book-recommendations

[gentle jasper]

Does anyone happen to know of either:

a) a lecture series or notes based on Axler's MIRA or
b) a good lecture series on measure theory that begins with the outer measure instead of sigma algebras.

[night star]

Does anyone know if Spivak’s calculus is good for someone coming back to review calculus after 4 years?

[sterile pelican]

Spivak is more like an analysis book, are you familiar with proof writing?

[night star]

Not at all

That’s what’s keeping me from it. I really want to relearn everything but I’m afraid it wont help me solve problems or anything when in a class or if I take a placement exam

[stray veldt]

why not just try it

[sterile pelican]

What’s your goal for revisiting calculus instead learning proofs then analysis?

[restive nexus]

What are some good books on model theory

I've read sets, models and proofs but there are only 100 pages

[restive nexus]

Even better if it has any applications to universal algebra or classical abstract algebra

[stray veldt]

might want to ask in #foundations plenty of active users there

[restive nexus]

Thanks

[heady ember]

#book-recommendations message

[restive nexus]

Damn yeah this is pretty useful

[raw bay]

Hey guys I randomly got this urge to do maths which I don’t know why but I decided to ask for assistances on good books for the basics and building my foundation again

After that I want to try get into maths competition because you only live once

But all in all what’s the best roadmap you guys recommend??

[summer lagoon]

I stopped math three years before but had to redo it again for my master, I took Lee's manifold book which have bunch of exercises that are straightforward and some random books on algebra

[summer lagoon]

wait what's your objective, like competitions or building up?

[molten gulch]

What consists of your "foundations"? Have you taken courses in calculus? analysis? topology?

[sturdy shore]

can you tell by these pics?

[deft mesa]

How to prove it

[gray gazelle]

Does anyone know any book that explains modern axiomatic set theory in full detail? (from the axioms to the definition of the integers + stuff like ordinals, cardinals, etc)

[remote sparrow]

this is a perfect bound book

i.e. gluebound

[sturdy shore]

yeah

I ordered my first springer hardcover recently, I assume it is going to be the same sadly

the CA book was absurdly cheap though on sale so I'm not complaining

[lyric storm]

Hi, any recommendations for diff. geo books with good problems? I have already taken a course where the professor used his own notes, but I dont have much practice with problems. Lee's book looks a bit too long and I am looking for something shorter and more effecient.

[sturdy shore]

jech is a standard reference for that stuff

[gray gazelle]

so jech is the title or the author?

[sturdy shore]

set theory by jech

[gray gazelle]

thank you

[sturdy shore]

wait actually, I recommended a reference because you asked for full detail @gray gazelle what is your math level?

[gray gazelle]

ZFC and a bit of real analysis

I learned with the peano axioms first

[sturdy shore]

okay, then probably look at introduction to set theory by jech and hrbacek instead

[remote sparrow]

is the paper like glossy and thick or more like regular paper

[sturdy shore]

regular

[remote sparrow]

i'd assume the former since there's lots of color graphics

oh

:(

[gray gazelle]

Ive read the first 7 pages and I find your first recommendation quite good

[solid narwhal]

is the novak book of game theory good?

did anyone read it?

[young fern]

Which books are best to accompany Khan academy’s app ?

I’ve started the pre algebra course once finished I want to find a book that challenges the basics I’ve learned from that course

[raw bay]

Actually become competent to compete in competitions

[raw bay]

Taken hs calc, and first year university maths that’s basically it

[raw bay]

By who?

A math competition would be like simon marais maths competition, check out their pdfs for the test

I wanna be build up and be confident in attempting those types of questions

What would be the perfect roadmap for something like that?

[molten gulch]

velleman

[raw bay]

Thank you

[molten gulch]

there's also hammack's book of proof, which is free

[raw bay]

Okay I’ll check those out

[earnest wolf]

The book by Enderton is solid as well

I like it a bit more than Jech since it's a bit more precise

But I ended up using both of them, since there can't be "the best" book

Altho Enderton probably isn't ideal for self study

It's a bit too thick for a first course — usually a first undergrad course in axiomatic set theory will cherry pick only some chapters from it

So either take a class, or have lecture notes / syllabus to know what chapters to skip on the first pass

[shadow river]

The Foundations of Mathematics by Kunen is excellent, it would give you the foundations to study more advanced set theory (either the sequel also by Kunen, or Jech)

[fathom elm]

Hi something to recomend for system of differential equations

[heady ember]

Are you mixing up Enderton and baby Jech? The latter covers a superset of the former iirc

[sturdy shore]

yes baby Jech has way more than Enderton

let alone the adult one

and enderton's set theory is meant to be introductory to math in general no?

okay ig not really

[raw bay]

Oh

[novel hound]

That's like the Putnam I believe? This Putnam problem solving seminar from MIT OCW and other Putnam guides (like Kiran Kedlaya's page) should be helpful. https://ocw.mit.edu/courses/18-a34-mathematical-problem-solving-putnam-seminar-fall-2018/pages/syllabus/ https://kskedlaya.org/putnam-archive/

[uncut hazel]

Hello, I'm making another attempt to study mathematics. After studying algebraic expressions, what else should I learn? Or are you all familiar with the algebra's chronological lesson?

[raw bay]

Yes it’s similar to it but I think it’s easier

[remote sparrow]

axler's MIRA is actually very well-made; the pages are sewn together. as far as the 4th edition of LADR, you might get a crappy gluebound like mine (but still with thick glossy paper) or you might get a sewn book.

same goes for the 3rd edition of LADR

princeton university press actually sells a very nice copy of a new translation for marx's capital, which i have at home

[heady ember]

Print it out and, then, bind it yourself

[weary fox]

is there any benefit in reading baby jech before reading kunen set theory given that i have read enderton?

[heady ember]

You can just read Kunen's Foundations of Mathematics in that case ig

You cannot jump straight into his set theory book, for you lack the logic prereqs if you haven't read a logic text.

[heady ember]

Or a logic book that suits your liking. E.g. Ebbinghaus, Rautenberg, etc

[weary fox]

gotcha, im currently reading this textbook: https://slc.openlogicproject.org/archives/f21/slc-screen.pdf
would that give me enough logic background, or would i still need to read foundations?

[heady ember]

Idk that text, so I can't say.

I'd rather go with a more reputable text, personally.

[weary fox]

gotcha, just reading this to skip a certain course at my school due to weird circumstances, and the prof said to use this

i'll check out kunens foundations as well

thanks!

[heady ember]

Np!

Check this out too #book-recommendations message

If you have logic questions, you can ask in #proofs-and-logic and #foundations, where all the set theory/logic bois gather.

[tacit isle]

What are some books you guys recommend for someone in grade 9?

[molten gulch]

what are you studying in "grade 9"

[tacit isle]

Last thing I remember studying was trigonometry

Sin, cos, tan, sine, cosine.

Before that Was functions and graphing them

If you are wondering my school follows igsce 0580 maths syllabus

[spring night]

Any good linear algebra books?

[trail hemlock]

Friedburg, Insel, Spence is nice. it has a good mixture of proof and computation problems

check pins for dami's recs also

[spring night]

Is that one book?

[trail hemlock]

yeah FIS are the 3 authors

[spring night]

Yeah I did, I'm looking for one comfortable book

and one problem book

[spring night]

like Spivak for calc

[trail hemlock]

this comes to mind for that

[heady ember]

The three musketeers

[heady ember]

If you're gonna do Spivak, you might as well do Abbott or Schroder.

[heady ember]

I don't think there's a reason you need three linear algebra books 🗿

[spring night]

Abbott is the other book I'm referring to for analysis/calc

[heady ember]

I see

[trail hemlock]

from the looks of it, apart from books written specifically for this syllabus (which u can just search for on amazon), i doubt there is a book that covers all of these topics. pretty much all of this stuff can be found on khan academy, and in my opinion, it is not worth purchasing a book. However for all of these topics, I like the aops books (which prob go into more detail than your classes). so for algebra, it would be the intro to algebra, for geometry it would be intro to geomeytry, etc (i cannot remember if vectors are covered in those intro books, but u can find a khan academy lessson for that).

[trail hemlock]

well its F, I, S, and axler, so its 4

[spring night]

So you recommend FIS and Axler?

[trail hemlock]

i would jus go with FIS, but its important to note that i used lang for la (DO NOT use lang), and ive just glanced as FIS as i need to reference linear algebra

unless u wanna move onto a text like roman, as grass said, 3 la books is a lot of work

[spring night]

wait dude is FIS one book or three

[trail hemlock]

1

[spring night]

😭

oh

send me the pdfs if u have them

[trail hemlock]

best not to discuss piracy here

[spring night]

oh okay, sorry

[zinc thistle]

I've read through Fraleigh this past semester and want to get a decent intro to galois theory and or elementary alg geometry before next semester starts, just to get a taste of both topics. I might do a reading course with my algebra prof and she recommended one of those two topics so I just want to know what i'd be getting myself into

can I get a text on both of those topics that would be readable with just knowing group/ring/field theory at the level of fraleigh

i know fraleigh has a section on galois theory at the end iirc, but i left my book back at my house which i wont get back to until the end of my winter break

[ebon cedar]

im trying to self-study statistics, what is the best textbook that has rigor but is beginner friendly

price is not a concern

[remote sparrow]

do you already know calculus

also by "statistics" do you mean just statistics or probability and statistics?

[sterile pelican]

One LA book I am curious no one talked about would be Berberian’s book

[golden topaz]

An Intro To Galois Theory by Andrew Baker and Commutative Algebra by Andreas Gathmann maybe? There are pdfs of both freely available

[remote sparrow]

Galois Theory by cox

as for elementary algebraic geometry, consider Ideals, Varieties, and Algorithms by cox, little, and o'shea

[ebon cedar]

no

[ebon cedar]

and idk whats the difference between the two 😭

[remote sparrow]

i feel it's a good idea to learn calculus instead

[zinc thistle]

Great!!! Thank you sm

[zinc thistle]

lmao this is perfect, I just checked w my school's "recommended texts" page for each class and the cox little and oshea book is the one they rec for alg geo

[zinc thistle]

may I actually ask what does comm. algebra actually entail? i guess it succeeds intro algebra, but does it go more into the geometry side of things

[pseudo forge]

a book on discrete math? [for someone looking to get into algorithm analysis and select topics in cs (starting with clrs).]

[zinc thistle]

rosen

[remote sparrow]

Undergraduate Commutative Algebra by reid is often recommended too

[fresh skiff]

i can smell algebraic geometry

[ebon cedar]

im homeschooled and i wanna be an industrial engineer which requires a lot of statistics which I need a rigorous and good book for. I currently dont have the skillset required for calculus

[remote sparrow]

it's hard for a stats book to be anywhere close to rigorous without calculus

[ebon cedar]

(highschool)

[ebon cedar]

what can i learn on the side without calculus

im trying to build my way up to calculus but i dont want to wait learning stats until I actually learn calc

[zinc thistle]

wait can you address my previous comment about comm algebra?

3 messages above yours

[vital bane]

Two should be fine, FIS -> Roman

[vital bane]

Linear Algebra

very important for anything

[heady ember]

I don't think there's a reason you'd need to read Roman

You could spend your time on algebra or something instead

[vital bane]

it is algebra

linear algebra and module theory

[heady ember]

Of course, if you like linear algebra, then feel free.

[heady ember]

1+1 is also algebra

[vital bane]

so is Teichmuller theory

[heady ember]

Modules \in algebra \setminus linear algebra

[vital bane]

"You can never know enough linear algebra"
-Neam 2025

[heady ember]

Actually, you're wrong. Knowing FIS levels of linear algebra is enough for general prerequesites. But knowing more doesn't hurt.

[fresh skiff]

Roman requires abstract algebra as well iirc

[viscid goblet]

Roman empire

[tender cobalt]

is Roman linear algebra = Serge lang algebra

like

both have like insane amount of content

[fresh skiff]

i believe roman is much harder

[tender cobalt]

both are GTM tho

[golden topaz]

Comm Alg is just the study of commutative rings and their modules. It builds the algebraic machinery applied in alg geo, e.g. Hilbert’s Basis and Nullstellensatz theorems

[dapper root]

And number theory

[daring lake]

I am pretty sure you can start from Roman if you have mathematical maturity

[tender cobalt]

yeah he told in preface that its very pretty self contained book

[daring lake]

yea, its just super terse

I am planning to go through sometime soon

[tender cobalt]

i gave up on his chapter 1 vector spaces lol

the examples are insane

really need some mathematical maturity

[sterile pelican]

Roman has another book I want to do called field theory

I am about half way from my self studies of abstract algebra and that book is in my list

[vital bane]

True

[fresh skiff]

Is lang'a book in GTM?

[fresh skiff]

Aren't there any prerequisites?

[daring lake]

mathematical maturity

[tender cobalt]

Serge lang algebra is GTM

Serge lang Undergraduate Algebra is another one of his, which is UTM

[tender cobalt]

how to get

[fresh skiff]

Oh i thought lin alg

Damn his Algebra book is known as Bible for algebra

[sterile pelican]

Anderson and Feil is an algebra book I think some people should give a go for undergrads

[fresh skiff]

It's beast broo

[tender cobalt]

Yeah

that's what i mean

[fresh skiff]

Oh, i will check it (maybe after an hour).

[sterile pelican]

I hear scary things of Lang's GTM Algebra

[tender cobalt]

I am saying Roman's linear algebra and serge lang algebra are probably on same level in terms of rigor, and also they're both very broad

[fresh skiff]

Is it an abstract algebra book?

[fresh skiff]

Same here

[sterile pelican]

Yeah for undergrads currently halfway myself

The other is Silverman's abstract algebra since I love Silverman's writing

[fresh skiff]

I think Lang's algebra is much harder

[fresh skiff]

Arithmetic geometry?

[sterile pelican]

Silverman has an algebra book

I had skimmed through it and I quite like it

[tender cobalt]

both are insane

but lets get someone who actaully went through both books to say something

[fresh skiff]

Oh i just saw it rn

[tender cobalt]

🤣

[daring lake]

contact me in 3 years

(both are pretty big)

[tender cobalt]

ok let us set a goal

and in 3 years

we shall meet

[sterile pelican]

3 years per book right? :^)

[tender cobalt]

and exchange words of both books

Wait

I got an idea

What if you struggle a lot on first few chapters of roman or lang

later chapters are gonna become easier, right??

right??

[sterile pelican]

This is not Rudin

Nor Spivak

[tender cobalt]

rather 100x harder 💀

[vital bane]

I'm pretty sure he says in the preface "Having taken an undergraduate course on linear algebra would be a good idea, but without that you can maybe manage"

[fresh skiff]

Seems reasonable

[tender cobalt]

should i try

[vital bane]

Have you learned abstract linear algebra before

I think you should do FIS first

[tender cobalt]

idk why i touched vector spaces chapter in FIS and axler

like did exercises

then didnt do any further exercises

just kept reading through

lol

[tender cobalt]

these cat emojis are based af

[tender cobalt]

"you can maybe manage" 🤔

[vital bane]

if you want to, go ahead, if you find it too difficult, you can always fall back onto something like FIS

[heady ember]

Neam moment

[vital bane]

to get on my level you need to spend at least 300 Mya per book

[tender cobalt]

Mya?

[heady ember]

Sorry, I don't think most people aspire to be on the same level as you.

[vital bane]

Million Years

[tender cobalt]

i want to be andrew wiles level

[sterile pelican]

I aspire to know GAGA

[tender cobalt]

Gaga?

[vital bane]

Geometrique Algebraique or something like that

[sterile pelican]

Algebraic geometry and analytical geometry

[tender cobalt]

these two are worlds apart 💀

ok nvm i thought typical analytic geometry

i dont think u mean that right

do u mean like differential geometry stuffs

[sterile pelican]

Yeah

[tender cobalt]

Ye now theyre not worlds apart

[tender cobalt]

To let you know

My goals are also same

[sterile pelican]

Brother!

[tender cobalt]

how much math have you covered so far

[sterile pelican]

Currently just half way on abstract algebra and just starting with limits from analysis

[tender cobalt]

oh you covered some algebra

[tender cobalt]

ohh

[sterile pelican]

While simultaneously studying linear algebra, set theory, logic, and projective geometry

Oh and sicp

[tender cobalt]

:o

all i am simultenously studying is some topology (includes set theory), linear algebra, and calculus/analysis i dont know what to call it im studying limits and continuity in R^n

and ye topology and linear algebra i am studying like introductory chapters

[sterile pelican]

Cool!

But yeah I will be old by then :^)

[tender cobalt]

how old are you rn if you dont mind me asking

[sterile pelican]

30

I am just doing this for fun at my own pace

Let’s carry this in #discussion

[distant shell]

When I can use seno,coseno y tangente??

[plucky rose]

presumably during your test

[vital bane]

Ubel

[tender cobalt]

serge lang calculus of several variables vs ch edwards advanced calculus of several variables

[sterile pelican]

You can, and hear me out, do analysis first then do multi-variable analysis

[remote sparrow]

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

[sturdy shore]

It just arrived, perfect binding with great paper quality is what I ended up getting

it still doesn't open so bad though, I can live with it

[remote sparrow]

what book is it?

[undone prairie]

i have a little problem understanding cosets and i thought about looking to other books but couldn't find a good one
i am studying fromFundamentals of Abstract Algebra
Textbook by D. S. Malik, John M. Mordeson, and M. K. Sen
and it explains cosets before quotient groups
can you guys help me out?

[slender cargo]

I think Dummit Foote’s chapter on quotient groups is very good

[bright epoch]

does anyone know of math ebooks or pdfs that are polished (have chapter divisions and whatnot) I feel like all the pdfs I get are at most high quality scans and never have that extra bit of polish

[molten gulch]

many many books do, our copy of abbott has chapter divisions and whatnot, we downloaded it directly from springer fwiw

[bright epoch]

that sounds nice

[marsh ingot]

Looks interesting

[trail hemlock]

DO NOT read lang's linear algebra 🙏 😭

[drifting urchin]

Hello, I would like to study the last 6 chapters of Artin's Algebra. How self contained are they? He says in the preface of the book that they are fairly logically independent of previous chapters, such as billinear forms, though I'm scared there may be a requirement of certain prior chapters to solve problems, i.e. problems requiring chapter 1 in chapter 2. I appreciate that Chapter 1 is very basic/treated almost as a pre-req, but I would like to get to those last chapters as quickly as possible. I'm using the second edition (have the hardcopy). Thanks!

We covered Group Theory in a class last semester but didn't do amazingly, we mainly covered some content in Chapter 2 and some bits and pieces from Chapter 7. I am planning to go through these chapters, but again not so sure on whether I will need the more detailed linear algebra chapters/ billinear forms/group representation chapters.

I hope this is the appropriate channel for this question!

[rain hound]

What you described (at most high quality scans) is common of dover in my experience.

Springer usually has everything LaTeXed though and is pretty good.

[remote sparrow]

https://qcpages.qc.cuny.edu/~zakeri/CAbook/ACCA.html

FYI zakeri's book has a companion website

[sturdy shore]

damn, didn't know

thanks

[fresh skiff]

Am not really lmao
I am using FIS

[vital bane]

FIS = best

[sterile pelican]

Berberian’s LA anyone?

Also what is FIS?

[trail hemlock]

friedburg insel, and spence’s linear algebra text

[sterile pelican]

Oh ew that text

Berberian is my LA book ❤️

[fresh skiff]

How is this book good?

[heady ember]

https://tenor.com/view/obi-wan-so-uncivilized-attack-of-the-clones-star-wars-gif-19823075

[sterile pelican]

It assumes you know abstract algebra and hits off with isomorphisms and all the good stuff

No matrices till later

I think it is the LA book for maths majors

Just my two cents I think FIS does its job though

[heady ember]

Yeah I jest

[heady ember]

Its published under Dover? Based.

[sterile pelican]

Oh I know! I meant that for Afzal’s answer

[sterile pelican]

Dover ❤️

Unlike the cursed Pearson

Overcharging darn books

[fresh skiff]

Wait let me check it

[sterile pelican]

A true hidden gem!

But FIS is for every STEM major so it’s better while Berberian is for solely maths major, you need to know rings by then

[sterile pelican]

Or just do all you know :^)

Like all is nice

I am doing all

[heady ember]

Tfw you need linear algebra to read algebra

[sterile pelican]

Bah there are good books that don’t need to assume LA first for AA

[fresh skiff]

well looks a good book to me. But I cannot betray with FIS

[sterile pelican]

I can do it for you

Just stab its back

[heady ember]

[trail hemlock]

what’s like acc wrong with FIS

it’s for stem not just smth majors doesn’t seem like reason enough

oh u alr answered nvm

[fresh skiff]

hey, one of my friend is graduated from CUHK (Chinese university of Hong Kong). Once he told me, they used FIS as well for linear algebra, so i check the web and found it. (https://www.math.cuhk.edu.hk/course/2425/math2040a) I found these lecture notes cool af. I hope you guys will find it useful as well.

[vital bane]

So your friend graduated from CUHK? ||They got an education from CUHK...ed from CUHK, they got CUHK-ED ||

[sterile pelican]

Sure and FIS is fine for the rest of science, tech, and engineering but like that if you are maths major I feel it’s a huge injustice to not see Berberian. I mean after seeing this book I wished I learnt LA this way

Just my two cents though I am just expressing how I felt of sharing such a wonderful book

[lime vessel]

Are you from hk

[fresh skiff]

No, I am from Pakistan.

[remote sparrow]

https://old.maa.org/press/maa-reviews/linear-algebra

[sterile pelican]

I don't exactly agree with his remarks some of the sections are there while the first half isn't "useful" the whole point of it is to learn that LA is no different than AA. You realised that a linear map being linear is akin to homomorphism, and if they are linear and bijective you can show such vector spaces are isomrophic - the whole point is to see its connections with AA.

You learn to also prove why the operations are what they came to be with the basis under AA

That makes you more than ready to study advanced topics

[vital bane]

when I saw the definition of a homomorphism for the first time linear maps are what came to mind

so it's totally okay to go the other way around like LA -> AA

[sterile pelican]

It's okay but this is better

This I like

[vital bane]

I wonder what you think of Werner Gerub's Linear Algebra book

[sterile pelican]

No

Me no like

Well actually I haven't read it lol

I heard of it but I never touch it

[vital bane]

it's also kind of AA oriented

[sterile pelican]

But it's a grad text. no?

[vital bane]

I'm not really sure tbh

[sterile pelican]

I was thinking after I finish Berberian's book cover to cover I want to try Roman's advanced LA

But like do I even need that level of LA for my trip to GAGA? I am not sure

[trail hemlock]

what is GAGA?

[heady ember]

"Gagaga (evil noises)! You shall be destroyed and reborn by my GAGA!" - Gronthedieck, probably.

[trail hemlock]

huh 💀 😭

[dapper root]

GAGA is by serre

[trail hemlock]

oh

ohh

[sterile pelican]

Yes GAGA

[rich sun]

GAGA HHAG

[vital bane]

John Piere Serre?

[vital bane]

Géométrie algébrique et géométrie analytique (GAGA)

Algebraic Geometry and Analytic Geometry basically

so in english, AGAG

ABBA when?

Algebraic Beometry and Beometric Analysis

[crisp horizon]

Biometry

[native shore]

anyone knows what books to refer for iit exam

[sterile pelican]

Algebraic Biology and Biological Analysis

[livid lintel]

Biological analysis sounds cool

[heady ember]

Oh oops my bad

[prisma lagoon]

yo... no new pinned book reviews in last 9 months?

[gray gazelle]

it's levioosa

[rich sun]

not leviosaa

[novel shoal]

Hi guys, which book for Introduction to Differtial Equations ? someone mentionned Zill, i don't know which one could be good for me, i learn calculus from Simmons book, and Linear Algebra from Gilbert Strang (emphasize with computation)

I do computer science, if someone knows

And im also thinking, should i do Discrete maths from Kenneth or Knuth ? i started with Kenneth, finished first chapter with 70h

[normal crystal]

Simmons has a DE text if you liked his style

[novel shoal]

i like his style

i was thinking, all the calculus book have the same problems so ODE book should have the same problems?

[turbid jackal]

does anyone have any book recommendations for an introduction to abstract algebra?

[molten gulch]

Artin

[turbid jackal]

thanks!

[grave fiber]

And also homeschool curriculums grades 3-12 is a good book

[silent nest]

Which trigonometry book would you recommend?

[sterile pelican]

If you are willing to try, since I haven't done this, you can do Gelfand's trigonometry book

[near idol]

Is there a super list or thread for book recs in this server

[molten gulch]

Check pins for a mini version of this

[molten gulch]

Does anyone have any good books to learn elementary number theory? This is a field I've occasionally come across but (none of us) have never studied it and at-least from what I know, one of our other headmates are very interested in ENT, yet I feel it prudent to learn at-least the basics. Everything I've looked through past very basic stuff like euclid's theorem, long division, gcd, etc... is very confusing and I just...don't find it very intuitive. Any video resources, notes, etc... will also be appreciated. Thank you

[formal bronze]

'Elementary Number Theory' by David Burton

[molten gulch]

Thank you

[normal crystal]

maybe Number Theory Step by Step - Kuldeep Singh

[fluid skiff]

Any good book to teach complex analysis to undergrads?

[formal bronze]

'Real and complex analysis' by Rudin

[remote sparrow]

gamelin

[fluid skiff]

I wish it to be a little visual and elementary.

[sterile pelican]

Currently doing Silverman's A Friendly Introduction to Number Theory

[floral lantern]

Rosen’s book is truly excellent. In general, elementary number theory might feel a little unintuitive because a lot of the material is really the result of basic algebra (for example, bezout’s identity is really just the statement that Z is a principal ideal domain, and euler’s theorem is just lagrange’s theorem).

[molten gulch]

AFAIK the way some of us did it was...to just start learning algebra, and yeah, flipping through, some of the stuff does seem kinda like "wut where did this come from", which is definitely kinda similar to how I felt originally looking at some number theory stuff a few months ago

I will look more into rosen tomorrow morning probably, very eepy rn

[floral lantern]

You kind of just have to smash through it and appreciate the elegance of some of the arguments.

Once you’ve done some algebra a lot of it will appear trivial (this is how it felt for me), but the intuition from ENT actually helps with understanding abstract algebra in my experience.

[molten gulch]

I see

thank you

[floral lantern]

@trail hemlock don’t u dare nerd emoji me

Mr munkres topology

[trail hemlock]

ew i would never

[floral lantern]

Ok bro

[trail hemlock]

i should lowkey learn number theory

maybe over summer i’ll use rosen

[floral lantern]

If you know algebra these books are too easy for you

💀

And you know algebra

[vague granite]

🤓

[floral lantern]

Watch out at primes conference bro

I’m sending my friends after u

[vague granite]

praying sobbing crying tweaking rn

[floral lantern]

Interview at 11 hours

[vague granite]

ur gonna nail it

[floral lantern]

Nah

[novel hound]

The book list here is nice. https://ocw.mit.edu/courses/18-781-theory-of-numbers-spring-2012/pages/syllabus/ If you are undergrad then NZM is good. If you are pre-undergrad then Burton is gentler. If you know abstract algebra then Ireland/Rosen is nice. Btw, Borcherds has a youtube series off of NZM for Berkeley 115 elementary number theory course.

[trail hemlock]

ok then what do i read

bro i be bored asf during lunch 🙏 😭

slide reading list

[remote sparrow]

nzm is good

you really don't need to do a deep study of ent

[trail hemlock]

ok

✍️

[fresh skiff]

nzm? is it number theory by zukerman (if i spell correctly)

[trail hemlock]

yeah

[remote sparrow]

zuckerman but pretty close

[vital bane]

ye ye Niven Zuckerman and Montgomery

Pretty cool book but intended for people with prior exposure to puremath

[ionic estuary]

guys what should i do for competitive geometry

[fresh skiff]

Meaning, the prerequisites includes mathematical maturity and some knowledge of number theory?

[trail hemlock]

evan chen has an olympiad level book, there is also aops intro to geometry which is a little lower level

[ionic estuary]

alright, thanks!

[vital bane]

no knowledge of number theory is required, it starts from the very basics, like what it means when b is divisible by a

just mathematical maturity

like one of the exercises in chapter 1 starts off with "for readers who are familiar with basic point set topology..." (51st exercise I think)

Lol but don't worry most of the exercises don't require knowledge from other fields of math

just 1 or 2 here and there

[sterile pelican]

T-there is Silverman's A Friendly Introduction to Number Theory too

I am currently doing it and I don't know much

[vague granite]

oly geo is really theory heavy so learn the theory first thru something like evan chen otis and grind isl 💪

[ionic estuary]

fair enough, thanks and will keep it in mind

[tender cobalt]

https://www.youtube.com/watch?v=ZWH-4GJaErM

[vital bane]

is your pfp mikasa?

[ionic estuary]

perchance

[fresh skiff]

Got it

[dawn holly]

Anyone got recommendations for someone that has a brief understanding of algebra to learn more? I need something that can break down how to do each equation and what symbols and words mean, and etc. I'm in my 2nd 7th grade semester looking to pursue math personally. Thanks!

[floral lantern]

AoPS’s book introduction to algebra is phenomenal at getting a good understanding of basic algebra.

[oblique hatch]

So I’ve just finished Silverman’s book on arithmetic dynamics, and I want to learn more
What would be a good source for that?

[old elk]

Hi guys I have some money to buy the dummit book, do you think it is worth it, also I am going to apply for a masters soon.

[timber mesa]

if you see yourself using the book a lot in your first year of MSc or so then yeah sure. most people here might tell you it's a good reference for algebra though a bit encyclopedic in tone and scope

see also this pin about abstract algebra books: #book-recommendations message

[tender cobalt]

what are the prereq of stein and shakarachi's fourier analysis?

[molten gulch]

we assume basic riemann integration theory and basic mathematical analysis/advanced calculus

[tender cobalt]

is it a graduate level book?

[molten gulch]

We don't really distinguish "undergraduate" vs "graduate" level books, you can kinda read any book once you have the prerequisites

[sturdy shore]

it's not a graduate level book

[tender cobalt]

alright, I'm reading pughs analysis rn and I was thinking what else can I study alongside it

[sturdy shore]

it's meant for someone who has taken a first course on analysis

you could just try reading

[molten gulch]

This is meant after you've finished up to the riemann integral section I think

[tender cobalt]

what about their 2nd volume complex analysis and 3rd volume of real analysis measure theory

[old elk]

I've been reading a little bit Artin's, it seems pretty good, I'm currently with gallian, only the dummit has caught my attention because of what you say it's encyclopedic, but it's difficult to take on a trip :/

[molten gulch]

vols 2 and 3 have the same prereqs and volume 2 assumes familiarity with analysis on R at some points AFAIK and book 3 is a book on measure and integration theory, which is a standard logical step up from real analysis on the line

[fresh skiff]

I believe Integration theory refers to real analysis here

[molten gulch]

fixed

[tender cobalt]

Oh I see

[tawny copper]

What are good books on the calculus of variations?

[molten gulch]

I believe that their functional analysis book (book 4) requires familiarity with measure theory (book 3)

[tender cobalt]

So after learning some basic analysis

I can start that series

And finish it sequentially

[molten gulch]

If you wished, also I would recommend checking the pins in this channel to see other recommendations on analysis

[tender cobalt]

Guys any suggestions what should I do if I want to learn to apply mathematics in physical contexts

Read some classical mechanics or E&M or quantum mechanics book?

[molten gulch]

Classical Mechanics and Electrodynamics are both useful

[tender cobalt]

any book recommendations

[molten gulch]

here's Dami's review (from pins) on S&S

[molten gulch]

Taylor for classical and Griffiths for electro

[tender cobalt]

That seems decent actually compared to others

[tender cobalt]

Alright thanks

[molten gulch]

Both do assume you're familiar with calculus

and maybe little bits of vector algebra but nothing too bad, some linear algebra may come in handy for intuition at points but AFAIK isn't a hard requirement

[tender cobalt]

do I need anything else like some general Physics course

[molten gulch]

Uhhhh most unis do have a sequence going over a university physics book (Halliday and Resnick or Young and Freedman are common choices) but I am unsure how..."required", I guess, they are

[molten gulch]

tensors will show up, just beware :)

[tender cobalt]

Ye thats what i am concerned about whether im required to read a text like resnick or young beforehand, cuz its gonna be time consuming and its not much mathematical either mostly

[tender cobalt]

Multilinear stuff??? 😮

[molten gulch]

yep

[tender cobalt]

In taylor or griffiths?

[molten gulch]

yes

stress tensor, field tensor, etc..

metric tensor (but that's GR)

[tender cobalt]

Wait taylor got stress tensor?

[molten gulch]

lemme check

[tender cobalt]

Isnt stress tensor in like continuum mechanics

[molten gulch]

yes, chapter 16

[tender cobalt]

Wow

[tender cobalt]

That looks cool now

Definitely gonna read Taylor

Have you read Taylor? @molten gulch

[molten gulch]

Bits of it but we have not read anything on physics much since highschool

[tender cobalt]

Oo

[formal parcel]

hey logic fans, what are some of your favorite books to learn logic with? I want to dive into ones that focus on primarely logic instead of learning it as a side topic in another book

[zealous coyote]

#book-recommendations message

[remote sparrow]

yes. just buy used if possible.

[bright epoch]

I want to learn more about QFT from a tensor bundle perspective, is there a QFT text that's mathematical and used that sort of language?

[old elk]

I was going to send it to print... cough cough, it's cheaper, besides I was reading a little bit and I got lazy reading the section of the permutation groups and the dihedral groups.

[remote sparrow]

it's kind of a huge book

if you print it, it could be gigantic given the paper used at printing centers might be thicker

[old elk]

I get it for $29, and the person I know is familiar with book printing, hehehe.

[tawny copper]

why not use a pdf?

[old elk]

My doctor recommended me to stop the long hours of screen time and to have my neck massaged.

I use a fairly small laptop

[ionic zephyr]

maybe they're worried about pirating idk

[tawny copper]

sublime's dark mode is quite light on the eyes, and there are anti blue light glasses and stuff like that. But I'm no oftalmologist

[old elk]

I am saving to buy a monitor, 27 inches to see better and with blue led configuration, besides improving my position.

[old elk]

I have heard of glasses, but the doctor wanting to damage the eyesight by making a small magnification on the glasses to further damage the eyesight.

I really use pdf books but it's really annoying.

[ionic zephyr]

have u tried audio books? those are more expensive but less of an eyesore lol

[bright epoch]

Or an e-reader

[ionic zephyr]

ooh fair

i kinda want one but idont have the oney so

[old elk]

Imagine the machine reading the mathematical symbols, it must be pretty funny.

[ionic zephyr]

loll even more reason to try

but i guess tbf i havent really tried listening to mathematics books.

[bright epoch]

Yeah, if you're using it for math PDFs you got a make sure you get a big-ish one

[ionic zephyr]

im ded

but i mean i have read math stuff on my phone

in the past

[bright epoch]

Yeah it's less bad on a phone because you can zoom and pan easier

[normal crystal]

if only there was something like a phone, but much bigger
hold on, about to sell this genius idea to Apple

[slate wedge]

Does anyone have any recommendations of math books that teach the fundamentals of math? Like I understand how to use formulas but I want to learn how they work and like how it makes sense yk?

[dawn holly]

Alright, thanks 👍

Anybody have books for somebody interested in aerodynamics? I'm not sure how math related it is, but I'm thinking of building a collection

[vital bane]

it is actually really cool

I've read Taylor

Harmonic oscillator chapter is goated🗿

make sure you do that thoroughly

[vital bane]

you mean like a (scalar, vector, spinor)-quantum fields are just sections of a (scalar, vector, spinor)-bundle right?

There is "Quantum Field Theory for Mathematicians" by Robin Ticciati but I'm not sure how good it is, I've never read it

maybe @median fossil can recommend a book on mathematically rigorous QFT

[median fossil]

Despite its name, it's very much a standard physics treatment of qft, with some more details and formalisation of the combinatorics

[median fossil]

I'd suggest asking in the physics server

There are quite a few mathy people there

[vital bane]

this is actually so true

it's crazy how many mathphys people are in the physics server, like the population is very skewed toward mathphys and hep-th and people who work with QFT

[vital bane]

that actually sounds nice I should check it out then

but by "standard physics treatment" do you mean it's similar to something seen in Schwartz and Peskin and Schroeder?

[sour mountain]

I have studied Linear Algebra using the books "Elementary Linear Algebra" from Howard Anton, and "Introduction to Linear Algebra" from Gilbert Strang.
What other books do you recommend for more advanced study?

[sterile pelican]

Axler or Berberian...some people like FIS here

Not sure what level is Strang though, does it have proofs?

[remote vortex]

Axler's LADR is a solid second read

With a more abstract perspective (I see that book very much as a stepping stone towards functional analysis)

[sterile pelican]

If you have background in abstract algebra, in particular after ring isomorphisms, Berberian is a great book

[median fossil]

Yeah, it's similar in content to P&S

[vital bane]

depends on what you mean by "advanced study" are you looking to learn linear algebra for applying it somewhere, or do you want to study abstract linear algebra that's usually seen in a math degree?

if it's the former Gilbert Strang is awesome no one can beat him

if it's the latter, I recommend FIS

[ionic zephyr]

i learned linear algebra from "Linear Algebra and Its Applications" by David C. Lay but it costs money so i guess it cant beat the Gilbert Strang person

[sterile pelican]

And Berberian (why is no one looking into this?) if you know abstract algebra

It's still considered a first course of LA too!

[sour mountain]

FIS = Further Linear Algebra, correct?
I will check out the reviews on FIS and David C. Lay books.
Cheers!

[spice stag]

is Contemporary Abstract Algebra by Joseph A Gallian easy enough to understand for the people who are studying abstract algebra for the first time?

[sterile pelican]

If there is one abstract algebra book I love it would be Anderson & Feil's A First Course in Abstract Algebra

It starts off with rings first

No linear algebra needed but a background of Proofs, at the level of Velleman or Bloch or Chartrand, is needed

[sterile pelican]

It's more like Freidberg, Insel, and Spence I recall also I despise Lay's book

[ionic zephyr]

fair although it is clear and concise imo

[sterile pelican]

It's like Stewart's Calculus but for LA

I feel there are better books out there that builds rigour and intuition but my two cents I don't force people to avoid it

[tender cobalt]

Ima do taylor

[ionic zephyr]

how would recommending a book be forcing it?

[sterile pelican]

I don't physically take your book is one

Since I don't physically take a book in favour of mines...you know...?

(I am funny don't hate me)

[ionic zephyr]

im ded

[vital bane]

More like Spivak but for LA

[vital bane]

Where do you feel FIS lacks rigor? I think it's a perfectly mathematically rigorous book

just because it also includes some computations doesn't mean it lacks rigor

[sterile pelican]

Oh I was talking about Lay

[vital bane]

Oh I see

[sterile pelican]

FIS is fine it does its job

[molten gulch]

FIS stands for Friedberg, Insel, and Spence

[vital bane]

I too thought that person was saying "FIS stands for Further Linear Algebra" but on second thought I don't think they did because that would be FLA

I think they meant "FIS is further linear algebra?"

but I could be wrong since they capitalized "Further Linear Algebra"

[molten gulch]

lol

[mossy flume]

FIS my beloved

[sterile pelican]

Berberian is the best LA ❤️

[hearty steppe]

Oh man where you been? You came back to life?

[sterile pelican]

I am still alive and still doing maths

Just erm slowly and now unemployed

[ionic zephyr]

pray ing for u man 🙏

[sterile pelican]

Thanks April

[tender cobalt]

I am using Pugh to learn analysis, should I read abbott alongside?

[fresh skiff]

Are you using a particular book or random?

[tender cobalt]

as i said i am using Pugh

Pugh's real mathematical analysis

[fresh skiff]

Ok cool

I have heard a lot of good words

Btw using Abbott as reference wouldn't hurt i believe

[tender cobalt]

as for complex analysis, hows stein and shakarachi complex analysis?

[fresh skiff]

Idk i will use other book when i will start

[untold thistle]

what's a list of books that i could read in order to master most/all aspects of pre-college math

[tender cobalt]

Any Precalculus/Algebra & Trigonometry book as well as a geometry book

And then James Stewart Calculus for calculus

Any O levels math book (10th grade typically) then transitioning to A levels math book (12th grade) is also a good idea, it gives you a sequential progression covering all of these topics

[untold thistle]

what are the recommended books for each of those subjects

[tender cobalt]

James Stewart Precalculus
Michael Sullivan Precalculus (Also has basic probability and counting like permutations and combinations)

These are the two books I used to learn most algebra and trigonometry things. For YouTube channels I suggest blackpenredpen, khan academy, organic chemistry tutor. You can also learn geometry trigonometry algebra from khan academy which is a solid resource for starting out math. A nice geometry book I used is Schaums' Outlines of Geometry.

After doing the above, now you can learn some calculus as you got fluebt with algebra and trigonometry.
For calculus things, pre college you have these following topics: limits, differentiation and integration, sequences and series. You will be learning them at pretty basic level. For these I suggest watching YouTube videos (blackpenredpen, organic chemistry tutor, khan academy ) and James Stewart calculus (most popular calculus book) for doing the exercises.

After doing all of these you'll pretty much have mastered entire highschool and you'll be able to ace any highschool exams of any grade.

[queen escarp]

Is Organic chemistry by Jonathan Clayden gud

[night flare]

Yupp get it ,if your serious for organic

[dreamy sierra]

For pre calculus what book should I get that is rigorous and well help me for amc 10/12 and algebra II solidification and just want to gain critical thinking skills

[dim pendant]

They don't make rigorous pre-calculus books. I think there's a book by Serge Lang called "Basic Mathematics" or something which does like high school algebra and trig and some other stuff rigorously. Assuming that is true, I have no idea if the chapters are self-contained, meaning that, in the worst case, you'd have to read extra chapters just to cover the content you're looking for, if the book even has it.

The reason why they don't make them rigorous is because the term "pre-calculus" is relatively specific to America, and each curriculum covers different topics. Some of them are trig courses, some involve limits, some are more of a second algebra course, etc, and covering certain topics like conics, limits, etc. may require a bit more intensity than you might be hoping for.

[trail hemlock]

aops precal is rly nice for contest prep

though specifically for anc 10/12 it’s not strictly needed

[dreamy sierra]

Ya aops is so good for math not taught in school

Thx 🙏

[trail hemlock]

its worth looking at this for contest specific books: https://artofproblemsolving.com/wiki/index.php/How_should_I_prepare%3F
and asking the ppl in #competition-math as well

[digital scarab]

hey guyz do yall have any books to reccomend thatll help me understand the history of maths like who came up with what and how

[queen escarp]

Get history of modern math by David Eugene Smith

@digital scarab

[sterile pelican]

I actually support Lang's Basic Mathematics alongside his calculus books

I wished we stop with books like Stewart just saying

Also I did read Gelfand's Algebra, and his Functions & Graphs book before I did Lang's basic mathematics

I did those aforementioned books cover to cover they are gems

[trail hemlock]

stewart books are good for what they are

imo

[vital bane]

They are good for non-math majors

I wonder what your take on Hoffman and Kunze is

[cursive orbit]

I disagree: there's really no reason to use stewart over any number of freely-available references.

[broken meadow]

i dont think it matters

if the goal is to learn how to compute derivatives and integrals and stuff and use them to solve basic modeling problems its a fine book

i myself used books like stewart and ended up just fine

[cursive orbit]

it does matter when you assign students to buy a specific edition of a book just to get access to hw problems/online homework autograders

although I guess the latter does provide an incentive for professors to assign stewart lmao

[broken meadow]

i agree, i had not thought about the monetary side of things

[trail hemlock]

i like larson more because of calcchat, and of course in terms of total coverage online resources r a lot better, but for the average student i doubt they care, esp non math majors

[sterile pelican]

Yeah personally I read Lang's Short Calculus book, which is kind of what you wish to teach for a student - to understand an integral and derivative. However, while I say that that doesn't mean you are at a disadvantage from Stewart. Again this is my super subjective view, and that I feel a STEM major like us deserve better

[vital bane]

That's not really an argument against stewart tbh

that's just an argument against any book that's not freely available

[sterile pelican]

I never read it but I guess it's like Axler? I just think after skimming through Halmos, FIS, and Axler, that I settled with Berberian after knowing rings and its isomrophism

There are some nice connections with Berberian is how I view it, like nice interconnected ideas with abstract algebra off the bat

[vital bane]

HK is different from Axler, HK also utilises some stuff from abstract algebra

whereas Axler does not

[sterile pelican]

Ah I see

[vital bane]

I am most excited for chapters 7 and 8 of Axler

[sterile pelican]

Let me have a look but for now I am really in love of Berberian

[vital bane]

they cover a lot of cool stuff

[sterile pelican]

Axler can be fun but his omission of determinants is not good for my heart lol

[vital bane]

same

[digital scarab]

ty bro

[vital bane]

it's just... kind of not good for a first course in abstract LA

[sterile pelican]

I agree

[queen escarp]

Np

[vital bane]

Axler is what you get when an analyst tries to write an LA book

[sterile pelican]

Wouldn't that be the same with Halmos? :^)

[vital bane]

I suppose Outsider did mention Halmos does the same with determinants

but I've yet to properly check out Halmos

[sterile pelican]

I skimmed it I hear from my friends it seems to be FA at times lol

[vital bane]

Lol yea Axler also teaches LA as if you're going to be doing FA right after LA

hence the banishment of determinants and trace to the end of the book

[sterile pelican]

Yeah that's something I feel one shouldn't learn off the bat but my attitude is that Axler is more of a "fun" book to read after you go through say FIS or Berberian

Not sure of HK though

(I tend to think HK as Hong Kong lol)

[vital bane]

this is true

[molten fractal]

Spivak Calculus is good for early university?

[sterile pelican]

If you mean some basic analysis then yes, as Spivak stated in his 2nd edition that it should have been called analysis

But his exercises are notoriously hard, you get better over time but likely due to ptsd

I heard Abbott is a good alternative but I never use it

[slender cargo]

Abbott isn't easier. Their exercises will be of similar difficulty, from what I saw

Nice thing about Spivak's book is that you can get a full solutions manual with it, which is great if you're self-studying

[sterile pelican]

That's true one analysis book I quite like, if you have an online tutor, is Bloch's Real Numbers and Real Analysis

A notoriously slow book but he teaches analysis right

Or Lang! Lang has a calculus book explicitly called Short Calculus with only 200 pages of single variable calculus

[vital bane]

Abbott is an amazing book

I'm using it right now

the exposition is brilliant

[vital bane]

ehh Abbott exercises are not too difficult, most of the exercises are doable

if I can do them, then anyone can do it

[sterile pelican]

I see

I like Bloch so far but I cannot recommend it to anyone unless you like some thorough foundations in your life

Bloch builds the real numbers from N, Peano axioms, which I do love but this meant you won't see a limit until like 3 long chapters lol

Also while this might be irregular by comparison sequences and series are much later in the book

[fresh skiff]

So true.

[trail hemlock]

my take is that if u don’t use it as ur main book, but ur at least interested in some stuff, it’s worth having on hand to look deeply into things

but like if u wanna learn basic computational calculus there are easier options

as for “early university” u can approach this book without much math prerequisite, the only thing is that u have to be willing to dedicate a significant amnt of time

[vital bane]

All I used to learn calculus was Khan Academy + 3Blue1Brown

and I turned out fi-... I didn't turn out fine

[trail hemlock]

my intro to calc was spivak

[trail hemlock]

i’m always scared to say “i turned out fine” cuz it’s easy for a mf to say “wellllll”

[vast jackal]

apostol or spivak?

[austere beacon]

I recommend the book, "Eleanor and park" I would like to warn that it is an intense book with bad language and a rough family. Eleanor is a girl who is "weird" and dresses odd and has a bad family background. On her first day at her new school where everyone is judgy, the bus is full and there's one seat left, a seat next to park. Park is self reserved and would rather not talk to any "weird" girls so he ignores her and hates the fact that she's weird and sitting next to him. They later get a friendship through parks love for comic books and start dating while park slowly learns about her family's issues. Soon those issues start to affect Eleanor and parks relationship. This is my second favorite book.

I am not a romance type of person but this is a perfect book

[trail hemlock]

either tbh

[tender cobalt]

Apostol starts integration first iirc

[trail hemlock]

yeah lol

[raw bay]

What would be the best way to benchmark where you're at math wise?

Initially I was just gonna do a test and see where I lack foundationally and kind of work on those areas, but the problem with that is I don't know a very good test to actually go about that.

anyone's input would be appreciated.

[austere beacon]

I don't know

[tender cobalt]

depends on what math topics youre studying

[acoustic jay]

what is a really nice book for reading physics?

[vital bane]

that depends on what field of physics you wanna read about

[acoustic jay]

theres nth in general?

[vital bane]

if it's general introductory physics then haliday, resnick, walker is good

[acoustic jay]

and what about the physics related to astronomy?

[vital bane]

you do mean a textbook for learning physics right? if you're looking for popsci books on physics I have other recommendations

[vital bane]

not sure, I've never learnt astronomy

[acoustic jay]

no i mean reading for fun 😭

[vital bane]

...yet

[acoustic jay]

oh it's alright

[vital bane]

then I would recommend "In Search of Schrodinger's Cat" by John Gribbin

that was a fun book

about how quantum mechanics came about

[acoustic jay]

i think i have heard about schrodingers cat

ill buy that

[vital bane]

You could maybe also check out Paul Nahin's books

they're pretty fun I'd reckon

[vital bane]

wait your "about me" section

Levi

[tender cobalt]

i wanna learn quantum mechanics and GR now lol

[raw bay]

Ordinary Differential Equations

3. Laplace and Fourier Transform Methods

4. Matrices and Linear Systems of Equations

5. Analytical Methods for Solving Partial Differential Equations

6.Difference Numerical Methods for Differential Equations

7. Finite Element Technique

8. Treatment of Experimental Results

9. Numerical Analysis

10. Introduction to Complex Analysis

11. Nondimensionalisation

12. Nonlinear Differential Equations
    .integral Equations

Calculus of Variations

[tender cobalt]

thats some beefy stuffs

so you wanna find out where youre lacking

to test yourself

[raw bay]

yeah

[raw bay]

Then fix the foundation to tackle those topics

[tender cobalt]

idk these topics but

1. try and see if you can do all the exercises/problems in the texts you are using
2. search online for university exams testing yourself and give one of these exams
3. try teaching someone the concepts, you will notice it if youre lacking somewhere, another good way is to write down the things you learnt about the topic and see if you can write definitions give examples by yourself and explain it in an essay

[raw bay]

Thank you !

[tender cobalt]

on the side note, curious if youre a physicist

or an engineer

[raw bay]

2nd year engineering

[vast jackal]

aops

[vast jackal]

if we're talking bout mechanics HRK fifth volume requires calculus

[vast jackal]

karttunen is really good for introductory for someone without any math experience

it considers both readers

trust me karttunen is really good!

well It's abit of an exaggeration because astronomy is interesting but yea he really considers people

[tender cobalt]

@vast jackal 😭 if you scroll down you will see that she was asking for a popular science book

[raw bay]

What’s this?

[vital bane]

https://artofproblemsolving.com/

[raw bay]

Just do any test off this should suffice?

Thank you btw

[vast jackal]

karttunen is like I said focused on both reader

[vast jackal]

yes

there's bunch of advanced shit there

[tender cobalt]

Same

Non rigorous

False sense of "applications" on the way

Too much digressions on things that arent related

But its fine for non math people

[sterile pelican]

Yeah basically this. Also the computations felt senseless, which isn’t the point of calculus. Your goal isn’t to only become a human integral and derivative calculator, computations are still important. But also you are suppose to be able to get a feel of making the rules of integration and derivative, which Lang does in a mere 2-300ish page for single variable

[tender cobalt]

Spivak too

Also have you read lang's multivariable calculus book

I have always wondered hows it

[sterile pelican]

I think it’s a fine book it does well for all of STEM

[tender cobalt]

I like Thomas calculus better than Stewart

[vital bane]

Thomas' calculus is good

[tender cobalt]

🤝

it's not actually

90% things are proved in thomas calculus

[sterile pelican]

Computations are still important it’s just Stewart is only computations

[tender cobalt]

And thomas calculus has proofs exercises too

[tender cobalt]

It also has some fourier series and complex functions on the new edition

[tender cobalt]

They're still not Spivak level computations 💀

Spivak be like:

Find the derivative of e^x(cos (tan^2 3x / ln x) ) * (ln x) ( log_2 (x^x ) )

[sterile pelican]

Spivak is an analysis book lol his second edition made a preface about it

He was like “too late to change the name now”

[tender cobalt]

can be called intro to analysis book

but its really a calculus book

it can be used to learn calculus

along with some analysis techniques

you can with spivak

[sterile pelican]

Yeah but if I learn calculus like that I would cry

[tender cobalt]

Many people do

[sterile pelican]

I am not many people sorry

[tender cobalt]

Also have you read lang's multivariable calculus book

[trail hemlock]

only computations are like absolutely fine for a first course in calculus

like even for math majors

[sterile pelican]

Nah you go into the details of understanding limits but if you never use it informally it would be a struggle, at least for me

You need a sort of high level view of calculus imho

[tender cobalt]

Spivak builds the necessary foundations on the way

You can skip the hard exercises

It's not an easy book for sure

You'll struggle a lot

But do need to make sure you have sound experience with algebra

[tender cobalt]

Yup

[trail hemlock]

u theoretically can, but its prob the worst way to learn analysis. a lot of analysis books assume that you the reader can motivate stuff with your prior calculus exposure, so it doesnt really make sense to jump into an analysis text. as slender mentioned spivak is a good way to bridge this gap

[tender cobalt]

That's what they do for first year

[trail hemlock]

like spivak -> rudin or smth would do you very well

[tender cobalt]

That's why I call spivak a calculus book with some analysis techniques

It really is meant to teach you calculus

[sterile pelican]

I know I wouldn’t but if you are confident go for it I took the slower path because I want to set my foundations well

I also don’t use Spivak rather I read Bloch then combine with some of Spivak’s exercises

[tender cobalt]

No one told me spivak was a great book when I was learning calculus

[tender cobalt]

well I would say I didnt have enough experience to acknowledge how good it was

[trail hemlock]

i feel like its important to note that regardless of your exposure to analysis beforehand, the best tool u can have going into analysis is a lot of spare time

[tender cobalt]

if i had the choice i would go back and struggle

[trail hemlock]

i used spivak as a first course in calculus, and it is an amazingly written book that asks a lot from the reader

[sterile pelican]

Also don’t underestimate Lang’s calc book it is still rigorous compared to every calculus book out there

[tender cobalt]

Lang's book is a substitute for spivak's book in some sense

Since it's also a proof based calculus book

[vital bane]

Abbott -> Folland

[tender cobalt]

(too) easy ones are the ones that ask you to plug in a formula

and get out an answer

Spivak is not like that

[trail hemlock]

lang basic mathematics -> roman's advanced linear algebra (intermediate stuff is fairly trivial)

[tender cobalt]

Most exercises are not really hard , it's just it requires you to work through

[tender cobalt]

lang basic mathematics is spivak of precaluclus

[trail hemlock]

i used the aops books for everything leading up to calc

lol

[sterile pelican]

I erm use Gelfand’s Algebra and his Function & Graphs, then Lanfg’s Basic Maths

Gelfand is not exactly an easy book there are better ones out there

[floral lantern]

aops calc book 🤤

[trail hemlock]

i lowkey hate it

[floral lantern]

tf you mean

💀

why would u dislike that book

like the only criticism I could see one make is that it's a "worse, less rigorous version of spivak"

[trail hemlock]

yeah

thats my thing

[floral lantern]

but it balances that with lots of more difficult problem-solving

which in my opinion is also valuable

[tender cobalt]

fuck problem solving

[floral lantern]

💀

[trail hemlock]

its a good book i just dont like it

[floral lantern]

fair enough

[trail hemlock]

literally no logical reason for it

[tender cobalt]

😭

[floral lantern]

I need to read aluffi at some point

[trail hemlock]

dude u should

like acc

[tender cobalt]

its not if you arent learning things rigorously and solving problems rigorously

also idk anything about aops calculus book

[floral lantern]

yeah ik bro

[trail hemlock]

mfs will tell you its a lightweight book but ppl jus be lying out here

[tender cobalt]

i just hate "problem solving" in general

[trail hemlock]

its fucking awesome

[tender cobalt]

whats aluffi

[floral lantern]

but the thing is I have to like actually pay attention in school

[trail hemlock]

algebra chapter 0

[floral lantern]

bc I don't go to shitty public school 😭

[trail hemlock]

god made apush for me to learn math

trust

[floral lantern]

I have to simulate a nuclear reactor next sem bro

in compusci

and make a neural net to simulate an evolutionary model

[trail hemlock]

ight why u hatin on me now

[floral lantern]

😭

no ur lucky

u can study ur math

[trail hemlock]

yeah yeah we get it u go to a magnet school

pissing me off bro

imma crash out

[tender cobalt]

wait

thats school

or

university

[floral lantern]

😭

[tender cobalt]

or what

[floral lantern]

school

[tender cobalt]

i dont get it

SCHOOL

[trail hemlock]

school

[tender cobalt]

WHAT KIND OF SCHOOL BRO GONNA SIMULATE NUCLEAR REACTOR

[floral lantern]

no bruh but I can't do my own math

because of time

[trail hemlock]

ug fr

[floral lantern]

like last sem I had no time to study anything but absalg 😭

[tender cobalt]

School or university what are we talking

are we talking

grade school

im confused

[trail hemlock]

ur lucky i havent touched algebra in months discounting winter break

[floral lantern]

high school

[trail hemlock]

yeah me and marlins are in high school

[floral lantern]

but you've been doing analysis

and topology

[tender cobalt]

i am in highschool too

[floral lantern]

hi in highschool too

I'm marlins

[tender cobalt]

ive been doing analysis and topology too

🤝 @trail hemlock

ay i thought i was alone in this world

[tender cobalt]

im slender

[sterile pelican]

I’m Kani

[trail hemlock]

dude now i gotta review algebra for rotman

[tender cobalt]

yea

[trail hemlock]

alg pmo

anyway this is veering off topic

[tender cobalt]

what kind of highschool got you simulating nuclear reactor

[floral lantern]

this is hype tho

[trail hemlock]

ive chosen to use rotman's first course in algebra to review

seems only natural

[tender cobalt]

#math-discussion

[trail hemlock]

couldnt bring myself to open D&F 🤢

[floral lantern]

is this an ug or grad book

[tender cobalt]

D&F is a ug book

[floral lantern]

I know rotman's full book is a grad book

[trail hemlock]

rotman's intro book doesnt even assume LA afaik

[floral lantern]

makes sense

judson doesn't either and neither does gallian

[trail hemlock]

yeah imma review for like a week and then open up rotman

[floral lantern]

when aluffi grind

😔

[trail hemlock]

bro summer

[sterile pelican]

Anderson and Feil is my AA book ❤️

[trail hemlock]

cuz it takes a lot of convincing to make algebra interesting

[floral lantern]

??

algebra is super interesting by itself

it's pretty

unlike analysis

[tender cobalt]

I agree

[trail hemlock]

ight bro never step foot in america

im swiss cheesing you on sight

[sterile pelican]

Foundations are fun…Bloch’s Real Numbers and Real Analysis build the real numbers starting from the natural numbers!

[tender cobalt]

Tao's analysis too

[sterile pelican]

Tao builds Dedekind Cuts?

[tender cobalt]

Ye

[trail hemlock]

dedekind cuts are like standard

[tender cobalt]

Pugh does dedekind cuts as well but assumes N, Z, Q first

[floral lantern]

I was in texas a week ago

[tender cobalt]

Tao builds Z from N, then Q from Z

Then R

[sterile pelican]

I like Bloch’s way more though as he is slower, way slower

[slender wasp]

"Experience has convinced me that it is pedagogically unsound (though logically correct) to start off with the construction of the real numbers from the rational ones."

Rudin

Also Abbott says the same thing

[sterile pelican]

Sure but if you know calculus first then you must start to construct things

It’s why you cannot skip calculus

[tender cobalt]

Abbott includes construction of real numbers at the end

[slender wasp]

no Rudin and Abbott are talking about analysis pedagogy

not calculus

[slender wasp]

yep, he says thats the right place for it rather than the start which seems pedagogically better (as opposed to Tao)

[sterile pelican]

I disagree with that approach but each to their own

[slender wasp]

Spivak also does construction of R in the appendix

[trail hemlock]

"rudin" and "pedagogy" in the same sentence 💔

[sterile pelican]

I started building R first but remember this is just my subjective view though

Bloch is to me the right book for that but is notoriously slower

[slender wasp]

Refer Rudin and Abbott for details since the quote is from Rudin and Abbott says similar. They base it on their teaching experience.

I'm gonna put a quote in discussion-2 since that's probably the right place for this.

[vital bane]

from section 1.3 of Abbott

[floral lantern]

A construction is more valuable to appreciate in my opinion once you've seen some number theory

[summer lagoon]

Do you guys know books on differential geometry with a big focus on de rham cohomology and very dense/condensed results?

[floral lantern]

the construction of Z from N and Q from Z helps motivate why we care at all about constructing R and the power of that

[floral lantern]

Tu's book is a very introductory book, but excellent and does have a section on de rham cohomology.

[summer lagoon]

I’m more looking for a book that does de rham mostly not as simply a section but as the main part of

Like backbone of the book is de rham

[vital bane]

I think they're looking for a reference book

[summer lagoon]

Between summary and course

[floral lantern]

yeah ok makes sense

I don't have a good answer for you in that case 💀

maybe look for summary papers on arxiv?

[summer lagoon]

Dont worry its quite specific

[floral lantern]

or like lecture notes from topics classes at universities?

[summer lagoon]

That would be ideal but no idea how to look for that

[floral lantern]

https://pages.uoregon.edu/koch/deRham-Course.pdf

does this work?

[summer lagoon]

Let me check

its actually a good summary 😮

thanks!! If there are more I would gladly eat anything

[tender cobalt]

Meanwhile Pugh:

We begin at the beginning and discuss R = the system of all real numbers from a
somewhat theological point of view. The current mathematics teaching trend treats
the real number system R as a given – it is defined axiomatically. Ten or so of
its properties are listed, called axioms of a complete ordered field, and the game
becomes to deduce its other properties from the axioms. This is something of a
fraud, considering that the entire structure of analysis is built on the real number
system. For what if a system satisfying the axioms failed to exist? Then one would
be studying the empty set! However, you need not take the existence of the real
numbers on faith alone – we will give a concise mathematical proof of it.

Bro called it a fraud

🤣

[slender wasp]

I'd point to the quote from Abbott i put in discussion-2. Fraud is too harsh if Cauchy, Bolzano, Weierstrass, Riemann did their work prior to rigorous construction of R.

[tender cobalt]

in that case, a radical's approach to analysis by bressoud is great

i never read it though

[vast jackal]

does it matter if we start integration before differential?

[tender cobalt]

nope

They should be seen as both independent concepts tbh

[vital bane]

???

they are very related

that's the core idea of the fundamental theorem of calculus

[tender cobalt]

Yeah

They are related

[vital bane]

?

[tender cobalt]

but until FTC you should see them as independent

[vital bane]

[tender cobalt]

otherwise a spoiler :3

the math-orgasm I got when I arrived at FTC

was insane

I was literally goign like HELL YEAH THIS HAS TO BE THE BEST THING ON EARTH

[vital bane]

wait till you see

[tender cobalt]

yessir stokes theorem go brrrr

i call it FTC