book-recommendations

[vital bane]

it's a good book

but it mostly covers only manifolds not general top spaces which is fine for the most part ig

[gray gazelle]

How are you defining formal? Like if the book had the same contents but was rewritten (transcribed?) into symbolic logic, would that make it formal?

[strange vector]

yes, that would be more formal compared to using only english words

[gray gazelle]

But that’s just a typographical difference

[strange vector]

and i think jech's definition of formal is similar because he says his book is informal and doesn't use symbols

[gray gazelle]

So long as the words are used consistently and precisely, the effect is the same as using symbols

[strange vector]

what formal/informal means then?

can't be as precise as using symbols

[gray gazelle]

How so?

[narrow crown]

Do you where I can find even numbered question solution for Kenneth H Rosen Discrete Maths & its application 8e book Indian adaptation?

[sick river]

symbols were made to shorthand the formalism

[gray gazelle]

If I take a text written in symbol logic and replace each symbol with how’s its word equivalent (so the for all quantifier goes to “for all,” etc) and I do this exhaustively, the resulting text will be no more ambiguous then the original

[strange vector]

that is not what we are discussing, i'm just saying thomas jech's definition of formal is same with mine

he defines his book informal and doesn't use symbols

anyone have a problem with that can talk with jech idc

[sick river]

he's not saying its informal because he doesnt use symbols though

[strange vector]

then why

[sick river]

it means that the book doesn't justify it's logical basis rigorously, that's all

[strange vector]

and it's done with using logical symbols almost all of the time?

can you write mathematical logic book without using symbols

[sick river]

Yes the symbols are shorthand for all the qualifiers and such

[strange vector]

wow, i didn't see any mathematical logic book without logical symbols

[sick river]

Because it’d be 10x as long lol

But still doable for sure

[strange vector]

and i think there isn't any, because you need symbols for formalism

[sick river]

There isn’t any because it’d be quite cumbersome that’s all

You do not need symbols for formalism, they’re simply shorthand for the underlying language of formalism

[strange vector]

if that was true i think there would be some logic books without symbols, you can't express symbols precisely with english, that is why mathematicians use symbols

english or some other langauge is not enough

[sick river]

If I live an hour (by car) away from where I work, we agree I can still just walk right?

[strange vector]

i can't

you might be able to walk

[sick river]

I can physically walk there maybe it takes 8 hours though right?

[strange vector]

can't be sure

[sick river]

Okay.

Like I said. It’s an hour away by car, so there’s land from my house to where I work, since there’s land and even a path, I can walk to work in some amount of time right?

[strange vector]

there are so much unknown factors, you might die from heart attack or something

[sick river]

Bro I’m done

Someone else take over

[cold elbow]

ggs

[gray gazelle]

Again, symbols are just shorthand. If you always you the phrases “for all” or “for every” when you could write the upside-down A, then this expresses the same thing to the same level of precision. Or, if you want, just think of works as long symbols

At any rate, if you want to read a set theory book that is formal by your definition, why not read the Principia?

[strange vector]

not only my definition, jech also uses in this way and most of the mathematicians i see

maybe in the future i can read principia btw

nice book

[mellow wren]

The principia is ironically a very bad book lmao

[strange vector]

people say bourbaki's books are bad too so they are just opinions

[gray gazelle]

Can I ask, why do you want a formal set theory book? I mean, formal language is more tedious to read than natural, and the non-formal treatments are pretty good

[strange vector]

i prefer symbolism to english

it's easier to read for me

[vital bane]

symbols ≠ formalism

you can be completely informal while using symbols

[vital bane]

example this message:

[strange vector]

yes, but you need symbolism for formalism

for being precise

[vital bane]

not really?

[strange vector]

yes

[swift dome]

concrete mathematics is all what you need

[vital bane]

that is not true, symbols are just a way to shorten certain phrases

[gray gazelle]

I agree. Or Naive Set Theory if you just need to brush up on set theory

[strange vector]

you can't be precise with english, other people can interpret differently

this can't be happen with symbolism

symbolism is necessary for formalism just think a little

[gray gazelle]

Yes it can

[strange vector]

how

[vital bane]

you can interpret the symbols differently it's not like a formal language

mathematical symbols dont form a formal language

[strange vector]

logical symbols*

not some random x,y,z

[vital bane]

yes neither do logical symbols form a formal language

[strange vector]

sure

[grim sinew]

percy jackson

[vital bane]

Percy Jackson and the Goblet of Fire

[grim sinew]

fanfic unfortunately

read rick riordan

[oak sable]

Is there a modern, substantially more readable version of Principia Mathematica by W&R? I'm not sure what the current field of set theory looks like. I'd really prefer a textbook written by a mathematician for mathematicians rather than philosophers. I've looked at some of the textbooks written by/for philosophy and there's something very uncomfortable about them.

Just a good, serious foundations book. Ideally, it'd work from introductory to intermediate. A two semester sort of book.

[vital bane]

@heady ember

[strange vector]

You can take a look at this link https://www.logicmatters.net/tyl/, It's a guide for learning logic and includes recommendations for each level and topic.

[gray gazelle]

Does it worth it to use this book for algebra 2 and pre calculus? :

Basic mathematics

[finite gale]

If you mean the one by lang, then yeah it's probably fine

But whether something is worth it or not is pretty subjective

If it's expensive for you to get (or if you don't like pdf versions) then maybe another resource may be better

[molten mason]

Yes, great book

[remote sparrow]

i don't think so

how about you argue this in #foundations and see what they think

[strange vector]

argue about what? I just asked formal set theory book and everyone argued with me

[vital bane]

[autumn spire]

can someone recommend me number theory book

i have already done andre's

[tiny stratus]

Hi guys

Can someone recommend me a good statistics book for a computer science student

[molten mason]

Sometimes in general it's better to ask for books in specific channels, since people active in those channels are more the experts in those fields and which texts to use.

[steel cloud]

@molten mason recommend book for set theory and logic

[strange vector]

so i need to ask in foundations channel for logic and set theory books

[molten mason]

Could be beneficial.

[molten mason]

Sorry, I've only read Naive Set Theory by Halmos, this isn't an area I'm knowledgeable in.

[steel cloud]

Is the Halmos is good for beginners?

[molten mason]

Yes

[strange vector]

should i ask for real analysis book in real analysis channel?

[steel cloud]

Okay

[gray jungle]

@steel cloud could be useful

[molten mason]

This is the main goto for this channel, it's in the pins. If you have more questions you can ask here or #real-complex-analysis

#book-recommendations message

I feel everyone has a different opinion when it comes to real analysis books, and it seems to be individual preference.

[strange vector]

makes sense, thank you

[molten mason]

Oh that's cool

[steel cloud]

Thank you

[tawny copper]

Andre Weil? Which one?

NT is very wide (and deep), you should specify what kind of NT you are looking for

[remote sparrow]

#chill message

@zealous light what do you think is a good treatment of multivariable calculus

[autumn spire]

i meant andreescu

i am just preparing for olympiads so anything related to that

[narrow prairie]

try modern olympiad number theory by aditya khurmi

you can get it here https://artofproblemsolving.com/community/c6h2344755

[autumn spire]

thanks

[tawny copper]

I second that. There is also Hojo Lee's collection of problems which I like

[livid terrace]

hey guys, i'm finishing calc 1 rn, about to head into calc 2 next sem

i'm finishing calc 1(ap calc AB at the hs level) with a 93, known to be a more difficult class at my school ||i'm not saying it's anything special, i'm just stating it for context to gauge||

do u guys have any book recs for calc 2?

i want to not only score high, but actually understand what it is that I'm learning

literally anything is helpful 🙏

[remote sparrow]

the same textbook you used for calc 1 isn't good enough?

[livid terrace]

we didn't have a textbook

[remote sparrow]

usually those books span all of calculus 1, 2, and 3

okay

[livid terrace]

i need to get a good grounding in calc 1 and 2 to take calc 3 at the community college next year through dual enrollment

[remote sparrow]

pick up either stewart or larson

an old edition is perfectly acceptable and much cheaper

for example, the 6th ed. of stewart only goes for several dollars on amazon, compared to a couple hundred bucks for the 9th ed.

[molten mason]

Most colleges use Stewart, Larson, or Thomas. Any is acceptable, but check which book your college will use and just grab that one. It'll cover Calc I through III

[remote sparrow]

there's also calculus for dummies

and obviously ap test prep books

[livid terrace]

im in hs rn, and calc 1 and 2 are at my hs

[livid terrace]

ye

[molten mason]

Plus the access code

[livid terrace]

ofc

[molten mason]

Yes that doesn't change what I said. If you're taking Calc 3 at the community college, grab that textbook early. That textbook will also have everything from Calc 1 and 2 if you want to study and practice

[remote sparrow]

my assigned textbook was stewart for ap calc

it had calc 3 material too

[molten mason]

That edit

[molten mason]

Also if it's Stewart, double check if it's Late Trancsentals or Early Trancsentals, they're different textbooks

[livid terrace]

def

[livid terrace]

fr? i'll def look into it

i'll look into my school textbook collections and see if i can find one

they prolly have em

[remote sparrow]

most use early transcendentals because colleges generally teach calculus to a diverse audience, especially science and engineering students

and science and engineering students need exposure to transcendental functions earlier

even though it's logically correct to delay them

[molten mason]

That's what we used, but I remember one of the first PDFs I found online was Late

[remote sparrow]

fwiw i think early transcendentals is better pedagogically

but i only ever used early transcendentals

and i used some of that stuff in my physics classes

[remote sparrow]

https://math.stackexchange.com/questions/43290/references-for-multivariable-calculus

https://math.stackexchange.com/questions/44522/theoretical-multivariable-calculus-textbooks

[willow basin]

Guys am in grade 11 looking for a free online book on combinatorics that is easy to understand

Pls ping if u have recommendations

[gray gazelle]

Alr

[heady ember]

Enderton is nice in my experience if you have little to no mathematical maturity.

Baby Jech may be more to your liking if you have more mathematical maturity.

If you wanna go grad level you'll need to learn mathematical logic as well . For that, Kunen and Ebbinghaus are some possible options, amongst others.

Check out Clerk's foundations recs too!

[lean pagoda]

Ebbinghaus happens to have a very very good introductory set theory text too, though unfortunately there is no English translation.
Quite odd considering all his other texts have been translated and the set theory one is already in its 5th edition (released just 2 years ago).

[gray gazelle]

When I finish the book: “Basic Mathematics “ where in the mathematics iceberg would I be like, does the next thing I would need to learn is geometry, trigonometry, calculus, physics etc…

[loud cradle]

Lang Basic Mathematics? Doesn't it cover geometry and trig?

i think from there you could go straight to calculus

[trail hemlock]

the german psychologist?

[trail hemlock]

if you think abt it, all books are free online 🏴‍☠️ 🏴‍☠️

[molten mason]

Basic Mathematics is considered a Pre-Calculus book. The next textbook afterward would be any Calculus book

You could supplement it with https://mecmath.net/trig/ for trig

[gray gazelle]

But does algebra 1 and age are 2 are covered?

[molten mason]

It has plenty of trig and geometry though

[gray gazelle]

Ty

[molten mason]

Yes

[molten mason]

It starts at middle school math and ends in Pre-Calc.

[loud cradle]

yea, should be pretty much everything you need to proceed with calculus

[gray gazelle]

Oh so I will be "setup"

[molten mason]

Technically it starts more at 5th grade US Math level, imo

But yes. It's an all inclusive book. Makes you ready from for Calculus

[gray gazelle]

Alr but I'm in 8th grade so secondary 2 in quebec and does thus book OK for me?

[gray gazelle]

Oh

Ww

Wow

[loud cradle]

yea i think it should be fine, i suppose there could be some topic you need that isn't covered but it's reasonbly complete as far as i know

[molten mason]

I know 10-year-olds to college students who are or have gone through the book.

You'll be fine.

[gray gazelle]

This is fantastic, should i buy it or read the free pfd I found

[loud cradle]

haha obviously up to you

[molten mason]

Personal preference. I have both PDF and physical copy

[loud cradle]

serge lang is dead, he doesn't care one way or the other

[gray gazelle]

He is dead?

[loud cradle]

yea died in 2005

[gray gazelle]

Ah rip

[gray gazelle]

Oh

[molten mason]

Yeah. And he has written many textbooks. From that textbook all the way up to graduate level math. Pretty much every topic you'll ever want, he's written about it, for better or for worse lol

[gray gazelle]

So the 10 yo learned pecalculus?

[loud cradle]

tbh there's nothing about precalculus that needs to be age-gated, just that most schools go very slowly through math

[gray gazelle]

Why no one told me about this book in elementary school bruh

[molten mason]

Yes

Yeah public education is painstakingly slow

[loud cradle]

hell i never knew about it until i was an adult, at least you found it while it's still useful to you 😁

[gray gazelle]

So ig I had bad environment and bad connection as a kid

[loud cradle]

i haven't read it but i've seen it recommended many times, i expect it's pretty good

[gray gazelle]

Yes, you right

[gray gazelle]

I'm gonna let it a try

[loud cradle]

yea do it

[gray gazelle]

Give it a tru

Try

[loud cradle]

if you get stuck on questions, just ask in the help channels here

[gray gazelle]

Alralr ty

Tysm guys

[molten mason]

It's a very... mathematical book.

It's very straight to the point. It doesn't have 10000 pictures and graphs and colored text.

So it covers a lot in the space given, but you might need to go on YouTube to have things explained better if you can't follow along.

[gray gazelle]

Yes

[loud cradle]

"It's very straight to the point. It doesn't have 10000 pictures and graphs and colored text." - his two calculus books have this virtue as well, in particular i quite like his multivariable calculus book

much better than wading through the multicolor picture-filled spam of the most popular calculus books

[gray gazelle]

Yes

Ima start read tomorrow

1 chapitre a day

[loud cradle]

^ sounds fast for a math book!

[molten mason]

I've heard about that one but haven't gone through it myself. I have a 1994 Calculus textbook from Howard Anton, while still a very modern Calculus textbook, isn't as bad as the more recent Calculus books. I feel like every newer edition of textbooks gets worse and worse with the spam lmao

I'm going through his Undergraduate Algebra and Undergraduate Analysis right now though.

[loud cradle]

but if you can do it and understand it then go for it

[gray gazelle]

Should I skim(especially if ik that) or read

[loud cradle]

yea, you can see it if you compare recent calculus books with ones from 20-30 years ago (they had a bit of color but not every color in the rainbow) or 50+ years ago (black and white)
intro physics books same deal

[molten mason]

Some days you might do a whole chapter. Some days maybe only a page. Only advance when you understand what you're learning.

[loud cradle]

really up to you, no need to spend extended time on stuff you already know well, skimming that stuff seems fine

focus on the new stuff

[gray gazelle]

Mhmm

[lean pagoda]

The German logician (I doubt there are many psychologists that care about set theory )

[molten mason]

IMO skim the problems if they're too easy, but read the text. You may never know what you accidentally skipped.

[trail hemlock]

nah i just got the craziest flashback to ap psych

the forgetting curve 🙏 🙏

[loud cradle]

^ yea, even if only to make sure you are aware of any notation conventions lang is using

[gray gazelle]

Yes yes it does happens something when I want to skim but end up reading and knowing that I almost passed a very important thing to revise, for a exam for exemple

[remote sparrow]

i don't know where you live, but schools generally try to give their students a broad education in things besides math, so they necessarily need to spread out the math curriculum a bit to accommodate other subjects

[gray gazelle]

Canada

[gray gazelle]

So, is it fine to use these books after covering Abbott?

[remote sparrow]

not really

[gray gazelle]

Oh! These books are such advance:O

[remote sparrow]

maybe you can do a few easy analysis problems but qualifying exam questions typically test you at greater depth

[gray gazelle]

I understood.

What is abbott

I guess having experience with few analysis books (including baby rudin) is enough

[remote sparrow]

qualifying exams are written for phd students. phd students take them to show they have adequate skill in some given area of mathematics.

[loud cradle]

intro real analysis book

[gray gazelle]

Okok

[gray gazelle]

Like réalise problems?

[naive eagle]

a really, really good underrated book that i found is called "Insignia" by S.J. Kincaid. its a trilogy about a boy named tom raines with a dark background, who has a very special ability, capable of ending WWIII

[gray gazelle]

Dayum

[loud cradle]

rigorous calculus, topology of the real line, convergence of sequences and series of functions, that kind of thing

[gray gazelle]

Bro what? Seems cool

[naive eagle]

i read the 3rd book in 3 days

[molten mason]

Graduate students normally complete an entire undergraduate math degree and 1-2 years of graduate school before attempting those questions. And still many fail

[naive eagle]

its super good

i couldnt put it down

[remote sparrow]

you might solve some analysis problems from the ucla basic exam (tests undergraduate real analysis and linear algebra), but you wouldn't be qualified for the analysis exam.

[gray gazelle]

How many pages my max is 450

No like 400

400 is my max

[naive eagle]

its like 300-400 depending on book

[gray gazelle]

I never finish a book after 350 page

[gray gazelle]

Ok

[gray gazelle]

Oh damn

[gray gazelle]

I got it. Looks something really challenging hehe

[gray gazelle]

What analysis exam gonna grant you?

[remote sparrow]

advancement to candidacy i think

[loud cradle]

i think the basic exam is taken just as you enter grad school at ucla
covers only undergrad material

[molten mason]

Those problems don't just have an answer. They have multiple possible answers, all given the "correct" solution, but there is some nuance about the problem or about the possible solution that can make the answer seem correct but actually be wrong.

[remote sparrow]

typically you need to pass another one or two exams as well

[remote sparrow]

yeah it's mostly ug real analysis and linear algebra

quals/comprehensive exams vary from school to school; ucla is just an example

[molten mason]

Yeah some combine real/complex, some separate them, some make the specific topics mandatory some give you multiple topics and tell you to pick 2 out of 3 or 5 out of 6 or whatever. All very different. All sounds like it sucks lmao

[gray gazelle]

Ok i know none of that let. Me do research

[molten mason]

Depends on the university, for most I've seen. If you pass, you are allowed to start your PhD. If you fail twice, you're kicked out.

[remote sparrow]

sometimes it's oral exams, like at princeton

[molten mason]

I've heard those can be easier, but I don't think any of the universities I'm interested in do them.

I've heard stories of some quals having 100% fail rate just depending on who wrote them that time 🤢

But anyway getting off topic of the channel.

[gray gazelle]

Oh ok

What happens after u get ur phd,nothing?

Or récognition

[remote sparrow]

some people pursue postdoctoral work, hoping to secure a position at a university (which is super hard). they might get work as an adjunct while doing this. others may pivot to nonacademic jobs.

[gray gazelle]

I understood. Once upon a time, I participated in math competition in my country. Where the question were taken from these books (especially problems in Berkeley university). Few months ago, when I read that book I suddenly remembered. To be honest, none of my answers in the competition was correct lol (except one)

Today, I know why the questions were so difficult hehe

[gray gazelle]

Ah

[gray gazelle]

any pdf for complex numbers?
I am weak at CM so i want a pdf from basics . _ .

[tiny stratus]

@molten mason do you know any good book on the topic statistics and probability for computer science students

[glossy zealot]

I actually ran across a book with that name ytd, statistics and prob for computer scientists

[zealous light]

For analysis, the usual choices for intro analysis or spivak com is nice, but if you want something with less rigor, something like Schifrin

[remote sparrow]

do you have a specific source(s) that you've personally enjoyed or found most helpful?

[zealous light]

When I TAed for a proof based course in multivar, I enjoyed using Schifrin

[remote sparrow]

https://tenor.com/view/sanae-fumo-nodding-nod-yes-gif-26471925

[remote sparrow]

good books on measure-theoretic probability?

[jaunty quail]

Alan Gut Probability: A Graduate Course

[glossy zealot]

Probably the one by Billingsley or Rosenthal

Those are common books for graduate probability course in a PhD stat program

[trail hemlock]

i would say for bc calc the best textbook to do well in the class is any ap prep book, but the the best way to learn it would be maybe the apps textbook or the spivak(most calc textbooks you can find are alright ngl)

[fierce hedge]

Theodore Shifrin?

[light glacier]

what are some good books for a secondary school student looking for more advanced than the curriculum

i can never find more advanced stuff for my level

[gray gazelle]

What’s your background? What classes have you taken?

[drowsy thicket]

Well you can still prepare for your qualifying exam like that I guess?

[graceful moon]

Probably some basic real analysis and linear algebra if youre at the end of highschool, maybe just look at like stewarts calculus if youre earlier in highschool

[drowsy thicket]

By picking harder texts

[sage python]

UCLA analysis quals as I recall are brutal

[brazen rivet]

Could anyone suggest a resource on convergence analysis of projected gradient descent, but in an abstract sense? Rather than projecting via minimizing the squared norm, I'm instead projecting via minimizing the KL-divergence

[gray gazelle]

Anyone have any sources for math books/pdf's that I might want to look into, as a complete beginner?

[brazen rivet]

What level are at instructionally? i.e. high school calculus, undergrad math student, etc.

[runic kernel]

In what context? Eg. are you 10 years old hoping to get into String Theory ? Are you a retired engineered interested in recreational number theory?

[rare dew]

How to make friends and influence people recommended to my mathematical friends

[lucid shoal]

Eh nah I will have to pass.

[remote sparrow]

https://maa.org/press/maa-reviews/computability-theory

[grand minnow]

Is there a good introduction book for linear algebra?

[lucid shoal]

Idk.

[grand minnow]

Why would you respond then 💀

[lucid shoal]

Because to let ya' know that I did not ignore ya'.

:>

[grand minnow]

Y'know what, I appreciate that

Thank you

[lucid shoal]

Np. <33

[gray gazelle]

Depends on your background. If you're already familiar with proof writing, and want to take a theoretical/general approach, then Linear Algebra Done Right by Axler and Linear Algebra by Friedberg, Insel, and Spence are both good. If you want something more computational, I believe Gil Strang's books are good

[grand minnow]

Thank you! I'll check those out

[heady ember]

Look in pinned

FIS is pretty good, but may feel a bit dry

Depending on your taste

[grand minnow]

What am I looking for in pinned?

[heady ember]

Dami's lin alg book review

[grand minnow]

Alrighty

[daring lake]

Hoffman & Kunze

[grand minnow]

Yeah, looking at the review it seems FIS or Hoffman and Kunze are what I'm looking for

Just gotta hope they're relatively cheap 😭

Not a bad idea, Salagos...

[remote sparrow]

#book-recommendations message

[molten mason]

FIS 5th edition is $33 on Amazon, it's what I have.

[remote sparrow]

@tame tree is a big fan of meckes

[remote sparrow]

that must be the international edition

i heard some pages might be missing

[molten mason]

I do not.

[molten mason]

It is, and I've heard that as well but I can't figure out which ones, if there are, not enough to make a difference

[remote sparrow]

you can corroborate page numbers with the pdf

[grand minnow]

USD?

[remote sparrow]

for example, the international edition of artin is supposedly missing its chapter on galois theory

[daring lake]

it is

i hate it for that

[molten mason]

They're about the same, ~600 pages.

Before I bought it I saw a review that it was completely missing Chapter 7 on Canonical Forms but my book has it. 🤷‍♂️ So who knows

[molten mason]

Oof that's an important one

[molten mason]

Yes

Yeah both are 616 pages

[trail hemlock]

what's a fairly rigerous treatment of multivariable calc? I was thinking Calculus, Vol. 2 by apostol or Vector Calculus, Linear Algebra, and Differential Forms by hubbard and hubbard? for reference i learned singlevariable calc mainly from the spivak

[remote sparrow]

hubbard is good

[trail hemlock]

gotcha

i just want something with interesting problems to work throiug, and not just straight computations

[remote sparrow]

Advanced Calculus: A Geometric View by callahan complements hubbard nicely

[trail hemlock]

ooo

ok i will check those out

tysm

[remote sparrow]

@tame tree

[heady ember]

Before I bought it I saw a review that it was completely missing Chapter 7 on Canonical Forms but my book has it. 🤷‍♂️ So who knows
The fourth ed doesn't have this chapter iirc

[pine kindle]

Comeing back to school and need a simple book for algebra (grade 9 if possible) Just want smth to kill time with and possibly learn from

[heady ember]

Not a book but Khan Academy is well-liked for hs algebra

and hs stuff in general

[pine kindle]

alr

[gray gazelle]

https://www.cambridge.org/core/books/logic-induction-and-sets/C359E91F59134B3AFEC8460798C62AA1

is anyone familiar with this book?

a combined text on logic and set theory

[remote sparrow]

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

[molten mason]

That makes sense

[native cargo]

i bought calculus made easy

is it good?

[remote sparrow]

it's okay

[lean pagoda]

I'm only familiar with the first 3 chapters since the Induction part of the text caught my eye and there are few textbooks that have dedicated chapters on this, but I found the presentation to be quite rough and think there are better alternatives.
I can't speak for the rest of the book though.

[hallow oriole]

if you're interested in induction specifically you might like mathematical induction: a powerful and elegant method of proof by andreescu

it's not exactly an uber-advanced book but it's fun and interesting

[lean pagoda]

Induction in this context means inductive definitions (and a bunch of other related stuff)
So it's not about the induction proofs you learn about in, say, a discrete math class

[hallow oriole]

ah never mind then

[gray gazelle]

I see

[olive bloom]

Any books for complex numbers ?

[vital bane]

complex numbers?

do you mean complex analysis?

[heady ember]

probably not

[heady ember]

Not a book but try Khan Academy

[round pelican]

Has anybody read “Introduction to Real Analysis by S.K. Mapa”? If so, did you think it was a good book? I’m considering purchasing it for self study.

[native cargo]

I'm not sure if this book will be enough for me. do you think I should cancel the order and buy the stewart singlevariable calculus book?

[versed coral]

any pre-calc textbook recommendations ?

[tame tree]

👀

What about its treatment differs?

[gray gazelle]

hey guys, so I took a course in which we covered an introduction to proofs (propositional logic, predicate logic, quantifiers, sets, relations, equivalence classes, induction, the division algorithm), while it is an introductory course, do you think It prepares me for reading spivak's calculus?

I've taken single variable calculus in highschool and I'm taking it in college (it's mandatory)

[heady ember]

eh I would say even without that you can reasonably learn from Spivak

[gray gazelle]

we use stewart, which I like and enjoy, but I also am interested in reading spivak

[gray gazelle]

that sounds great

[heady ember]

Just need to have some patience, as with any proof-based math book.

[gray gazelle]

I do have time

[heady ember]

You're gonna probably face a learning curve when first writing proofs

Enjoy!

[gray gazelle]

thank you!

I may go over what we had learned the first term using stewart, this time with spivak

[proud junco]

guys

any reccomendations for grade 9 algerbra?

[vital bane]

khan academy

[vital bane]

the curve when using Abbott: f(x) = x

the curve when using Rudin: f(x) = x^x^x.....^x

[peak knot]

what are the best books for learning about elliptic curves?

[vital bane]

damn you love krill

[peak knot]

https://www.youtube.com/watch?v=rU0mLB-stU0

[heady ember]

I also experienced a skill issue using Jacobson yesterday

Missed something obvious for like 2 hours

[gray gazelle]

happens to the best of us

[gray gazelle]

U 14?

Or 13

[vital bane]

yes Rudin's skill issue in writing a textbook

[gray gazelle]

What are your reviews on Analysis by amann. I saw the table of contents of all volumes. The book seems comprehensive to me.

[strange vector]

I think they are really good

different than other analysis books, starts from abstract which i really like

[gray gazelle]

The table of contents suggests, there is no need of any prerequisites. But Idk why, after some overview I feel the book is equal to the level of rudin in the view of rigour and abstract.

[gray gazelle]

Oh yes. It starts from abstract algebra

[strange vector]

I think it's because it requires some mathematical maturity and abstract thinking, but i think with basic set theory knowledge, it's readable.

[gray gazelle]

I got it. Thank you.

[strange vector]

You're welcome

[remote sparrow]

calculus made easy is more of a supplement. it doesn't cover some more standard material

[remote sparrow]

incoming college freshmen with high school calculus background sometimes take honors calculus, which is usually taught from spivak or apostol

[remote sparrow]

it really thoroughly treats R^2 and R^3 (even though these are special cases, a lot of the geometric and physical intuition can be found here). just because it focuses on these cases doesn't mean advanced ideas don't show up (like pullbacks and push-forwards).

[peak knot]

i am once again asking

[remote sparrow]

@left cloud

[left cloud]

[left cloud]

i'm obliged to recommend silverman and tate for an intro

obliged since it's the canonical intro book ofc

[peak knot]

ty

[gray gazelle]

is honors supposed to be like, more mathematically mature students than usual highschoolers?

[remote sparrow]

no

just harder because you're expected to do proofs

[gray gazelle]

ah sounds fun

[remote sparrow]

not many colleges offer honors calculus a la spivak

if yours does and you want to do it, just try it

[gray gazelle]

they don't unfortunately, just one program

my prof told me we will take proof based linear algebra though

next year

[remote sparrow]

proofs in analysis usually give students a lot of trouble

[gray gazelle]

because they're under-prepared?

[remote sparrow]

they're just really tricky, even for people who have done proofs in a different, more straightforward class like linear algebra

[gray gazelle]

yeah I think that's why we took an introductory course on that, although I should revise and practice more on proof writing

[trim kayak]

I will be helping to support high school students with Alg I and II and Geometry. I've been teaching Alg I and Geo for a few years but am rusty with Alg II. I have the high school text. Should I go through Alg II concepts and quickly review or is it best to take notes and spend alot of time on it?

[remote sparrow]

can you let us know what "algebra 2" material is?

[trim kayak]

Graphing, equations

[remote sparrow]

what kind of equations exactly? could you give us some examples?

[trim kayak]

Nvm

[stoic river]

Hi, does anyone know a good book that covers enough of differential geometry to understand De Rham’s theorem ? I don’t want to get too deep into diff geo, just know what is necessary for De Rham stuff.

[foggy fiber]

You don't need a book then. Just search for documents covering de Rham's theorem.

[stoic river]

Yeah but I have little higher differential geometry background

That’s why I’m wondering what is needed for that

[mossy flume]

What do you need De Rham's theorem for

If not differential geometry

[stoic river]

I need to know integration on manifolds for De Rham’s theorem right ?

[sage python]

Not what De Rham is needed for

What is needed for De Rham

Like how much background do you need to understand it

[mossy flume]

Ohhhh

I can't read

[dim sierra]

Can anyone recommend books that are in the style of Atiyah Macdonald, i.e. force you to develop the theory in the exercises?

[molten mason]

Take notes and spend a lot of time on it, go through all the odd-problems. That way when they have questions you'll be prepared and know exactly what they're going through.

[mossy flume]

For what area of math?

[trim kayak]

@molten mason Think it would be a good idea to go through the book and make a note of the sections I need to review or just start practicing problems?

I have a student book and no answers. Its a bummer that I won't be able to check my work.

[dim sierra]

Geometry/Topology/Algebra

Basically just not combinatorics or number theory lol

[modern ruin]

yeah atiyah macdonald

(sorry)

what kind of thing are you looking for? just any subject?

[remote sparrow]

if you haven't worked through lang, maybe try that?

[dim sierra]

Anything that’s not NT or combinatorics

[mossy flume]

I mean most good texts will develop theory through exercises in the text + exercise sections

[modern ruin]

all roads lead to do carmo

[remote sparrow]

hartshorne algebraic geometry?

[dim sierra]

His riemannian geometry book or the other one

[remote sparrow]

any book that gets bad reviews from the average reader for being too unhelpful would work

[dim sierra]

LOL

[modern ruin]

I know that people really don't like his riemannian geometry book, but I like it personally

[dim sierra]

Are problem books generally like that? I saw springer had a problem book series

[modern ruin]

I have not read his other books

[modern ruin]

based af

oh oh @dim sierra you should check out Davis & Kirk Lecture Notes in Algebraic Topology and see if the exercises in there are what you want

SUCH a good writing style

and there are like projects at the end of the chapters

basically the way a book should be written

[dim sierra]

That’s cool

Does this require hatcher

As a prerequisite

[modern ruin]

you should probably read chapters 1 and 2 of hatcher, it's good for your soul. I don't really think books have other books necessarily as prerequisites, but it sort of assumes you're a bit familiar with homology. you should try reading it and if it's too difficult then try hatcher and then this book.

I guess it doesn't need that much prior familiarity with homology if you're a strong algebra person, since it contains the construction

you seem to enjoy cohomology after all :P

plus, if you're trying to develop the theory on your own, it has stuff that you can fill in - for example "one calculates that del^2 = 0" can be seen as either a blackbox or a computation, and you can treat it like an exercise if you want

ah here are prereqs straight from the authors:

The prerequisites for a course based on this book include a working
knowledge of basic point-set topology, the definition of CW-complexes, fun-
damental group/covering space theory, and the construction of singular ho-
mology including the Eilenberg-Steenrod axioms

[dim sierra]

lol make no mistake that word is mostly a buzzword to me atm lmao

[heady ember]

Massochist moment

[molten mason]

Both. At that level, you can probably figure out all the answers using Desmos and YouTube though

[molten mason]

Like to check your work

[sage python]

😠

[dim sierra]

Hehe

[crude sage]

Is Abbott enough analysis background to read Folland? Maybe with basic stuff relating to metric spaces from Rudin or Carothers or something like that

[remote sparrow]

abbott isn't enough

you can read axler tho

https://measure.axler.net

[crude sage]

I guess folland assumes much more maturity than anyone coming out of abbott will have?

[chrome coral]

are there any books that high schoolers can read about proof writing

[cunning elk]

plenty

[remote sparrow]

students who did well with rudin are probably prepared enough for folland

[crude sage]

Is that because rudin expects more independence from its readers, or because it covers material abbott doesn't, or both? (I remember both are true)

[remote sparrow]

abbott technically has a bit of material on metric spaces, but it's just a series of very short exercises that don't go into much depth

[crude sage]

I see

[vital bane]

spivak

[vital bane]

nah you got it bro Abbott is enough

just change |x - y| in abbott to d(x, y) and you got it

and just read some notes for general metric space theory

[glossy zealot]

https://www.jirka.org/ra/html/frontmatter-1.html
You can try this book too, it is both for a slower, more beginner course or a faster one, cuz the author used to teach in both type of classes

It has metric spaces in chapter 7

[vast jackal]

hey any book for classical mechanics introduction?

[gray gazelle]

how introductory

[loud cradle]

kleppner and kolenkow?

[gray gazelle]

my class used young & freedman university physics

im planning to read landau if you mean university level though

[vital bane]

"Classical Mechanics" by John Taylor

amazing book

[gray gazelle]

Is book channel closed?

I mean the one without ability to write in.

[heady ember]

Archived

[molten mason]

Oh I forgot about those, I remember seeing it once, like a vague memory

[gray gazelle]

Thanks

[livid bobcat]

sears and Zemansky's University Physics or Giancoli --> Introduction
David Morin ---> 1 step ahead

[proud junco]

yup

[solemn sigil]

could anyone reccomend books for recurrence relation ?

[gray gazelle]

im 13 cool to young people learn

@proud junco u should use the book « basic mathematics «

Hello, I am @reef escarp looking for book recommendations covering all the basic algebra and geometry before precalculus, which i believe includes: functions, polynomials, factorization, linear equations, quad equations, complex numbers etc. So all that stuff. I have a few requirements:

1. Physical copy must be easily available for cheap (under $25, it doesn't matter if it is used)
2. Has good enough explanations that I can use it for self-studying
3. Plenty of problems (preferably with their solutions)

(trying to help him that why i copy pasted his message)

[scarlet steeple]

Discrete Mathematics by Biggs, it has a chapter on recurrence, his chapters on Generating functions to find closed formulas for certain types of recursion equations is great

[solemn sigil]

ahh ok ty

[grand thistle]

any introductory books for statmech thats mathematically rigorous but doesnt require like an extensive phys background

[naive trellis]

whats books for geodesics on rfolds

[burnt jackal]

Any books covering Vieta's Formula? Collage algebra books from here: https://youtu.be/pTnEG_WGd2Q?si=T8mKnUZcjNW4Kb0B aren't covering it

[molten mason]

I don't know any textbooks off the top of my head that have it, but there's tons of websites that talk about it

[molten mason]

https://www.geeksforgeeks.org/vietas-formula/

[vital bane]

rfolds?

orbifolds?

[sage python]

I don't know of a particular place for that unfortunately

Write some finite ones down I guess and play with them until they make sense?

Tbh indices ruin everyone's lives even after however much time doing math

[naive trellis]

rfold

[vital bane]

what are rfolds

The final section in the 2nd chapter of Abbott covers the theoretical basis of infinite double sums

[graceful moon]

Khan academy is free and fits all of that although it isn’t a book

[vital bane]

Khan acadmey is very good for all the basic geometry, algebra, precalculus and even calculus

[graceful moon]

Yeah anything at a highschool level I’d recommend Khan academy for NA students, it’s very comprehensive

[lime vessel]

Riemannian manifolds?

[gray gazelle]

@reef escarp there is ur answer

[ember slate]

I know this is cs but, any book that goes through the math needed to understand cryptography?

[vital bane]

new riemannian manifold course in khan academy coming soon

new and improved with ricci flow

[lime vessel]

rfolds

[vital bane]

oh is that what she meant by rfolds

[lime vessel]

Idk

[gray gazelle]

^repost :/
Anyone got Complex number pdf ,book , or smt?

[vital bane]

Complex numbers?

khan academy covers that

https://www.khanacademy.org/math/algebra-home/alg-complex-numbers

[gray gazelle]

I want DPPs not lectures .-. (I found a few DPPs on Khan Academy, but they do not match the level I am seeking for)

[vital bane]

DPPs?

[gray gazelle]

Daily practice paper

like module and stuff

[vital bane]

oh you want practice questions?

[gray gazelle]

yes C:

[real marsh]

What level are we talking about? End of high school?

[gray gazelle]

Competitive exam level? like IMO and few entrance exam

[real marsh]

Uh I mean IMO, beyond problems which use complex bashing for geo, which you can find on aops, it’s not really a thing

[gray gazelle]

thx bro btw do you know some good website/resource for an entrance exam?

[acoustic cliff]

There's a book on Complex Numbers by Andreescu

The book contains contest problems and Olympiad problems

[somber linden]

Book recommendation for advanced axiomatic set theory and logic?

[vital bane]

@heady ember

[heady ember]

How advanced

Grad level?

In that case you might get better answers from#foundations

[somber linden]

I went through Schaum's outline on set theory, but I want to learn it more rigorously, if that helps

[vital bane]

jech - intro to set theory

[heady ember]

Not familiar with Schaum's but is it naive set theory?

[somber linden]

Yep

[heady ember]

Ah I see

Is there a reason why you wanna learn axiomatic set theory

If you're not interested in set theory for the sake of set theory, maybe picking it up more rigorously isn't that necessary/helpful.

[somber linden]

Wouldn't it help with my understanding of formal logic and related concepts? I'm also planning to take real analysis next sem

[vital bane]

it would not

taking real analysis helps with that

[somber linden]

What about group theory? Or can axiomatic set theory be considered a more 'isolated' topic?

[heady ember]

You are really using any formal logic for real anal

[vital bane]

it's a topic for unhinged people

[heady ember]

You probably won't need to learn mathematical logic if you're not specing into foundations.

A naive understanding generally suffices

There will be exceptions of course

But you can learn those as you go

[somber linden]

I'm kinda working towards a physics-math double major, so I assumed having strong foundations in set theory and logic would help with later courses

But if not, should I just focus more on logic instead?

[heady ember]

[modern ruin]

having set theory will not help you in math or physics unless ur gonna do like, logic or something or you just want it for your own sake

[heady ember]

Yeah

[modern ruin]

i like set theory because it’s cool

[heady ember]

Same

[somber linden]

I'm also studying analytical philosophy and logic, so that's something I plan to get into eventually I'd say. Though I don't have much experience with how much rigor is required or where it gets redundant 💀

[modern ruin]

well then you might like set theory

[heady ember]

If you wanna see if you'd like set theory, a nice intro is Enderton's Elements of Set Theory, if you have no mathematical maturity like me when I picked it up.

If you're more mathematically mature, baby Jech (the ug book) is well-liked

Have a look at this

And this

[somber linden]

It's called 'baby Jech'?

[heady ember]

nope

its the informal name i call it by

This is the actual name

[somber linden]

XD. Alright, I think I can get started with these

[heady ember]

Seeing as how you said you haven't taken real anal, Enderton might be more suitable.

If I used baby Jech back in the days I would have probably died much harder lol

Don't be afraid to ask qns too! You can always ask in #proofs-and-logic

[gray gazelle]

If you want to work on your proof writing skills, I’d also recommend a book on discrete math or (proof-based) linear algebra if you haven’t taken it. Proofs in math are a little different than just formal logic, so it could help you prep for real analysis

[somber linden]

Yeah, I'll definitely need that

[somber linden]

For proofs, I currently have the book by Chartrand. Would that suffice?

[heady ember]

Some good pointers

• Don't use multiple implications in one sentence
• Don't use the word "suggest" --- it has a connotation that what you're suggesting may be false
• justifying very basic logic makes stuff too long (if you're new to writing proofs don't worry about this too much)
• Use short sentences instead of long ones
• Good grammer

[native cargo]

should i buy anything after calculus made easy

[tepid kindle]

Hi, can i ask? If may i

[heady ember]

And don't worry too much about being unable to write good proofs when you start. It takes time; my first couple dozen proofs were terrible. With that said, trying is key!

[somber linden]

Yeah, I've recognized they require a very different kind of intuition than what I'm used to

[marsh ingot]

Yes

[heady ember]

Yeah I would say that, if you have the luxury of time, try to focus on having fun and not how much time you're spending. Easier said than done ofc.

[gray gazelle]

I take set theory this sem

[gray gazelle]

That should be good. So long as you’re getting some exposure to reading and writing proofs before the prose monstrosity of analysis

ig id just work through enderton

[tepid kindle]

Dm please

[marsh ingot]

You can ask here

[tepid kindle]

I’m scared, maybe there’s someone who will criticize me

[gray gazelle]

wdym by prose monstrosity?

[marsh ingot]

No judging here, come on ask

[gray gazelle]

if they do, ill bonk them in their heads

[tepid kindle]

These questions are about in our activity, i’ve tried to answer those questions several times, but i can’t. These are the questions. Just need some solutions about quadratic functions into vertex form. I just need some solutions, could someone help me out. Thanks if you will. If i bothered you, just ignore this message😄

1: “f (x) = x² - 6x + 7”
2: “f (x) = x² + ,4 x + 8”

3: “f (x) = - x² + 10x + 12”

[gray gazelle]

Having lots of quantifiers grouped together (q.v. epsilontic definitions) makes it harder to write well/pleasantly. And throwing symbols at the matter makes the prose ugly in its own way

[somber linden]

I sure hope Tom Apostol isn't guilty of that cuz I'm following his book

[gray gazelle]

hmm

[tepid kindle]

I have no idea how to solve those

[heady ember]

If you wanna jump staright into analysis, that can work too. Check out mathematical analysis: a concise introduction, by Bernd S.W. Schroder.

[somber linden]

Alright, will do

[heady ember]

Why Schroder is nice #book-recommendations message

Some pages of it #book-recommendations message

[gray gazelle]

I know that book

it's in our library

[vital bane]

Abbott

[gray gazelle]

I’m sure he’s fine, I meant more on the student side. There’s just some adjustment in writing style to be had

abbott has a really tongue and cheek approach to analysis

i like it

[vital bane]

what does that mean?

[gray gazelle]

doesn't give away everything

gives you space to grow and develop

[native cargo]

this room is not for help, you should look #❓how-to-get-help

[gray gazelle]

throws in hints if you are careful enough to notice

it's an extremely good book

[vital bane]

yes exactly!

half the time some ideas of analysis are developed in the exercises

and half of the proofs you have to do by yourself (well guided proofs but still you kinda have to do it, the author doesn't provide a proof)

[bright vortex]

hey any good books I can use to learn trig from? I am trying to take it before the end of summer next year (as I plan to take calculus and I need to take trig on my own to do so) I don't want to use kahn achademy because I know a decent bit (like a bunch of formulas, what cos and sin and tan are and their inverses. I know some identities and such and a bit more) but I still do need to learn some stuff that I do not know. any good books out there for self teaching?

[modern ruin]

me too! exciting stuff

[gray gazelle]

oh nice

what do you plan to cover?

[molten mason]

https://mecmath.net/trig/

[molten mason]

Going to add that to my list, thanks

[naive trellis]

Any books for geodesics on rfolds

[wispy idol]

currently reading "The Algorithm Design Manual", it's written in a philosophical way, a good read for now (still in chapter 1 :3)

[remote sparrow]

you are using ordinary reasoning in plain english 🤓

[remote sparrow]

most math majors never investigate set theory and logic deeply beyond intuitive notions they pick up and they do fine

[remote sparrow]

any standard calculus textbook

[vital bane]

what is an rfold??

[wispy idol]

a research paper

[naive trellis]

riemannian manifold

[vital bane]

doesnt any book on riemannian manifolds cover geodesics?

[molten mason]

Any Calculus book, Stewart, Thomas, Anton, whichever.

[trail hemlock]

Spivak

[bright vortex]

many thanks!

[naive trellis]

i mean specfically on geodesics

[bright vortex]

woah only 180 pages. I was expecting more lmao thats great

[gray gazelle]

there isn't a dedicated book focused solely on geodesics on r-folds, i guess it's very specific thing to have a book about but there's differential geometry and string theory by matthew duncan and there this paper which is very good actually but wants a deep background "u-folds from geodesics in moduli space " and there's an intro to it in string theory and m-theory: a modern introduction by grishachugen "ig that's its name"

[naive trellis]

Cool

[molten mason]

It's actually a lot lmao, I was expecting like 30 when I first downloaded it

[bright vortex]

well a lot of it is examples and I only do maybe 1 of every ten lol

and I have till the end of summer

[remote sparrow]

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

[remote sparrow]

this link is down

i pulled the pdf from the webarchive though

[molten mason]

Works for me, is it giving you an error?

[remote sparrow]

yeah

[molten mason]

Works for me on three different devices. I think it's just you lol

[remote sparrow]

The connection has timed out

An error occurred during a connection to www.mecmath.net.

The site could be temporarily unavailable or too busy. Try again in a few moments.
If you are unable to load any pages, check your computer’s network connection.
If your computer or network is protected by a firewall or proxy, make sure that Firefox is permitted to access the web.

other websites work

[molten mason]

Weird

[pale scarab]

What would be an equivalent style book in real analysis to Algebra by lang. Like notoriously difficult problems.

[trail hemlock]

baby rudin

[pale scarab]

I see I thought that was an undergrad level text. I have already gone through understanding analysis by Abbott and do about all the problem sets. I was looking for the next level up that would prepare me to eventually read actual research papers. Like I went through Algebra by Gallian and lang is proving quite difficult but seems like the right step up

[molten mason]

Baby Rudin is undergrad. I haven't gone through it personally, but I've heard Folland's Real Analysis is the next step and is graduate level.

[vital bane]

papa rudin

RCA

[vital bane]

based Abbott fan

[molten mason]

Funny enough, I have Lang's Real and Functional Analysis book near me right now lmao

[molten mason]

I've heard Folland is a more modern version of RCA, what do you think?

[vital bane]

hm really?

[molten mason]

I plan on getting Folland at a later date for that reason, but I haven't gone through either of those so I don't know

[pale scarab]

Yeah it was honestly the easiest to read math textbook I have gone through. I'm looking for a more modern/ general approach. (Kinda like what lang does)I'll check out folland thanks

[vital bane]

yup best textbook for beginners ever!

[vital bane]

all I know is rudin = difficult

[heady ember]

(I also have a skill issue )

[trail hemlock]

woah ur him :🙏

[remote sparrow]

https://precalculus.axler.net/

@molten mason have you heard of this

it's supposed to be a standard treatment of precalculus, just significantly more concise than other competitors

[molten mason]

Yes, I have seen/heard of it many many times. It's like a modern alternative to Lang's Basic Mathematics, I haven't personally gone through it, just seen a few pages here and there.

I feel like anything by Axler can probably be trusted

I'm going through it right now, honestly I should probably recommend it more

[pale scarab]

I used the problem sets for a sophomore class for precalculus and it's good. Most textbooks at the high school level are awful and just not suitable for anyone looking to go further in math.

I personally think AOPS has the best treatment of precalculus. Their intermediate algebra book and precalculus book will prepare you well. I think most math majors would still find many of the problems quite difficult.

[rough umbra]

How is the presentation of category theory in algebra: chapter 0 by aluffi? What background would one need

[vital bane]

I think it's used a lot in AT and AG

and in any algebraic field no?

[sick river]

as someone who has used aluffi, category theory itself provides great motivation and cohesion between the different kinds of algebraic structures and imo if i was taught it that way as undergrad it would of been better (used judson, book sucks imo)

[distant galleon]

any good books on integration problems
especially for substitution, quotient rule, partial integration
on different functions (sin, cos, arctan, e, ln, polynomials etc)
as well as improper integrals
(it is the end of real analysis 1 and we have to do a bit of pracitce on these integrals)

i have found stewart calculus early transcendentals is this good?

[silk sigil]

I really don't think baby rudin has "notoriously difficult problems"

[marsh ingot]

The real problem is understand it

[gray jungle]

i would say the next step is learning measure theory, functional analysis and complex analysis if you want to progress further in analysis you dont want to stay stuck doing real analysis.

[normal reef]

Hello, I'm looking for a real analysis book that treats Reimann integrals in R^n ; something like baby Rudin in terms of what the excercises should be, I don't care for the computation ones.

[vital bane]

"mathematical analysis" by tom apostol is a good one

[molten mason]

For just a bunch of regular calculus problems, it's fine

[gray jungle]

Just a piece of advice, don't get stuck too much with Reimann integration on R^n for n>1 as there is a more suitable integral for this task you learn later in measure theory.

but its still useful in certain areas ofcourse (multivar lmao)

[normal reef]

Yeah I know but I have a stupid exam to pass

Thanks for the advice

[normal reef]

Thanks, the book looks promising from the table of contents

[marsh ingot]

Any books about machine learning and anomalous diffusion? Need for an introduction to a project

[vital bane]

anomalous diffusion? sounds like an SCP

[marsh ingot]

Its a weird stuff tbh

[gray gazelle]

do you guys have a book on optimization or on complex analysis

[vital bane]

they are very different subjects

[gray gazelle]

I know

[marsh ingot]

Convex optimization?

[gray gazelle]

yes

[vital bane]

Do you have a link to where I can read about it?

[marsh ingot]

Boyd convex optimization

[gray gazelle]

thanks

[marsh ingot]

I dont have so much about it tbh

First steps in random walks, Klafter and Sokolov

[dense loom]

Someone (not me), who had very bad experience with math and has discalculia (can't do 7*3), is looking for a book to self-learn.
Any ideas ?

[marsh ingot]

If anyone know pls ping me

[vast jackal]

AOPS

[vast jackal]

does it have lots of problems where i can solved it? what are the prerequisites?

[solar void]

Calculus book recommendations

Please

🙏

[vast jackal]

Calculus by Spivak

[strange vector]

Calculus by Tom M. Apostol

[solar void]

Good for self study?

[strange vector]

Yes, and have solutions in web if you need

https://www.stumblingrobot.com/index-of-solutions/solutions-to-calculus-exercises/

[solar void]

Ok thanks

[strange vector]

There are one more calculus book by courant, if you like applications of physics you may like it.

[solar void]

Man

It's like the book like looks like white and black

[gray gazelle]

can you guys recomend me a intrudoction to analitic geometry?

[solar void]

Hey man yes yes I am need calculus for physics. I am like in 10th grade and in this age I want to learn calculas by my own

[solar void]

I search the book online by Tom . And see the math sourcer vid . He said it like very hard

[strange vector]

you can choose one of apostol or courant, courant gives more applications of calculus in physics

i don't think it's very hard

[solar void]

Is it going to teach from beginning. And do you also learn calculas from that book?

[strange vector]

yes, all of them are calculus books and starts from beginning

[solar void]

🆗 Thanks 😊

[strange vector]

You're welcome

[sullen raptor]

do I need baby rudin for the fourier analysis book from princeton lectures?

[brazen rivet]

Could someone recommend category theory-free resources on fine moduli spaces?

[sage python]

You won't need the full force of Baby Rudin, maybe if your background is on the level of Spivak Calc that might cut it

[molten mason]

I read your Complex Analysis pin. Has there been any new thoughts or changes on it since your last edit? Do you have anything to say about Lang's Complex Analysis?

Do you have any recommendations on books about Fourier Analysis or is S&S your recommendation?

Would you recommend S&S Complex Analysis with S&S Fourier Analysis

End goal is to eventually have a solid graduate-level understanding of both topics.

We'll say background would be Lang and Folland for Real Analysis and Lang's Undergraduate Algebra

Are there any other topics/books you feel would be a prerequisite or fill a gap for Complex and Fourier Analysis?

[loud cradle]

yes, it has good, mostly nontrivial problems (but not too insanely hard for self-study). should be readable if you know calculus and basic things about vectors - dot products, cross products etc. It doesn't require any previous knowledge of physics

[loud cradle]

fyi, S&S Fourier Analysis is a very good book but only uses/requires the riemann integral, so it can't deliver the theory at "full strength" as you would do at graduate level. their later volumes (vol 2, complex analysis, vol 3, real analysis and vol 4, functional analysis) all have additional material on fourier analysis so if you read them all, you'd get decent coverage

for a more focused introductory treatment that assumes knowledge of the lebesgue integral, i like katznelson "harmonic analysis" and pinsky "intro to fourier analysis and wavelets"

[lime temple]

Can someone recommend me books that will help me study and master the basics of math

[molten mason]

#book-recommendations message

[molten mason]

Thanks!

Is the fourier analysis spread out through the volumes or are there dedicated sections/chapters?

[loud cradle]

there are some dedicated sections but iirc there are spread out bits as well
they're all good books but if your immediate goal is fourier analysis they're probably not the most efficient path (although vol 1 does give you a fair amount of material, by all means check it out, it's my favorite of the four books)

oh btw, another riemann-based book you might want to take a look at is folland's "fourier analysis", has lots of interesting applications (mathematical applications, not engineering stuff) that i haven't seen elsewhere

[molten mason]

Not immediate, long term and efficient is the goal.

[molten mason]

Oh cool, that's good to know.

[untold eagle]

Opinion of Art of Problem solving the Basics ?

[molten mason]

General consensus is that AOPS are great books in general.

[untold eagle]

nice thanks u :D I got the 1st volume

I hope to upgrade my self thinking bcs bruh I suck at it

[hasty eagle]

Removed the studying! role from you.

[oak sable]

Can anyone recommend an intro mathematical logic (first order logic, set theory, etc.) book by a pure mathematician? It's not just my intention to learn, I'm also very curious about how a pure mathematician would write such a book.

Virtually every book on logic seems to be written by someone who is also a computer scientist or mathematical philosopher. There's nothing wrong with this at all. I'm not supposing that a pure mathematician would write a better book or vice versa. I'm just curious how they'd tackle the subject. It's obvious that someone interested in logic would also likely be interested in CS or philosophy.

Any pure mathematician who hasn't published in CS or philosophy would count.

[remote sparrow]

You have some options.

A Mathematical Introduction to Logic by Enderton

A Friendly Introduction to Mathematical Logic by Leary and Kristiansen

Introduction to Mathematical Logic by Mendelson

Modern Mathematical Logic by Mileti (assumes a first course in algebra and uses many algebraic examples)

Logic and Structure by van Dalen

Foundations of Logic: Completeness, Incompleteness, and Computability by Westerståhl

[molten mason]

@remote sparrow

Rest of my Springer order just came in. So I did get my full original order.

[remote sparrow]

my last package should come in later today

[oak sable]

Thanks a bunch!

[sleek ice]

Any self study books for abstract algebra and galois theory?

[remote sparrow]

didn't you just ask a couple weeks ago?

[sleek ice]

I thought I didn't ask for those, I can check again then, sorry. I forget fast.

Ah, I only noted down the website books. Let's see.

[remote sparrow]

#book-recommendations message

[sleek ice]

Ah, alright.

Does that include abstract algebra or does it presume knowledge in that field ( )?

[remote sparrow]

it's a standalone book on galois theory

judson or pinter give enough background for it, and they're both low cost

[sleek ice]

Ah.

[remote sparrow]

http://abstract.ups.edu/

https://www.amazon.com/Book-Abstract-Algebra-Second-ebook/dp/B00VDGA1JA

[sleek ice]

Alright. I don't just want it for Galois but that will do, thanks

[faint snow]

Any recs for a good fantasy series? I already read some of of lord of the rings, Joe Abercrombie books, red rising series, and rage of the dragons

[rare estuary]

If you haven't read the Earthsea series, I'd highly recommend it

My second fav. behind LOTR

[faint snow]

I’ll check it out, thank you!

[lean pagoda]

Hmm, I think van Dalen's text is the odd one out in this list.
He puts considerably more emphasis on proof theory than the other texts and he also included a treatment of intuitionistic logic (understandably so considering his background).
Not to say that mathematicians don't care about this at all, but the trade-off is that the book contains less model theory than some of the more classical texts.
It is probably one of the very few interdisciplinary logic textbooks, not having a huge CS/Philosophy/Mathematics bias but containing a little bit of everything.

[remote sparrow]

kingkiller chronicles

[remote sparrow]

any other "interdisciplinary" books that come to mind?

[faint snow]

Oh yes, the first one was fire but I didn’t get to the second one bc there’s most likely never a third book

[remote sparrow]

you should read the second book anyway

i mean, i've still been waiting all this time

[remote sparrow]

i liked the mistborn series by brandon sanderson

the first few books of wheel of time are good

but the middle books are a slog to go through because robert jordan is so overly meticulous

the last couple books were finished by brandon sanderson. i've never completed the series but i like the universe

if you're okay with light novels, overlord, youjo senki, and ascendance of a bookworm are good

[lean pagoda]

Hm, hard to think of any off the top of my head

[lean pagoda]

The Malazan Book of the Fallen series, though that is quite the time investment considering its length

[faint snow]

Yeah I have Malazan and Brandon Sanderson on my reading list

I also have wandering inn and the cradle series

[storm juniper]

if youre into anime would suggest frieren really got me into fantasy stories that made me give hp a try, but if you're looking for a book perhap a wheel of time have heard a ton of good things about it

[faint snow]

Yeah, I need to watch frieren lol. There aren't many good anime this season

[fierce hedge]

Is it really that good?

[storm juniper]

i liked it enough to read the manga and catch up to everything, I plan on rereading it too, but if there was one thing i could improve it would probably be the fight scenes theyre not horrible, but i wish stark(the red head could have more or atleast make some a bit more cool i'm sure the anime wont disapoint though)

[sullen raptor]

so be comfortable with elementary analysis? At some point I’m pretty sure they use some fancy stuff like weirestrass M test and lebesgue dominated convergence theorem which looks like it’s beyond basic analysis.
I’m most likely wrong though… I haven’t done any analysis yet so this stuff could be chapter 1 stuff

[sage python]

Wait in the Fourier book?

[crimson leaf]

Dominated convergence theorem doesn't seem to be introduced until the 3rd book which makes sense

I don't even think they say the word dominated in the first book

[remote sparrow]

let me know your thoughts on axler's precalculus book when you can

[heady ember]

There are a decent number of nice animes I'd say. E.g. The apothecary diaries which is continuing from last season

[daring lake]

There are many good trash anime too

[tough stag]

Hey guys. I just joined, I had a very specific interest. I was looking for a maths book, preferable physics focused, that purposefully uses terrible methods for solving problems. As a perfect example of what I would love to find in this book: if you were to do a closed surface integral for finding flux in physics, you would only ever use a sphere for symmetry, but I would love to see someone using a square or worse. Stuff like this.

[wispy idol]

trying to learn number theory, needed some resources for abstract algebra, anyone got beginner friendly suggestions? 👉 👈

[tepid notch]

Hello, I'm trying to get back to the basics, do you have any recommendations for books for: Basic Algebra, Trigonometry, Pre-Calc?

I was looking at:

1. Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by George F. Simmons
2. Precalculus: Mathematics for Calculus by James Stewart

Are these any good? Are there any other books that you would recommend?

[sullen raptor]

Ah my bad, I am using another book as well and they use the theorem to prove continuity of the Fourier transform. I assumed that this Princeton book would use the same techniques

[sullen raptor]

yes, I was referring to that

[wheat trout]

Could you be more specific on what you want? The difference between fine and coarse moduli space is easily described by whether the moduli functor is representable, that just uses the basics of category theory (Yoneda lemma and such). If you want to learn a certain moduli space, like Teichmüller spaces, there are notes which uses almost no category theory. But for a general fine moduli space, almost all sources I remember will say something about representability.

[daring lake]

For Abstract Algebra : Dummit & Foote. It's a huge book but starts from scratch so you should be fine. Just a huge list of exercises , idk about number theory but I know Ivan Niven is used by many

[wispy idol]

i'll look at both, thanks!! :3

[silk sigil]

For abstract algebra, there's a list of a few of the best books with a short description so you can see which one might be best of you (it's also pinned) #book-recommendations message

[wispy idol]

could you reply to it? (can't find it in pinned for some reason)

[silk sigil]

The link is in my message, but sure, here you go

[vast jackal]

one last question is is it a good foundation book for mechanics. I'm trying to participate for the IPho but we don't know ?

[vast jackal]

is it good for beginners?

[modern ruin]

i’ll look for something for you, this is a really fun idea. i know that the michael penn youtube channel has a series called “overkill” where he’ll prove elementary results using way more machinery than needed, which is pretty fun

[crimson leaf]

@tough stag @modern ruin you guys might like the book, https://en.m.wikipedia.org/wiki/Mathematics_Made_Difficult

[vital bane]

[fossil arch]

What's a good text to grab topology exercises from

Just exercises, not reading the content

[mossy flume]

I mean most good topology texts have good exercises

[fossil arch]

hurb

The source does provide problem sets so ig I'll work with those

[mossy flume]

What source lol

I mean ig the prototypical example of an intro topology text is Munkres

[finite gale]

You can take munkres and do problems from it without reading the actual material I guess

[mossy flume]

Yea lol

[fossil arch]

I found these really nice topology notes from a Harvard class that make me want to give math a try again

[finite gale]

Or like idk just find some course page online from some uni

[fossil arch]

https://people.math.harvard.edu/~bullery/math131/

[mossy flume]

Wait there are problem sets on that page lol

[peak knot]

mathematicians inventing pointset topology:

[fossil arch]

Ya! I forgor hehe

[vital bane]

https://www.math.toronto.edu/ivan/mat327/?resources

Check the link named "Big List of Problems"

[dim sierra]

did u get that from aleph 0 👀

[vital bane]

I think so

[fervent marten]

should i get the nspire or the plus ce ?

[brazen rivet]

Well, I'm reading this paper on the space of linear dynamical systems modulo coordinate transformation, and this paper says this forms a fine moduli space. As an engineering PhD student, I don't have a good graspe of category theory other than the basic definition. I suppose there's no way around it then. Anything beginniner friendly would be helpful.

[wheat trout]

I assume what they are saying is that this space itself can be viewed as a dynamical system (or has some geometrical structure). Not very sure but for this statement you do not need category theory.

[brazen rivet]

To me, it means its a quotient space, its not hausdorff, but it still has nice geometric properties. that was my take from that.

[wheat trout]

I guess that is fine. I really do not think an engineering student needs to know what is a coarse moduli space.

Or I just do not know enough about dynamical system.

[brazen rivet]

I agree 🙂 but I think the basics of moduli space could assit me since this paper does use alg geo quite a bit. I found this one article Intro to Algebraic Stacks by Behrend that seems very beginner friendly and avoids category theory. I might read this.

[wheat trout]

Well, I am not sure reading about stacks is going to be helpful.

It is a very hard topic.

[brazen rivet]

Well it uses moduli spaces a bit in it, and it has lots of pictures of triangles for examples lol

[brazen rivet]

Yea this AlgGeo stuff is crazy

I just saw the zariski topology isnt hausdorff ever and I'm like...wow

[vital bane]

it's cursed that's what it is

[storm zinc]

Doing a Masters Statistics program rn but the last time I took Calc and Linear Algebra was 5 years ago.

Want to find a good textbook to review these subjects in prep for studying Real Analysis and Measure Theory. Any advice?

I'm able to do computations but my theoretical knowledge and more complex problem solving skills have atrophied greatly so maybe a book with good practice problems?

[remote sparrow]

so you're saying you want to review calculus and linear algebra?

[storm zinc]

Yes

Just added the context in case that helps

[remote sparrow]

why not study real analysis beforehand? it's a lot more useful than going over calculus again

[molten mason]

That's the gist of it, I can give you a more in-depth answer tonight or tomorrow though

[molten mason]

Probably perfect candidate for Spivak's calculus and Friedberg's Linear Algebra

[storm zinc]

I was told that Calc 1-3 and Linear Algebra are prereqs for it and it's been a while since I had a good theoretical understanding of those subjects so was worried it'd be a bit heavy if I jumped straight to real analysis.

If you know of some Real Analysis books that ease you in though I'd for sure try them out

[remote sparrow]

what kind of calculus class did you have where you gained a real theoretical understanding of calculus?

it's mostly problem solving

#book-recommendations message

anyway here's some intro analysis and intro linear algebra books

[storm zinc]

Thanks! I was worried since I don't remember many of the Theorems in calculus (even if we don't prove them) and only know how to problem solve, but it sounds like I'm closer to being prepared than I thought I was.

[molten mason]

Abbot would be good.

Feel like Spivak would be a good bridge too though to be refresh on calc and ease into real analysis

[storm zinc]

thank you!

[molten mason]

Amazing resource

[fervent marten]

what is the best book for basic introductions to calculus?

[graceful moon]

It depends what youre looking for really. If you just want to calculate but also have a very complete understanding of the subject, Stewart is very good, if very long. I believe the books on openstax by Strang are supposed to be quite good too plus theyre free.

If you want a more theoretical understanding really any analysis book will treat you well, I like Tao but its hard to go wrong with analysis books

Calc is such a widely taught and well understood subject that theres about a million different books and sets of notes which will treat you well, so id say the best book is the one you have

[fervent marten]

thanks

[warm cradle]

What is a good Differential Calculus book that teaches fundamental understanding / isn't scared of proofs?

[remote sparrow]

spivak or apostol

[warm cradle]

I don't want a computational based / memorize formulas Differential Calculus book

[warm cradle]

could you say the title?

[remote sparrow]

they're both titled calculus

[warm cradle]

do you mean Spivak's Calculus

oh

[remote sparrow]

yes

[warm cradle]

so that will cover the differential calculus content?

[remote sparrow]

yes

[warm cradle]

okie thanks

[warm cradle]

just curious, what are the main differences / benifits of spivak & apostol

I was going to read spivak's as an "intro to analysis"

but I keep on hearing apostol

[remote sparrow]

apostol starts with integration first

it covers standard applications like related rates that you would see in a normal calculus textbook, while spivak does not

but either are good choices

[molten mason]

I like Apostol

[loud cradle]

the writing styles of spivak and apostol are very different, probably you should preview both and decide

[rigid barn]

Anyone here read Second Apocalypse?

[manic cairn]

i just wanted to pop in here and recommend lang’s undergraduate analysis, going back through it and doing the problems.

the problems he gives are always just the right level of difficulty, and the sections are concise and to the point while remaining perfectly clear.

[molten mason]

I'm going through it right now

[manic cairn]

in particular, there’s this amazing section on path integrals and the winding number

[molten mason]

What page

[manic cairn]

chapter XVI

it feels so clean, and it doesn’t assume you have some topology background

(besides what the book has already covered in an analytic setting)

[molten mason]

Yeah I'm reading it now

[molten mason]

Good read. Taking a small break to read Stillwell but I'm going through Undergraduate Analysis and Undergraduate Algebra currently. Liking the books so far. I have his Real and Functional Analysis book too for after

Have you read his Complex Analysis?

[manic cairn]

i’m going back through CLRS too, trying to implement all the algorithms inside in haskell and rust. that, and doing all those ap classes on khan academy.

there’s something soothing and refreshing about revisiting old introductory courses, or picking up a new subject you haven’t done before. in the first case, it’s great to tune up rustiness and shows you how far you’ve come. in the second, it does the same thing, but on the other end of the spectrum. picking up biology and economics, the things i’m learning feel like brand new things.
it’s also interesting with biology that it’s taught with so many things blackboxed, not out of laziness, but out of necessity. what many things even are on a chemical level is largely unknown.

the other thing that’s different is that you’re able to read significant parts of actual papers, published in the last 20 years, in an introductory course on the subject.

you’re already in the more recent 1900’s by the time you’re studying the chemistry of DNA.

[manic cairn]

no, but it looks like it’s good

[molten mason]

CLRS, haven't heard of that one in a long time. Haven't gone through it myself, probably should though.

[molten mason]

Yeah I'm still about a year out from ordering a Complex Analysis book, thinking on getting Lang and then either S&S or Freitag and Busam as a second text. Will make a decision when I get to that point

[manic cairn]

also, i recommend tadoku’s japanese graded readers

they are good for all ages

if you don’t know how to read japanese

or you want to teach children to read japanese

tadoku is great, given a very basic vocabular and grammar.

many of them are free because tadoku is a nonprofit that just wants to increase literacy

[magic raft]

https://archive.org/details/the-cartoon-guide-to-calculus-by-gonick-larry-gonick-larry-z-lib.org/page/25/mode/2up?view=theater

[wispy idol]

is terence tao "Analysis" series written with beginners for mind?

[dusk wind]

its good

[deep summit]

I wanna learn real analysis UG by using two books that are different in approach and questions which two books do i choose ?

[frank frigate]

ello, i am dumb as rocks but need to learn graph theory. I know math upto some multivariable calculus, where start?

[chrome yacht]

abbott and pugh. pugh for the problems

[chrome yacht]

i used graphs and digraphs by chartrand and zhang a while ago

[frank frigate]

thnx 👍

[deep summit]

alright what about abott and bartle. or abott and rudin ?? (cuz those are easily available to me)

[chrome yacht]

abbott and bartle are similar books in the content they cover, you shouldn't need to buy both

abbott and rudin sounds like a better investment

[deep summit]

yo this pugh looks like higher level

like it finished differentiation and integration in one unit

[chrome yacht]

pugh and rudin are at the same level...

[deep summit]

and proceeds to multi

[sage python]

Pugh is Rudin but with somewhat better multivariable calculus treatment and (imo) somewhat awkward topology treatment

[deep summit]

but they are higher level than abott ?

[sage python]

Yes

[deep summit]

cause abott takes a good 1 unit for just series

limits

diff

int

[glossy zealot]

Are you self studying?

If not then you should check out the course material first

[deep summit]

i am self studying

[glossy zealot]

Ok if you are beginner, you can do Abott or Jay Cummings

They are both beginner friendly

If you want a more verbose book, check out Tao

[narrow prairie]

30 pages per hour is way too fast

[remote sparrow]

read to comprehend, not to meet an arbitrary page quota

[finite gale]

although spending more than a day on a single page feels really bad

[dusk wind]

reading is hard

reading 100 pages a day is true progress

30 an hour is even better if you can do that

[daring lake]

depends on what you read

[daring lake]

Atiyah 100 pages in 1 day

[vital bane]

you can do analysis on R^n and general metric spaces just using Abbott

just replace |x - y| with d(x, y)

[vital bane]

I agree, also it's not about the pages you study, it's about how many exercises you solve

70% of the actual learning happens in the exercises

[wicked summit]

I kinda want to jump on the self-learning train I was on again but for Maths instead this time. I've tried to look for a way to start and right now I'm thinking of grinding Khan Academy on stuff that seems easy, and going up until Pre-calculus to solidify foundations and knowledge gaps (and just generally getting into it again). For Pre-calculus I'm thinking of working through Stewart's Pre-calculus. After pre-calculus, I'd get into some book on proofs e.g Book of Proof or How to Prove it. After proofs, I'd jump into Apostol's Calculus.
I've two questions: does this seem like a solid pathway to get to calculus for someone who's already studied it but forgot all of it, and will those books on proofs prepare me for the style of book that Apostol's Calculus is, since I've heard its pretty difficult?

[deep summit]

uhh, i dont think u actually recommend that

[keen orbit]

is modular arithmetic/elementary number theory a necessary prerequisite to study group theory

[fierce hedge]

No not strictly necessary, the amount of modular arithmetic/elementary NT used is usually introduced when needed in the group theory book/course itself.

[real marsh]

no but it makes it significantly easier if you've worked with it

Cos Z_n provides a lot of good intuition to start out

And a lot of elementary nt results end up being corollaries of group theory results

[vital bane]

I'm not kidding btw

analysis on normed vector spaces (like R^n) is literally the same as on R

only one thing that differs is that you need some basic linear algebra knowledge to define derivatives

it's defined as a linear transformation

everything else is the exact same

you just replace the norm

[deep summit]

so R^n includes n=1 right ?