to you really

[devout hollow]

Yeah, I thus far managed to do 90% of the exercises and prove almost every theorem before looking at the proof. I think I am happy with my current progress.

[loud cradle]

maybe chapter 12 of lang is not so important (depending on your interest of course), but the rest of the content seems fine

i think he's missing the SVD, which would definitely be good to learn at some point
but there's no linear algebra book that has everything, so well worth taking a look at several

[sturdy shore]

oh wait you are that guy that was proving every theorem in lang and insecure about your progress

[devout hollow]

I might as well at least try to work through it since I bought the whole book.

[devout hollow]

Yes. It just feels like I don't actually understand what I am proving.

[sturdy shore]

convex sets are really important for a lot of things, it is just not part of linear algebra proper (generally)

[sturdy shore]

it takes time, nobody develops perfect intuition overnight, you will get better at it too once you start using LA

[devout hollow]

Thank you for your encouragement.

[loud cradle]

and i'm guessing, they're taught better elsewhere, maybe either rockafellar or boyd and Vandenberghe

[sturdy shore]

but if you are at this level I would advise finishing lang then jumping to halmos or h&k or both, FIS is probably too low level for a second book

[loud cradle]

if you're interested in exploring the numerical side of LA, there are a number of nice choices there as well

[hazy elk]

You can also try a different subject other than LA

[devout hollow]

Okay. Quite conveniently, I already bought Halmos (because it was only 30 dollars for the hard covered version, I couldn't resist it)

[hazy elk]

I think that's more fruitful tbh

[loud cradle]

halmos's book is good (like all of his books), that's not wasted money

[hazy elk]

You really don't have to read like 3 books on LA

[sturdy shore]

sort of true, I do think reading a 2nd book on LA is very much worth but at the same time you should start actually using what is in them by now, or else it will feel dry

unless you already do

[hazy elk]

Artin is an inspiring book but it has its own style

[loud cradle]

agree, LA is so ubiquitous that it's worth viewing from several perspectives, no one's saying you have to focus on it exclusively though

[hazy elk]

If DW is going to major in math, they will probably have to do an LA course there as well no? So I'd say it's more profitable to explore new math like analysis and algebra

[loud cradle]

(and topology)

[devout hollow]

I want to eventually study differential geometry, as well as abstract algebra. But I've heard that Differential Geometry requires a lot of LA, and that advanced knowledge of LA makes abstract algebra easier. I guess, that is the main motivation behind my study of Linear Algebra.

[sturdy shore]

have you studied any analysis?

you should start, same with algebra

by now not knowing any algebra is actually gonna make your life harder in LA, both H&K and Halmos assume you know algebra at an elementary level

[hallow oriole]

huh, would you say there's not much worth in reading multiple books abt other subjects too? c i kinda wanted to get a few different anal books/algebra books but would that actly help me?

[loud cradle]

a first course in algebra doesn't require a ton of LA (just enough for field theory and some matrix groups, unless you're covering representation theory as well) but it certainly helps to have seen things like quotient spaces and isomorphism theorems in the LA context

[sturdy shore]

there is definitely worth for those too if you want to solidify your knowledge, it's just that LA is more well-suited to multiple perspectives imo

[loud cradle]

it's worth looking at several books in order to find one whose style and content you like, but then again if you're doing this in the context of a math major, that choice is gonna be made for you by the instructor

[hazy elk]

You might wanna pick up some multivariable calculus (differentiation, chain rule, implicit and inverse function theorems) and read Do Carmo/Pressley

[devout hollow]

I did went through some multivariate Calculus, as well as some vector analysis, but not rigorously. Thus, I will probably relearn calculus using two volumes of Apostol Calculus.

[hazy elk]

Good luck

[devout hollow]

thanks 😊

[devout hollow]

Can you recommend me a good elementary text in Abstract Algebra? For now, I would prefer a short book on the topic. I will commence my thorough study of abstract algebra, but only after I have gained reasonable proficiency in Linear Algebra.

[heady ember]

You can also see the pinned recs btw

[devout hollow]

okay I will do that

[hazy elk]

Armstrong is also a nice book for beginners imo (it's not in pins)

But it's just group theory

[sturdy shore]

personally not very knowledgeable on elementary AA books

I've read a bit of Fraleigh and thought it was pretty good but that's it

[remote sparrow]

pinter is cheap and good

judson is also decent

[karmic thorn]

Judson is nice

[broken meadow]

was going to suggest dummit foote but then i saw Short

[karmic thorn]

In that case I suggest MetalNinja 💟

[broken meadow]

Short kings rise up

[karmic thorn]

[crimson leaf]

Herstein has a short book not topics but the other one

[rugged sable]

brief history of violence

[unique ice]

sounds like algebra

[spiral lynx]

Any recommendations for complex function books?

[broken meadow]

Ruel V. Churchill complex variables and applications

soft introduction to material with no proofs, designed for math adjacent students

if you want pure math you will need some more background

[gray gazelle]

can any one advice a book about modeling with differential and how to make differential eq ?

[karmic thorn]

I like Mathematical Modelling with Case Studies by Barnes and Fulford

[gray gazelle]

is this book help me to percept modeling better? because I want to code(differential modeling) in MATLAB

[karmic thorn]

The book has MATLAB code for its examples

You should check it out

[gray gazelle]

thank you a lot , i Certainly check it

[karmic thorn]

👍

[turbid sequoia]

Any good calculus II books for self learning

[crimson leaf]

Stewart and Thomas for the standard Spivak or Apostol for more rigorous proof based calculus and there's also paul's online math notes not a textbook but you can learn calc 1-3 from there

[turbid sequoia]

Thanks

[spare ridge]

what is your height

[undone pine]

hi, i'm searching for some litterature on gaussian distribution and it's applications (entropy maximisation, likelihood estimation etc.). If someone could recommend something I would appreciate it, thank you!

[tropic thorn]

+1

[broken meadow]

,w 5’5” to cm

[hasty eagle]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by MetalNinja27#7212

[broken meadow]

Lmao

[dapper root]

Bro you’re 5’5??

Your photos didn’t seem to indicate that

[broken meadow]

I give off average height vibes but im actually a short king

[dapper root]

I think I’m 179

,w 5’10.5” to cm

[hasty eagle]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Chmonkey#9767

[dapper root]

Yah

Literally a heightcel because I’m not even 180 cm

Now I’ll never find love

[sudden kindle]

Bro legit added the 0.5 inches to his height

[dapper root]

Look, the reason for this is because when I was in middle school I said exactly that I want to be 5’10.5

And then I became that height down to the half inch

I shoulda said I wanted to be 6’4 or something fr

[willow pecan]

Very book recommendation

[dapper root]

Okay “ange”

[vital bane]

chmonkey

what are the prereqs for commutative algebra? ring theory?

what's a good comm alg book with low prereqs but also like pushes you towards alg geo towards the end

[dapper root]

Undergraduate commutative algebra by Miles Reid

[vital bane]

huh 172 pages quite a short book I suppose

[dapper root]

It is geometric

[vital bane]

i guess you need some topology as well since apparently people care about the topology of spec(Z)

[dapper root]

I mean

You need the definition

I’m pretty sure the book includes the definition of a topology

[vital bane]

oh so they just define the zarski topology on it and that's it? they dont do any topological stuff? (both in the book and in comm alg)

[dapper root]

I mean

You use properties but it isn’t like using theory

[vital bane]

I see

[dapper root]

The Zariski topology is very odd and behaves unlike the things you’d study in a topology class

[vital bane]

non-hausdroff

[dapper root]

So you mostly just need definitions and then develop the properties in a commutative algebra book or AG book

[vital bane]

ooh okay makes sense

[dapper root]

If topology is what stops you from learning AG you suck

To be brutal

Like that is by far the least hard part of the subject at an elementary level lol

[vital bane]

no I was excited about AG using topology

alright thanks for the book rec

[icy knot]

Anyone familiar with Nearing’s Mathematical Tools for Physics? Granted I have Kreyzig’s Advanced Engineering Mathematics, but this looks like a good book on the same topics. I would eventually like to work and get a MS in Applied Math, so I need to learn stuff like PDEs, Complex Analysis, etc.

[foggy relic]

@broken meadow send pics

for research purposes...

[broken meadow]

Huhhh

nuuuuu

im too cute…

anyways its wrong channel we need to stick to Book recs

[grave thorn]

(i could be wrong): most of the topology you use in commutative algebra is definitions; it doesnt seem to use lots of hardcore topology results (urhysohns lemma, tychnoff etc)

[dapper root]

ChmonkaS

Scroll down a little bit from that first message

[cobalt flume]

how many editions does spivak* have?

[remote sparrow]

i'm not aware of a spavik, but i have heard of a spivak

spivak has written multiple books; which one would you like to know about?

[grave thorn]

[blazing parcel]

What do you think about The Joy of X ?

[cobalt flume]

sry i misspelled

[cobalt flume]

i saw it has 2 editions
3rd and 4th. but what abt 1st and 2nd
or am i asking a dumb question?

[remote sparrow]

i'm sure there's a first and second edition, but i've never bothered to look for those editions

for his calculus book

[snow lintel]

HI, I want to know more about wavelets

any good book recommendations?

[gray gazelle]

Four editions

Has anyone read this book?

[snow lintel]

if it is only mechanics you can choose "Hibbler" more focused on the mechanics

[marble solar]

I've read parts of it

Spivak has sadly passed away so it won't every be complete

[gray gazelle]

Who is the book for? Can someone who's never taken course in physics dive in this?

[remote sparrow]

that's his goal, but one of the prerequisites he stated was differential geometry

[spare ridge]

wait what

oh he died in 2020, damn

[marble solar]

I don't recommend it

You should know basic physics

I'd say a freshman year of university physics is a pre-req

[gray gazelle]

But basic physics is incredibly boring

[marble solar]

Roughly equivalent to Halliday & Resnick, Young and Freedman (Sears & Zemansky) or some other equivalent

[gray gazelle]

Yeah this ^

[marble solar]

Halliday & Resnick is a fun book

[gray gazelle]

Absolutely most boring thing you could ever hope to study

[marble solar]

I don't think so

I think that goes to programming ^_^

[gray gazelle]

Programming itself yeah, but computer scientific programming fun

[marble solar]

To be seen on my end

[gray gazelle]

1200 pages of fun yeah sure )))

Why is this larger than a calculus book

no way highschool physics has this much material

[remote sparrow]

there's mechanics, e&m, and special topics like qm, optics, thermo, special relativity, etc. to be chosen at an instructor's leisure

mechanics and e&m are pretty standardized

special topics classes are more varied

so 1200 pages is also fitting at least 3 semesters' worth of material like those big calc books

[forest sleet]

apparently Monday is AMS day so if you are an AMS member you get 40% off many of their books

[willow pecan]

<@&268886789983436800>

[vital bane]

such contempt for AMS books...

[grave thorn]

Does Springer have Korn & Korn?

[vital bane]

[dense glen]

No

[grand thistle]

ams books look so pretty

[balmy isle]

Can someone recommend the best financial book for beginners? how to handle money etc

[gray gazelle]

1200 page calc is done in 1 semester tho right?

is there a difference between mechanics and classical mechanics?

[rich sun]

classical mechanics is a subfield of mechanics

[vital bane]

classical mechanics is just what it's called (a branch of physics or one of the 4 pillars), I dont think anyone refers to "mechanics" as a field on it's own

[rich sun]

mechanics also includes quantum mechanics and relativistic mechanics

[vital bane]

mechanics is just any physics that quantitatively describes the...well motion of things, i myself have never heard of people refer to "mechanics" as a field

[remote sparrow]

? that's three semesters worth

calc 1, 2, and 3

[gray gazelle]

So what is the mechanics chapter about in highschool physics books?

[remote sparrow]

mechanics also covers stuff like energy

and momentum

not just motion and forces

depends on the book but it should take several chapters

[vital bane]

newtonian mechanics

basically f = ma or f = dp/dt if it's calculus based and momentum and impluse and of course the rotational equivalent of all that

[gray gazelle]

thanks guys

[forest sleet]

what happened lol?

[willow pecan]

Someone posted something against the rules

Advertising if I remember correctly

[forest sleet]

oh ok I thought someone hated AMS books so much they said something that got deleted

[junior heron]

For Christmas I can wish for many books from Springer. Which ones would you recommend?

[gray gazelle]

Introduction to topological manifolds by Lee

[rigid barn]

Followed by Introduction to Smooth Manifolds and Introduction to Riemannian Manifolds

What's a good introductory algebraic geometry book besides Fulton or Cox? Same for commutative algebra that isn't AM/Eisenbud/Reed.

[dapper root]

Bro

Reid is really elementary

Idk what else exists that’s at that level

It doesn’t even cover the tensor product

[next thicket]

I'm gonna be studying Ring + Field Theory next semester. Any book recommendations to read over the winter break?

[gray gazelle]

I don't think they are a series that you should read one by one, but those are the other options

[rigid barn]

I know, but I simultaneously like and dislike his casual style.

[rigid barn]

I'm fine with tensor products, the book doesn't have to be completely elementary, just not something like Hartshorne that requires all of commutative algebra.

[dapper root]

You named like 3 entirely different books on commutative algebra

AM Eisenbud and Reid are all very different so idk what to say lol

[rigid barn]

Shit, you were talking about CA? I thought you meant Reid for AG

[dapper root]

But…

You put Reid down…

[rigid barn]

Then say nothing 🤐

[dapper root]

In the CA portion…

[rigid barn]

I know, but I spaced for a second and thought you meant Reid's AG book

[dapper root]

Anyway, if you didn’t like AM then idk why you’d like this but if you know a lot of algebra I like Matsumura

There’s also a book by Antoine-Chambert Loir (I think that’s the name) published recently

Idk, maybe that one is good

There’s also Zariski-Samuel, Nagata, Bourbaki but

If you prefer those idk, you’re built different, those books are ancient

[rigid barn]

Thanks.

[sick river]

Any recommendations on birational projective maps?

[remote sparrow]

https://www.youtube.com/watch?v=M1RrI3gXVsU

[valid ferry]

Wow a math socerer

[gray gazelle]

hello!

What book do you recommend to start with linear algebra from 0?

I am in the first year of my degree, in physics, and I am quite lost

[willow pecan]

Do you have experience with proofs

[marble solar]

Schaum's outline to Linear Algebra

Doesn't matter if you're good w/ proofs or not, it will help you

[gray gazelle]

what are proofs?

sorry, I am spanish, my english is not very well

proofs are demostrations?

[willow pecan]

@broken meadow

[gray gazelle]

Thank you!

[alpine rover]

https://youtube.com/playlist?list=PL49CF3715CB9EF31D

[gray gazelle]

ohh, thank you!

[terse basin]

What books do you recommend to get a grasp of limits in calc1? specially the indeterminate ones that require factorization

[gray gazelle]

is this book rly good?

[remote sparrow]

it seems fine based on an online copy i have

[fast wasp]

hey, sorry but do you have a book of integrals?