book-recommendations

[vital bane]

yup

[deep summit]

and n=0

n= i

nvm

lol

[vital bane]

[real marsh]

n dimensional space is just 3 dimensional space with a different number of lines

[deep summit]

the formulas in such analysis would be functions of n right ?

general formulas

[real marsh]

idk it's been too long since I last saw an actual formula :(

what even is calculation

[keen orbit]

tysm

tysm

[real marsh]

Not quite cos anti differentation is like real and true

in R^1

[vital bane]

as opposed to anti-differentiation being complex in R^n?

[deep summit]

u are talking about multivariable analysis right ??

R^n to R

function analysis

right ?

not R^n to R^m

[vital bane]

I was thinking about R^n -> R^n

[deep summit]

where do u study general R^n to R^m ?

[rich sun]

multivariable analysis

[vital bane]

differential geometry

[sage python]

R^n -> R^m is part of multivariable

[vital bane]

it was partially a tongue in cheek response

but also partially not

because the only books you see covering things like divergence and curl rigorously are diff geo books

I have never come across an analysis book that does that

[vital bane]

in the form of more general and abstracted versions on manifolds but still

[wheat trout]

iirc, Mathematical analysis by Zorich did this in vector calculus part.

[sage python]

I'd say divergence and curl are a step up from just, analysis of functions R^n to R^m

The latter is stuff along the lines of the inverse and implicit function theorems, things like that

While the former is where you start to get into analysis on curves/surfaces/manifolds territory

Not necessarily full blown differential geometry, but yeah it's getting to that level

Though there are analysis books that do that story as well

[forest trellis]

Hi guys, I'm a guy who goes to high school and does computer science but since I like mathematics, I would like to deepen and carry on as a self-taught and I would like to ask you for a list of perfect books from algebra up to calculus and if you can also add something related to computer science such as algorithms, thank you

[gray gazelle]

Any good recommendations for multi − variable calculus books. I am thinking of using william wade's "introduction to analysis" book is it okay?

My background : single variable calculus and currently studying analysis 1.

[vital bane]

"Concrete mathematics" by Donald Knuth, Oren Patashnik, and Ronald Graham

[vast jackal]

anyone have the manual for Introduction to Algebra Solutions Manual 2nd Edition AOPS?

Hey are there any good free resources for foundation in Algebra up to Calculus? I'm planning to join the national team for the IPho in our country since it's not too popular compared to IMO and basically i still have wayyyyy lots of time practicing my problem solving skills and the problem with AOPS is it's hard to find some electronic copies and due to financial constraint i can't buy it i do have the pdf for Introduction to Algebra but i don't have the solutions manual for it

[marsh ingot]

For algebra

[vital bane]

Dummit and Foote the bible of undergrad algebra

🙏

[glossy zealot]

Both of their names are very weird though

[lime vessel]

DF

[loud cradle]

even weirder, someone told me that foote's name is pronounced to rhyme with boot

[vital bane]

Differential Fields

[fierce hedge]

Like boot-e?

[loud cradle]

like "boot", no "ee" at the end

i don't know if it's true, but this guy seemed pretty insistent that it was

[fierce hedge]

Yeah, NO

[graceful moon]

DF is a fantastic reference but if you’re working through the book do yourself a favour and use Artin, DF is extremely dry imo

[dusk wind]

https://realnotcomplex.com

[remote sparrow]

it'll always be foot to me

you can't change my mind!!!1

[remote sparrow]

check out zorich's Mathematical Analysis II

his Mathematical Analysis I also has a chapter on functions of several variables and a chapter on differentiation in several variables

the books are logically independent of each other though since he develops the necessary material in greater generality in volume 2

[rigid estuary]

Hi guys, I wanted to self-teach myself math from 0 so I needed your help to forge a path of books (paper ones) I could follow and be guaranteed that if I go through it, by the end of it I would have a very solid grasp on math.
Probably this is something asked a lot and probably this roadmap of books already exists, so I'm hoping you guys can point me to it.
A thing I should mention is that I'm not good at memorizing something like a formula if I'm not explained why it works, so the books I'm looking for should all aim to give the reader an understanding of things rather than just a bunch of formulas with little or no explanation.
And of course, every chapter of the books should be accompanied by many excercises 🙂

[graceful moon]

Im aware that you have specified books but give Khan academy a fair try if you haven't already, Its pretty hard to beat as an all in one place to learn high school maths

[rigid estuary]

I've gave it a fair shot in the past (I have 2.000.000 energy points in it), it didn't worked for me 🙂

[graceful moon]

What is your basic level right now and what would you like to learn it for? For example, if your fundamentals are ok and you'd just want to solidify your basics to lean more advanced maths from text books, Langs "Basic Mathematics" would suit, if you your level of maths is weaker or if your goals are different I think more standard highschool books would probably suit you better

For example a text book on GSCE maths, should be relatively easy to get in many places in the world

and should start from a pretty basic level and build your foundations

[rigid estuary]

my current knowledge is 0, there where too many holes randomly scattered in my understanding to begin with, and my last attempt with khan was probably 6y ago, so it's all lost.
But aside from that, a single book recommendation is not the way I would like to approach it because then it falls to me to understand what to read next and I don't like trying my luck with things. That's why I'm interested in a "well/time tested progression of books" 🙂

[graceful moon]

This is why I'd reccomend a book on like GCSE maths, there is a natural next step to take (A level) and it is used all over the world (Primarily in England, Wales and Northern Ireland but a lot of international students use it too) so there is a plethora of resources. Plus it starts from a very basic level and covers a wide range of topics

[remote sparrow]

https://precalculus.axler.net

try axler's precalculus book

[rigid estuary]

this is essentially me choosing a book, right? That is also trying my luck, that is why I'm asking others 😄 I don't have the money to afford trial and error

[graceful moon]

Probably not a great choice for someone looking for a complete understanding of maths and starting from basically nothing IMO, It seems to be a perfectly fine book (just from skimming the free chapter, its not a book ive used) but not sure its the best option all round

[graceful moon]

Well the other good thing about GSCE, as i mentioned, is its so popular that theres a million resources online, you can try youtube, BBC bitesize or the million websites like this https://thirdspacelearning.com/secondary-resources/gcse-maths/ which have resources to get a taste for what it teaches

Obviously you do you, but i think if youre starting from nothing, self studying and have a wide range of gaps, following an established course is a good idea

[rigid estuary]

so far I've found this "roadmap" on a reddit post, in case anyone can comment on it https://i.imgur.com/rF8C5e5.png

[graceful moon]

I presume its not in order becasuse if so its wild

[rigid estuary]

https://www.reddit.com/r/learnmath/comments/13qmsh9/foundationalhigh_school_math_best_books_for/

this is the post in case you want to check

[gray jungle]

whats the roadmap here exacty?

[graceful moon]

Ok so back to my origonal question, what is your level of knowledge and goals? That list goes in quite a pure maths university level, is that what youd like to learn? And what exactly do you know?

Like could you comfortably do most of the GSCE course i mentioned or are there parts of that youd struggle with? If so is it one specific topic or a lot of thing?

[rigid estuary]

my level is 0, I don't have a specific goal for it yet but is probably game related and involves programming in c++

[gray jungle]

level 0 means you cant count to 10 , you have to be more specific

[graceful moon]

As i said, could you do a GSCE course, if so we can reccomend more specific textbooks, if not I strongly advise just following that first

[rigid estuary]

you give me an equation, I cannot solve it. You ask me to do a division by hand, I don't remember how. I can get confused on multiplication and division

that for me is 0

xD

[graceful moon]

If you want to do game dev you also dont really need to do anything more than computational LA so most of that list is somewhat pointless for you

Ok if you really know that little, start with a course in like GCSE maths or any basic highschool algebra book you can find

[rigid estuary]

well, last time I ragequitted because the book I was following about programming 3d graphics used matrices and told me to memorize formulas using sin&cos without telling me what they where doing or how they worked

I just want to understand things, not memorizing thing not understanding why they work

[graceful moon]

then try something like precalc and trig, then you could move onto a book like nicholson linear algebra

[rigid estuary]

I don't know... if someone can provide me a full tested/widely approved roadmap, I can get started with it - without, to me it seems just me left alone to figure out what to learn, and for me that really doesn't work...

[graceful moon]

This is why i am reccomending GSCE maths, this is exactly what it is

millions of students do it every year and have done for many years

its comprehensive and has a plethora of resources

[rigid estuary]

what comes after GSCE maths?

[graceful moon]

A level

Then a book on discrete maths and applied linear algebra

[rigid estuary]

and how do I find that A level? What do I google for?

[graceful moon]

this is all you need for most coding purposes

A level is the follow on course for GSCE, also done all over the world, sam things apply

[rigid estuary]

but how do I google an A level book on amazon... do I write A level and it comes up?

seems too generic of a word

[graceful moon]

A Level maths

A level and GSCE are specific exams taken primarly by UK students (except scotland) and many many international students. If you google either A level or GSCE maths you will find loads of stuff, more than you could ever need

[rigid estuary]

what comes after A level maths?

[graceful moon]

As i said, a book on discrete maths and computaional LA if youre intrested in coding, after A level maths youre at the same position as any good first year of university student and its far easier to make recommendations

[rigid estuary]

what is an example of book about "discrete maths and computaional LA" ? Would like to read the index

[graceful moon]

Computational LA - Nicholson "Linear Algera with Applications"
Ive not read this but ive heard its fantastic and very comprhensive, Keneth Rosen "Discrete Mathematics and its Applications"#

Theres about a million books you could reccomend when you get to that level though

So id say start with GSCE and A level maths, these are well vetted and comprehensive with a clear path, which seems to be what you want

[rigid estuary]

yes, definitely need to get up there, I'm seeying from the index lot of the arguments that stopped me the other time with the "programming graphic" attempt

[graceful moon]

Computational LA and discrete maths are the courses that comp sci students take at most institutions so they should serve you right, and after doing a full course in highschool maths (which is what GCSE+A level is) you’ll be in the same place to understand them as anyone else

[rigid estuary]

(computational LA and discrete maths are two separate things, right? Or is meant to be read as a single thing?)

ok then, I'll start with the GCSE math book. There is one widely recommended? 🙂

which includes a lot of exercises with solutions

because I don't have noone to check if I'm solving things right

[dusk wind]

Khan Academy would be good for this, or any precalculus/algebra books. For a roadmap you can check for a syllabus of what you want to learn and pick books specific to each area. Otherwise there are an infinite amount of lists like #book-recommendations message

another issue with roadmaps is you might have to have supplementary materials anyway so you would have been better off finding that one book you needed to read

[rigid estuary]

I'm going with this, if anyone can check the index and let me know if seems all good 🙂 https://www.cambridge.org/ar/education/subject/mathematics/cambridge-igcse-mathematics-2nd-edition/cambridge-igcse-mathematics-2nd-edition-core-and-extended-coursebook?isbn=9781108437189

thanks for the help @graceful moon 🙏 🙂

it's called "igcse", don't know if that "i" changes anything significant

[graceful moon]

IGCSE = International standard certificate of education, it’s just the GSCE exam board (there’s loads of different boards idk how it works exactly I didn’t do GSCES) for international students, no problem though

[remote sparrow]

bump

[trim kayak]

Anyone ever use the CPM texts for math at all?

[gray gazelle]

I am currently on second chapter of Abbott. Would I still handle the abstract book like zorich ?

[remote sparrow]

you could try hubbard and hubbard instead if zorich doesn't work for you

[gray gazelle]

I understood, I shall try this book. I have overview it and the table of contents looks fine.
Thank You

[molten mason]

I feel like most Pre-Calc and Calc books today are pretty modern and standardized; you can't go wrong with any of them.

Axler covers very similar material with tons of overlap between his three books Precalculus: A Prelude to Calculus, College Algebra, and Algebra & Trigonometry

The third is surprisingly the longest by far with much the same material.

His Precalculus book is definitely more concise and the only real big difference between that one and his College Algebra text is the precalculus has a chapter on Polar Coordinates, Vectors, and Complex numbers. The overlapped material also appears to be more geared towards Calculus. I think the only subject his precalculus textbook is missing compared to the other two textbooks is a section on matrices.

It is FILLED with motivation for those who needs it, and many varying example topics to make sure a wide-variety of students can find something concrete, such as a relatable real-world application, to assist in learning the material (goes hand-in-hand with the motivation). It is well organized and is filled with imagery and graphs. There are tons of problems to attempt until your hand falls off.

The main issue is it can be inaccessible for many people. There's not much online presence and it's a bit pricey.

If someone is able to get the book, and they require heavy motivation to learn the material, it's definitely a recommendation. He's a great writer.

For someone who wants to study mathematics at the university level, I still recommend Basic Mathematics to start developing mathematical maturity early and getting used to more "dry" and abstract type of texts.

I do find Stewart annoying for Calculus but my biggest positive for it is just how much presence it has online.

For example, Quizlet has a collection for Calculus: Early Transcendentals 9th ed. that contains a fully explained solution to nearly every single problem, organized by chapter, then section and in order, for the entire book.

On top of that you can find YouTube videos also explaining solutions to many of the WebAssign problems.

I think online presence and ease of obtaining assistance matters a ton when selecting a text, especially for self-study.

[fervent marten]

I've been striving over math competitions so far in 8th grade, and I want to get more progress done before I hit high school. I get near perfect scores in mathcounts and have been struggling over AMC 10 and 12 lately. I think the biggest problem for me is number theory and combinatorics for some reason. I will appreciate free pdfs and resources on the web thank you

[novel hound]

I would say you could skip book on proofs and start with Apostol calc directly. Intro of calc I (45 pages) is mostly about proving stuff with induction and proving stuff about sets and real numbers from basic axioms. If that feels hard then do a proof book but there's a chance you'll be fine without it. Esp since you've done calculus before.

[novel hound]

Have you tried the AoPS website?

[remote sparrow]

as far as which book has the most official resources, it would probably be the books by larson. i used https://www.calcchat.com/ for calc 3.

[molten mason]

Fun fact: that guy who came in here wanting to do the whole math Undergrad in a month is now 10 days in. Random thought in my brain.

[molten mason]

Now that's neat

[slender wasp]

Hello, how much PDE prereq is needed for Complex Analysis (Churchill/Brown and perhaps Conway/Ahlfors after that)? Can I get by with Apostol Calc intro to PDE or need more in-depth?

[daring lake]

I don't think you will need concepts of PDE theory for complex analysis (atleast from what I know)

[trail hemlock]

prob just check out the free prep book: https://www.omegalearn.org/mastering-amc1012

also any aops books 🏴‍☠️🏴‍☠️

[gray gazelle]

hello

[trail hemlock]

fuck i forgot to reply

[gray gazelle]

where are you from

[trail hemlock]

idk

[trail hemlock]

@fervent marten

[modern ruin]

asking for a friend: what is ur favorite rep theory material?

[gray gazelle]

hello

[modern ruin]

hello!

[flat lantern]

For what? Introductory rep theory?

[modern ruin]

yeah

[flat lantern]

I read James Liebeck for my introduction

It starts off slow but covers a lot of finite group rep theory well

[modern ruin]

cool okay great thanks my friend will like this

[grim hinge]

Why is #books #books-old now?

Anyways, I remember coming across a real analysis textbook which began with the motivating example of heat transfer, but don't remember its name... maybe someone here does?

[fervent marten]

yup

[fervent marten]

yeah I just ordered the precalculus AoPS book

[trail hemlock]

how r u gonna u gonna understand all of undergrad math in a month 😭🙏

[grim hinge]

Found it, it's A Radical Approach to Real Analysis

[karmic thorn]

Have you read Steinberg's rep theory book? Any thoughts on how it compares?

[sage python]

@karmic thorn I've glanced at it

It's quite gentle and it does hit cool stuff like probability and finite Fourier

[karmic thorn]

Yes, that is why I was curious. The major difference I noticed with Liebeck is that it switches to the FG-modules language at the onset, which (at least in my course instructors opinion) has its merits. I still want to read more of Steinberg though.

Maybe just to motivate myself to do harmonic analysis this summer

[sage python]

If you're comfortable with module stuff then yeah maybe there's some other books. Hmm

[mossy flume]

Serre has been serving me well for rep theory

[molten mason]

@sage python any thoughts on this?

#book-recommendations message

[sage python]

No edits yet. Lang Complex, everyone I know who used it says it's boring. For complex I don't like S&S somehow, but if you wanna combine with Fourier that might be good. My preference is Freitag-Busam or Narasimhan

Idk much about Fourier, S&S's book on it doesn't assume you did measure theory, so it's a Riemann integral take. Accessible but not having full power of L^2 is limiting (though he seems to do well given that constraint/does well at situating Fourier within math at large). There are others like Schlag or Grafakos if you know measure theory, and if you want the more rep theoretic harmonic there's Deitmar-Echterhoff

[molten mason]

Thanks!

[real veldt]

any recommendations for modeling with differential equations?

introductory stuff

[marsh ingot]

Topological Manifolds from Lee

[foggy fiber]

https://sinews.siam.org/Details-Page/celebrate-the-new-siam-online-bookstore-with-40-off

Solid deal if you're in the market for some applied mathematics texts.

[gray gazelle]

does anyone know of good resources about calculus of variations? I need basic stuff

[whole hazel]

Hey what are good "advanced" logic books

Im in the midst of reading forallx which is a free online intro book to formal logic

It introduced propositional and predicate logic, their semantics and it has a chapter on proofs i havent gotten to yet

[remote sparrow]

#book-recommendations message

[heady ember]

@whole hazel

[viral heath]

https://tenor.com/view/yeah-i-play-among-us-amogus-hop-on-among-us-yeah-i-play-among-us-gif-26469692

[finite gale]

Memes and gifs go in #chill

[tough stag]

Thanks heaps, Ill take a look

[karmic thorn]

Serre sounds scary. I tried reading his Complex Semisimple Lie Algebras last sem, and the concise writing was really too much for me

[copper axle]

Hi! Anyone have book recommendations on ODEs or PDEs for undergrad physics students? Thx!

[sage python]

I think Serre "Linear Representations of Finite Groups" is what was meant, and it's probably easier. It's the book I see most cited for finite group rep theory, and it is smooth

The reason I didn't jump to suggesting it is if you wanna see the Fourier analytic picture (which is a good desire to have), I'm not certain that's in Serre

[karmic thorn]

Oh yeah, I'd prefer the Fourier analytic bias here

[wind radish]

does anyone know a book that covers Algebra & Geometry in general

[marsh ingot]

For algebra

[karmic thorn]

At what level?

[wind radish]

In general

[karmic thorn]

That is kind of vague. Are you comfortable with high school mathematics?

Do you want a textbook recommendation, or something that makes for an enjoyable reading?

[sage python]

Yeah I don't know a good book offhand other than Steinberg so do that

[karmic thorn]

After that I learn either compact Lie groups or some harmonic analysis this summer

[sage python]

Or both 🙂

They connect a lot

Unless by harmonic you mean stuff like singular integrals. That won't feature the group theory as prominently

[reef escarp]

Sorry for the late reply, I completely forgot I posted here. I have tried KA, and I am personally not a fan of it. I prefer learning through text.

[molten mason]

Same. Any PDF, such as Basic Mathematics, should be less than $25 to print out.

My favorite part of this channel is when people ask for algebra books and people immediately recommmend abstract algebra

[molten mason]

Algebra pre-university and Algebra for math majors in university are two very different things. Also algebra pre-university varied slightly from state-to-state and between countries. For example, the United States often splits up Algebra 1, Algebra 2, Geometry, and Trigonometry into different classes but not always.

That's why we're asking your current level, what your background is, and what exactly you're trying to learn.

[reef escarp]

yeah, someone recommended me a book for abstract algebra, and I haven't recovered yet.

[molten mason]

I'm crying rn, but it's also hilarious lmao

[molten mason]

Free, legal, and online. They also offer printed versions.

https://openstax.org/subjects/math

[trim kayak]

@molten mason That website is awesome. I'm looking for more practice with quadratics - the formula, equations, graphing, parabola and more. Which Algebra book would you suggest I download?

[karmic thorn]

I'll see what flavour I get to learn it in; I have my eyes set on Dietmar-Echteroff for now but I'll go with whatever the supervisor recommends

[molten mason]

I'll let you choose for yourself, any of these 3. You can review the table of contents, then honestly just download all 3 and skim them yourself. They all cover the material you asked got but they're either written slightly different or written with different focuses. For example I think the first one knig briefly covers quadratic while it was the second or third link below that covers it in detail.

https://openstax.org/details/books/algebra-and-trigonometry-2e

https://openstax.org/details/books/elementary-algebra-2e

https://openstax.org/details/books/intermediate-algebra-2e

[molten mason]

Also Brian McLogan is great in YouTube all the way up through Calculus.

https://youtu.be/lNTe5uQjcKA?si=r9MNX6RwRwBLTx-5

https://youtu.be/l76asUJFmXs?si=eEogIJ7dOuzwCRck

[trim kayak]

Thank you!!!

[dusk wind]

some of the openstax content is written from other open source works

better to just find some university book on algebra

[trim kayak]

They aren't good books to use or reference? I don't see Geometry there. Maybe its included in another book. I'll look at the TOC.

[dusk wind]

when I used them some had errors, there are shorter books that are more efficient

you can learn from them but any book is fine

you might want to do a lot of problems so take a look at college algebra & trigonometry by Leithold

they also have just college algebra

[molten mason]

Oh yeah the original original OP I saw said they were 13 and that's why I recommended OpenStax lmao

If you're an undergrad, there's tons of more books.

The algebra and trig from openstax has geometry near the end.

But there's those books, honestly the College Algebra book on OpenStax might be best if you use that website. IIRC it's basically the same subjects but for an adult learner.

A lot of what you're wanting will be covered in any College Algebra text and Precalc text after.

There's what Renji mentioned, AOPS has great books if you Google those, and I'm personally biased to Serge Lang's Basic Mathematics

[dusk wind]

still looking for a short book on algebra but really in the long run anything around 1K pages would serve you well

[trim kayak]

Ahh okay thanks. I love math and just want to practice a few concepts that I don't remember from high school and college. And I will be helping some students in my classes with various algebra concepts.

[molten mason]

1k pages

[dusk wind]

If Leithold isn't good, there is also Algebra for the practical man

or well AOPS

and unironically khan academy but dat UI

[molten mason]

You can find great problem solving workbooks, and then YouTube the concepts. That helps a lot for me when I need to relearn sonething.

I hate Khan academy lol

[dusk wind]

I think websites are too distracting when learning/practicing

you want as little interferance as possible

[trim kayak]

So books on OpenStax are good to use then? I will look into those

I agree. I prefer a hardcopy book to learn from too

[dusk wind]

OpenStax is ok if you really don't care

[molten mason]

Yeah there's nothing bad to use. They're all options. Some are easier to get online as a pdf, some you can order on Amazon, etc

[dusk wind]

you can pick something from one of these places too https://realnotcomplex.com https://www.opentextbookstore.com/catalog.php

there's not really much else for Algebra beyond unis in your area

[trim kayak]

I like the realnotcomplex site too

[pliant wadi]

Okay kinda off-topic, but I remember there being a book list channel with quite a few threads on various disciplines that I can't find (I am not talking about the archived old books channel; I remember seeing another channel. I know it's not that one because I can't find one of the books that I picked up from there.)

I have been looking for the past 15 mins, can anyone please help me find it or confirm that I was hallucinating or something?

[molten mason]

A lot of those threads/posts on that channel I think are missing/deleted, maybe that's why?

[pliant wadi]

oh that makes sense. Any idea why? I found some interesting books there.

[trim kayak]

These texts on OpenStax seem pretty good. I'm surprised the entire book is available for free

[molten mason]

No sorry

[trim kayak]

Would any of you suggest reading a section and possibly taking notes, working on the problems, and then checking my answers?

[molten mason]

That's how I do it

[trim kayak]

Sounds like a good idea to me. Salagos, did you say you're a student or no? You have some good advice and book recommendations 🤓

[molten mason]

Nah I'm still learning a ton myself lol I'm a university student, math major.

[trim kayak]

Oh nice

[smoky zephyr]

click on channels and roles at the top of the server, click show me the archived channels, then you can access this https://discord.com/channels/268882317391429632/873809533615628308

[ancient bison]

Books from B&N I’m interested in:

• Weapons of Math Destruction
• Thinking Fast and Slow (not math really)
• Golden Ratio
• The Irrationals
• The Drunkards Walk

anyone have a comment on any? I already have a math degree so also comment if I would already know it all. I’d send an image but don’t have perms, please ping / reply :)

More so books to learn and enjoy instead of strictly enjoy like a textbook

if you also have any recommendations also feel free to say books that are a good learn and a good story / enjoyable

[dusk wind]

looks like there are a lot of reviews for them, but some might be clickbait

[pliant wadi]

Oh thanks

Worked

[dusk wind]

any notable topics in there?

[pliant wadi]

I haven't checked out a lot (which was why I was looking for that channel) but I found an interesting book in point-set topology thread: Topology - A categorical approach. Builds up point-set topology from a categorical point of view. I am going slow as a snail but whatever I have seen so far looks good.

It's sad that a lot of threads like the game theory one is empty though.

And the complex analysis one doesn't have enough entries.

Imho

[dusk wind]

seems interesting, I'll check it out

[molten mason]

Yeah a lot are empty or only have one book in them. Many of them are uncommon, not books I normally hear recommended if at all

[dusk wind]

Hmm I've seen this book before

[pliant wadi]

Ikr that's why I wanted to check it out. I have been out for some not well known books recently. Worth giving a shot ig.

Ooh

[molten mason]

Yeah same. I try to use the mainstream book my school uses and then one extra non-common book

[dusk wind]

covering all bases

[pliant wadi]

Oh same, I used Baum's Book on the side with munkres for point set topology. It was nice.

And visual group theory with dummit and foote

[molten mason]

Sweet, I'll add those to my list for when I get to topology.

[pliant wadi]

Also, G. F. Simmons. That was the main reference for our course but that book just feels impossible to get through as a beginner. I remember ramming my head through it for a month. Our prof didn't help, introducing Zariski topology in first lecture and all.

But looking back, the exercises in that book were decent.

It gives me PTSD though, yes.

[molten mason]

I love those kind of books. A month of slamming head against the wall, crying about how could someone expect anyone to read this alien text, put it away for a bit, reopen it later and you're like oh duh all of this makes so much sense.

[remote sparrow]

ODEs:
Differential Equations by Blanchard, Devaney, and Hall
Elementary Differential Equations and Boundary-Value Problems with Boundary-Value Problems by Boyce and DiPrima
Differential Equations and Linear Algebra by Goode and Annin
Differential Equations, Dynamical Systems, and an Introduction to Chaos by Hirsch, Smale, and Devaney
Nonlinear Dynamics and Chaos by Steven Strogatz
Ordinary Differential Equations by Tenenbaum and Pollard

The "elementary" texts in this list are Blanchard, Boyce, Goode, and Tenenbaum. Only a good understanding of calculus is required. Only Boyce and DiPrima covers boundary-value problems. An old edition works fine. My professors prefer the 10th edition. Blanchard has a very different focus compared to other elementary differential equations texts at its level (e.g. Boyce, Goode, Tenenbaum, etc.). It deemphasizes closed-form solutions and instead emphasizes qualitative analyses and modeling. It's written as a kind of soft intro to dynamical systems for sophomores.

Strogatz assumes a tiny bit of knowledge about separable ODEs and linear algebra. Hirsch, Smale, and Devaney can be used by scientists and engineers who have previously studied elementary ODEs and linear algebra, but it is preferable to know some real analysis and linear algebra.

PDEs:
Partial Differential Equations: A First Course by Choksi
Applied Partial Differential Equations with Fourier Series and Boundary Value Problems by Haberman
Partial Differential Equations: Theory and Completely Solved Problems by Hillen, Leonard, and van Roessel
Partial Differential Equations: An Introduction by Walter Strauss

Other than Choksi, these are books specifically concerned with solving specific, common classes of PDEs. This is probably more useful for the physics major. Hillen has complete solutions to all problems in the book. More advanced treatments concern themselves either with numerical solutions and simulations or the existence and uniqueness of solutions. An example of the latter kind of treatment would be Evans or Taylor. These assume functional analysis and measure theory (though someone remarked the first few chapters of Evans is a brief treatment of solvable PDEs, which do not require either), advanced mathematical topics.

[molten mason]

Sour Drop with the drop

[pliant wadi]

They are good and all. Imho it helps to start a bit early with those books, like summer break, etc. They need time. A lot of it.

[molten mason]

That Haberman one sticks out as super interesting to me. Have you gone through hat one at all? I'm reading the reviews online rn

[molten mason]

I start at least a semester early on all my classes, I'll rather be partially lost than completely lost when there's looming deadlines closing in.

[pliant wadi]

Oh wow that's great. For me it was a lesson learned after some bloodbath.

[molten mason]

Same

[remote sparrow]

no, it's just a standard text.

[molten mason]

Pde for scientists and engineers by Farlow I see recommended a lot as well, for applied peeps.

Haberman and Staus seems like great recs. I don't plan on taking pdes anytime soon though

[remote sparrow]

farlow restricts himself to R^3 fyi

[molten mason]

Good to know

[remote sparrow]

https://maa.org/press/maa-reviews/partial-differential-equations-an-introduction

strauss is standard, but it's not well-liked

[molten mason]

I saw a post that said Haberman for undergrad, Evans for grad, and Srauss is somewhere in between.

[remote sparrow]

my institution uses strauss as a senior-level intro to pdes. it only assumes background in elementary ODEs.

@stoic sleet https://www.amazon.com/First-Course-Partial-Differential-Equations/dp/048668640X

did this book help you with your particular PDE class?

[molten mason]

Yeah looks like mine does too. Strauss for undergrad, Evans for grad

[trim kayak]

I've been reviewing some math stuff. Ya'll are still in here?

[modern ruin]

I was not in your computer to begin with

[trim kayak]

In the book recommendation channel, smay

😒

[molten mason]

We're always here, lurking, watching, refusing to answer

[trim kayak]

I hope not. Salago, you're always very helpful 🙂

[balmy crown]

Does anyone have good book recommendations for numerical analysis?

[remote sparrow]

burden and faires i guess

[foggy gorge]

A thing I am trying to understand is why the graphs of functions are the way they are. Like, why quadratic functions are curved, cube functions have like idk

Does anyone know any written source about this

?

[molten mason]

I feel any algebra textbook should explain that when explaining graphs, quadratic, and polynomials.

There shouldn't be any dedicated texts to just that, you can set your y and x axis in such a way that a "curved" equation looks straight on a graph, such as using a logarithmic scale.

[novel hound]

you can take a handful of points and think thru what it looks like (e.g; at x=-1,-2,0,+1,+2). If you have more complicated polynomials you may need more than a few points and a plotting tool. And/or an understanding of it's zeros, etc.

[trail hemlock]

probably not any written sources, just play around on desmos.
also if you just mean functions in general, there is this video: https://www.youtube.com/watch?v=92wXQYcYLMg

smh embed 🤦‍♂️

[rare forge]

what's a particularly great algebra book?

[weak solstice]

Lang

[molten mason]

#book-recommendations message

Of course Basic Mathematics by Serge Lang

[rare forge]

its my understanding that this is not actually an algebra book?

but I'll read it

[molten mason]

It covers roughly American 5th/6th grade to all of Precalculus.

Algebra is definitely in there.

Unless you meant Abstract Algebra

[rare forge]

no, no.

[molten mason]

In which case that's a whole different subject

[rare forge]

just enough algebra to do calculus with

[molten mason]

Oh yeah then yes that book is perfect

[pliant wadi]

Dummit and foote covers a lot of ground and has good problems. You might wanna refer to artin too for group theory and rings and modules.

[molten mason]

That book is written specifically to prepare people for Calculus, starting from scratch

[rare forge]

that's more abstract/linear alg

[pliant wadi]

Oh you meant that, algebra

[rare forge]

artin, right?

[pliant wadi]

My bad

[rare forge]

yeah, that algebra

[modern ruin]

straight up: there are no good algebra books in that sense

lol

[molten mason]

There's no perfect book, you just get close enough before diving in to a higher level class

[modern ruin]

just go to your classes/find a youtube series

[molten mason]

Brian McLogan and Professor Leonard are great

On YouTube

[rare forge]

I'm doing leonard, will start serge lang

want to be able to do calculus relatively well enough to do ai stuff

idk how much time i need

but maybe a year

[molten mason]

I mean that's mostly linear algebra and stats

And if you're doing calc-based stats, that'll probably take more than a year

[rare forge]

eep

idk what calc-based stats is

i thought it was just prob/stats.

lol

[molten mason]

You sweet summer child

There's a lot of applied stats for various fields and simplified that doesn't require calculus

But the real upper level stats is A LOT of calculus.

Just depends on your goals and needs

[molten mason]

https://realnotcomplex.com/probability-and-statistics/statistics/theory-of-statistics-by-joseph-c-watkins

[molten mason]

https://realnotcomplex.com/probability-and-statistics/statistical-and-machine-learning/mathematics-for-machine-learning-by-marc-peter-deisenroth-and-a-aldo-faisal-and-cheng-soon-ong

Don't be discouraged.

The sooner you start, the sooner you'll reach your goal.

The more you learn, the more you can do.

Quality work takes quality time.

It'll be worth it in the end.

In a lot of places Pre Calc is 1 semester. Calculus is 3 semesters. Probability and Statistics take 2 semesters. Linear algebra is 1 semester.

[rare forge]

good to know

still doing algebra, but I can definitely use this as a framework

[molten mason]

If you want to do math and study real math, and learn algebra trig and other pre-calc topics then Basic Mathematics by Lang is definitely great.

Get used to reading concise and plain or dry texts. Get used to math notation and thinking. And go at your own pace.

[rare forge]

agree with everything you've said here. current workload is 2 hours a day but I'm consistent and trying to manage other fields of study too

aspirationally even if it does take 1.5/2 years, I'll be pretty good

even if I am a bit older

[hearty turret]

whats a good book for an introduction to measure theory?

[grand thistle]

folland

[heady juniper]

I know that Harmonic Analysis is a very large field and the exact meaning can often depend on the subject (it seems to encompass a massive amount of mathematics). But for an undergrad who just wants a taste of the general themes, is there a good introduction?

I know that "pure harmonic analysis" is a pretty nonsensical term, but I hope you understand what I mean. Not completely devoted to just, say, Harmonic Analysis within Number Theory. It would be fine if it's a book which covers lots of different areas while focusing on harmonic analysis. E.g., it shows its applications in number theory, etc.

I just find it to be a bit of a hard definition to really grasp. I'd like to see its work at a somewhat beginner level. Assume 3rd-4th year undergrads.

[marsh ingot]

Bartle

[marsh ingot]

Folland

[upbeat vine]

Classical Fourier Analysis by Grafakos seems apt; once you have covered Folland

[steel narwhal]

can you recommend me some class 9 grade math book

[heady juniper]

Awesome. Thanks folks. 🙂

[vital bane]

measure theory

[foggy gorge]

I'm also on the road for precalculus. What do you think of the book "Schaum's Outline of College Algebra - Robert E. Moyer"?

[magic zinc]

book recommendations for trigonometry and congruency

targeted class 9th,10th

[rigid marsh]

Hi. I need help to understand how to do mathematical problem formulation and describing / modeling of a real-life problem into a mathematical equation or set of equations. I am working on a machine learning project which requires transforming the problem at hand into a mathematical set of equations so that I could run code for analysis across the dataset. Any help or recommendation for the same would be appreciated.

[amber cave]

hello, i want to learn algebra, i'm in 10th grade in France. Can you recommand me a book that cost less than 20€

[hollow bone]

Good morning everyone (I hope this message doesn't get put in spam pls 😢).
Would anyone be interested in joining a tiny science group?
If anyone wants to, here I send the link
https://discord.gg/MmgKb4STg5
Please, don't put it in spam....

(I know it's not a message about a book, but there's no other channel to say it xd).

[dusk wind]

there are free ones posted above but in English

[amber cave]

english isn't a problem

[dusk wind]

ok, pick any from either list #book-recommendations message

khan academy or openmath could help for problem sets

[amber cave]

thanks, is there execices in these book ?

[dusk wind]

They should yea, but I recommend the one by wallace or yoshiwara

[amber cave]

okok

[foggy gorge]

What is the difference between arithmetic and prealgebraa

Aren't them quite the same

[dusk wind]

same thing with algebra, precalculus, college algebra etc

naming conventions and switching around content

[foggy gorge]

Do they show proofs?

[dusk wind]

these are just for problems

if the author wrote a course on openmath it's supplementary exercises for practice

[foggy gorge]

Ic

[molten mason]

100%, I love Schaum's books

Math is not a spectator sport

Use a textbook or YouTube series to learn thr material.

Use Schaum to just practice practice practice and apply what you learned.

[molten mason]

Sharing that in this channel is literally the definition of spam.

#discussion and #chill would be more appropriate than book-recommendations, however they also might consider it spam.

Delete please.

[dusk wind]

there are literally like 4 discussion channels lol

[molten mason]

That he had to scroll past to even click this channel lmao

[molten mason]

https://mecmath.net/trig/

[molten mason]

Basic Mathematics by Lang is the only text at that level with proofs. Very elementary but it gets new people used to and in the mindset to prepare them for texts with proofs.

It's why I recommend it to anyone wanting to study math.

[foggy gorge]

I see. It is that I am studying discrete mathematics and proofs too, so I wanted something that really uses it, so I can practice altogether

[molten mason]

That whole pre-algebra, algebra 1 algebra 2, geometry, college math, and pre-calculus are all arbitrary divided and definitions that basically cover the same thing.

Honestly anyone over the age of 10 could probably skip right to a pre-calc or college math book.

You're covering the same material but instead of 500-1000 pages each textbook for 4 different textbooks, you knock it all out in 1 textbook.

[molten mason]

Discrete math, are you studying computer science?

[foggy gorge]

Yes

I'm really liking it so I want to get deeper into it

For discrete mathematics I am using that book of susan

[dusk wind]

There are some solid college algebra books, a talented kid could probably blitz through with just that alone

also for discrete math you might want to go with something more rigorous or just rosen

actually nvm, just use these https://discretemath.org/ https://discrete.openmathbooks.org/dmoi3.html

[molten mason]

The only discrete I care about is the discrete Fourier transform

Those look like good links though.

[unborn jackal]

could anyone who has worked through "the power of logic" if they would recommened it

[broken willow]

Hello, I would like to learn some pre-calculus. Can you please recommend some books? Thanks!

[marsh ingot]

I think Spivak

[alpine rover]

Stewart is a good one

[placid coyote]

this is not a textbook, but has anyone here read Diaspora by Greg Egan? in contemporary scifi circles i feel likes its extremely underappreciated bc most people glaze over the math parts. i just finished it and i think it's one my favorite novels now

[modern ruin]

thank you for the recommendation

I need to read more novels

[molten mason]

[marsh ingot]

What?

[placid coyote]

@modern ruin it's so good. he reviews riemannian geometry and it's very fun, it's rare to find someone who can both write and understand. im chock full of recommendations if u ever want another

[tender river]

what precalculus book did spivak write

[dusk wind]

use leithold

actually just use this and hope for the best
https://amazon.com/Precalculus-Made-Difficult-Seth-Braver/dp/B0CCCLJ6YH

[molten mason]

For pre-calculus? In preparation for Calculus? Does he have a book for that?

I like how this channel goes through waves. Last week was people asking for set theory and logic every 5 minutes, this week is pre-calc

[molten mason]

What a title

[dusk wind]

and at 200 pages too

[dusk wind]

yeah I've noticed the pre-calc phase as well

Full Frontal Calculus? Who is this guy lol

[molten mason]

The Dark Art of Linear Algebra is giving me a mix of like, Harry Potter and 14th century alchemy

[dusk wind]

There is a certain air about it, I'll check them out at some point

[marsh ingot]

The book is about infinitesimal calculus. He start with basic stuff at the first chapters before start with the derivative

For you whats pre-calculus?

[rare forge]

not findign a pdf, if you rec i'll buy it

[dusk wind]

can you link it?

alright this guy definitely wrote these to be modern

they're all 200 pages or less

[marsh ingot]

Google it by Spivak Analysis, its the first result

About 900 pages

[dusk wind]

buy it anyway

[molten mason]

The only version I found is in Spanish, and I agree that's pre-calculus content in Parte I and II

[molten mason]

Yeah I haven't found (didn't really look either) any PDFs but I love concise books.

[molten mason]

I literally found out about this book 7 minutes before you did lol I don't know anything about it to recommend it.

[molten mason]

My recommendation would be Basic Mathematics by Lang -> Linear Algebra by Friedberg, Insel, and Spence

Then there's many Calculus books to choose from. If you suceed with that linear algebra book, get a rigours Calculus book such as the one by Michael Spivak. If you struggled a little bit and need to do a more computational calculus book with tons of applied problems then literally any calculus book e.g. Stewart, Thomas, Anton, etc...

[dusk wind]

Well MAA recommends it and no one like to read too many pages so... these 3 books by him are definitely worth a shot, if not for the meme content inside

[rare forge]

do you generally want to do linear algebra before calculus?

[dusk wind]

You kinda do it before calculus anyway

And learning linear algebra helps with calculus

if you want to look at another linear algebra book like the one by Seth try Tea Time Linear Algebra

[molten mason]

Generally do? No

Generally should? IMO, yes

[molten mason]

That's good to know. Yeah I'm gonna try to look for it later when I'm not busy.

[rare forge]

oh hmm. ok then

always thought it ought to be algebra, calculus, linear algebra

will go the other way around

[lavish orbit]

Hey all, I'm almost finished with my undergrad degree and I'm looking for a more advanced treatment of linear algebra
it's something i need to revise, but probably not starting from scratch

[dusk wind]

If you do get it, I hope you post a preview of it somewhere

[dusk wind]

#book-recommendations message not advanced, but maybe one of these has a treatment of it you'd enjoy

[lavish orbit]

ah ok ill have a skim through, thx for that!

[molten mason]

That's how most education systems go. Or they might put linear algebra between Calc II and Calc III (Vector/Multivariable)

Should be algebra -> linear algebra -> calculus -> More Linear Algebra -> Even more Linear Algebra -> Linear Algebra don't stop

[remote sparrow]

https://linear.axler.net

[molten mason]

Friedberg or Axler

[molten mason]

Boyd has these 4 books. The first one, Introduction to Applied Linear Algebra might be of interest to people.

He also includes lecture slides, lecture videos, additional exercises, and companions in both Python and Julia

https://web.stanford.edu/~boyd/books.html

[trim kayak]

Hey Salagos

[lavish orbit]

yeah I was thinking 4th edition of axler
i am a bit of a determinant lover though
i'll see how it goes

thanks guys

[molten mason]

That's what makes 4th edition the best

[molten mason]

Hello there

[lavish orbit]

oh what changed?

[molten mason]

Chapter 9, Determinants

[trim kayak]

How's it going?

[unkempt gorge]

Good math textbook for topics covered in high school?

And thoughts on these books?:

• Essential Prealgebra Skills Practice Workbook by Chris McMullen
• Schaum's Outline of Basic Mathematics with Applications to Science and Technology, 2ed by Haym Kruglak

[dusk wind]

stick with Schaums and use khan academy

[unkempt gorge]

Already using Khan Academy, was planning on buying Schaum's too

Just thought a workbook would be beneficial

[dusk wind]

schaums is a good series

[unkempt gorge]

Ight

[molten mason]

Good, another mathtastic day

[molten mason]

+1 to Schaums, for all levels

[rigid marsh]

Hi. I need help to understand how to do mathematical problem formulation and describing / modeling of a real-life problem into a mathematical equation or set of equations. I am working on a machine learning project which requires transforming the problem at hand into a mathematical set of equations so that I could run code for analysis across the dataset. Any help or book recommendation for the same would be appreciated.

[round sage]

When you say “machine learning” do you mean a generic algorithm/data structure that can “learn” or do you mean specifically neural networks?

[copper axle]

Thank you sooo much!!!

[slim bramble]

what do you think of ODE by vladimir arnold

[rigid marsh]

I am using CNN / neural network. For the dataset preprocessing / feature extraction task, I need to model the problem into set of equations, and then solve the same for extraction of features for neural network training purpose.

[vital bane]

this

you can never know too much linear algebra

[rare forge]

i dont even know algebra, so everything is new again

[heady ember]

You can never know too much set theory

[rare forge]

tbh idk what nunber theory, graph theory, set theory all even is

maybe ill take a day out to wikipedia it all

[molten mason]

Find a book in discrete math and it'll cover all of that plus combinatorics

[molten mason]

The only set theory I need to know is whatever is in the first chapter of a textbook

[unkempt gorge]

Is Schaum's really that good lol? I'm pretty new to mathematics

[molten mason]

Math is not a spectator sport

For the most part, any textbook is fine. The meat is in the exercises. You can supplement any textbook, no matter how big or small, with any decent workbook. The repition of problem solving is where you actually learn.

Schaum's has a workbook for every level and literally thousands of problems.

[vital bane]

"Math is not a spectator sport" you know I have been thinking about this recently

the first couple of times I heard it I was like "oh yeah definitely! 100%"

now I'm like wait what even is a spectator sport?

every sport has spectators

but like you only get good at the sport if you actually play it

so...no sport is a spectator sport?

[molten mason]

I actually really dislike that phrase because of what you're saying, I agree with you, but I don't have any better one lol

Oxford defines spectator sport as "a sport that many people find entertaining to watch" so I guess in that sense it's true

Similar to the idiom "Clear as mud" often being used to describe something that is easily understood. Quirks of languages we just have to put up with.

[vital bane]

[dusk wind]

play it while spectating yourself

[fossil arch]

Any recommendations for getting comfortable with tensor algebra & tensor calculus computations? I'm learning the theory but it's just not going to set in unless I have some concrete numbers to work with lol

[vital bane]

GR book

[fossil arch]

Why would that not just be another glob of index mashing

I want numbers or functions or something more than just ijklmnpq 😭

Or YouTube videos or whatever, literally anything to get comfortable with this

I will be perfectly comfortable working with abstractions after I've seen some numerical computations

[modern ruin]

where are you learning the theory from? I think LADW has a good section on tensors (personal opinion) but unfortunately doesn't have any actual computation iirc

[fossil arch]

I am learning it from a physics/engineering book but it is very theoretical and all of the problems are like "Verify this identity" bla bla

Unhelpful things like this

I suppose doing computations in the abstract like this isn't unhelpful

I just don't feel comfortable with it until I've seen some examples with numbers/given tensors/matrices/etc

[vital bane]

https://www.youtube.com/playlist?list=PLRlVmXqzHjUQARA37r4Qw3SHPqVXgqO6c

my go to recommendation for tensors\tensor fields

[gray jungle]

learn tensor product through distribution theory , thats like the main subject you cant say is useless for you engineers

[fossil arch]

Like

Distributions as in Dirac Delta and probability?

I didn't even know tensors were used in those wtf?

[gray jungle]

dirac delta yes

[vital bane]

tensor product of space of distributions when

[gray jungle]

convolution is defined through tensor product

[modern ruin]

tensors are everywhere

[fossil arch]

WHat??

[vital bane]

"tensor" is just a fancy word for "multilinear map"

[fossil arch]

What are the prerequisites for this approach? And why would learning it this way help me understand/conceptualize the tensor product better?

[fossil arch]

I know!

[vital bane]

he's kidding lol

[modern ruin]

it's like the adjoint, you never expect it to come up when you first learn about the word but then suddenly it comes up everywhere

[fossil arch]

I got baited

[vital bane]

jebaited

jamesbaited

[gray jungle]

id say measure theory and multivar is the only real prerquisites

[fossil arch]

Well adjoint is easier for me to see how it shows up everywhere because determinants are everywhere and adjoints give a nice way to compute determinants of expressions

[fossil arch]

wait so you're not baiting? LOL

[gray jungle]

distribution product is not well defined

so we use tensor products

[modern ruin]

adjoints are EVERYWHERE

[gray jungle]

but its mainly a gateway to convolutions lmao

[vital bane]

this is the sort of computations you are looking for?

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

the wikipage has them

[gray jungle]

i recommend checking this book if you are interested

[vital bane]

Beware: James is paid by Big Distribution to advertise distribution theory

[fossil arch]

Yes!!!!!!

[gray jungle]

but in all seriousness it wont really be this eye opening tensor product subject but its the one where it made the most sense to me

[fossil arch]

But preferably problems with numbers too

Numbers are just so much less tedious lol, I'm perfectly comfortable with variables but I like the concreteness of numerical answers

[vital bane]

just take this example and plug in a bunch of numbers and you come up with some examples

[fossil arch]

I guess 😭

[vital bane]

engineer moment

[fossil arch]

How about computations with other stuff like inner products and so on? Magnitudes?

How about higher dimensional tensors?

Also I thought the tensor product was an operation on vectors, not matrices?

Oh well

I guess

they're all tensors

[vital bane]

tensors form a vector space

[modern ruin]

tensor product is an operation on tensors

who knew

[vital bane]

so...anything you can do with arbitrary vectors, you can do with "tensors"

inner products, norms, etc.

[vital bane]

matricies are just linear maps represented using a basis

[gray jungle]

now its time to spew comm algebra propaganda as the only way to learn tensor products

[vital bane]

bring forth the universal properties!

[modern ruin]

i’m just confused - is the problem that you just have not seen an example of a tensor? you should make an example and follow the theory of some book with that example.

[fossil arch]

Computations with rank n > 2 tensors?

[modern ruin]

then it’ll be more clear

[vital bane]

import tensorflow as tf

[fossil arch]

I think I see the problem with what I'm asking

[fossil arch]

Exactly this

You're right Smay

But still how about for rank n > 2? Just to get really fully comfortable with "visualizing" or "working with" all the various symbols and indices

[modern ruin]

okay, here is what you should do: go through your book and whenever they say “for an arbitrary [x thing]” come up with a concrete thing

[fossil arch]

I will try

Would I go to diff-geo-top for questions about tensors multivariable calculus and linear algebra don't feel appropriate (plus they're a lot more clogged)

[modern ruin]

probably, and if someone shoots your question down just ping me and I'll ask an extremely basic question to take the heat off

[fossil arch]

🥺 💚

[modern ruin]

fwiw #linear-algebra is appropriate as well if you would rather post it there

[gray gazelle]

Is zorich analysis 1 and analysis 2 are good books for the second course in analysis?
(Any reviews about these two books of Zorich).

Moreover, three volumes of Amann look also comprehensive.

Which will be the good choice for second course in analysis and for multivariable calculus?

I don't like physical problems (such as some mentioned in zorich). Is it worthy to do that physical problems?

[round sage]

I always took “Clear as mud” to mean the opposite. Basically, a reversal of expressions like “crystal clear” or “clear as day”. Of course, it could then be sarcastically reversed, leading to a double reversal, so it means “easily understood” again, but I don’t see why one would want to use it sarcastically.

[molten mason]

That is the actual/original meaning, but the last couple years I've heard it almost constantly used in that reversed sarcastic sense.

[molten mason]

What did you use as a text for your first course in analysis?

[remote sparrow]

he wrote abbott

[molten mason]

Oh yeah I remember him now.

[round sage]

Weird. I’ve never seen that. Although, to be fair, I don’t remember ever coming across that expression very often, so maybe I just haven’t seen it within the last couple years when the meaning was reversed.

[molten mason]

I mean they're all fine books, it just depends on what you're interested in, how you learn, what your background is, and what your goal is.

Amann II and III would be good afterwards.

Zorich is comprehensive.

Axler is a good writer and he has Measure, Integration, & Real Analysis

Munkres Analysis on Manifolds

Get real good through the first half of Abbot first and see how you feel then.

[brazen rivet]

Book recommendation for vector bundles with emphasis on diff geo and Riemannian geo? I have intro to smooth manifolds by Lee, but it doesn’t go deep enough.

[marsh ingot]

Not enough diff geo in Lee? Lol

Try Tu

[tawny copper]

What are advanced differential geometry books

[fast pawn]

Any book recs for learning how to solve complicated integrals? Like integration bee level integrals?

[heady ember]

Doesn't hurt to know 1000 facts about forcing and large cardinals

[livid elm]

Where should I look for math books to read during the summer? If it helps, I would want something that might help me prep for calc 3.

[lyric turret]

how do you even use these in cosmology studies

[molten mason]

Review all your Calc I and II notes, textbooks, cheat sheets, etc.
Review parametric equations
Review Trigonometry: https://mecmath.net/trig/
Study your textbook ahead of time, it should be the same as your Calc 2 textbook, just the other chapters you didn't cover.
Study on YouTube. Brian McLogan has a bunch of stuff on calc in general. Professor Leonard has the full Calc III lectures as a playlist that you can start ahead of time.

[molten mason]

No idea, not my area of expertise. I would imagine it doesn't have a direct application but it prepares you for the advanced books that would have an application.

[molten mason]

[graceful moon]

https://www.youtube.com/@DrTrefor this guys calc 3 videos are quite good too

[molten mason]

I love his hyperbolic function video

It actually made me upset afterwards how simple he made it lmao

[desert anchor]

rec: Paul Nahin - The Imaginary Tale of i

[livid lichen]

whats the website to read math books for free I forgot it

[molten mason]

https://realnotcomplex.com/

[livid lichen]

Tha mbks

[gray gazelle]

can you recomande any geomatry books

about

like

cos sin and tan

that like talk about it deaply

[molten mason]

https://mecmath.net/trig/

Maybe this

[gray gazelle]

ay

can you recommend a physics book about forces

[livid elm]

Thanks much 👍

[proud horizon]

dracula by bram stoker

slow read but good nonetheless

[gray gazelle]

Yes. It was Abbott

[gray gazelle]

My main goal to study analysis is to develop mathematical maturity and be comfortable with proof.

Ok, I shall see how I feel after completing the first half of Abbott. Thank you.

[grizzled tulip]

If ykyk

[heady ember]

You can also try Schroder

[gray gazelle]

Oh I have pdf of this book. I have took an overview of the text. I found the text concise (as mentioned in the title of the book). Moreover, I guess (here) I have read that this book is good for proof writing too and it can be used for first course too.
Is it right?

[mellow oriole]

Anyone know a book that covers differential eqns up to state space models, without really touching the physics applications? The few books I surveyed seem to teach differential eqns for the purpose being applied to physics, which I don't really have a background in

[remote sparrow]

I would want a solid understanding of real analysis and linear algebra going into it.

[remote sparrow]

Yeah, Zorich is good for a second course in analysis. You can skip the physics problems without loss of continuity.

[remote sparrow]

The physical situations you're given examples of in an introductory ODE class are usually fairly elementary (and easy to watch demonstrations of on YouTube, such as a spring). You can skip discussions of circuits.

[remote sparrow]

rudin or carothers are also good for second courses in analysis (i.e. courses taken after analysis on a real line from a book like abbott)

[heady ember]

Yes

Why Schroder is nice #book-recommendations message

Some pages of it #book-recommendations message

[vital bane]

or spivak's 5 volumes of DG

[vital bane]

2nd course in analysis is a book on measure theory

you can learn general metric spaces from some lecture notes

[gray gazelle]

Ok I got it. I am thinking of using zorich or Amann with rudin or paugh as a reference book.

[gray gazelle]

This book has good reviews. I shall try to read this and maybe use it for reference.

[gray gazelle]

Like axler's book on measure theory and royden ?

[remote sparrow]

royden has a lot of typos

axler is good

you only need to be good at single variable analysis for the first five chapters

[near jewel]

How is Dicrete Mathematics by Martin Aigner? Does it have its own pros and cons compared to like, Concrete Mathematics (Knuth), Discrete Mathematics (Rosen)?

[mystic orbit]

Where can I learn about history of analysis?

[vital bane]

I am interested in this as well

[mystic orbit]

Preferably something brief and focuses the stuff after newton and Leibniz

[vital bane]

tbh newton and leibniz stuff is interesting as well, like newton's "fluxions" or whatever

they were literally sotruing calculus into existence

[mystic orbit]

Yeah I mispoke, I meant newton and Leibniz inclusive

[gray gazelle]

I understood. First I shall study Abbott then move on another book.
First five chapters of Abbott are prerequisites for Axler measure theory?

[vital bane]

my plan is Abbott -> Donald L. Cohn

[remote sparrow]

you should certainly know about the riemann integral (which i believe is chapter 6 of abbott)

just finish abbott

it's designed to be completed in one semester

[gray gazelle]

Okay. Currently i am in 2nd chapter. I hope to complete remaining sections within 4 − 5 months.

[gray jungle]

4-5 months is a ocean of time

[vital bane]

and I wasted all of it

[gray gazelle]

For real?
I used to do self-study from Abbott. Also I study 5 other subjects in university. So, I didn't get the whole day for Abbott but certainly I got 4 − 5 hours.

[vital bane]

damn 4-5 hours everyday?

[gray gazelle]

Same here uf

[vital bane]

I also have that much time but I am bad at manging it

[gray gazelle]

Yes. But I can only study 1 and half hour effectively.

[gray gazelle]

Oh I made a schedule for selfstudy (2 subjects per day in these 4 − 5 hours). But idk why I always get distracted. That's why I study effectively only 1 and half hours effectively.

[fierce hedge]

Is that the one called the Bible of measure theory

[vital bane]

is it?

pretty sure bogachev is the bible of measure theory

[fierce hedge]

Ah, maybe I confused with that one

[steel cloud]

Is there any server for logic?

[remote sparrow]

Not that I'm aware of, but The Affinoid Union gets activity in the #foundations channel at least several times a week

[steel cloud]

Ok

[molten mason]

Man I wish I had 4-5 hours a day, that's about how much time I have per week.

If responsibilities could stop that would be great

[gray gazelle]

I always used to think, I had less time. But I feel, it's more than enough.

[cloud heart]

hi everyone, i am new to this channel. can i have your opinion (especially singaporean if u sb here is singaporean) on which book should i use for the smo (senior and open) . tysm

[grave thorn]

It is a reference book though

it covers way too much to learn from

[sharp helm]

Guys

Hello

I've got a quastion

well did any of you know more about math then other classmates?

Like your studing in 7th grade,but teachers know that your good so they gave you 8th grade book

How do I be like that???

[vital bane]

You finish studying grade 7 math, then you start studying grade 8 math

that's it

[molten mason]

You ask them. Study over the summer and normally they'll have you take either a placement test or they'll have you take the class final exam and then bump you up a grade .

[brazen rivet]

Rather, not enough content about vector bundles, fiber bundles, group bundles, etc.

[sharp helm]

thanks

[dusk wind]

courant or abbot

[molten mason]

You've said this already

[proud horizon]

nice, thanks

[proud horizon]

🙄

[gray gazelle]

https://openstax.org/details/books/statistics?Student resources
is this website reliable

[dusk wind]

no

[gray gazelle]

Why do u say that

[dusk wind]

because you can get a real book or use something else

[gray gazelle]

Are u familiar with these books or are you just avoiding them on principle? They are used by professors and are relatively well known. Most people say they are average with no overwhelmly bad reviews

[dusk wind]

they are bad because they have typos and errors and those errors will cost you in the long run

besides there are plenty of better books for statistics anyway, I avoid openstax

[gray gazelle]

I see.. i was hoping to use free resources. If there are better alternatives I'd love to use them

[dusk wind]

check some of the posts for statistics in this sub, I don't know what your goals are so can't recommend anything specific

[gray gazelle]

I wanna learn high school level math

[dusk wind]

khan academy, is what most would say

heck I think there is even statistics on there too, should be decent enough

AOPS if you want an alternative

[gray gazelle]

This url? https://artofproblemsolving.com/

[dusk wind]

yea

how good is your geometry

[gray gazelle]

Very bad

[dusk wind]

well you don't really need it but

I wonder if you should focus more on Algebra or Trig at current

[gray gazelle]

Trig gives me headaches especially differentiating trig

[dusk wind]

there is geometry on Khan Academy too if you want to review

you need trig

its incredibly important

[gray gazelle]

Aw

[dusk wind]

I'll give you some random links but strong Algebra and Trig will take you far

[gray gazelle]

Sure

[gray gazelle]

Does Khan Academy have test questions

[dusk wind]

https://mecmath.net/trig/index.html
https://archive.org/details/collegealgebra0000leit
https://stat110.net/

yeah

any college algebra/intermediate algebra or algebra with trig book will carry you

but if you get good at trig now you won't have to deal with it later

[gray gazelle]

I guess I can learn to like it haha

[vast jackal]

AOPS will do

[dusk wind]

for AOPS I think volume1 is what you want

[vast jackal]

but it will give you a hard time

you will learn math techniques so it be better to go from the start prealgebra

[dusk wind]

could also try https://amazon.com/Precalculus-Made-Difficult-Seth-Braver/dp/B0CCCLJ6YH or one of the free books in this list #book-recommendations message

For free there is Yoshiwara or Wallace

[gray gazelle]

apparently i need a class code to sign up for khan

[dusk wind]

pick the date then it'll let you sign up with an email

[gray gazelle]

thx it worked

[molten mason]

I knew there was a free stats link I was missing. Need to re-save this.

I seen a lot of PDFs on archive.org but I wasn't sure if it was scammy or anything, do you just make an account and then you can read all the PDFs? Is there anything else?

[gray gazelle]

do u have a link to one of them? I could check

[dusk wind]

its legit, you can make an account and rent the books for 1 hr or 14 days

libraries digitally archive them

[molten mason]

Is it free though, or a fee, or what?

[dusk wind]

no fee

[molten mason]

What's the cooldown timer?

[dusk wind]

public internet library

[molten mason]

Nah not on me

[dusk wind]

not sure

[molten mason]

Interesting interesting, cool!

[dusk wind]

good way to get really old books and such

unfortunately a lot are paywalled by the source so you would need to get a bit creative

[molten mason]

creative

[keen orbit]

what are the prerequisites to self study real analysis from baby rudin

[gray gazelle]

Discipline and khan academy

[glossy zealot]

Sanity

[keen orbit]

what are other good analysis books and is baby rudin among the best of these ?

[finite gale]

there are many, e.g. abbott, tao

personally I don't think baby rudin is really worth it (in terms of efficiency) as a first read, but if you manage it well, you'll learn a lot

but it also isn't really fit for a second course since you'll just be mostly reviewing stuff at that point

[keen orbit]

so if i manage to grasp its ideas fully then it will be the best choice?

[keen orbit]

also what do you recommend

if not rudin

[gray gazelle]

only one way to find out

[keen orbit]

is to try

[gray gazelle]

yes

[finite gale]

I never really used any of them, so I can't really give an opinion, but I have heard good things about both abbott and tao

[keen orbit]

ok but in terms of content for example does it have more content than the other textbooks ? also in terms of rigor etc

[finite gale]

but of course you can just choose one and try to work through it and supplement with others as needed

they're all roughly the same in terms of content though baby rudin has harder problems i think

[gray gazelle]

abbott is very suggestive

which i like

[keen orbit]

then what did you use if i may ask

[finite gale]

my prof's lecture notes

[keen orbit]

ive heard that abbott's is nice too

[keen orbit]

ohhh ok

[gray gazelle]

honestly just try a bunch of books and see what works

[finite gale]

I read a bit of tao prior to taking analysis and i thought it was nice, but I didn't really get very far

[keen orbit]

yea sure i will start with rudin's and see what happens

i wont really know until i try

[gray gazelle]

there is this series of lectures which follows rudin

it's by francis su

[keen orbit]

it cover same content as rudin's or does it serve as a continuation to rudin

[gray gazelle]

idk tbh

[glossy zealot]

Rudin is good but it lacks exposition, so beginners will have trouble reading it

It’s like a book that you read after you have read another introductory analysis book

Its content is harder than Abott

[heady ember]

Why Schroder is nice #book-recommendations message

Some pages of it #book-recommendations message

[keen orbit]

tysm everybody

[vital bane]

insanity

Rudin is a terrible "text book" (something one uses to learn from)

it is a good reference book

there are several good textbooks for real analysis

like abbott, tao, schroder, bartle etc.

[vital bane]

all anaylsis books cover pretty much the exact same content

you can easily fill in any discrepancies on your own

[vast jackal]

you can download tho?

[distant spear]

I've liked Coddington so far

[rose geyser]

good recs for a measure theoretic probability theory book?

idk measure theory yet, but do plan to learn, so just something to note down for now

[gray jungle]

Then i recommend robert ash probability and measure theory , it builds all the measure theory needed in the early chapters and is a great book imo

[dusk wind]

@molten mason they have pdfs for their trio on lulu for $9 each. Here's a sample of their precalculus book https://www.bravernewmath.com/_files/ugd/3327e0_e05cc59e7b574d25b34ce7095dcc0a44.pdf their illustrations look ok but could be a bit better, it has solutions and their writing is active enough to encourage. Would be good for high school tbh or as a refresher.

They managed to fit in a lot of content it seems and there may well be very little bloat

[fervent marten]

Any resources other than AoPS for AIME and USAMO? Still in grade 8 and taking alg 2

[finite gale]

might be helpful to ask in #competition-math (as well)

[molten mason]

Yeah it looks great, hopefully it becomes more popular, I hate 1000 page textbooks but 200 pages also seems crazy lol Basic Mathematics is roughly 400 pages of content and I feel it's pretty terse, but there's also some things I feel like shouldn't be in there (Do determinants really need to be taught before Calc I?)

Basic Mathematics Also starts at the very basics, around 5th grade level. While Precalculus Made Difficult already assumes Pre-Algebra, maybe even Alegbra 1 as a prerequisite. The meat in between is similiar though.

Imma write my own textbook

https://xkcd.com/927/

[sacred abyss]

I need a starter book on pde

[gray gazelle]

Group theory books please

[molten mason]

Rotman's An Introduction to the Theory of Groups

[mossy flume]

Rotman my beloved

[gray jungle]

introductory or advanced?

well either way i like artin as a first run at groups to have some fun and learn the basics and then i would move to kurzweil and stellmacher "The Theory of Finite Groups" i cant really say i can compare the latter to other books available as its the only book i used aside D&F and robinson as references

[sharp helm]

Did anyone read Ender's Game

???

I am reading it

And its super cool

its science-fiction

anyone who like science fiction, i recommend this book

[mossy flume]

wrong channel (server?) but you aren't wrong lol

[wary radish]

It’s a good book, and a recommendation, ‘feel free to ask about other literature’

[molten mason]

Any time I have to read fiction is just spent on more math lol

[left cloud]

what’s the difference?

[molten mason]

[lone wave]

anyone here arabic ?

[stuck zephyr]

it's one if my fluent languages

are you looking for a book that is written on arabic

what kind of book are you looking ?

@lone wave

[lone wave]

no for someone to help me

sorry channels and roles kinda missed up for me

[stuck zephyr]

#❓how-to-get-help if you need help

you can try translate it or if you want I can look at it

[molten mason]

Keep trying. Don't just post "Arabic Calculus", post the problem too.

[lone wave]

@stuck zephyryes pls

it's a homework and it's this symbol

∫

[stuck zephyr]

thats integral

can we move to a help channel?

[lone wave]

sure

wanna do it on dms maybe ?

[stuck zephyr]

I mean sure

go ahead

[hearty steppe]

I guess I won’t find an Ergodic theory text that doesn’t feel like very rigorous math gibberish…

[rigid barn]

That's like wanting to read about topological quantum field theory in the form of a novel, the rigorous "gibberish" is the whole point.

[indigo mesa]

Advanced mathematical subject is mathematically rigorous, shocking news

[marsh ingot]

Lol

[tepid notch]

Hi do you have any book recommendations (can be several) for calculus, specifically covering these topics: Differential, Integral and Multivariate Calculus?

[marsh ingot]

Apostol

Spivak if you talk spanish

Bournaki has books about spectra theory but in french, any chances that is translated?

[glacial badge]

I recently got Stewart Calculus and I enjoy it so far. It has both single and multivariable.

[tepid notch]

will give it a try :) thank you

does it have a lot of questions to it? i’m looking for stuff to just grind out problems to practice

[keen orbit]

are you looking for something more rigorous ?

if yes then go for spivak i didnt learn from that book but everyone says that its the best bc it enables you to get into real analysis more comfortable later on (thats what i concluded from what others say)

[tepid mural]

does anyone have books with lots of exercises for an undergraduate computer science, first-year, probability (and preferably stats) book?

i already have my course book for theory but this book has only 10 questions for each topic (so a total of ~60-70 questions per chapter)

usually that's enough but i'm really struggling with conditional probability, bayes theorem and total probability theorem, so i'd like some extra practise for that

[orchid mortar]

Are you able to get the 1000 exercises in probability?

[tepid mural]

can you send a link to that book?

is it this one?
https://www.amazon.com/Thousand-Exercises-Probability-Geoffrey-Grimmett/dp/0198572212

[orchid mortar]

Yes

That's just exercises by the way

There is a textbook, but Grimmett and Stirzaker is a harder book

[coarse arrow]

Book on discrete math with difficult problems

[tepid mural]

that's alright

im looking for something like that

thanks for the recommendation. i'll take a look at it

[orchid mortar]

try to find the textbook too it's great reference material

[tepid mural]

got it

[tawny copper]

Engel, Pranav Sriram, Soberon

[vital bane]

huh?

[marsh ingot]

Literaly the first result for Spivak is his book for infinitesimal calculus but in spanish

Idk if there is a english version

[hearty steppe]

I’ll probably just stick to general measure theory and probability reads then that are on my reading list

Folland’s real analysis was a good read for me, kicked my ass but I was able to work through it

[vital bane]

maybe spivak was secretly spanish

[marsh ingot]

Dunno, never read his calculus book

[reef escarp]

What is the prerequisite for Sullivan's Algebra and Trigonometry?

[silent nest]

Book about Linear Algebra and Computer Science with answers in former case

[remote sparrow]

#book-recommendations message

[dusk wind]

The Dark Art of Linear Algebra

[rigid barn]

There's this French book called smth like "The Grimoire of Commutative Algebra" and it has a whole arcane theme to it (star signs, sigils, etc.). Really wish the author would translate it to English. More textbooks need to have a bit of stylistic flair to them (w/o that overtaking the contents, ofc).

[dusk wind]

I agree, will check it out

[molten mason]

I only found a Spanish version, I can't find that book in any other language which is so weird, I wonder if a university in Mexico specifically requested it or something.

Luckily I read Spanish

[marsh ingot]

Good

[molten mason]

Stewart isn't the best Calculus book, but it has nothing but TONS of problems. Hundreds and hundreds and hundreds of questions. The paid version of Quizlet has a verified collection for Stewart that has answers to all the problems in the book, including the even problems. It also gives explanations and shows the work for every single one.

[molten mason]

What's the pre-reqs for that textbook?

[molten mason]

Organizing the book into zodiac signs is... interesting.

[dusk wind]

their blog is written in English but they wrote the book in French lol

[molten mason]

The mad lads

[dusk wind]

will just use deepl and the french I do know

[molten mason]

Could be a good way to learn somw new French

[glacial badge]

i think so though i haven't gotten too far into the book. se lessons have around 60 problems. most odd numbered questions have answers in the back

[hearty steppe]

Well I’m going to try to give billingsley’s Ergodic theory and information a shot. A quick skim finds it to be far more approachable

[rigid flint]

Any good books on Vector Calculus, especially ones with lots of questions in them?

[spring cave]

If you only want problems, Demidovitch's Problems in Mathematical Analysis might be for you...

[gray gazelle]

Spivak’s Calculus on Manifolds for a slimmer option, Shurman’s Calculus & Analysis in Euclidean Space for a thicker volume

[rigid flint]

Tyty

[karmic yarrow]

Can someone suggest me a good book for differential equations?

[vital bane]

what kind of book?

a book containing methods and stuff like the usual undergrad diff eq course?

or a book that studies ODEs mathematically rigorously?

if it's the former then I would suggest "Differential equations with Applications and Historical Notes" by Simmons

if it's the latter then Arnold is usually recommended, I haven't gone through it so I'm not sure how readable it is

[distant scroll]

Hey guys! So i am going to take calculus next year, but afraid would not do so good since i have bad algebra skills, i want to learn algebra 1 + 2, geometry, precalculus all over again by myself in the summer by using textbooks, and then take the calculus course, and hopefully do good. Do you guys have any textbook recommendations?

[vital bane]

the usual recc is khan academy

[trail hemlock]

trigonometry for the practical man
humongous book of trig problems - older editions very very cheap
Intermediate Algebra - a lott cheaper used
Precalc aops

u can prob find these online 🏴‍☠️

oh and this seems to have "Algebra, Geometry, Trigonometry, Logs, Coordinate Geometry"
https://archive.org/details/mathematicsforp00howegoog/page/n4/mode/2up

[distant scroll]

I want textbooks though, i tried khan academy, but didn't like it since they are missing some stuff and it is not organized

[distant scroll]

Thank you

[dusk wind]

you can try Precalculus made difficult

its very short and should have what you need

[distant scroll]

Thank you, the book sounds perfect, i will take a look at it

[dusk wind]

let me know how it goes

[molten mason]

Yes, it's perfect for your needs, +1 to that

[gray gazelle]

Please recommend me an intermediate algebra textbook I have finished pre-algebra, algebra 1 and now I wanna move on to an algebra 2 textbook.

[distant scroll]

Did you finish an algebra 1 textbook?

If so which one was it

[gray gazelle]

algebra 1 for dummies

workbook*

I just wanted to revise the algebra 1 topics so I did it but I don't know some algebra 2 topics so I need a brief textbook

[distant scroll]

K

But where did you learn algebra 1

[gray gazelle]

youtube

[distant scroll]

Isn't there a sequel to the series for algebra 2?

[distant scroll]

Which channel

[gray gazelle]

its the khan academy youtube channel

but I prefer going through a textbook

[young grove]

I know this is math, but can anyone suggest a good book for thermodynamics

[marsh ingot]

There is a physics server

[keen orbit]

you can find it in english if you want

[orchid mortar]

US Calc of some kind at an undergrad level.
Mostly better if you have done proofs before

[vital bane]

Schroder's Thermal Physics

[young grove]

thanks!

[molten mason]

Do you know where? We tried looking for it the other day.

[keen orbit]

yes i cant tell you that you may find that in anna's archive or z-library

[vital bane]

mfw "I can neither confirm nor deny any details of the mission without the secretary's approval"

[keen orbit]

there you can find what you are looking for

[molten mason]

I can't tell you that it doesn't show up on either of those.

Spivak has Calculus, which is about 680 pages.

There's also a Cálculo infinitesimal written in Spanish that's 944 pages for Spain and Mexico.

The Spanish version is great and the material is a bit different (about 300 pages different amirite)

We were just hoping to find an English version of that book but I don't think any exists, I think it was specifically made specifically for some Spanish calculus curriculum.

[keen orbit]

did you check the editions and compare table of contents for example

i checked a book named calculus for spivak which is in spanish and is 691 pages 3rd edition

so it is the same

i have 3rd and 4th editions of spivak's in eng 3rd ed is 682 pages and 4th ed is 704 pages

[keen orbit]

i translated the table of contents of the 944 page spanish book and with the table of contents of the 4th edition of the english version and they were the same

so they are the same content

but the 944 book is 2nd ed so there might be slight changes ofc 4th edition will be better bc there are corrected mistakes for example

so they are the same dw abt that

[molten mason]

Lmao, you're right.

@marsh ingot @dusk wind I think when we talked about this I opened up an English Calculus PDF and scrolled straight to table of contents. I thought I click Spivak but I think it might have been a different Calc book completely and haven't looked since. However looking at it again with the correct PDF and I see they're the same textbook. That was my fault.

[keen orbit]

so you found it long ago ?

[keen orbit]

no problem these will be useful for future reads

[molten mason]

We were talking about if the beginning of Spivak is enough for someone wanting to learn pre-calc. Then they can go straight into Calc while already being in Spivak.

Versus buying a separate pre-calc book and then going into Spivak.

[keen orbit]

ohh idk about that tbh

but it probably is i saw sections like graphs and functions

so it probably builds background from start

[molten mason]

Yeah I read Part I and II in the Spanish version lmao

When I have time I want to go through various Algebra 2, College Algebra, Pre-Calc, Trig, and the beginning of Calculus textbooks and get a true perspective on that level of math and more appropriately recommend texts.

I personally recommend Basic Mathematics -> Any Calculus text 99% of the time.

[keen orbit]

college algebra is something more advanced than calc

college algebra is referred to stuff like linear algebra/abstract algebra etc

these are proof based such as real analysis unlike calculus which is more computational

one note you will notice that spivak is more rigorous than any other calc book prob unlike stewart's

[molten mason]

In the United States, College Algebra is the course taken before Pre-Calc at the college/university level, but it also overlaps a lot with Pre-Calc.

It's like coordinates, functions, the quadratic formula, the parabola and hyperbola, logarithms, and polar coordinates.

So in secondary school you'll have algebra 1, geometry, algebra 2, trig, pre calc, calc

University is commonly College Algebra, pre calc, calc

[dusk wind]

I've looked at countless 'College Algebra' books and the material looks mostly the same

There might be a chapter or two of differing content though

[vital bane]

Lol yea I've been confused by this nomenclature before

I too once thought "college algebra" meant abstract algbra

only to find out it's elementary algebra for 1st years

[dusk wind]

Unis gotta make sure you learn algebra in case you sneak in somehow

Precalc is better to take up though if you already have solid algebraic skills

[fierce hedge]

Isn't college algebra just a US thing? Or maybe US+Canada

[vital bane]

yea I think it's only like a NA thing

[keen orbit]

I mean generally college algebra should LA/abstract algebra etc

Otherwise what would you call these

[vital bane]

....abstract algebra

[dusk wind]

???

[molten mason]

I try to think of it as College Algebra texts are targeted towards an adult learned. And teenagers get more of the "Algebra 2", "Geometry", and "Trigonometry" texts.

And then the difference between College Algebra and pre-Calc are minimal. I think College Algebra often has a chapter on probability or something and Pre-Calc doesn't?

I know locally, Non-STEM majors have to take and pass College algebra, while STEM takes Pre-Calc and Calc I at a minimum.

Either way it seems dumb

[dusk wind]

'modern algebra'

[vital bane]

yes it is

[molten mason]

My favorite thing is when a 13-year-old comes in here asking for help with Algebra and everyone just blindly recommends D&F or Artin to them

[vital bane]

high schoolers should be taught real analysis, it's way more intuitive

[dusk wind]

just take precalculus for the functions+everything else

[vital bane]

and what doesn't help is there are 13 year old in this server who have finished D&F or Artin

[molten mason]

Yeah

[dusk wind]

so confusing

[molten mason]

I've always known Abstract Algebra = Modern Algebra. And basic algebraic functions you learn during school-age years is Elementary Algebra

[dusk wind]

Its better to be introduced to a subject by using it rather than learning all of it's intricacies

Abstract Algebra is something you can learn in college but it's not necessarily 'college algebra'

[molten mason]

I need a mix of and

[open birch]

Guys I am 16 years old and i want to work in cybersecurity. Do anyone has a good book for me ?

[molten mason]

Terence Tao

[dusk wind]

any book on computer networking

[molten mason]

Cybersecurity is a vast and broad field.

For example, you can probably study everything for the CompTIA certs now and then when you can afford it take the certification exams and start getting into the workforce in a couple years.

[open birch]

I want to join secret service there is any achievements i need more ?

[dusk wind]

[molten mason]

LIke... the United States Secret Service?

[dusk wind]

maybe try interning at a company

[open birch]

No the DGSE I don't know if you know what it is but its the french equivalent of the FBI

[dusk wind]

maybe they have requirements on their website

[molten mason]

They're more like the CIA than the FBI

[open birch]

I have visited and not in particulary

But I prefer ask