book-recommendations

[slender cargo]

(I'm in an Introductory Real Analysis class currently so this is just me having fun. I am no expert.)

[tribal crow]

dw I am too lmao

we use spivak

[slender cargo]

Oh. Spivak is a bit idiosyncratic though. He structures his book like a calculus book, so sequences come much later.

[tribal crow]

yeah...

[slender cargo]

Where as Bartle, Abbott, Rudin, etc. introduce sequences earlier.

[tribal crow]

we did sequences first anyways lmao

started with spivak's chapter 22

[slender cargo]

Oh wow haha

[tribal crow]

I'll take a look at Bartle 👍

[dim sierra]

Anyone know any books/notes/lecture series dedicated to visualizing 3-4 dimensional stuff in topology/geometry?

[violet shuttle]

Thurston's 4 3-manifolds

The Wild World of 4-manifolds

[dim sierra]

can u write the exact title i couldnt find this

[violet shuttle]

oh The Geometry and Topology of 3-manifolds

[dim sierra]

got it, thanks a ton

[violet shuttle]

and

https://bookstore.ams.org/FOURMAN

[vocal violet]

any recommendations on how to refresh my math skill? Been a few years after high school and i wanna go to college and major in math

[violet shuttle]

This is a panorama of the topology of simply connected smooth manifolds of dimension four.

Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but too small to have room to undo them. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today.

The first part of the book puts things in context with a survey of higher dimensions and of topological 4-manifolds. The second part investigates the main invariant of a 4-manifold—the intersection form—and its interaction with the topology of the manifold. The third part reviews complex surfaces as an important source of examples. The fourth and final part of the book presents gauge theory. This differential-geometric method has brought to light the unwieldy nature of smooth 4-manifolds; and although the method brings new insights, it has raised more questions than answers.

The structure of the book is modular and organized into a main track of approximately 200 pages, which is augmented with copious notes at the end of each chapter, presenting many extra details, proofs, and developments. To help the reader, the text is peppered with over 250 illustrations and has an extensive index.

Chapters 1 to 3 mostly describe basic background material on hyperbolic geometry.

Chapter 4 cover Dehn surgery on hyperbolic manifolds

Chapter 5 covers results related to Mostow's theorem on rigidity

Chapter 6 describes Gromov's invariant and his proof of Mostow's theorem.

Chapter 7 (by Milnor) describes the Lobachevsky function and its applications to computing volumes of hyperbolic 3-manifolds.

Chapter 8 on Kleinian groups introduces Thurston's work on train track and pleated manifolds

Chapter 9 covers convergence of Kleinian groups and hyperbolic manifolds.

Chapter 10 does not exist.

Chapter 11 covers deformations of Kleinian groups.

Chapter 12 does not exist.

Chapter 13 introduces orbifolds.

btw til what a train track is

train track is a family of curves embedded on a surface, meeting the following conditions:

The curves meet at a finite set of vertices called switches.
Away from the switches, the curves are smooth and do not touch each other.
At each switch, three curves meet with the same tangent line, with two curves entering from one direction and one from the other.

they are used to study laminations

which are families of locally parallel curves partitioning a subset

[tribal crow]

Chapter 12 does not exist.
hmmm

[dim sierra]

what kinda superstitions are we dealing with here 😂

[vocal violet]

any recommendations on how to refresh my math skill? Been a few years after high school and i wanna go to college and major in math

[molten mason]

Check out Basic Mathematics by Serge Lang

[gray gazelle]

3blue1brown's essence series on calculus and linear algebra might be a good place to start

[vast jackal]

Hey can anyone recommend me a book in Algebra I and II
Not too rigorous it's for Physics Olympiad and I need like most of it will come out of the round in our country

Khan Academy slows me down the video is not explained too well

[trail hemlock]

well for olympiad prep i would say AOPS Intermediate algebra is great.
there is also 101 Problems in Algebra From the Training of the USA IMO Team

[torn crypt]

Chapter 10 does not exist
What the heck

[quasi umbra]

anyone have a good book on loop quantum gravity for mathematicians?

[gleaming summit]

anybody know where i can find a lot of hard trig questions? in looking primarily for identities

[molten mason]

I don't know about hard but check this
https://mecmath.net/trig/

[gleaming summit]

theres some good ones in there thank you, although im looking more for just a large quantity of them, not rly explanations

[vital bane]

Khan Academy, 3Blue1Brown, "Basic Mathematics" by Serge Lang and also the book "Mathematical Proofs: A Transition to Advanced Mathematics" is very good if you wanna major in math, also "Understanding Analysis" by Stephen Abbott (it is the best mathematics textbook of all time)

[heady ember]

The one time Neam doesn't shill Abbott

[vital bane]

oh right, I mean to do Abbott (or any analysis book) you have to want to do analysis

They said they just wanna refresh their math skill before starting college

[jaunty harbor]

Can anyone recommend me a good book for calculus undergraduate

[vital bane]

undergraduate what? math? physics?

[jaunty harbor]

Maths

Calculus

[vital bane]

the usual recommendation for everyone is Stewart or Thomas

but if you're into mathematics then maybe Spivak's "Calculus" would be good

[jaunty harbor]

Okay

[vital bane]

that's kind of proof based

it's like in between calculus and real analysis

[jaunty harbor]

I want that book which have good quality of questions

Like some difficult

And also have final solutions at the end of book

[heady ember]

Imo if you're gonna do Spivak, might as well just learn analysis.

[vital bane]

yea Stewart and Thomas is good then

[jaunty harbor]

Thomas have solutions of odd problems only

[vital bane]

that's good enough imo

[jaunty harbor]

Stewart is similar to thomas?

[vital bane]

yup

[jaunty harbor]

Do you have its pdf?

I wanna take a look

Before buying

[vital bane]

you can find it online

[fervent crypt]

does anyone know any good books on cryptography for hs students? i'm going to start a course in july with a professor based on his book, but i just wanted to build a base first
link to his book: https://www.amazon.com/Cryptography-Springer-Undergraduate-Mathematics-Rubinstein-Salzedo/dp/3319948172?refinements=p_27:Simon+Rubinstein-Salzedo&s=books&sr=1-2&linkId=7d1a910c228e337d67e37b2cc9cb7e75&language=en_US&ref_=as_li_ss_tl

[jaunty harbor]

Okk

I found

Bro but what should i follow? Thomas or stewart?

Which is more better?

[vital bane]

they are both good

you can choose whichever one you want

which one do you like more?

[jaunty harbor]

Thomas

[vital bane]

Then use that!

[jaunty harbor]

Okay

Do Thomas have beta and gamma functions?

[vital bane]

What do you want to learn in relation to beta and gamma functions?

because that can be a huge topic

[jaunty harbor]

I can't find , and this topic is in my syllabus

[heady ember]

Lame joke ||what transformation do you need to compose the beta/gamma function with to become an alpha function||

[vital bane]

convolution

[vital bane]

it's not in Thomas, but I'm sure you can find a book that has beta and gamma functions

[vital bane]

sigma function when🗿

[heady ember]

That's just a permutation

[vital bane]

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

let's goooo

I guess lower case sigma could also be a measure

[heady ember]

Let 📏 be a measure....

[vital bane]

Lmao that would be so funny

imagine measure theory notes where the measures are denoted by ⚖️ 📏 📐 emojis

[heady ember]

Do that in your measure theory assignment, when you take that class.

[vital bane]

I'll do it when I teach a measure theory class

[heady ember]

Never?

[vital bane]

what did you just say

You will see

[remote vortex]

Right, now I know what to do when updating my notes for the next time I teach MT

[remote vortex]

Ah, great minds think alike, it seems

[vital bane]

[remote vortex]

And so do ours

[vital bane]

or...feeble minds go for the same low hanging fruit...

I love that phrase

it's like a counter to the "great minds think alike"

[high heath]

After I've learnt Linear Algebra (from Axler), does anyone have any good reccommendations for textbooks on Analysis and Algebra? Preferably ones that aren't too boring

[grand thistle]

theres an algebra book review in the pinned messages i think

[high heath]

I'm fairly comfortable with proofs (know the whole of the Further Maths course, and I also do Maths Olympiad)

[grand thistle]

ah if you're comfortable w proofs

maybe you'll like rudin

for analysis

or abbott

[high heath]

I already tried this one, found it to be very boring

[vital bane]

Abbott!!

[still panther]

dummit and foote is the absolute bottom tier algebra book

[vital bane]

I will find you

[grand thistle]

fax

[hallow oriole]

iirc the full quote is “great minds think alike but fools seldom differ”

[open steeple]

I want to get into ai and neural networks from scratch, is Before Machine Learning Vol.1 - Linear Algebra a good start ?

[woeful pagoda]

something for a total beginner?

[hallow oriole]

wrong reply smh

[toxic smelt]

Good morning guys,do someone have any book about analytical geometry?

[covert mauve]

any good books on starting out with physics

[gray gazelle]

I’ve only read a little bit of it, but I’ve heard good things about Spivak’s Mechanics book, if you already have some mathematical background

[covert mauve]

what are the prereqs?

[gray gazelle]

You can read the first part of it if you’ve gone through the calculus sequence

I believe

Later parts might need some diff geo

[covert mauve]

yeah, i am not very familiar with diff geo

[flat marten]

Grillet doesn't fuck about and is more interesting in my experience

[gray gazelle]

I’m considering reading Grillet, since it seems like he puts a lot of emphasis on commutative algebra & field/galois theory. Would you recommend it for these topics?

[flat marten]

I'm only on chapter 4 right now I'm afraid

What I've read so far seems to confirm alot of field stuff going on

You'll definitely want linear algebra for it; he takes for granted that a field extension is a vector space over the base field, for example

[gray gazelle]

I have a fair bit of background in LA, so that won’t be a problem

[flat marten]

👍

[gray gazelle]

How are the exercises?

[flat marten]

Outside of the group theory chapters he places alot less emphasis on those stupid calculational exercises that D&F have everywhere

[gray gazelle]

Fantastic 🙏

[flat marten]

Which I like, alot. They're mostly proof based and will sometimes ask you to prove more advanced or niece material in the exercises, for example a fun one is monoid rings

Oh and he places alot more emphasis on universal properties

He'll frequently discuss, prove, and use them in proofs

[gray gazelle]

Cool cool

[flat marten]

Another thing I appreciate is thoroughness, and how it doesn't feel like there's alot of material left out

He refuses to delegate a proof outside of the book, even if its by a while, for example delegating the proof of the classification of finite abelian groups to when he discusses modules

[gray gazelle]

Sounds perfect

[cosmic steppe]

Does anyone have a review of the book Problem-Solving Strategies by Arthur Engel?

[fervent crypt]

yeah it's amazing

[remote sparrow]

abbott is good. schroeder and bartle/sherbert are other good choices. browder is similar to rudin. aluffi's Notes from the Underground and shahriari's book are good for algebra. pinter and judson are good too.

[trail hemlock]

rudin mentioned 💯 🔥

[high heath]

It's average

[trail hemlock]

[mossy shell]

Could ask the physics server

I have one i think is decent i need to remember the name though

Ah yea university physics by freedman

[remote sparrow]

https://www.amazon.com/Classical-Geometry-Euclidean-Transformational-Projective/dp/1118679199

[white pollen]

Terrence Tao’s books on analysis are comprehensive. I would say they are a good step between Rudin and Calculus.

[dim sierra]

Anyone know a book/resource that lays out a list of problems that helps you build up to the proof of a result? We’re doing this in my complex analysis class for the PNT and it’s pretty fun, so I wanna try it on some other results.

[gray gazelle]

Quick question, should I buy a book for differential geometry by lipschutz or barrett o'neill?

[remote sparrow]

kristopher tapp has written a good book on diffy geo

[gray gazelle]

I can only choose those

[remote sparrow]

are you thinking of getting a used copy?

[gray gazelle]

Many people say barret o neill is a classic

[gray gazelle]

Yas

[remote sparrow]

well do carmo is a classic too

it's available as a dover for very cheap

[gray gazelle]

I have that one too to print it

[remote sparrow]

btw there's a springer sale going on

https://link.springer.com/book/10.1007/978-3-319-39799-3

[gray gazelle]

Should I just save my money to print that one, instead of buying one of those (barret o neil/lipschutz)?

[remote sparrow]

i heard the coupon codes 50off and HLT23 work

[gray gazelle]

K thanks then, I will use Do carmo

[remote sparrow]

i'm not super knowledgeable about differential geometry books in general; i'm only really familiar with tapp and do carmo

[vast jackal]

Shouldn't I do Introduction Algebra before Intermediate?

[trail hemlock]

intro to algebra is algebra 1 so yes, but i assumed physics olympiad would have prepped you for that as well

and if you are looking for just the simple basics of alg 1 and 2 any “for dummies” or similar book should be fine

[vast jackal]

Are you sure?

I mean I just need the foundations up to algebra based physics and Calc based

And I want to progress fast lol

[lusty ermine]

which book is good for learning about maclaurin polynomial

maybe a good intro to series aswell I need

single variable though

[lost bobcat]

What is the best book to learn precalculus

[high heath]

For olympiad prep you should try BMO1 problems, then BMO2 problems, then IMO shortlist

IMO shortlist is really your best resource

If you're struggling with Geometry you should try Euclidean Geometry in Mathematical Olympiads by Evan Chen

[vast jackal]

I'm doing physics Olympiad

[high heath]

You can try HRK and KnZhou handouts, but I'm not that good at physics Olympiad, there must be more experienced people here

[vast jackal]

Yeah you're right but I'm still doing on my foundations I'm still in high school

[high heath]

I think HRK is ok for foundations if you're familiar with calculus

I didn't really learn calculus from a textbook so I can't really help you

[vital bane]

<@&268886789983436800> yooo crypto gang! let's get in on this!

[flat lantern]

YO?????? I LOVE bits coin...

[modern ruin]

guys. i have this epic new shitcoin we are gonna go to the moon with this. TO THE MOON I SAY!

[gray jungle]

they doubted jesus too, dont doubt my dogecoin!

[bold kite]

hello

i need help, im preuniversity and i want to start self study grad and post grad mathematics fields to master quantum studies . , which ones do u recommend me

[slender cargo]

Don’t skip undergrad

[bold kite]

i dont

i want to start like from now studying more about math

because we are doing optimization

[slender cargo]

Did you learn Calculus yet?

[bold kite]

this year im going to university

i guess we are gonna complete claculus high school level yes

[slender cargo]

I would just focus on preparing for university. Look at a book about proofs

And ace your calculus class. Take both Calc 1 and 2 if you can before university

[bold kite]

yes but the thing is i dont plan to go mathematics bacherlor , id like to do computer science

[slender cargo]

Oh

Uh if you want to “master” post grad math fields then that is a math major

[bold kite]

yes, i want to learn about quantum computing and essentials mathematics for machine learning and other stuff that would be helpful

[bold kite]

i wanted to say master quantum computing field

sorry

[slender cargo]

No worries. I can’t help you there then

[bold kite]

u dont have any book recomendations like calculus stewart and that? , its just from the beginning , ofc im not gonna start with quantum books, ill need a base

[graceful moon]

You’ll need a bit more maths if you want to start learning quantum computing

At least calculus and linear algebra

[glad rampart]

Yeah learn linear algebra

Very useful I’ve heard

[graceful moon]

It’s very useful generally, but essential as a prereq for quantum computing stuff. You’ll struggle to understand tensor products if you don’t know linear algebra

[bold kite]

oh okay guys, ill guess its first calculus and then linear algebra ( ill study at the same time but im meaning the importance order)

[graceful moon]

I will give a recommendation to a book I haven’t actually read, Quantum Mechanics by Arjun Berrera and Luigi Del Dobio

The book was written based on the course for mathematical physics students at my uni, so I can assure you that linear algebra, calculus and DEs will be enough for it (I believe it also covers some symmetries, which will require group theory but I’m sure this can be avoided if computing is your interest)

I started out doing that degree and most of my friends are still doing it, hence why I know the prereqs, I know it covers computing and I’ve heard it’s good

But yeah as a book with minimal prereqs that covers a good amount of modern quantum mechanics, I think that’s a good place to look@

[lusty ermine]

😛

[narrow relic]

I just found a neat looking book on functional analysis. This is a topic I have not studied yet so I'm not qualified to recommend this but I thought I'd mention it here: https://www.amazon.com/Functional-Analysis-P-K-Jain-dp-1906574677/dp/1906574677/

The writing is super clear from the few parts I sampled.

[daring lake]

Will look at it

[narrow relic]

Cool, I'd love to hear what you think.

[daring lake]

Ordered it 👍

[narrow relic]

Wow alright! Well, let me know what you think after it arrives.

[daring lake]

yeah, it was only like $7 on amazon.in

[narrow relic]

Nice. Can people from outside of India order books from there?

[daring lake]

Not sure, and most Indian publishers primarily publish in paperback to cut back on the cost (and I honestly dont mind that, hardcovers are often very expensive).

[narrow relic]

That makes sense, I don't mind it either, hardcovers are heavier too.

[high heath]

I've been finding this very good. It's fairly concise and interesting, but not difficult

I've found analysis a lot easier than Abstract Algebra as it's much more intuitive and easier to picture

Linear algebra I've found is somewhere in between

[celest furnace]

For high school level mathematics (even though I assume you did American high school), try Bostock and Chandler A level mathematics textbooks, (between Pure Maths 1 and 2 and Further Pure Mathematics, its pretty much everything you need for university level maths and then some). They are ncredibly thorough (a little too thorough). They are a little outdated but the calc, geometry sections are well explained

There is also Calculus for the Practical Man by Thompson which I found helpful.

[bold kite]

thanks brother, im from spain

[celest furnace]

Ah, pardon me.

I recommended them just because I had to teach myself maths (I did three different systems in four years) and they were really good.

[bold kite]

Malaga

dont worry , i dont mind

[celest furnace]

Real southerner then. Pretty cool.

[bold kite]

valencia so cool to

[remote sparrow]

i prefer algebra over analysis

[next condor]

For an introductory study of Contemporary Algebra, if you had to choose between Pinter and Gallian, which one would you choose and why? These are the two books I have available to study.

[slender cargo]

If I had to choose for self-study I would go with Gallian. That book is used at a lot of places so it'll likely be easier to find solutions and syllabuses online, and it has way more exposition. Pinter is more of a problem set book. However, I hear Pinter is very good. That's from my limited understanding between the two.

[remote sparrow]

pinter

#book-recommendations message

[dapper inlet]

hi does anyone know where i can get an equivalent chapter of holts basis and dimension (7.3) in a different book?

[vast jackal]

Like I said I'm still on my Algebra

Working with foundations

[west spoke]

Can someone give me a good suggestion for a book that's more or less situated between analysis and calculus? I am literally 0 interested in the computational part as anything other than a challenge to strengthen intuition I hope this makes sense. Without being arrogant, moat calculus books start like this: when Newton invented the lightbulb, gauss played a guitar gig, Leibnitz, bla bla. There must be some book where I can learn it more "in bulk" and "top down" involving things I know bout more contemporary style math

[glad rampart]

Spivak perhaps?

[west spoke]

It would be cool if it was as rogourus analysis as possible

[slender cargo]

Spivak is rigorous analysis.

[west spoke]

Just said it as an add-on

Ok

[lusty ermine]

how do I get rigurous about real analy, without proofs

[west spoke]

Just with the computational aspects in-between.

[west spoke]

You don't?

[lusty ermine]

and also I suck at math

[west spoke]

Rigor is just a word tho

Also complex analysis looks much more fun

[slender cargo]

If you don't want the computational aspects, then... you can read a Real Analysis book, although I don't know if that's a good idea. I think Bartle and Sherbert or Jay Cummings would be good for a book that can "replace" Calculus. Pick up Rudin if you're crazy.

[west spoke]

I would love to replace calculus

[acoustic cliff]

If you mean as rigorous as possible while still being suitable for a regular Calc class there is Velleman's Calculus book

[west spoke]

I don't want to take a class necessat

I don't think I'd fail one

So I wouldn't be that afraid

I literally want to use all (albeit limited) knowledge I have of set theory, topology, discrete math, abstract abstractions, groups, algebra and linear algebra and so on in order to 1)replace anything inqanr to know about abalysis

While also building strong computational skills

I literally only know what differentiation and integration are theoretically but wouldn't know to apply them. Yet.

But I couldn't do them surfing through a calc or analysis book

But when I look at a problem I can immediately use everything I know

So I thought.computarion maybe better

Computation

Idk I hope this doesn't come off as completely dumb

I thought about doing Tao or Zorich and ask if someone can just shower me with exercise papers on calculus stuff

I hope i don't read like a procrastinerd

[west spoke]

Nice rudin has well documented exercises

It's strange I want to make the shift from recreational to serious, so I can literally not skip analysis I think?

But then again I never linearily finished a single textbook so far I think.

So a calculus book .ight be a good choice

[west spoke]

I don't want to miss out on math because I can't do calculations

Is practically the point

I can do abstract math

Which kind of bothers me

[slender cargo]

Spivak's Calculus is probably the best choice for you imo

[west spoke]

Are you sure?

Why?

I am genuinely interested

[slender cargo]

Spivak's Calculus will teach you introductory Analysis while also including the computational stuff in Calculus.

[west spoke]

Ok. I also don't know about the calculus focused educational systems btw

I know that many societies prime people on calculus

Most likely because of the applicability of it in applied science and the history of the subject or something

And also its attractive as a discipline or something idk

Analysis that is

Whatever I am being nonsensical

[graceful moon]

I’m confused about what it is you’re looking for here, do you want a calculus book?

[west spoke]

I want to be able to intuitively work with limits series differentiation and integration as much as I am with every other piece of math I know

If my knowledge of math subjects were a record analysis would be a scratch on it where the needle bumps

[graceful moon]

That’s a complicated way of saying you’re looking for an analysis book

Abbot or Tao are good. People like Rudin, I don’t, but the problems are good

Spivak I’ve heard good things about

[west spoke]

📉

Don't blame me I am scared

Ok thx guys

[graceful moon]

What are you scared of?

[west spoke]

Something I say being inconsistent, setting a date of me being inconsistent and therefore being debilitating

An irrational fear as I have control over it

Is there a book that literally only has problems on analysis and calc

That would actually maybe be best suited

[graceful moon]

[glad rampart]

Listen you just gotta pick up a book at some point

Pick one and stick with it

[west spoke]

I do often

Pick up books

And read them

And do the problems

But not a to a I admit

But a uni course is usually denser than a textbook anyway

Just a textbook*

[west spoke]

Replies like that are what scares me.

[glad rampart]

It’s what you gotta do if you wanna learn

[west spoke]

Thanks sherlock

[glad rampart]

Or take a class I guess

[west spoke]

Sorry for being blunt but I am not trying to not learn

I am just trying to ask how to develope computational skills based on my level of intuition informed by other things I know

A sensible question tbh

[glad rampart]

So you just want to be better at computation?

[west spoke]

And how to do the things done in analysis

[glad rampart]

So read an analysis book

[west spoke]

From the perspective of things that I know

[glad rampart]

Then read an analysis books that you have the prereqs for

[west spoke]

Efficiently

[high heath]

The main "things that are done in analysis" are proofs though

[west spoke]

That could be any analysis or calc book based on the fact that I don't know what the prereqs considered are for most analysis books

[west spoke]

As with any other discipline of math

[glad rampart]

You could Google the prereqs for the various good analysis books

[west spoke]

I literally have 0 discomfort with engaging in proofs

[glad rampart]

Spivak is part analysis part calc and it only assumes knowledge up to trig iirc

[west spoke]

Also prereqs is one thing. Flavor is another

[glad rampart]

In the time you’re spending trying to find “the perfect book” that might not even exist you could just pick up a good book and already have learned a lot of analysis

[west spoke]

I literally can't refute this

While also not having wasted more than 30mnuites
Which is valuable time, which to be honest could've saved by thinking of a better wording

Thanks

[glad rampart]

Np

[west spoke]

Googling the prereqs is a good piece of advice

The style rash. But whatever. I might just be sensitive

The advice was valuable

What would be considered the most hardcore real analysis book

That still embedded into how analysis is taught on undergrad

[glad rampart]

I’ve heard baby rudin is hard but maybe not good as something to learn from

[west spoke]

What defines good to learn from

[glad rampart]

Something that teaches the concepts in a good way instead of being more like a reference book

[west spoke]

Ok. I see. So a book with "tense proofs" and nothing else would be considered a reference book

O am not afraid of abstraction is what I wanted to say.

Whatever thanks for the suggestions I'll delete my messages now

[molten mason]

Mostly this, yes.

A lot of "good" learning/teaching textbooks will hold your hand and answer questions you didn't even know to ask.

A lot of the "reference" type of textbooks basically expect you to already know the content and have gone through a class and another textbook successfully.

[molten mason]

I would say this is false. I did 3 semesters of Calculus and we skipped a lot of sections, paragraphs, exercises etc. It was very rushed.

Going through a textbook yourself you can actually dive deep into the material and learn it.

You can 100% do Analysis without Calculus, but I would recommend at least either skimming through a Calculus book over a week(end) or watching some concepts on YouTube. You said you already know about derivatives and integration. I don't know how much you know but I'm sure it's fine.

I would for sure NOT skip through any chapter about Series and Sequences. This material is generally covered in a Calc 2 class in the US and is pretty independent of the rest of the Calculus textbook. It's important knowledge overall and I would go through as many of those exercises as possible.

@west spoke if there's any section about theorems I would look at that too. For example Stewart is a very computational Calculus textbook but at the end of the book in Appendix F is a whole section, Proofs of Theorems

[still panther]

yeah this is like wildly untrue

especially if you dont skip exercises

[trail hemlock]

why would you do analysis without calculus

[still panther]

here we dont have calculus we just have analysis

[trail hemlock]

a rigerous calc textbook is good prep for maturity imo

but if it works it works

[still panther]

and honestly its much better that way, i dont understand the separation at all personally

[molten mason]

Yeah they were already recommended Spivak above

[trail hemlock]

my fav 😍

[molten mason]

Money

American Math departments make their money teaching computational Calculus to all the engineers and physicists and medical students

[molten mason]

Some Calc classes here are in the hundreds of students

[still panther]

having a math course without or with little proofs is just insane in general

like ridiculous

[gray gazelle]

Just make the physics majors take analysis anyway

They’ll benefit from it down the road

[still panther]

here all the stem courses just take analysis

both physicists and computer scientists

and engineers

[west spoke]

I prefer deep diving yes, I just mean that optimally while a course requires you to learn the things in a short period of time, theoretically if undistracted and optimal, it should be the "richer experience" to draw from. That practically it isn't like this I know

My question remained badly asked and therefore unanswered but I thought of a route to take. I'll maybe rephrase my question

At a later point in time

[gray gazelle]

Optimal textbook study is more efficient than a course

[west spoke]

Argh I know

But I am also asking more or less

Ah whatever I'll ask at a later point in time and maybe contribute later

[graceful moon]

Literally just read a book it’s not that deep

[west spoke]

I am reading books all the time

When I get the time

Just saying

But whatever

[west spoke]

This reply is good but you missedy point and misread, which is due to my writing style probably, what I wrote. It's not important I'll just tailor an analysis study route

[west spoke]

It should be maybe is what I mean. Maybe, produces more written symbols. I had the experience that the hand holding on the linear algebra courses I took was more or less an additional guard rail where essentially someone just does proofs that if you do them or equalthings yourself too, you can draw from the things presented in a manner that if you combine the theorem by theorem atusy of the book with a well prelared course , both things together form a nice reference that would not be there the other way around
It is probably the same if you do this all by yourself, which is exactly what I am asking

Could also be considered more superfluous or paced to the didactic part of it idk. So maybe I am asking for a good reference book or something idk.

Dense usually means dense formal proof as in as abstract and dense as possible. I know this is not true. This whole discussion is literally me DID'ing.

I'll drop it until further notice

But my question was not: how do I study precalc calc ana, but rather how do o use undergraduate analysis best effectively as a reference since never having taken analysis, to engage on everything I will need it for and I'll just set up a study path for myself.

With considering suggestions

[gray aspen]

Hi Everyone,

Where an I find Elementary Linear Algebra with Applications, Student Solutions Manual 11e PDF to buy?

[west spoke]

Forget what I asked

In this thread on book recs. I'll delete it soon.

I'll just stick to the things I am studying and ask specific questions

[quasi haven]

Which book is recommended for Linear Algebra, especially for engineers?

[rare tundra]

Good book to learn caculus?

[trail hemlock]

what’s your end goal? pass a class or learn is for analysis or something else

[rare tundra]

Well really learn it really well

To be able to use it

[trail hemlock]

probably go for a more rigerous book like apostol or spivak

they focus less on intense computations

but for computations and not many proofs or rigour there is stewart

[gray gazelle]

Got one for beginners?

Absolute beginners

[trail hemlock]

my intro was spivak actually. but for no rigour hand holding, go for thomas or stewart. if you care about proofs and difficulty. spivak, apostol, or mcculer’s honors calculus are good

[gray gazelle]

I love you blackbeard

Best guy in here fr

Nohomo btw

Thanks

[trail hemlock]

anything on this list is considered good

https://www.amazon.com/shop/themathsorcerer/list/SKD9TCJQOZAI

[gray gazelle]

🥲you are too good

Thank you man

[trail hemlock]

sure

[gray gazelle]

C-can i add you

[trail hemlock]

ion add ppl idk irl

[gray gazelle]

Its ok brother

I still like you

Have a great day

[trail hemlock]

u2 💯

[gray gazelle]

🙏

[quasi haven]

Which book is recommended for Linear Algebra, especially for engineers?

[next condor]

I think that Gilbert Strang's book "Introduction to Linear Algebra" adequately fulfills the requirements of an applied field. If you're into programming, you might also be interested in Philip Klein's book "Coding the Matrix".

[gray gazelle]

Does anyone know of a good text on the history of math? Particularly of NT?

[remote sparrow]

you might be interested in books that combine linear algebra and differential equations together

[trail hemlock]

does hubbard and hubbard do that? its in the title but ive never read it

[remote sparrow]

it says differential forms, not differential equations

[trail hemlock]

genuinley whats the diff

[gray gazelle]

differential forms are objects you can integrate... very different from diff eq

[marble solar]

heh

Exact equations are always fun

[trail hemlock]

oh 😳

[marble solar]

There's a connection between them

Differential forms are definitely objects you can integrate, and you can do PDEs on Manifolds in different ways

[marble solar]

Also complex analysis exists, which gives you a way to go back and forth from these forms to derivatives

[slender cargo]

A retiring professor gave me his copy of Spivak’s Calc on Manifolds, with handwritten notes inside! Now I feel compelled to go through the book in his honor.

[trail hemlock]

you might be the luckiest person oat

i plan to go through that book with lee's itm it looks fun ]

[slender cargo]

I am very lucky indeed

[trail hemlock]

i think darq said we can pivot the reading group to spivak after rudin is done so 🤞 maybe

[slender cargo]

My course for multivariable analysis is going to use Edwards Multivariable book, but I might try to read Spivak concurrently

[trail hemlock]

never heard of edwards, is it good?

for multi iplan to use "advnaced calculus a geometric view" and hubbard and hubbard

[slender cargo]

It's older, and I think it's more like Shifrin's Multivariable Math book

can't really say

I know Spivak in his Calculus book compares it to his little book in the book recommendations section

[trail hemlock]

PepeMonkaHmmm

[slender cargo]

(and it's a Dover book so it's cheap)

[trail hemlock]

🏴‍☠️ most books are pretty cheap iykyk

[marble solar]

Spivak's Calculus on Manifolds is a wonderful little text with the right guidance

It's hard to read on your own, there's lots of errors, and gaps in his proofs

[tribal crow]

[marble solar]

I had it as my last math class at Community College, and it was essentially at the graduate level

[trail hemlock]

yeah thats why i hope the rudin reading group will pivot.

[tribal crow]

amukh and I are going to try our hands at ITM + Spivak(/Folland) in a few weeks

[slender cargo]

holy shit that's a crazy community college

[trail hemlock]

why not finish rudin first tho

[tribal crow]

well I'm not reading Rudin lol

idk about amukh

he's doing Abbott afaik rn

[trail hemlock]

bruh

literally a worse book

[marble solar]

yUh, we did an honors calculus sequence that used Spivak's Calculus. Honors Calc 3 was intro to differential geometry: frenet equations, fundamental forms, etc. Honors Linear Algebra/Diffy Q was 8 weeks of point-set topology, then 8 weeks of exterior algebra

[trail hemlock]

than my hero walty

[slender cargo]

That's ridiculous

in a good way

[trail hemlock]

😬 my local community college only goes up to..... linear algebra

💀

[marble solar]

Yeah, most of the people at my CC went to UCLA or UC Berkeley

[slender cargo]

most prepared math student coming out of that community college

[marble solar]

The ones in the honors math, at least

[trail hemlock]

oh wow

this aint abt books yall shud prolly move to advnaced lounge

[tribal crow]

I mean it's his choice yeah?

but yeah, if you ever want to join us with ITM/Spivak, you're always welcome to

[trail hemlock]

i will never stop hating on amukh

[trail hemlock]

🙂 over summer ?

[tribal crow]

I suppose we're starting in like

early May

it's not an actual reading group or anything though

just going through stuff

[trail hemlock]

cool

[hollow shore]

can I get an invite?

I am gonna restart Real Analysis too

[tribal crow]

I mean there's no invite necessary

we're planning to open a thread in #point-set-topology where anybody can type

[hollow shore]

is it spivak com?

[tribal crow]

ITM is for topology, and we'll be (hopefully) reading CoM as well

also, we should move to #serious-discussion if you want to talk more

this isn't the channel

[hollow shore]

okay

[trail hemlock]

jus join rudin reading goop

we pivoting

[tribal crow]

I can't make that type of committment

[west spoke]

Seconded idk why I worded it like that.

[west spoke]

What is ITM?

[daring lake]

Intro to Manifolds

[rich sun]

Topological Manifolds

[heady ember]

Pivot in what way

[heady ember]

[gray gazelle]

Hey I am currently in Grade 12, can anyone suggest any books or pdfs(I do not want videos) that can explain why and how the taylor expansions work?

[dense loom]

Is there a Rudin reading group in this server? Can I join it ?

[clever elbow]

Does anyone have any recommendations for a first homological algebra book? Ideally one that includes Hochschild (co)homology but that's not strictly necessary

[earnest wolf]

https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/pages/lecture-notes-and-readings/

see lecture notes for week 11

but beware u will likely need to be familiar with at the very least derivatives and Mean Value Theorem

by 'how does it work' u meant the proof/construction of it, right?

ow for intuition 3b1b's video is just a m a z i n g

[gray gazelle]

Yes

[gray gazelle]

3B1B has a video on this?

Nice

Thanks a ton

[lusty ermine]

how to get started in vector analysis?

any readings?

[torn crypt]

Uhhh, no idea how Rotman compares, but Weibel isn’t bad (if you can check the errata and all that)

[clever elbow]

Alright cheers

[versed meteor]

guys please give some good lecture series for complex analysis, i searched a lot but cant find any good resource (videos) for it

and i am looking for undergrad level material

theres richard borcherds lectures on this but i dont know if they are complete or not, i think he is still yet to upload them all

[gray gazelle]

You can probably find someone’s lecture notes from when they taught it

[versed meteor]

i mean i am kinda looking for videos to watch

[versed meteor]

but thanks for the suggestion

[lusty ermine]

which book has good exercises on taylor expansions

[eternal yarrow]

does the book Cracking the AP Calculus AB Exam any good for the ap exam ?

[trail hemlock]

yes. any barons / princeton review stuff is great for ap review

[eternal yarrow]

is it still worth going through the book if i have got a month till the exam? it's a 1000 page book i mean

[trail hemlock]

your teacher should have some material for you, and there is soooo much online stuff

i didn’t use a prep book for the calculus bc exam

[eternal yarrow]

actually i am not in america and didn't know about the AP exams being held in my country till recently. I just signed up barely making the last date for apps

i am studying for it all on my own

[trail hemlock]

so you haven’t studied calculus before?

[eternal yarrow]

no i have studied calculus, i know all of calculus 1

[trail hemlock]

oh then you will be alright with online stuff

[eternal yarrow]

in my country calc 1 is taught in the junior and senior year of highschool

[eternal yarrow]

could you like link some resources ?

please

[trail hemlock]

just watch shit tones of videos and read the rubric for tjr frq. they are super stringent on notation

[trail hemlock]

1 sec

[trail hemlock]

https://www.beyondcalculus.com/

[eternal yarrow]

oh i see... i realized while looking at spivak that a lot of the notation we use here didn't match with what was in spivak. So maybe i will have to look into that

[eternal yarrow]

thanks a lot

[sleek python]

Wasn't there a channel with a book list per topic?

[eternal yarrow]

huh? it doesn't show that to me in my channels list, could you link to it maybe?

[trail hemlock]

u learned calc from spivak? yeah just check out the notation stuff

[sleek python]

Idk I'm asking, I remember such a channel existing but maybe it's been deleted since

[eternal yarrow]

no i didn't learn calc from spivak, i just looked at it recently

[trail hemlock]

yes it’s #books-old and you need to go into channels and give yourself access

[sleek python]

Ok thanks

[eternal yarrow]

thanks for the resource i will get back to studying

[tribal crow]

besides the sections in LADR and LADW, what are some other sources to learn multilinear algebra from?

I want to weigh my options

[gray gazelle]

Greub has a multi linear book

That being said, multilinear is probably just best picked up as you go

Rather than studying it in isolation

Are you familiar with Halmos’ treatment of the determinant?

[tribal crow]

I've not read Halmos, no

[tribal crow]

fair enough

how does Halmos treat the det?

[gray gazelle]

He treats it as a number corresponding to a linear operator on the space of n-linear alternating forms

It’s worth checking out

If you’re interested in multilinear

[tribal crow]

let me take a look...

oh I've had a somewhat similar treatment of the det in my LA course

a bit different, but I recognize some similarities

that being said, I'll take a look at Greub too

thanks eigenpuppet

I think virtually any calculus/analysis textbook would cover Taylor series in good depth

[gray gazelle]

Looking for some math resources. (Ping if posible)..

[tribal crow]

math resources for... what exactly?

[gray gazelle]

I have a program.

Can I show you?

[tribal crow]

this doesn't tell me a lot

lol

[gray gazelle]

I have a program that have every topic I need to master. What do you mean?

[tribal crow]

okay, then show it

[gray gazelle]

We need to chat in dm-s. I want to exprot the messages.

[tribal crow]

if possible, I would prefer to stay here

and not take things to DMs

[gray gazelle]

We can try.

Firstly:

I need some math resources made for self learning. No teachers. Without colors and in black and white form. It should provide answears in the end of the exercise. (Only the x or smth.)

[glad rampart]

Books

[tribal crow]

we cannot recommend any resources without knowing what kind of math you want to study

[gray gazelle]

Can you fullfill this before going to the next step?

[tribal crow]

well, it depends on what you want to study...

this is really odd

[molten mason]

If you need to master Algebra then Serge Lang has a great book called Algebra

[gray gazelle]

First thign to find:

[tribal crow]

you want resources that meet your constraints, but you haven't stated what you even want to learn

[gray gazelle]

Cant I send images here??????

[tribal crow]

...sure?

[gray gazelle]

I have.

[molten mason]

New accounts can't

[gray gazelle]

I have told you 3 times I have a program.

[rigid forge]

imgur exists

[tribal crow]

that isn't useful information

I don't know what you mean by program

what's in it??

[gray gazelle]

How cna send some images for me?

[gray gazelle]

Program is a kinda plan with all what I need.

[rigid forge]

just copy the image, go to imgur, paste it and share the link

[gray gazelle]

Program. 4th time.

[tribal crow]

alright, now I'm just confused

I don't know what you mean by program at all

[gray gazelle]

A program Is what I have to learn.

1. vectors (blablabla)

[tribal crow]

tell me what's in the program.

[gray gazelle]

Nvm

GEOMETRY IN THE PLANE
• Understanding the distance of a point
from a straight line.
• Properties of angles with a
common vertex: additional,
complementary, opposite angles at
the vertex, etc.
• Corresponding angles
formed by the straight line
parallel.
• Congruence of any
triangles (BKB, KBK, BBB)
and triangles
right angle.
• Basic criteria of similarity
of triangles.
• Properties of the isosceles
triangle.

• Circle theorems referring
to angles, radius, tangent,
chords.
• Equation of the circle in the
form (xa)2+ (yb)2= r2.
• Equation of the line in the plane.
• The condition of parallelism and
perpendicularity of two lines.

[molten mason]

So just Geometry

[glad rampart]

Just pick up a geometry book dude

[gray gazelle]

Not just geometry.

[tribal crow]

I'm just confused why it took this long for you to state what you're learning

[molten mason]

But you could have written "Geometry" instead of all that

[gray gazelle]

My teacher told me find resources that are seperated only for one topic.

[gray gazelle]

Not the whole geometry...

I have wasted time last time on trigonometry learning 90% while 30% was needed.

[glad rampart]

Trig will be super useful

You should learn all you can of it

[gray gazelle]

I have 1 month to my final exam.

[glad rampart]

And you haven’t been keeping up with your studies?

[molten mason]

There's never any waste in trig. You'll need it for pre-calc and calculus

[gray gazelle]

No, not at all. Studied 70% of my program in 3 months.

[gray gazelle]

I have to learn 30% of program in 1 month.

Dont have time to flex.

[glad rampart]

Study hard then

[gray gazelle]

Resources...

[molten mason]

Good luck

[glad rampart]

Book

[molten mason]

Youtube

[glad rampart]

I read an entire ent textbook in like a month

You can do it

[gray gazelle]

I like to study with paper sheets.

Look an website:

(To get an idea on what i am talking about.)

Look: https://www.mathcentre.ac.uk/courses/mathematics/trigonometry/

I like this but the away that they explain is not bad but not good.

[glad rampart]

Why are you so adverse to reading a textbook

[gray gazelle]

Elon Musk away. Long story.. dont ask.

[glad rampart]

I’m not sure what Elon musk has to do with math studying, pretty sure he never did that

[gray gazelle]

Any website I can search papers in certain topics like: "Understanding the distance of a point
from a straight line."

Lets say I just want to learn this.

Example: https://www.mathcentre.ac.uk/resources/uploaded/mc-ty-rcostheta-alpha-2009-1.pdf

[hallow oriole]

so true, everyone should be forced to learn that $$\sum_{n=1}^\infty (-1)^{n+1}\arctan{\left(\frac{1}{F_{2n}}\right)}=\arctan{\left(\frac{1}{\phi}\right)}$$ where $F_k$ is the $k$th Fibonacci number and $\phi$ is the golden ratio

[hasty eagle]

valley

[glad rampart]

Holy shit that’s cool

[gray gazelle]

Studying is never waste of time, but I dont have that lux since I have bomb ticking.

[hallow oriole]

isn't it??

[gray gazelle]

Anyone can help?

Any website I can search papers in certain topics like: "Understanding the distance of a point
from a straight line."
Lets say I just want to learn this.
Example: https://www.mathcentre.ac.uk/resources/uploaded/mc-ty-rcostheta-alpha-2009-1.pdf

[glad rampart]

So do I

[rigid forge]

is there actually a good book on how modern hardware works? like to build a good mental model, I am not trying to implement a kernel driver or something.

[violet shuttle]

wait lemme see why

[hallow oriole]

like a proof?

or will u do it urself

[violet shuttle]

sum of arctans is arg of product of complex numbers

[hallow oriole]

ooh sick

[violet shuttle]

so
arg{\prod_{n=1} (-1)^{n+1}(F_{2n} + i)}

well this diverges

(ofc this doesn't prove the angle diverges)

((like i'm saying it's not a contradiction))

[gray gazelle]

Any geometry pdf? 12 class.

[violet shuttle]

idk here

[violet shuttle]

Lee's Riemannian Manifolds

[hallow oriole]

do u want hints

[violet shuttle]

Or perhaps those lecture notes on symplectic geometry

[violet shuttle]

yes

[gray gazelle]

Selfstuding textbook?

[violet shuttle]

i mean i used it yes

[hallow oriole]

xela wrong geometry

[violet shuttle]

shhhhhh

oh!

you want Hartshorne, gotcha.

[tribal crow]

😆

[gray gazelle]

Lee's Riemannian Manifolds textbook = 3 * schoolbag full of books.

[violet shuttle]

no don't get the whole series

[gray gazelle]

And still none of the topics that I am looking isnt there.

[violet shuttle]

get smooth manifolds if you don't already know the basic DG

[gray gazelle]

https://www.maths.ed.ac.uk/~v1ranick/papers/leeriemm.pdf

[violet shuttle]

but riemannian manifolds are where there's a metric thus making it geometry

[gray gazelle]

All I am looking for: • Understanding the distance of a point
from a straight line.
• Properties of angles with a
common vertex: additional,
complementary, opposite angles at
the vertex, etc.
• Corresponding angles
formed by the straight line
parallel.
• Congruence of any
triangles (BKB, KBK, BBB)
and triangles
right angle.
• Basic criteria of similarity
of triangles.
• Properties of the isosceles
triangle. Circle theorems referring
to angles, radius, tangent,
chords.
• Equation of the circle in the
form (xa)2+ (yb)2= r2.
• Equation of the line in the plane.
• The condition of parallelism and
perpendicularity of two lines

BRUH

[violet shuttle]

okay but like gauss bonnet helps you out there

the "condition on parallelism and perpendicularity of two lines" is literally false

[hallow oriole]

1: ||you can bring the (-1)^(n+1) into the arctan||
2: ||note that (-1)^(n+1)=F^2_n-F_(n+1)F_(n-1) and that F_(2n) = F^2_(n+1)-F^2_(n-1)||
3: ||recurrence relation of fibo ||
4: (big hint) ||can you get this into a telescoping series with arctan(a)-arctan(b)=arctan((a-b)/(1+ab))||

[violet shuttle]

"equation of circle and line" you'll get from Hartshorne's Algebraic Geometry.

(something something schemes something stack something homological magic something blow up uhhh idk)

[gray gazelle]

Math is hard to be found.

😭

[glad rampart]

Just read a geometry book??

[violet shuttle]

1. umm i actually don't remember uhhh uhhhhh -atan(y/x)=atan(-y/x) right

[tribal crow]

I didn't realize Xela could be a troll

I love it

[violet shuttle]

there's a lot of geometry

[glad rampart]

A high school geometry book

[violet shuttle]

trolling? what are you talking about? i do this all the time

[hallow oriole]

arctan(1/F_2n) is always positive 😭 so yes you can bring it in

[violet shuttle]

i started reading my purchased copy of Riemannian Manifolds in highschool, does that count?

[violet shuttle]

yeah okay that's what i thought

[tribal crow]

I am inclined to say that you're a persistent troll then

[gray jungle]

born to love awful notation

[violet shuttle]

2. what

[glad rampart]

Xelas training data got contaminated oh no

[tribal crow]

but, I know that you did do stuff like this when you were in hs

[hallow oriole]

first one isnt that hard to prove, second follows from binet

[violet shuttle]

excuse you it's much better than Wald's notation

because physicists amirite

[violet shuttle]

...binet?

[hallow oriole]

binet's formula

[violet shuttle]

for the orbit?

[hallow oriole]

$$F_n = \left(\frac{\phi^n - (-\phi)^{-n}}{\sqrt{5}}\right)$$

[violet shuttle]

of a body in a central force?

this is false

$F_n \ne ($

[hasty eagle]

valley

[hallow oriole]

proof? smh

[hasty eagle]

Xela

[violet shuttle]

right just from linear algebra

[hallow oriole]

yeah yeah anyways the identities follow

u can use them for free

[gray jungle]

almost forgot why i even came here, anyone know a good reference on representation theory? not sure what the "classics" are

[violet shuttle]

fulton and harris for that of lie groups and algs

then look at the freudenthal magic square

then quiver in bliss

[hallow oriole]

xela the fourth one is actually a fairly big hint combined w the other three

so if u wanna fully solve it dont look at that

[molten mason]

You have no idea. It's so beautiful

[molten mason]

All of that sounds like a great convo for #math-discussion

[dapper root]

Bro is calling Xela beautiful oooooooooo

[violet shuttle]

awwwww

[molten mason]

You choose this to be your first comment here in two weeks

[violet shuttle]

It's a book recommendation.

Xela is Beautiful, by Salagos the Salad God

[glacial coyote]

I don't believe i fell for that and searched for the book

[trail hemlock]

after i finish baby rudin, to learn measure theory, is this good?
https://www.amazon.com/REAL-ANALYSIS-THEORY-MEASURE-INTEGRATION/dp/9814578541
yes i am aware of papa rudin, but i dont have a reading group for it, so im not sure how much i can benefit from its brevity

[loud cradle]

this is like the opposite of rudin, all proofs given with full details
it's quite dry reading but it could be a good choice if you are self studying

[remote sparrow]

clarinetist likes this book

uh he used to be here, he's only on the stats server now

there's an accompanying solutions manual

[loud cradle]

there's a separate volume with full solutions to all the exercises, btw

[trail hemlock]

i read the maa review, and the dude siad it was very terse, and i got so scared 😭

[remote sparrow]

wonder what that reviewer would say of folland then

[trail hemlock]

its my understnading that rudin is good for learning cuz it forces you to understand stuff yourself

does a book with all the details diminish from that ?

[remote sparrow]

you can just cover up the details if you want

[trail hemlock]

honestly i might just use papa rudin for exercises

[remote sparrow]

or just...don't read them? blackbox them, try a few problems, see if you understand the details after

you don't have to read a math textbook linearly

[trail hemlock]

hmm ok maybe

[loud cradle]

i like papa rudin, but i wouldn't recommend it as a first exposure to measure theory

[trail hemlock]

so like read hte definitions and try to proive the theorems myself? hm

[trail hemlock]

fair enough but i think the baby rudin problems are so interesting, so i might just take papa rudin problems after learning from somewhere else

[remote sparrow]

if you're planning to finish a certain syllabus in a given time frame, you may lose something spending all your time proving the main results instead of possibly trying to apply those results to new situations or extending them

as you become more advanced, you'll need to spend less time trying to understand everything

[trail hemlock]

this feels so counter-intuitive

[trail hemlock]

i dont wanna finish it by any time frame, i jus wanna learn it tbh

cuz its summer 🤷‍♂️

[mossy shell]

Anyone ever tried statistics by devore peak?

I mean jay devore

[violet shuttle]

i know you want it so badly

[molten mason]

I'll be going through this book but not until fall or next spring

[trail hemlock]

i’m doing it over summer, i think it will be fun

[molten mason]

Yeah I won't be ready that soon, plus that feels fast paced lol but let me know how it goes

[trail hemlock]

salute

imma finish rudin nicely b4 i start jus for prep

hopefully thats enough maturity 🤞

[vital bane]

james rep theory arc

[vast jackal]

guys who have an solutions manual to introduction to algebra by AOPS

[gray gazelle]

I need a quick calculus refresher. Can be a book or lectures. For a book I'm more interested in the "definition-theorem-proof" style rather than long chatty explanations. For lectures it would be good if they were fast paced and dry (quick proofs and no obvious examples).

[ocean mulch]

So... Bourbaki?

[gray gazelle]

not sure if they have a calculus text but it will definitely be above my level of mathematical maturity

after a bit of wandering around, Baby Rudin looks like a good option

but any other suggestions and opinions are welcome

[vital bane]

Rudin is perfect

has very little explanations
very short proofs with no explanations

[vital bane]

oh nvm you already did look at it

[gray gazelle]

I just looked at the ToC

[gray gazelle]

but this is good

[heady ember]

Real men prove everything themselves

[vital bane]

real men invent analysis from scratch instead of learning it from a book

they stand on their own two feet instead of on the shoulders of giants

[heady ember]

[gray gazelle]

wish I was a real man then

[supple sandal]

Hello o/
Can someone give me a book to learn calclus? ||idk but I feel this is a stupid question and I shouldn't be here when asking this but ok :D||
or any book that gives me a good foundation just ping me or dm thx

[supple sandal]

Thx

[gray gazelle]

I’d also recommend Browder, which is similar to Rudin, but has better measure theory + multi variable

[gray gazelle]

thanks, I was concerned about the multivar portion of Rudin looking kinda weak

[amber galleon]

calculus made easy by silvanus p thompson is a nice thin book that imo gave me a good foundation

nice little book to read before you move on to the big boys

[uncut zealot]

You might have a reading group! We'll see.

The book that I used for real analysis was Royden-Fitzpatrick.

[earnest wolf]

can u guys suggest some software to kind of create the contents page for a pdf?

I have a bunch of ebooks that are basically scans, and it's really inconvenient to navigate through them

If that matters, I use the vanilla iBooks + (Apple) Preview combination

preferably open source stuff, and maybe light weight?

but anything else works as well

[hallow oriole]

you can 100% do this in acrobat

ur uni might have an adobe license

or there are also alternative acquisition methods

[earnest wolf]

i think it isn't open source + paid

[hallow oriole]

.

[earnest wolf]

yeah exactly — most probably not

[earnest wolf]

i meannnnnn...

pĩråtïņğ pdfs is safer than pĩråtïņğ binary executable files

[tribal crow]

is acrobat not free?

[hallow oriole]

who said anything abt pirating

smh

[trail hemlock]

happy_excited

oh god that emoji isnt what i thought it was

but anyway i would rather have a spivak calc on manifolds group cuz its like exponentially more terse than yeh

[heady ember]

Massochist mindset

More terse = better

[trail hemlock]

💯💯

[remote sparrow]

acrobat is free, but you cannot edit PDFs with the free version

[earnest wolf]

oh, so it's useless for my purposes then

[graceful moon]

Just re-type them all in TeX and use \tableofcontents

[uncut zealot]

I'm not really qualified to run a group for calc on manifolds given that it's a topic I don't know

[trail hemlock]

zorn is all wise and all knowing. it follows that this account has been infiltrated by a bad actor

[torn crypt]

Infiltrated by a pde hater

[molten mason]

There should be a free trial

[gaunt path]

Any book recommendations for finite group representations for an undergrad?

[mossy flume]

Serre's text

https://link.springer.com/book/10.1007/978-1-4684-9458-7

Alternatively if you want a focus on something of a smaller scope, but quite combinatorial and beautiful

Sagan's text is fun

https://link.springer.com/book/10.1007/978-1-4757-6804-6

builds up the representation theory of the symmetric group over the complex numbers

and all the associated combinatorics

so I guess it depends if you want something broader or something more combinatorial

[gaunt path]

Do any of them go over more than just linear representations?

[mossy flume]

?

[gaunt path]

Forgive me because i haven't learned the subject yet, but can you represent groups with more than just linear transformations?

[mossy flume]

I guess technically yes

but you'd be amazed how far you get with just linear reps

[gaunt path]

Is that not standard for a first introduction?

[mossy flume]

I think non-linear stuff is very advanced and very specialized

no

[gaunt path]

Ok, thank you for the book recommendations!!!

[mossy flume]

I think this would be the best option tbh

unless you know you want to do more combinatorial stuff

and even then at least look at the first chapter of the Serre text

[gaunt path]

combinatorics is one of the subjects i have not looked into yet. Would that be ok for this one?

[mossy flume]

eh sure but then just start with the Serre text

[gaunt path]

ok!

[mossy flume]

if down the road you get more interested in the combinatorics of the symmetric group

you can come back to the Sagan text later

[pine widget]

ah combinatorics is so so so *(1/0) beautiful when we understand what is really happening and why we use that one specific method to get the answer

[earnest wolf]

guys, what do you think of Carother's real analysis book?

Is it a good resource to learn lebesgue integral?

I opened it recently (idk how it ended up in my ebook collection) to find smth, and I really liked his style

I'm wondering if his book is considered a good one for that purpose (ie motivates and explains in detail the lebesgue integral)

sure, there isn't the best book on a subject, but maybe there are some problems with his exposition I don't yet know of that make it not worth spending time on it

okay, I did a quick search and @remote sparrow seems to like it a lot

Ig I will give it a try then

[vital bane]

a measure theory book would be a good resource to learn the lebesgue integral innit?

[earnest wolf]

i just liked his writing and saw he has a section abt lebesgue int

[candid creek]

linear lagebra textbooks people?

for a 2nd course

would love one that talks about intuitions to concepts rather than just dump proofs

i.e., would love to have some geometric intuition that 3b1b gives

not essential doe

[vital bane]

I would recommend LADR by Axler 4th edition but look at #book-recommendations message for a more comprehensive review of books

[gray gazelle]

Halmos is the best

He does a good job of (in an albeit terse manner) distilling the geometric intuition for the subject

[narrow relic]

I found his "bracket" notation confusing.

[narrow relic]

You might want to check out Lang's Linear Algebra, that book has really clicked with me.

[gray gazelle]

Oh the dual space notation?

[narrow relic]

Yeah I think so, I just found it all confusing. I've been reading Lang and I haven't gotten to that part yet but I have a feeling it'll be less confusing than the Halmos book.

[gray gazelle]

He does that because it specializes to inner products once you prove riesz representation

[narrow relic]

I've heard Halmos is a highly recommended book just somehow it didn't click for me.

[gray gazelle]

That’s fair

[narrow relic]

Similar with Lax, couldn't stand that book.

[gray gazelle]

His approach is weird

Since he presents it as finite dimensional FA

[narrow relic]

So far, Lang has been super solid for me at least

[gray gazelle]

Nice

[narrow relic]

I think a lot of this is subjective, different things work for different people in my opinion

[earnest wolf]

I mean, I'd bet if you really want to have intuition for the 'advanced' linear algebra, you will have to leave the three dimensions and forget abt any visuals : (

[earnest wolf]

LADR is life

[narrow relic]

The only downside to Lang is that there's a key proof where he uses a fact about matrices that I have a feeling doesn't work when you go to infinite dimensions

But I haven't discussed that with anyone so who knows, I might be wrong.

[earnest wolf]

wait, doesn't most of finite dim lin algebra ||(say the results that are typically taught during undergrad)|| break when u go to inf dim?

[narrow relic]

I have no idea! 🙂 I'm not that advanced.
So maybe it's not a big worry. Here, can I run it by you?

[earnest wolf]

I mean, neither am I
better ask in the appropriate channel

[lusty ermine]

readings for euclidean geomtry from the groundup?

[vocal owl]

you guys know any good websites for practicing/touching up on quick mental arithmetic to prepare for interviews?

[dusk wind]

@earnest wolf use pdfxchange

[earnest wolf]

oh wow, looks exactly like what i need

thanks!!

[dusk wind]

yeah I had the same problem as you before

with that you can 'fix' any document even with the free version

[narrow relic]

Just asked about it in the linear-algebra channel and a nice person helped me, he said that indeed the result I was talking about doesn't hold for infinite dimensions and Lang's approach of using finite-dimensional tools to show it is a fine one and that every linear algebra book does it that way.

[narrow relic]

This book has some major issues, I'd personally be careful with it. I found two major mistakes in it when working through the first few chapters and someone in the analysis channel told me "get a different book."

[remote sparrow]

https://aaron.na31.org/Carothers_Errata.pdf

there's an errata sheet on the web

[gray gazelle]

This is the selling point of Halmos: he tries to write every proof in a way that easily generalizes

[candid creek]

I mean, from what I have encountered so far in linear algebra and calc, most higher dim concepts are motivated from generalising the finite dim cases

so in my case, I find reasoning by analogy much easier to gain some intuition of certain concepts

[earnest wolf]

see this thread I started a few hours ago : ) #advanced-lounge message

I mean, you risk tricking yourself into understanding a thing this way

But I do agree that type of intuition is probably important at least as a 'guide' to how to approach more abstract things (although justification later is almost surely essential)

[candid creek]

any "trickery" or major misundrestanding should reveal itself when doing practice Qs

cue the Groethendick quote on proofs

[violet shuttle]

no!

there always exists an orthonormal basis

the spectral theorem for bounded compact normal operators holds

to an undergrad, those are the only operators

[gray jungle]

well compact operators are a special case of "operators that behave as we expect a matrix to", but for other operators, things do break

[hazy elk]

Undergrads encounter many differential operators in courses on ODE and PDE

[violet shuttle]

shhhhhh

they don't know that those can be studied like this i don't think

at least the physicists have some clue

[gray jungle]

its the best introduction to unbounded operators

makes it click why we have to define each one on its own domain

[violet shuttle]

yes physics is indeed why i'm like "okay but my operators are unbounded, my representations are infinite dimensional, and i haven't even done anything beyond x and \partial_x"

also "distributions pls"

"rigged hilbert space or something"

[hazy elk]

I've been meaning to finally study some quantum stuff

Follands book looks interesting

[noble wren]

Hello, I'm studying physics and currently taking a math course for physics students. We started with a little bit of topology(metric spaces, open ball, completeness) and normed vector spaces, banach spaces, bilinear forms. Normally it's supposed to cover differential equations, multivariable calculus, further linear algebra and maybe differential forms. Do you have any book suggestions that also has solutions? It shouldn't be something like Rudin I'm not that comfortable with math.

[gray jungle]

do you want a book on the "topology , normed vector spaces,..." part or the "differential equations, multivariable..." part

[noble wren]

Well I would need all of them 🙂

Our university library is big so I can find most of the books there.

[gray jungle]

for the first half i would recommend kreyzig introductory functional analysis, its a friendly book compared to other books. As for linear algebra i think hoffman kunze is very good, its very detailed but it is not as friendly as other books.

i dont think i can recommend a differential equation or multivar book thats not aimed at math students

because i didnt read much of those

[noble wren]

Thanks for your suggestions! I'll borrow them from the library tomorrow.

[gray jungle]

but if you are interested, i do like arnolds book Ordinary Differential Equations, and spivak books "calculus on manifolds"

[remote sparrow]

https://www.amazon.com/What-Quantum-Field-Theory-Mathematicians/dp/1316510271/ref=tmm_hrd_swatch_0?_encoding=UTF8&qid=&sr=

https://link.springer.com/book/10.1007/978-1-4614-7116-5

see also these books by talagrand and hall

[flat ruin]

guys any book recommendations for someone looking into astrophysics thanks^^

[oak hazel]

I think three body problem, dark forest, and death end are pretty interesting

but some parts are kinda unrelated to astro physics

second and third are more Psychology/physics

[glad rampart]

I agree, great series

[violet shuttle]

wald's general relativity

there's some good astrophysics books I haven't read, covering plasma stuff and star stuff and inflation and whatnot

[remote sparrow]

carothers is mostly on metric and function spaces. there's some discussion on measure theory, but it doesn't replace a dedicated text.

[hallow oriole]

and what

[violet shuttle]

no, "and whatnot"

[hallow oriole]

i was thinking about the thing before it

[violet shuttle]

inflation?

what about it?

[hallow oriole]

tf does that have to do with astrophysics

oh

[violet shuttle]

Physical foundations of cosmology and astrophysicists for physicists

[hallow oriole]

inflation of the universe

[violet shuttle]

obviously

inflation is what we think happened early on

[hallow oriole]

im sorry xela i was confused and i didnt have faith in u

[violet shuttle]

some unknown effect caused it

[molten mason]

Imagine not having faith in Xela

I could never

[violet shuttle]

https://en.m.wikipedia.org/wiki/Inflation_(cosmology)

[hallow oriole]

might as well call urseld xela's #1 simp 😒

[violet shuttle]

i have simps now?

i mean i am objectively amazing

[molten mason]

That should be the name of the server at this point

[hallow oriole]

i have more dont get a big head

[violet shuttle]

inflate my ego

[hallow oriole]

it'll pop like a balloon

[violet shuttle]

So like an example is the cosmological horizon problem

We see homogeneities in the cosmic microwave background

Despite some regions being predicted to not have had enough time to thermally equalize with us early on before becoming causally disconnected by the expansion of the universe (and then of course later causally connected as light reaches us)

[tribal crow]

what book is this?

[violet shuttle]

(read)

[tribal crow]

I still have some interest in astrophysics

[tribal crow]

ah, I didn't realize that was the name lol

[violet shuttle]

yeah a friend of mine appeared to stop caring about astrophysics the moment it started getting like actually physicsy and mathy in highschool

so sad

[tribal crow]

tough

I lost most of my interest in astro when I got invested in math lol

though I still like the subject

[violet shuttle]

you should read goldstein's book on classical mechanics. it's clear and easy

[tribal crow]

I will!

Goldstein and L&L are on my to read list

[violet shuttle]

i've been having a fun time with it

[tribal crow]

Arnold too

[violet shuttle]

Landaufschitz's for statistical mechanics I will read later

[violet shuttle]

not a word of landau, not a thought of lifschitz

[tribal crow]

indeed!

[stone void]

Does anyone have the answer for OCR MEI a level 2023 past paper on pure and statistic

[foggy gorge]

Can someone recommend me some geometry book

[graceful moon]

What type of geometry? What do you know?

[foggy gorge]

I have about to zero understanding in geometry. I mean, I have basic understanding about lines, triangles and circles, and basic knowledge about coordinates geometry aswell

But I want to learn more

[vast jackal]

Khan Academy

Or Introduction to geometry by aops

[coarse arrow]

Introductory graph theory book with difficult problems along with solutions

[quick hornet]

you probably wont find any "serious" graph theory books with solutions included

thats a practice that disappears as you go higher in mathematics

you, as a student, are expected to be able to verify your solutions yourself

that said, Diestel is the gold standard text and therefore has a lot of solutions published by third parties online - as to whether theyre good, i can't say

you really should be reading Diestel if youre interested in anything nontrivial, graph theory is one of those fields where every other textbook is either too low-level (i.e. written for CS students) or too high-level (i.e. written for people who've already read Diestel)