book-recommendations

[drowsy nacelle]

im the same way but i dont know of books at this level, maybe someone else here does but khan is pretty good

[queen rain]

okay

so ima finish the algebra course and then geometry and then trigonometry

then i learn physics

btw, quantum physics requires calculus right?

[drowsy nacelle]

i would recommend learn basic trig, then go finish the algebra and geometry stuff concurrently with the physics stuff if you want to start learning

you dont have to wait

[drowsy nacelle]

a lot of it and much more lmfao

if youre very interested in physics i suggest getting a really good grounding of math and especially calculus

but like i said if you wanna start learning from the intro physics class on khanacademy i dont think you have to wait

just make sure youre continuing the math side by side

[queen rain]

it said i needed to learn those courses, so i dont know

[queen rain]

alright

thanks for the advice

[drowsy nacelle]

np

honestly just check it out and see if you can follow it

cause it can't exactly predict what everyone will know its just a general guideline

youll have to kinda figure that out for yourself

[queen rain]

ima watch some videos on youtube for trigonometry so

[drowsy nacelle]

good luck

[native cradle]

thanks

[hearty steppe]

Anyone familiar with this text? https://books.google.com/books?id=wOQbEAAAQBAJ&pg=PA1&source=kp_read_button&hl=en&newbks=1&newbks_redir=0&gboemv=1#v=onepage&q&f=false

[remote sparrow]

yes

[uncut crater]

@remote sparrow have any recs for the history of algebra?

I have read van der Waerden

Just feel like reading some more

[hearty steppe]

How is it?

[fierce hedge]

Saw this book recently on maa reviews - https://old.maa.org/press/maa-reviews/a-history-of-abstract-algebra-0

A History of Abstract Algebra by Jeremy gray

[gray gazelle]

check on stewarts website you can see the description of him with history of algebra might helps:)

[mossy flume]

https://bookstore.ams.org/hmath-15

not all of algebra

just rep theory

but I like this book

Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer

[uncut crater]

Perfect

[mossy flume]

very easy read

[uncut crater]

I've been reading some rep theory over the summer

[mossy flume]

I got it for free from my school's library at my undergrad (they occasionlly give away books no one checks out, mostly math CS and physics)

[uncut crater]

Quick question

Is it a problem if someone fusses over definitions?

As in, I've been doing lie groups and lie algebras over the summer and idk why but the entire time I'm reading lie groups, i need to read a lot of manifold stuff

And that irks me because I don't make progress with the material in hand

[mossy flume]

I mean

you aren't going to make progress with lie groups and lie algebras without manifolds

because lie groups are manifolds which are groups as well

that's like half the definition 😭

[uncut crater]

True

But lie algebras can surprisingly be studied on its own iirc?

And idk why but my guide for the summer insisted that this topic can be dealt with even if i know multivariable calculus

He's like, just take the definitions for granted

Is it a problem if I can't?

[remote sparrow]

it's good

[gray gazelle]

Differential Geometry and Lie Groups: A Computational Perspective: 12 (Geometry and Computing) https://amzn.in/d/00Q14jZD

Hi has anyone used this before

[visual gate]

Hey, what books are used to teach logic in university or collages

I wanted to self-study mathematical logic cause I think I will enjoy it and I wanted to study it before real analysis and linear algebra

I thought I would start that stuff after this

I am almost done with highschool maths

So do you know any good books for learning formal matematical logic?

[torn crypt]

Sour Drop might not be a fan, but Rautenberg I think is fine?

Peter Smith has a blog with reviews, but he’s kinda uhhh…..

yeah….

[normal crystal]

if he's still in high school math
maybe a discrete math textbook that introduces the topic
before a more advanced book on mathematical logic

[visual gate]

Yeah, I don't have any background with pure maths before this

so if the book teaches logic and then goes on to give proofs that are from those fields, I would not understand them

Set theory is fine tho, I also have some programming knowledge

Is computability and Godel's theorem part of studying logic?

[visual gate]

I have heard many people say that it is not a good place for the first introduction to logic

[torn crypt]

Yes

[torn crypt]

I like it, but I’m obviously a little further along

So as a first intro it’s hard to judge

[visual gate]

It doesn't matter if it's hard

I am just concerned about the prerequisites

When you started the book, did you know much pure maths? or do you need to know some maths above highschool level to start?

I know basic set theory

[torn crypt]

Yes I knew, but it should be fine

Whether it’s the best may be a bit different

[visual gate]

that's ok, I just need a place to start

[west basin]

Guys what about real analysis?

Book recommendation

[torn crypt]

Mendelson is an option too, etc

Just pick one, and if it doesn’t work, trying another might

[vital bane]

Understanding Analysis by Stephen Abbott

best anal book ever

But the other common ones are very good as well

lile Bartle, Tao, Cummings, etc

[sage plank]

First time seeing someone shorten the word analysis

What’s an introductory book to probability I can read?

I’d also like a recommendation for game theory

[sudden vale]

Can someone suggest some good introductory book on Sobolev spaces? I've had a course in function spaces where I studied Lebesgues integrable function with theorems such as Lebesgue DCT, Fatou's lemma etc, along with L^p spaces and some basic fourier analysis.

[visual gate]

ok, I am scared to ask

but what does anal book mean?

ok

short for analysis

💀

[torn crypt]

I dunno how suitable it is wrt prereqs, but Leoni has a book on a first course in Sobolev?

[foggy quest]

"Introduction to Partial Differential Equations" By G. Folland and "Partial Differential Equations I/II/III" by M. Taylor are good.

[sudden vale]

Would I find something relevant in Evans PDE? How does that compare to these two?

[gray gazelle]

bruh you can see lots of shorten words in #No-access tho

less words more efficient = less energy to use on fingers

[foggy quest]

Yeah Evans covers them as well, but I prefer the other two books. The books by Folland and Taylor develop the L^2 theory fully first and use it immediately. Only much later does Taylor introduce L^p Sobolev spaces.

[gray gazelle]

I heard Evan Chan is good in math's

or maybe is it a different Evan

[crude lava]

any good books about cellular automata?

[uncut crater]

Iykyk

Truly a moment of all time

[normal crystal]

does M Taylor have any cookbooks or gardening guides you recommend?
that guy does everything🤡

[dull fog]

im in middle school looking to study law, any book recomendations

[nimble osprey]

I technically finished highschool today, so does anyone have any recommendations for math textbooks for calculus 1 ?

[mossy flume]

I like Sheldon Ross's text (I forget the name it's something generic)

[sudden vale]

There's Feller as well ig

[remote sparrow]

#book-recommendations message

i would avoid mileti since you don't know any algebra as he uses many algebraic examples

i would use leary and kristiansen as it's the simplest of the list

i'd also recommend goldrei even though he only does propositional and predicate logic

[nimble osprey]

?

[gray gazelle]

Stewart's calculus

Early trascendentals

[nimble osprey]

Alright thank you

[gray gazelle]

https://a.co/d/03gopI0P

[west basin]

Thanks

[foggy quest]

nah he only writes math

[quasi haven]

Any book on mathematics which brings out the joy of doing and reading mathematics ?

[trail hemlock]

wait whats wrong with peter smith

[trail hemlock]

Spivak's Calculus is my fav

[uncut crater]

Well, let's just say

He was the diddler

And he fiddled with little...yeah you get the point

[trail hemlock]

ok ok

👍

understood

[glacial spire]

Anyone knows from experience whats the minimum background to go through Fulton's Representation Theory?

[dawn shoal]

Any recommendations for a good problem book with solutions for probability theory?

[remote sparrow]

https://www.newappsblog.com/2012/03/philosophy-prof-convicted.html

[trail hemlock]

bruh

only suspended for 3 months?

get bro gone

[elder kraken]

does anyone have any opinions on the book "Probability Through Problems"? I want to learn measure theoretic probability and my understanding of probability is a little shaky (I understand all of the topics at a high level but would probably struggle at first if I had to solve some problems; I also feel like learning probability from the ground up with measure theory would help). I've taken real analysis and this book seems like a great way for me to learn measure theoretic probability and to solidify my understanding of probability, but I was curious if people had any thoughts on this book

[maiden glen]

good books for galois theory?

[sudden kindle]

Sour has a recomendation

[remote sparrow]

Galois Theory by david cox

[maiden glen]

is jean-pierre good?

[remote sparrow]

no clue

[maiden glen]

thank you anyway

[fiery steppe]

if anyone wanna learn git, python related things or wanna contribute
do check my github and support guys
thank you

https://github.com/Orcus-IRL

[sudden kindle]

Whats a good book introducing the geometry of riemann surfaces ?

@sage python

[sage python]

What are you thinking of exactly? The books on RS that I know of are Forster, Miranda, and Donaldson

[sudden kindle]

Miranda kinda whack

[sage python]

What I've heard was, Miranda is more AGish, Forster spends more time going through analytic details on stuff like sheaf cohomology, Donaldson is big on geometric topology

[sudden kindle]

I liked Forster gmfrom what little I read but I need so.ething more intro

Like I want to introduce undergrads to uniformization and fuchsian groups, riemann surfaces as hyperbolic surfaces, systoles

Yeah I want more of the complex analysis and hyperbolic geometry, not so much the ag side

If it talks about complex jacobians and period lattices, holomorphic 1 forms, translation surfaces, even better

[sage python]

What do you think of Donaldson?

[sudden kindle]

Havnt looked into it

[sage python]

I don't know much about it but I've been told it's the more topology angled book

Which at a glance... I can see it

[sudden kindle]

Thats the whole book?

[sage python]

Nah there's more

[delicate hemlock]

Donaldson is hard

[sudden kindle]

I need easy books

I need to get undergrads into the geometry of riemann surfaces

[tawny copper]

It is

[delicate hemlock]

I like it but I don't think it's good for a first pass

[sudden kindle]

That book definitely has a lot of the things I'm looking for

[delicate hemlock]

You should check it out and see if you think it's expository enough

[sudden kindle]

I might have to go through it and select parts of it selectively

[delicate hemlock]

Admittedly I never looked at the hyperbolic geometry parts of it

[sudden kindle]

Did you know

Uniformization theorem allows you to equip any compact riemann surface genus >1 with the structure of a hyperbolic surface

[delicate hemlock]

The best theorem

[sudden kindle]

YesA

Uniformization theorem is one of the top best theorems in all of math.

[tawny copper]

You might also want to consider Kirwan's book on algebraic curves. I haven't really look at Forster, but I'd like to read it, it looks quite efficient

[sudden kindle]

Forster is good but I don't have the energy to work through it

[nimble osprey]

Ok thank you

[foggy quest]

Riemann surfaces are discussed in this intro complex analysis text: https://mtaylor.web.unc.edu/notes/complex-analysis-course/

[marble solar]

I'd say Forster is for a rigorous introduction to it. If you like an Analytic approach, the last few chapters of Marshalls Complex Analysis has an analytic approach to the uniformization theorem

Miranda is really great because it's full of insight, but sparse on calculation. Forster is heavy on calculation, but light on insight

I don't recommend Donaldson or Ahlfors book

[marble solar]

Terry Taos 246C from 2018 has a nice intro to Riemann Surfaces without much background needed. It won't go as far as you'd like, but it can be a good focused starting point for Riemann-Roch

[marble solar]

Forster was painful for me. My class just used this, and I wasn't a huge fan of the algebraic/topological flavor of it

[nimble schooner]

I want to learn statistics from scratch,

What should I read?

[visual gate]

do you mean linear algebra?

I don't know linear algebra, like vectors and all too much, I use them in physics but I have no idea about the mathematical definition of them, I am very eager to start Sheldon Axler tho

I also watched first few videos of 3b1b's series on the essence of linear algebra so now I am exited

lol

[silk kernel]

Anyone have book recommendations that I can find online in pdf (or some other etext format) for algebra1 and 2? I'm a recreational learner who finished algebra 1 and 2 a long time ago, and would like to go through all the topics again for a comprehensive review, and deeper understanding. I'm particularly interested in understanding each section of algebra in relation to their practical real world applications.

[gray gazelle]

Khan Academy or Openstax

[normal crystal]

what he said or look at these recommended books
https://textbooks.aimath.org/textbooks/approved-textbooks/

[inland grove]

hey does anyone have any textbook recommendations for classical mathematics? prefereably with problems or a supplementary resource for them

[signal mountain]

what do you mean by classical mathematics ?

[inland grove]

as in its taught through explaining classical methods

deductive logic and stuff iygwim?

[vital bane]

what are classical methods

[vital bane]

do you mean rigorous mathematics as opposed to just mindless computations "calculuate the roots of the polynomial x^2 - 4x + 2"

[gray gazelle]

I want to learn caculus and i'm beginner what book to start with

[stable flicker]

Have you tried the usuals, like Spivak or Apostol

[mellow delta]

I'd actually recommend Pauls Math Notes, it's an online 'course' that covers calc 1-3, and differential equations

[stable flicker]

This is also a good one

[maiden glen]

how is Serge Lang's Complex Analysis book?

[native cradle]

isn't spivak quite hard

I'd personally say lang is decent for a beginner( though I've had it for less than 12 hours )

[vital bane]

thomas' calculus is good

[vital bane]

yea it's basically like an analysis book

it's halfway between regular calculus and real anlysis

[native cradle]

I bought it thinking it would be a hard calc book 💀

oh well, I want to learn RA anyway, no problem

[daring lake]

Spivak is in a very odd place

[vital bane]

truly

[molten mason]

You can just get a calc workbook with a bunch of problems for cheap

Amazon has a bunch for like $10-$20 USD

[vital bane]

but his differential geometry books are in a very good place

[daring lake]

People who want to learn calc would pick something easier, people learning RA would go for a RA book, I can't pinpoint Spivak's audience

[vital bane]

Hardcore calculus fans

[molten mason]

People who join a math discord

[vital bane]

marh

marlth

[molten mason]

Spelled math on the first try

[native cradle]

I'm starting uni and @tribal crow recommended it, so I bought it

[daring lake]

I went hard into Rudin as my first RA book , then I had to backtrack

[molten mason]

Yeah there's nothing wrong with it, or any textbook really. I'm just saying you don't need to buy a second textbook for more problems/practice, they make tons of Calculus workbooks to get your practice in.

Like you can find a workbook with harder calc problems

[tribal crow]

it's a good book, but quite tough if you have little prior experience

[native cradle]

the harder the problems are the better

[tribal crow]

also, don't take my word as absolute lol

[native cradle]

I'm taking all green's words other than mine as gospel

for "reasons"

[tribal crow]

but why?

[native cradle]

We've been over this before, 99% of greens are at top unis

[tribal crow]

makes me want to take not very ppl now

[molten mason]

Higgins is definitely at a higher education

[tribal crow]

well, that doesn't matter as much as you think and also, there are plenty of users who are at top unis here and would recommend differently than us

[native cradle]

may be true in the west, but it does make a difference in developing countries as far as I know ( though someone here may say that's not true anymore, in which case, good)

[tribal crow]

eh, point is: green name neq all knowing. and especially for some topics, there are ppl here I would trust a lot more to give me book reccs than any green name

[native cradle]

[tribal crow]

mostly because I don't know of a single helpful who does, say, analytic number theory

so I couldn't ask any of them for a recc

[native cradle]

I meant for 1st to 3rd year topics

but point taken

[tribal crow]

AnaNT can be a first year topic too

[molten mason]

There's a lot of green names that are high school level too IIRC since a lot of the help is middle and HS level math

[native cradle]

wait,what?

[tribal crow]

nothing

[molten mason]

Don't give Deltoid any ideas

[tribal crow]

I won't say anything lest I summon a certain somebody

dang it

[gray gazelle]

LOL

[remote sparrow]

i do not mean "linear algebra"

[remote sparrow]

all i can say is that it has a complete solutions manual written for it

[maiden glen]

Are there anyone else present who may be able to give me a review

[left cloud]

this doesn’t say much but one of his better books

[maiden glen]

can you say more?

[left cloud]

been a while since i looked at it. what do you want to know?

[gray gazelle]

I know this is old as fuck but I was scrolling up through logs that mentioned Hamkins and saw this. If you are still interested, I think either Thinking about Mathematics: The Philosophy of Mathematics by Stewart Shapiro or Introduction to the Philosophy of Mathematics by Mark Colyvan would do here

[winged bluff]

Is there a problem book in algebraic topology similar to "Analysis and Algebra on Differentiable Manifolds"? I enjoyed the structure of that book. And I guess more generally, are there other books similar to that one?

[quasi haven]

What are some maths books that an engineer or a mathematician must read during their free time?

[bright epoch]

if you're asking for books that are less intensely rigorous, Strogatz's Nonlinear Dynamics is a good recc

[maiden glen]

if it is a good extensive text involving introductory information

[molten mason]

Lang's books are known for being written to the deranged learners. A lot of his texts assume you already know the information, or that you know how to look up an explanation on your own without guidance.

His CA book is one of the few that is more "normal" and easier to comprehend. It doesn't assume much going in, I think just calculus and some real analysis.

Is there a reason why you selected that book?

[maiden glen]

Thank you, I'd chosen it because I ignorantly thought it was good for self study

is/are there such (a) book(s) you may recommend please?

[foggy quest]

I can recommend https://mtaylor.web.unc.edu/notes/complex-analysis-course/.

[molten mason]

#book-recommendations message

[gray gazelle]

Does anyone have any good set of lecture notes on abstract algebra? I think I learn best from lecture notes

I think I found one but I want to know if there is something better

Here is what I found

https://math.berkeley.edu/~apaulin/AbstractAlgebra.pdf

[foggy quest]

you can try chapters 4+ of https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/linalg.pdf

[gray gazelle]

Seems quite good to me.

[willow merlin]

best measure theory book/resource

[fresh skiff]

I have started Axler from the previous week and till now I am enjoying it.

[gray jungle]

royden is great for beginners and folland is great as a 2nd pass/reference/with intructor notes

epsilon of room for a quick summary

[solemn rover]

i love forster and i'm happy to shill it

[solemn rover]

fake news

it's fun to read

[gray gazelle]

I would personally recommend textbooks, however.

[gray gazelle]

I learned a lot of my algorithms class stuff from lecture notes

And a good amount for my automata theory

class

Interesting.

The process is literally just read lecture notes and then do problems

I recommend textbooks for the problems.

Yeah I will probably find textbooks for problems but I don't like reading textbooks lol

You do not think textbooks elucidate these concepts adequately?

No, it's not that. Reading textbooks just annoys me for some reason.

[maiden glen]

when should I read gtm 211

[molten mason]

After reading at least one other algebra text

Or you can start today of you're feeling feisty

[maiden glen]

like what

[narrow relic]

I think the Linear Algebra book is pretty well written

[visual gate]

But I do know normal algebra lol

I know coordinate geometry and polynomials and all...

does that come under "normal algebra"?

[remote sparrow]

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

[visual gate]

oh

abstract algebra lol

yeah I do not know that

I know how to solve a cube tho

but you don't need to know group theory to do that

[molten mason]

https://math.berkeley.edu/~apaulin/AbstractAlgebra.pdf

[molten mason]

Yeah I agree

[molten mason]

#book-recommendations message

[visual gate]

Most courses, I think start with linear algebra and analysis but a lotta my friends who self-study started with group theory

as in "Their journey of pure maths" if you will lol

[molten mason]

I mean groups are normally the first chapter or two in an abstract algebra textbook. And you theoretically can take linear algebra, analysis, and abstract algebra in the same semester. They're three separate courses.

I think one or two textbooks do rings first

[drowsy nacelle]

group theory technically doesnt need anything but most books ive seen will assume familiarity with certain things from linear algebra

its not really a big impediment though in my opinion for concurrent study

[molten mason]

Yeah and you can just look up things as you need

[drowsy nacelle]

yeah

[molten mason]

I'm self study and half my time is spending looking things up and wondering why all the links are already purple

[drowsy nacelle]

too real

im doing math in school but im still self studying cause im studying ahead

[maiden glen]

when should I read Serge Lang's real and functional analysis

[viscid comet]

I LOOKED UP A BOOK EARLIER AND I WAS LIKE WHY THE FUCK HAVE I LOOKED THIS UP BEFORE

And then I have this PhD math guy constantly send me the strangest fucking math pdfs

[maiden glen]

really?

[viscid comet]

And then I'm reading on the side like circuit analysis stuff for my job, I think I'm gonna fry my last 2 brain cells

[maiden glen]

show me screenshots 🙂

[viscid comet]

Yeah he's pretty chill, one he sent me today was a PDE book from the AMS

And last night we were talking about connectedness in topological spaces

It's just fun banter

[maiden glen]

screenshots 😁

[viscid comet]

No? It's dms

[maiden glen]

oh

what are the pdfs

[viscid comet]

Idk where he got it from other than it's an AMS book called "Partial differential equations: a first course"

[molten mason]

Have you done any real analysis before?

[maiden glen]

I'm getting to it

[molten mason]

After that then.

All of the textbooks you've been asking about are graduate level texts; they expect you to already have 1-2 semesters of undergraduate level understanding in the topic.

You're more than welcome to skip ahead to them, just ve warned you night need to do a lot of extra work and/or get a lot of extra help

[maiden glen]

there's a sale

im buying them now to save money

[molten mason]

What sale

[maiden glen]

4th of July sale on Amazon

[molten mason]

Oh it looks like 18% and 36% off?

Springer does sales twice a year. I got Real and Functional Analysis for $20 during their Christmas sale

[maiden glen]

good to know

[molten mason]

They had 50% off like a month ago or so

[winged bluff]

Dummit and Foote, Aluffi Chapter Zero, and Rotman's books. But Lang is a good reference for its chapters on field and Galois theory. The rest I would probably learn from somewhere else.

[silk kernel]

Thanks! The openstax books on algebra look pretty good.

[silk kernel]

Nice recommendations. Added the algebra books to my library.

[silk kernel]

I am looking for math book recommendations that focus on game development; specifically the applications of trig, geometry, and linear algebra to game development.

[uncut crater]

Always wondered whether a rings first approach to abstract algebra is beneficial or not

I remember reading two such books, Aluffi's 'Notes from the Underground' and Rotman's 'Advanced Modern Algebra'

Of course, by a read i mean a casual flip of the pages

Does it have any benefits compared to studying groups first? Usually, groups being simpler structures (and rings being abelian groups), it's preferred to study them before rings

But most of the results in ring theory that I know of/have learnt do not specifically use results from group theory

As far as examples go, i think rings are better since we all know of the integers and the polynomials since young age

[dapper root]

I think that’s the idea behind it

People are more familiar with those examples of rings versus like

The symmetric group

[uncut crater]

Hmm, and the fact that groups should actually be taught as actions

Which aren't always intuitive

[drowsy nacelle]

you know what is intuitive though

is that a group is a groupoid with one object

[uncut crater]

Makes sense

[drowsy nacelle]

thats actually what aluffi does in the chapter 0 one

[uncut crater]

That statement rocked me off my chair the first time I saw it

Yep

[dapper root]

I don’t think he ever explains how to interpret a group as a 1-object groupoid explicity tho right?

[drowsy nacelle]

yeah im going through that book rn its good but maybe not for a first introduction

[dapper root]

I don’t remember it at least

[dapper root]

It was my first introduction 😎

[uncut crater]

He's cheeky, gives the Vsauce way of defining it casually and going 'or is it? is it trivial?'

[drowsy nacelle]

yeajh

[dapper root]

Hey Undergrad, Aluffi here

[drowsy nacelle]

i started off with artin

[uncut crater]

Artin...

Mixed reviews tbh

[drowsy nacelle]

its not my favorite but it was the only one id even heard about at the time

[uncut crater]

I think it's not nice jumping into GTM/GSM and then looking down on ug texts

[drowsy nacelle]

that and d&f

[uncut crater]

That's me

[drowsy nacelle]

wait artin is undergraduate right?

[uncut crater]

Yep

[drowsy nacelle]

ah

[uncut crater]

He covers groups nicely iirc

The rest was meh

[drowsy nacelle]

yeah and good linear algebra review in the beginning

[uncut crater]

💀 I skipped that

[drowsy nacelle]

at least for me cause we didnt cover permutation matrices and all that in my firstlinear algebra course or even block matrices

[drowsy nacelle]

fair

[drowsy nacelle]

1. Definition of group
   1.1. Groups and groupoids.
   Joke 1.1. Definition: A group is a groupoid with a single object.

LOL i didnt notice this

"Joke 1.1"

I mean he does go into it a little but there's not that much to go over specifically with that tbh

at least to understand the reasoning behind that definition

[dapper root]

Oh I thought he just didn’t explain

Like morphisms form a group

[drowsy nacelle]

Nah hes like every arrow is an isomorphism etc etc and the group axioms are recovered from it

but its not that long

[dapper root]

Ah

Guess I skipped that

Or my brain just forgot

[drowsy nacelle]

probably yeah

[gray gazelle]

Like Lang isn't that good for any chapter except field and Galois theory?

[winged bluff]

Not exactly. Lang has its uses, it’s a good book to have around. For a person self-studying, and learning the content for the first time, it’s probably better to look elsewhere.

[gray gazelle]

I see, that's fair

[halcyon wasp]

I heard Lang is a good graduate textbook

[rigid lichen]

@quaint seal

[languid valley]

i want some good book to improve my trigonometry

[plush topaz]

James stewart's Precalculus book?

[languid valley]

i do have that

oh wait its the early transcendental one

does it have good questions?

[narrow relic]

My impression from his graduate analysis book is that I do not like the style at all. His undergrad stuff is a lot better IMO.

[gloomy jasper]

Hi, a short time ago I have interested in topics like minkowski adding, convex analysis, convex optimization. How should I find good materials on this topic? Unfortunately I hadn't learnt it very much at university.

[visual gate]

figures

Yesterday the price Rautenburg was 830 ruppess

Today its 1,332 ruppes

Did he die or what? /j

I am thinking nobody buys that book from amazon so when they saw me looking it up yesterday they were like "quick increase the price, someone is looking for it"

[native cradle]

any book suggestions for uni level algebra?

[snow valley]

What is a good book for learning integration techniques (don't say interesting integrals by nahin)

[fierce hedge]

Algebra as in linear algebra or abstract algebra?

[native cradle]

other than lin alg

idk tbh, I just know I don't have a book for algebra

I have one for lin alg

[gray gazelle]

I've been reading Grillet's book and enjoying it

it's fairly comprehensive

Herstein's Topics in Algebra covers less, but has good problems

[fierce hedge]

Standard textbooks are :
Gallian - pretty much the standard nowadays at ug level
Rotman - like gallian but expanded and has more lore
Herstein - covers less (no galois theory), weird notation but better quality problems
Dummit and Foote - encyclopedia textbook, good problems but can be dry asf

Newer books I liked
Silverman - Abstract Algebra_ An Integrated Approach - alternates between groups, rings, fields and LA
Brešar - Undergraduate Algebra_ A Unified Approach - tries to give a unified approach to abstract algebra like quotient structures are introduced for rings, groups simultaneously etc

[native cradle]

thanks

are these expensive?

[fierce hedge]

you're in India right?

[native cradle]

yes

[fierce hedge]

you can find cheap versions of some of them but the paper quality would be terrible

especially dnf and Herstein

gallian you can probably find a cheaper, decently quality but older edition

or just print whatever you want using printster

[signal mountain]

theres also artin and vinberg

(two books not one)

[wintry hornet]

Of the two Alexandrov books of Alexander-Perunin-Kapovitch, which is more accessible?

acc should i ask this in #diff-geo-diff-top

[maiden glen]

how is gtm An Invitation to Mathematical Logic?

[hexed jolt]

Algebra in Action - Shariar Shahriari

[zealous tusk]

what abt RD sharma

[gray gazelle]

what is a good problem book for testing skill (in preference to be considered hard) something like a benchmark

?

[native cradle]

for undergrad maths?

[native cradle]

thanks

[gray gazelle]

what skill in particular?

[gray gazelle]

problem solving

[gray gazelle]

but , wait, what other skill are books about?

[gray gazelle]

there's lots of topics?

[gray gazelle]

Algebra, Calculus?

idk

alot

Real Analysis?

oh, but that are topics rather than skills

i mean what in particular do you want to problem solve?

I dont know, that's why I need a benchmark

any problem

well what's your highest level in math?

2 year of math undergraduate

💀

i shouldn't have respond

I'm still in algebra

but , anyways, i do not consider that a level

just wait

there might be someone

oh lol, dont worry

[gray jungle]

any combinatorics book should do the job

i think graph theory specifically is great for building up problem solving skills

[gray gazelle]

andreescu books?

[gray gazelle]

no no , but not for building up, for testing .
probably i wont able to solve any of that, but the idea is to have a reference of what is hard and what is easy

[gray jungle]

thats mostly subjective and depends on the subject, you can try olympiad problems from any book

my recs for graph theory are a bit advanced unfortunately

[gray gazelle]

how can i make that subjective a little more objective?

[vital bane]

just do exercises from math books

[gray gazelle]

it doesnt matter , I like graph theory (i know just the basics) but having a reference is a good idea, if you can reccomend something i would like it

[gray jungle]

diestel is a great book

[gray gazelle]

is that considered hard?

[gray jungle]

again, depends

but in terms of graph theory its a nice book with good proofs and problems

if you want real analysis problems rudin pma is good

for linear algebra i think hoffman kunze problems are good

and general competitive math problems can be found in olympiad or putnam exams

[gray gazelle]

what I am intuiting is that graduate level math books are considered hard, right?

Anyway guys what do math degree holder's usually get as a job after finishing college?

do they do like cryptography or something?

[gray jungle]

again...it depends

why do you care?

[gray gazelle]

(more appropiate to a discussion channel)

[gray gazelle]

#No-access means no

[gray jungle]

if you want to improve at problem solving, pick a subject you like (seems like graph theory is one) and try to cover it

[gray gazelle]

i have perma-studying for less distractions

[gray jungle]

combinatorics is known to be a subject thats good for problem solving skills

[heady juniper]

I'm taking an honor's calculus sequence soon that teaches from Apostol's book. It's a very rigorous course from a good university, and I'd like to prepare so I don't completely fail.

I'm looking for some advice on preparation. I'm obviously going to look through Apostol's book, but from an analysis perspective, I find Tao more approachable.

Would good preparation be Lang's Calculus (for more traditional calculus teaching) and Tao's Analysis? I don't really know what to expect from Apostol. I like Spivak's book, so I'll look through that as well. Just want to know if Tao's analysis will give me a good start on a book like Apostol.

[sage python]

Apostol calculus is probably at a lower level than Tao Analysis, no?

The former a priori doesn't need background in either proofs or calculus (assuming it's at the level of Spivak, which is what I've heard people compare it to) the latter I think assumes some experience

[heady juniper]

I can't comment on this since I haven't read either in full. But the first several chapters of Tao's Analysis (the ones I've read), are incredibly structured and don't seem to have any assumptions about background.

It starts with the peano axioms (arguably the longest course on peano axioms in any book lol), so it starts pretty much at the bottom.

If you're familiar with Apostol's book, would you be able to set some expectations for the material? There's multiple different sorts of calculus books (proofs based, lots of applied problems, analysis, etc.). Spivak is pretty clearly an intro analysis book, imo. And on the other side, I'd say Stewart and others are pretty obviously engineering books. Not sure where Apostol fits and what to expect from a problem set.

I can look at problem sets, but I don't have the background to know what I'm looking at.

[molten mason]

Do you not have access to Apstol right now?

[heady juniper]

I do not, though I can get it online easily. My issue is that I do not know calculus (I am taking my Calc 1 course this fall), so even if I flip through it and read problem sets, I won't really know what it means (and thus the expectations).

[molten mason]

Most Calc 1 Classes do derivatives first and then Calc 2 is integrals. Apostol is reversed and starts off with integrals. Do you know if your Calc 1 class itself is starting halfway through Apostol with derivatives, or is it following the same order as Apostol with integrals?

[heady juniper]

I can post the notes to the course. Based on the ToC, it looks like we will do linear algebra > derivatives > integrals. Not sure if this will be my professor though. Others might do it differently.

https://www.math.columbia.edu/~rf/honorsnotes.pdf

I'll be taking a standard calc 1 course before this. I will take this course in the spring.

Just want to begin preparing for proofs, etc., ahead of time. I'm a slow dude and I'll get outpaced very fast.

[molten mason]

Yeah just trying to get more info before giving you a right answer

[karmic tangle]

Hello sorry for pinging but since this is pinned and seems to be quite comprehensive I just wanted to ask about Michael Henle's book "A Combinatorial Introduction to Topology" if you've encountered it and potentially what your thoughts on it would be? I've seen good reviews for it

Also this isn't really a "book recommendation request" per se but more like a "topic recommendation request" if I may ask that here

I'm reading through Axler's Linear Algebra Done Right and while it is super nice I'm having this problem where I've seen (so far, will of course change later into the book) much of the material already and it's feeling a bit demotivating sometimes

I've had a course on groups, rings/fields, lattices and some universal algebra basics + some set theory basics

and basically I think ideally I'd enjoy doing 2 topics in conjunction switching between them, with one of the topics being something "novel and new"

I've this book, then Aluffi's "Algebra: Chapter 0" and George Bergman's "Invitation to General Algebra and Universal Constructions" that I'd all like to read and think I would benefit much from

doing the exercises is a blast but what all 3 of these books have in common is that significant parts of them (especially near the beginning) are things I'd already seen so while I definitely will benefit from going through them very much it feels not too good to have a big list of things I'd already kinda seen soem of that would be all that I'd be learning for the foreseeable future

so idk what to do

maybe just going through with it would be the best and I might be being impatient (be being feels weird/not right to write xD?)

[trail hemlock]

[karmic tangle]

I'm in a similar situation with the analysis side of things too, basically have had some courses on calculus then single-variable and multi-variable analysis and metric space basics but again it was kinda to the extent that I understood the material but think I'd gain a ton going over all the proofs and whatnot myself once more too

[molten mason]

Yeah this PDF seems pretty linear algebra heavy and then does derivatives first.

First, check out https://tutorial.math.lamar.edu/classes/calci/calci.aspx if you haven't already, you'll use it a lot.
Second, check out Brian McLogan and Professor Leonard on YouTube, they have tons of Calc 1 lectures, problems, explanations, etc. NancyPi also has a few great videos on Calc 1 material but then she disappeared.

Apostol is a great book, I would really have you go over the Introduction chapter a few times. It's the first 47 pages of the textbook and is the foundation for the rest of the book regarding how to read math and write proofs.

I would then still read up to page 60, because it's where the book truly "starts" and you can see how Apostol writes and explains things up until he introduces the integral, then skip to Chapter 4 on page 156 and have fun.

Utilize a lot of #calculus channel too.

[signal mountain]

if youre feeling confident on these early sections then i dont think its worth your time or mental effort to slog through them if thats how it feels

skim it so you know whats going on with respect to that specific book, but otherwise move ahead

[molten mason]

This discord like #calculus will help you figure out what you're looking at and can explain it. Apostol has a good balance of proofs and computational problems.

[karmic tangle]

I feel like I still gain a lot going through and doing the exercises/proofs myself

but also like I am able to follow later proofs/arguments somewhat alright too

[signal mountain]

i think you have your answer then haha

[karmic tangle]

yeah I am definitely going over them all again just wondering if you guys think I could also in the meantime be getting familiar with some other topic too

basically I have a lot of time right now during summer break so I'd like to split the time somewhat

[signal mountain]

personally id work through in order, but i dont know that you HAVE to

[karmic tangle]

so I'm not just doing "going over x topic" all of the time

[signal mountain]

if you book has a 'chapter dependancy chart' that may help you see what you could start on

[sage python]

Don't really know it unfortunately

[heady juniper]

Thanks a bunch for the detailed response. I'll definitely look into the first 47 pages, etc. Hopefully I do well!

[willow merlin]

best book for basic set theory

[remote sparrow]

#book-recommendations message

[molten mason]

Enderton is actually pretty nice, pretty easy read

[upper eagle]

any recommendations for a good competition counting and probability book? for context, I know most of AoPS's intermediate counting and probability, and am looking for something to supplement my way to AIME/USA(J)MO

[sudden kindle]

I wanna read biographies of famous mathematicians

Any recommendations?

Like a biography of riemann or Klein or poincare

[analog lava]

fermats last theorem

[gray gazelle]

I'm looking for a book for groups, rings, and fields. Someone recommended Artin's? I'm not really into number theory, my focus is on algebra, is that book applicable? I'd like to eventually study Category Theory.

[gray gazelle]

I guess maybe it would do with Algebra chapter 0 by paolo aluffi?

Since it starts with light categories

[sudden kindle]

No thanks

[gray gazelle]

Guys I need a General Topology book. It needs to be graduate level. I've seen Kelley's but I think it's too old. Munkre's is kinda not very deep. So I would like a suggestion, for a point-set topology textbook or lectures notes

this is rlly good

if u want more adv stuff its volume 2 is also v useful

https://link.springer.com/book/10.1007/978-981-16-6509-7

why isnt the embed working

[gray gazelle]

Thank you, I checked it.

It seems great, I appreciate your help.

[upper eagle]

any recommendations for a good competition counting and probability book? for context, I know most of AoPS's intermediate counting and probability, and am looking for something to supplement my way to AIME/USA(J)MO

[remote sparrow]

willard

[remote sparrow]

#book-recommendations message

[native cradle]

An Introduction to Homological Algebra by gallian is what you're talking about?

[fierce hedge]

WHAT

[fierce hedge]

No, contemporary abstract algebra by Gallian
You wanted ug algebra books right

[native cradle]

Yes

[fierce hedge]

I didn't even know Gallian had a homological algebra book

[tribal crow]

absolutely not

that is not a usual UG topic

[fierce hedge]

Yeah homological algebra in graduate algebra

[native cradle]

Oh

[fierce hedge]

I think DnF and Rotman covers some homological algebra but idk to what extent

But yeah they are grad topics

[native cradle]

I think I better wait for uni to start, I'm getting ahead of myself

I can't decide between these books anyway 😭

[fierce hedge]

Just start with a standard book and see if you like it

For Indian unis, Herstein is the canonical algebra book

Especially for group theory

Rings and fields will be usually done using DnF

[native cradle]

What about basic abstract algebra by Bhattacharya

Just realised I already have that

[fierce hedge]

Which one?

I have heard good things about it but I have never used the book myself cause the pdf I have is horrible

I think it does some LA also right

[native cradle]

Yeah

[stray veldt]

there is a book called men of mathematics which is quite cute

it has small biographies of many famous mathematicians from ancient ones to modern ones

it focuses more on the lives of the people rather than the mathematics they did though

other than that "the man who loved only numbers" is a decent biography of erdős

there is one about perelman called "perfect rigour" but its quite controversial

[delicate hemlock]

I like the unreal life of oscar zariski

[stray veldt]

ah nice, maybe i should check that

[uncut crater]

Why do people still use this book?

[sage python]

I learned my group theory from Herstein and kinda liked it tbh

(That + Keith Conrad notes)

[trail hemlock]

i learn all math from terrence howard

thats the best book rec i can give tbh

[fierce hedge]

If by people you mean students, they don't, most students use Artin or Gallian or DnF. It's the instructors who are hell bent on using the books they used.
Honestly the worst part of Herstein is the notation, the problems are good.

[uncut crater]

The God

I had a copy of herstein bought when I was in highschool

Back then, i had zero idea what algebra was

I sold that copy the day I joined college cuz i aint touching that 🙏

And the library is equally trash, they've got 10 copies of herstein mf bring aluffi instead 😭

[gray gazelle]

Thanks!

[trail hemlock]

🤓

alright bro 😭

[uncut crater]

You'd be disappointed with the stuff I did back then

[trail hemlock]

i highly doubt that to be true

[uncut crater]

I got my copy of PMA and apostols analysis then too lmao

Did i solve them? Ofc not

[trail hemlock]

then why get them

[uncut crater]

I have a weird obsession with books

Now that I'm an undergrad, i have the means to read them

Back then, I'd just casually flip the pages trying to understand and making no progress whatsoever

Except for Burton and Tucker, but those are books on the easier side

[trail hemlock]

tucker?

i barely know er 😔

[uncut crater]

Er?

[molten mason]

This was down for the last week and let me tell you how big my anxiety got

[sage python]

Lmfao

Now that you know there's a risk of access being removed you gotta download them all and put them on a Drive folder or smth

Or save it right now on web.archive

[molten mason]

You wouldn't believe what I've been doing since I sent my last message

[sage python]

Incredible

[tribal crow]

wait what

wdym

[sage python]

Apparently the website with the Keith Conrad notes was down for a little bit

So it's like damn this is a warning that that website is mortal

[tribal crow]

I see

[heady juniper]

Off-topic from my previous question. Anyone know where I can find Olympiad Style problem sets (at various levels) for different subjects? E.g., combinatorics, geometry/trigonometry.

Not for any particular reason. Just fun.

Not exactly problems sets on the Olympiad tests, but “practice” problem sets.

[tender river]

See the channel description of #competition-math

[languid valley]

is there some book about how newton invented calculus

or any book about him

im really curious about the thought process he had to invent an entirely new tool

[upper eagle]

any recommendations for a good competition counting and probability book? for context, I know most of AoPS's intermediate counting and probability, and am looking for something to supplement my way to AIME/USA(J)MO

[gray gazelle]

Principia Mathematica

actually

Philosophiæ Naturalis Principia Mathematica

[languid valley]

thank you :D

[gray gazelle]

well if you liked a history about him

just search isaac newton story

actually there are two person who made calculus

i forgot who's the other one

[languid valley]

leibnitz

is there a book abt him too?

[gray gazelle]

check

i think there are

[gray gazelle]

in google

[onyx mantle]

Ok

[languid valley]

okay

[upper eagle]

any recommendations for a good competition counting and probability book? for context, I know most of AoPS's intermediate counting and probability, and am looking for something to supplement my way to AIME/USA(J)MO

[willow merlin]

best book for order theory

[sudden vale]

There was this book iirc, "Principles and Techniques in Combinatorics" I found that to be a good book. Other than that, you can always look into books by Titu Andreescu

[steel cloud]

What is prerequisite for lie Algebra and group representation

[willow merlin]

what would be the pre reqs for order theory?

[karmic tangle]

is this good for a more or less first encounter?

I've had a few weeks of lectures on metric spaces as part of my analysis course and will go through Abbot's Analysis beforehand also

[uncut crater]

I'd stick to munkres tbh

[karmic tangle]

I was thinking of "Topology Through Inquiry" by Su and Starbird but the one you'd recommended seems to take a similar approach

I ideally wanted a book where you're expected to "explore and fill in the proofs" as you go along,

[tribal crow]

@remote vortex do you have a book recommendation in mind that treats measure and integraton like you describe?
#math-pedagogy message

[remote vortex]

Axler's "Measure, Integration and Real analysis", certainly.

Also most measure theory and real analysis books do that.

It's rare to treat Lebesgue integration specifically, because most people agree with me (or rather I agree with them) that it's a bad ida.

[tribal crow]

thank you

[sage python]

This is correct yeah. This is why I don't like Royden, Stein-Shakarchi (from which my TA in measure theory lectured for Fubini and this actually made things a bit confusing), etc

[gray jungle]

it could be a good approach to someone without much maturity to appreciate the full abstraction i guess? but then again if you are doing measure theory you should have that maturity

i think royden does it that way, its a good book but seems like a waste of time

ouf sniped

[sage python]

Even if someone doesn't have maturity, I feel like you can always just introduce the example of Lebesgue measure early

So they have something concrete to latch onto

If it's just that people are scared of reasoning about set systems with axioms then they need to be redoing Baby Rudin or... Linear algebra

[gray jungle]

you can also just put a exercise for people to show what integration with the dirac measure and counting measure looks like

which should give some insight on how integration doesnt need to be just lebesgue integration

[sage python]

And it's not just the convenience of generality or applicability to probability (which are of course important), it's imo more informative to know which theorems are theorems about set systems, which theorems use that you're a Borel or Radon measure, what actually relies on the fact that we're R^n, etc

[remote sparrow]

#book-recommendations message

[gray gazelle]

Sorry for asking about physics books but what's the word on university physics

And Thomas calculus

[placid needle]

Best book to understand the basics of geometric series and how to approach/solve them?

[gray gazelle]

I don't have any particular book recommendations (honestly, any calculus book should do), but if all you want to cover is geometric series, they can be explained pretty easily:

Starting in the finite case, a (finite) geometric series is a sum of the form $\sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$.

[hasty eagle]

eigenpuppet

[gray gazelle]

To obtain a nicer expression for this sum, let $s = \sum_{k=0}^n r^k$.

[hasty eagle]

eigenpuppet

[gray gazelle]

Multiplying both sides by $r$, we get $rs = r\sum_{k=0}^n r^k = \sum_{k=1}^{n+1} r^k = r^{n+1} + \sum_{k=0}^n r^k - 1 = r^{n+1} + s - 1$.

[hasty eagle]

eigenpuppet

[gray gazelle]

Rearranging, we have $(r - 1)s = r^{n+1} - 1$.

[hasty eagle]

eigenpuppet

[gray gazelle]

If $r \neq 1$, then we can divide by $r - 1$ to get $\sum_{k=0}^n r^k = s = \frac{r^{n+1} - 1}{r - 1}$

[hasty eagle]

eigenpuppet

[gray gazelle]

In the infinite case, just take the limit to get $\sum_{k=0}^\infty r^k = \frac{1}{1 - r}$, when $|r| < 1$

[hasty eagle]

eigenpuppet

[gray gazelle]

Can I get some suggestions on whether or not it'd be right to buy this book?

https://link.springer.com/book/10.1007/978-3-030-46040-2

I do have a copy of Loring Tu's book but this one seems to cover everything better especially Lie Groups which I really need to learn about.

[drowsy nacelle]

for intro books its usually taylor for classical mechanics and griffiths for e&m

i mean there are others though

and i assume you arent asking about gr and qm

[trail hemlock]

https://www.amazon.com/exec/obidos/ASIN/0817643176/artofproblems-20

both volumes of Enumerative Combinatorics by Richard Stanley are good as well

[drowsy nacelle]

Any recommendations to learn about forcing?

And inaccessible cardinals and related topics

[foggy quest]

there are good Lie group notes here: https://mtaylor.web.unc.edu/notes/lie-groups-and-representation-theory/ Though they assume you know manfiolds and some differential geometry

[molten mason]

OH BOY DO WE HAVE THE GROUP FOR YOU

@torn crypt @strange sentinel

[strange sentinel]

LOL

[drowsy nacelle]

i like what im hearing

[molten mason]

We're going through Combinatorial Set Theory: With a Gentle Introduction to Forcing by Halbeisen

[torn crypt]

At least nominally

[drowsy nacelle]

How far through it are you?

im def interested

[torn crypt]

I’ve been distracted by research project so uhh

Not as far as I should be

[torn crypt]

Kanamori and Jech also cover related topics

[drowsy nacelle]

ah i see

[torn crypt]

But Halbeisen is obviously forcing-centric and combinatorics pilled

[drowsy nacelle]

yeah im still interested

[torn crypt]

Kanamori’s “the higher infinite” does different but related things, etc

[torn crypt]

Just pick up Halbeisen and start reading

[drowsy nacelle]

Which is the first kanamori book you referred to

[torn crypt]

If you’ve seen set theory before you can start at chapter 4

[drowsy nacelle]

got it

[torn crypt]

“The higher infinite”

It’s more large cardinal-y

Jech feels like Lang’s algebra

[drowsy nacelle]

ok i see

[torn crypt]

But a bit more chill before going into a topics course sorta

[drowsy nacelle]

Jech meaning set theory not introduction right

[torn crypt]

Lot of deep stuff, but could spend a course going over some later chapter topics as opposed to a chapter or smth

Ye

I’m not the set theorist, so I am not the one to ask on what’s good, but I know what covers a lot, even if I can’t tell how well it does

[drowsy nacelle]

Well yeah from this i have more than enough to get started i think

what does the group entail btw

[torn crypt]

Just read Halbeisen, I kinda blundered in the organization of it

[drowsy nacelle]

alright ty

[torn crypt]

I should read it more later tonight to “catch up” oop

And prep for questions

[drowsy nacelle]

Yeah ill go through and see what im familiar with and stuff

[molten mason]

Crying so hard at this IRL right now, it's kinda true though lmfao

[halcyon wasp]

How do I decide materials to learn if I want to go into geometric topology?

Maybe I gotta begin with knot theory

[foggy quest]

Doesn't it all start with differential geometry

[halcyon wasp]

Yeah maybe I should learn the coordinate free form computations

And basic DG

Thanks!

[foggy quest]

Like Brouwers fixed point thm and De Rham Cohomology are part of DG

[halcyon wasp]

Indeed, well but

Isn't DR Cohom more difftop/algtop?

[heady ember]

Clerk's recs #book-recommendations message

[foggy quest]

I guess DR cohom doesn't use the metric, so maybe it doesn't count as Differential Geometry?

[halcyon wasp]

Oh, hmm

[vital bane]

@heady ember forcing!

oh you were already here

[nova cape]

anyone got any good imo prep book recommendations?

[willow merlin]

which book explains egyptian fractions for dummies

[gray gazelle]

If someone knows this please ping me too. I’m curious if that specific book exists.

[gray gazelle]

hi, what are some book for mathematicial logic?

from introduction to graduate?

[vital bane]

introduction or graduate?

[willow merlin]

well he is looking for a reference that goes from undergraduate to graduate

but idk if thats tangible

[gray gazelle]

well , do you know what are the reference books for logic quals exams?

maybe a progression is asking to much, but at least ,
what is the standard?

[vital bane]

graduate level logic is kinda niche, maybe asking in #foundations would help you

[gray gazelle]

thanks

[hexed jolt]

Yeah

[remote sparrow]

#book-recommendations message

these are mostly advanced undergraduate/beginning graduate references except leary/kristiansen

[zinc lantern]

does someone have any recomendations for a comprehensive and thorough book for multivariable calculus?

[trail hemlock]

hubbard and hubbard

[zinc lantern]

Thank you.

[remote sparrow]

https://ww3.math.ucla.edu/qualifying-exam-dates/

https://math.wisc.edu/graduate/current-phd/qualifying-exams/topics/

here are a couple of examples

[maiden glen]

what are some lengthy real Analysis books that are perfect for self study

[marsh ingot]

Did you see a bit of real analysis before?

[maiden glen]

yes, but I wouldn't mind something containing introductory

the problem is that I cannot achieve what I want when the books are restricted due to student use

i need something that gives me more than just semester worth

[fallow cypress]

It sounds like you want Cummings's "Real Analysis: A Long-Form Mathematics Textbook"; I never read it though

I personally like Abbott's book Understanding Analysis and William Wade's book An Introduction to Analysis

I assume you mean a first-course in real analysis, although William Wade's book also does a second course (in multivariable analysis)

[maiden glen]

thank you Eric, is there something similar for complex analysis?

[fallow cypress]

I don't think there's a long-form textbook for that. My course used Bak and Newman personally though, and it was fairly easy to understand, but nothing special.

ALSO

I'm trial running a new factoid command. Enjoy!

!bookrecs

[hybrid sparrow]

Check out the official Mathematics Discord website! https://mathematics.gg/books

[molten mason]

[fallow cypress]

Wait

I think that date is just wrong

Whatever

[iron badge]

Any recommendations for quant books?

[maiden glen]

maybe try leonard susskind's books for introductory

other than that, I have no other suggestions for you

[iron badge]

I will check that out

[normal crystal]

Susskind is a physicist, was that a misunderstanding?🤔

[maiden glen]

most likely, I assumed he was talking about quantum physics

[fallow cypress]

I thought they meant quantitative finance

[maiden glen]

give the guy a good book concerning quaternions

[daring lake]

quant is definitely quantitative finance

[grand thistle]

sus

[trail hemlock]

!bookrecs

[hybrid sparrow]

Check out the official Mathematics Discord website! https://mathematics.gg/books

[tribal crow]

nice

this list is still incomplete though

[onyx mantle]

Ok

[willow merlin]

is rosen best discrete math book or?

problem is I want to learn about posets but maybe an order theory reference is too much for me

[lime vessel]

Try any decent book on proofs and logic

Enderton is usually recommended

[willow merlin]

is it set or logic

i think he has many books i will check out the logic one i presume

[lime vessel]

Enderton Elements of Set Theory

[gray gazelle]

Halmos Naive Set Theory is also good

[willow merlin]

i will

[uncut crater]

@tribal crow Körner's A Companion to Analysis?

It's a meaty book, even tho it's a gsm undergrads can handle it

Will prolly read this during PhD cuz I have no time now

[gray gazelle]

thanks a lot

[analog sentinel]

Any good books on learning how to write proofs that y'all can recommend?

[signal mountain]

how to prove it, velleman

[graceful moon]

There are books specifically about proofs, but I’ve never been convinced that they’re worth the time. I think reading something like what Loch wrote in the pinned messages of #proofs-and-logic and then diving into whatever textbook you want to learn from is the best thing to do

[stray veldt]

i recommend not reading a book on this

what Nope said is even better

[graceful moon]

The only way you will learn what a good proof is and how to write one well is to read and write a lot of proofs, this just comes from experience

[stray veldt]

proofs in different subjects vary too much and books like velleman only do set theoretic manipulations

which are important but you dont need to do 200+ pages of them

i also like https://math.hawaii.edu/~pavel/Aluffi_notes.pdf, which is an intro proofs but mixed with intro to modern mathematics

[graceful moon]

I think a big part of learning a subject in maths is just learning the bag of tricks and methods typically used in those proofs, no book can be a catch all for every subject of that

[graceful moon]

If this interests you @analog sentinel there is a similar book called “A Concise Introduction to Pure Mathematics” by Liebeck which does a similar thing, it gives a taste of different areas of maths while teaching you basic set theory and proof techniques which is very approachable to people with a highschool level of maths

I actually think that book is an amazing recommendation to anyone considering maths at uni, just to get a taste of what its like because it can be quite different from highschool

[vital bane]

Lol I was so confused by this

"wait susskind wrote a quant book??"

[gray gazelle]

Lol same

I would like suggestions for a rigorous introduction to mathematical logic, can be graduate level but has to be of a building up from Axioms approach

[civic python]

I think if you don’t have a mentor that can give you feedback on your “proofs”, using a book such as Velleman becomes more relevant.

[graceful moon]

That is a valid criticism, it’s certainly easier to improve your proof writing at uni when you’re getting constant feedback but I’m still not convinced reading any of those how to prove it books is even half as effective as just reading an introductory textbook and taking it all in

The actual mechanics of writing proofs isn’t that difficult, it’s picking up all the tricks and stylings of each subject that takes some time

[vital bane]

I think actually doing proofs is how you learn to do proofs, like just pick up a analysis/algebra book and grind it

that's how I learnt it

and half the time the proof exercises are just applying the definitions properly

[lusty escarp]

Brezis is dead.

[molten mason]

Neam's analysis arc never ends.

[crimson leaf]

This is why I liked Lay's analysis book I felt like it would be a very good first book for someone learning math

[daring lake]

same here

I just grinded through bartle and rudin till i got the hang of them

[narrow relic]

I asked a professor about things from Bartle and Sherbert every week. But I did "grind" it too

[neat seal]

I think for people starting back house will always be reliable

[torpid gorge]

hi, can i get some textbooks recommendations about linear algebra and/ or calculus?

[foggy quest]

A good linear algebra book is https://mtaylor.web.unc.edu/notes/linear-algebra-notes/. How advanced of a calculus book are you looking for?

[remote sparrow]

#book-recommendations message

#book-recommendations message

[remote sparrow]

#book-recommendations message

[torpid gorge]

i'm looking at calc 1 and calc 2.

[torpid gorge]

thanks

[mossy flume]

!bookrecs

[hybrid sparrow]

Check out the official Mathematics Discord website, or ask in #book-recommendations. If you want to submit your own book review, please DM ModMail.

[mossy flume]

this exists as well

if you wanna see more recs + some written reviews

[stuck zephyr]

since when this was added

[tribal crow]

very recently (yesterday)

[willow merlin]

that is really really cool

i always hated to go through the pins on mobile

[stuck zephyr]

yeah me too

[gray gazelle]

Well I've been looking towards working on some physics this month... sadly ive lost touch with physics I only remember the basic stuff, is there a book for quantum mechanics geared more towards math people

[mossy flume]

also the pins don't have every review

[tribal crow]

conversely, the website doesn't have many of the ones in the pins

[remote sparrow]

https://www.amazon.com/What-Quantum-Field-Theory-Mathematicians/dp/1316510271/

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

[gray gazelle]

Are you sure i can jump right into that

It seems a bit difficult and is also a 'graduate' level textbook

[compact ore]

"graduate level" is meaningless

i read multiple GTM books as introductions to undergraduate topics

it seems that to be a graduate student to springer you merely need to "graduate" your first year

[gray gazelle]

Ah okay

I guess it's fine then

Thank you for the advice and the recommendations

[compact ore]

at the bottom of the book description it tells you the prerequisites

[willow merlin]

what would be the pre reqs to differential geometry, is it possible to self study or ?

[trail hemlock]

i’d like to add that callahan’s Advanced Calculus: A Geometric View is also excellent

[remote sparrow]

depends on the book

@tame tree how are you finding hubbard and hubbard

@median saffron are you still working through velleman's calculus book?

[tame tree]

very good book

although i have been on a long break from math

[gray gazelle]

Hey

[willow merlin]

best book for diff geo

[gray gazelle]

Are you all a mathematician

[willow merlin]

only me

[mossy flume]

oh hm maybe we should migrate some of those

[trail hemlock]

i wish

only 938c2cc0dcc05f2b68c4287040cfcf71 is tho

[gray gazelle]

Oh

I am also not that much but I like math

[trail hemlock]

m2

[willow merlin]

I am not, im taking precalc, I was just joking

[willow merlin]

same

[gray gazelle]

Wannabe friends then

I have some friends who are good at math ➗

[molten mason]

This channel is for book recommendations, if you want to talk about something other than books then head over to #discussion or #chill

[gray gazelle]

Ok

[gray gazelle]

please consider uhh #discussion

But what matters

[drowsy nacelle]

Bluds tryna boost his chances of getting mod

[median saffron]

Yep! I am. I’m about a little over halfway through the book which might seem slow but i have other things I’m currently studying rn 🤣, been a great book so far tho

[edgy cliff]

Kafka on the Shore

by Haruki Murakami

[willow merlin]

Tokio blues haruki murakami

[uncut crater]

Woit, and if you've done functional analysis, then Takhtajan

[bright epoch]

I'm sure this has come up before, but what is the best book out there on forcing for someone fairly new to set theory

[copper plaza]

does anyone know a book which teaches calculus from scratch till detailed

[willow merlin]

prolly thomas and stewart

can i get some recommendation for modular arithmetic

[ashen compass]

recommend me some in depth diffgeo books with exercises

[willow merlin]

what are the pre reqs for diffgeo?

[ashen compass]

calc 3, optionally topology, real analysis

[drowsy nacelle]

@molten mason

[drowsy nacelle]

@bright epoch

check the message linked in that message

[bright epoch]

ty

[heady ember]

You could have just linked Clerk's message

[willow merlin]

is diffgeo taught in undergrad math major or

[rich sun]

depends on where you're studying

it might even not be offered at all as a course

[willow merlin]

?

in ur uni

[rich sun]

for example

[willow merlin]

example what

[rich sun]

for example, it's not offered in my uni

[willow merlin]

are u grad or ug student

[rich sun]

I'm a PhD student

[willow merlin]

but u don’t care about diff geo or

[rich sun]

I do care a lot about diff geo

[gray gazelle]

mod matters

[rich sun]

Fortunately, there was a one-time project in my bachelor's related to diff geo

[willow merlin]

is it hard getting into a funded phd program?

[rich sun]

That's where I began learning about it (third year)

[rich sun]

That really depends on a lot of factors

[covert folio]

if i want to go back and actually understand calculus, instead of treating it like a black box that i can use for computations, which kind of book (stewart/thomas' vs. apostol/spivak) should i use?

[real marsh]

the latter

[daring lake]

yes

[gray gazelle]

Thoughts on Gilbert strang's linear algebra?

[marsh ingot]

Sources for presheaves and sheaves in a friendly way?

[tawny copper]

Vakil or Hartshorne

[marsh ingot]

Thanks

[vital bane]

this reminds me, today I saw a streed named "scheme"

[drowsy nacelle]

LMFAO

I wasn’t thinking

That’s actually hilarious idk why I didn’t do that

[trail hemlock]

size matters 😔

[gray gazelle]

perma-studying matters for having No-Access (not arguable)

How to go about using Intro to Linear Algebra by Stang?

[molten mason]

Probably with the online course

https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/

They use the 4th edition originally and should have it updated for the 5th

[gray gazelle]

I ahve the 6th edition book

How do the 2 balance each other?

Do I need to use both simultaneously, or the lectures more of a supplement

is linear algebra needed for calculus based physics?

[molten mason]

If you can just use the book, then do that. If you need someone to give you direction and help explain things, that's what the lectures are for.

Honestly the lectures will the be the same, the difference will be that the course-provided homework and solutions might not match the edition you're using.

[gray gazelle]

I see

Okay

Thanks

[molten mason]

LA is used all over physics. Your first intro course should teach you what you need to know for that course, but if you're planning on taking a lot of physics classes or majoring in physics then you should actually learn LA.

[gray gazelle]

is there a way to watch lectures on good notes or on ipad or something, sorry i got my ipad yesterday

[molten mason]

It should be the same on any device. Access the internet, go to the link, click play

[gray gazelle]

aight

thanks bro

[gray gazelle]

damnn you will get the new feature soon

[gray gazelle]

should i do Calculus first before LA?

[molten mason]

I mean...you don't necessarily have to, but if you're getting ready for calc-based physics then aren't you doing calc anyway?

Calc is 3 semesters, you can do LA while you learn Calc 1 and Calc 2 and have it ready to by Calc 3

[gray gazelle]

Yo

[drowsy nacelle]

I highly recommend doing this

[gray gazelle]

what were books that change the way you used to do math , and also change you skill level?
I mean, what are those books you can name as THE BOOKS.
those books that you would have wished to read/do* early when you started
("do" for the problems, since its not just about reading)

[drowsy nacelle]

Which level?

aops books tend to be good generally

assuming you mean pre-university stuff

[gray gazelle]

any, since for any level should* be at least some book that makes you progress to the next level
(maybe it doesn't)

[drowsy nacelle]

idk if any single book did that for me tbh, its more like understanding what a concept means well enough to prove it and to be able to explain it yourself, which may take a variety of resources to make it click

and those may differ person to person

[gray gazelle]

khan academy

[gray gazelle]

I remember talking with you, , remember that I am trying to learn pure math, so khan academy is not very good idea, but thanks for replying

[gray gazelle]

i think Khan Academy is very good resource

either way if you're working your way up to pure math's you either solid your foundations

like basic operations and stuffs

for me even Khan is hard

especially when you're self studying on your own

but that's up to you imo

i recommend Basic Mathematics by serge lang if you want to do pure math's

i think most here really recommends it

there's the fundamental which you can review if you have anything left out..

[gray gazelle]

I have al ready done that book
bro , I remember asking for books last time, and you also replied something similar, then you say something like:
"I am not even at college"
then I said you :
"dont worry"

xD

Spivak Calculus would be the best for you then

..

[molten mason]

I mean we have people here under 18 doing graduate-level math, being in university doesn't mean anything

[gray gazelle]

yeah