book-recommendations

[gusty smelt]

at this level just pick one, and start reading

[sturdy shore]

I just skimmed through the independence video on that playlist, there are 0 proofs

which tracks with the strang books I've looked at

[tender river]

any analysis or topology book for naive set theory and enderton for axiomatic

[crimson leaf]

This is MIT's proof based linear algebra course
https://ocw.mit.edu/courses/18-700-linear-algebra-fall-2013/

But this is based on LADR

[solemn haven]

What about Hrbacek's book?

[sturdy shore]

hrbacek is great, but it requires a bit more maturity than enderton

[tender river]

Pick and stick with one, just do h and k ig if you're a beginner with proofs and keep a reference or two for variety

[viral halo]

what abt Paul J. Cohen?

[gusty smelt]

what kind of set theory book do you want? I like kunen's books on the topic (his book on forcing) if you want something a bit advanced

[sturdy shore]

I'd say mid/late undergrad level while enderton is early ug

[ocean mulch]

Cohen? Like the Cohen?

The guy that finished the work on Continuum Hypothesis?

You kidding, right?

[sturdy shore]

lax is good from the parts I've read, if you've already done some LA before

covers some topics that you won't see in other LA books that are still important

[solemn haven]

I've seen some springer books about linear algebra, but it seems some people hate them lol

[gusty smelt]

just pick one

and see if you like it. For LA it really isnt the most important thing, which book you choose

[crimson leaf]

So has anyone read Lay's analysis book our professor picked it for this semester and I'm not sure how good it is

Though I'm leary cause Lay's LA book was not very good imo

[ocean mulch]

pick one and try it out. rinse and repeat

What works for other ppl might not work for you and vice versa.

[heady ember]

Enderton is good if one doesn't have any mathematical maturity but if one has some basic mathematical knowledge & maturity, Jech might be a better choice

[remote sparrow]

advanced undergraduate/beginning graduate textbook

[ocean mulch]

Lol, a hundred is too many

But do pick a few couples. Maybe like first 10, 15 when you search on Gg for recommendations

I often try 5-6 books before I find something I like

[gray gazelle]

Or just skip the set theory refresh part

[sage python]

This was me first year

But yeah I work best with some kinda structure or a very good book I can go through linearly

Got soooooooo many things I wanna read

[narrow relic]

I hated Lax

[narrow relic]

There are other books which cover those topics far better in my opinion

[sturdy shore]

like what? the latter parts are mostly stuff I never see in other LA texts

which makes sense because they are applications of LA that are in other disciplines, so you'd likely just see them there

[wicked lagoon]

Hey guys got any books covering normally hard/unintuitive math problems tackled from a work perspective?

[sage python]

Work perspective?

[wicked lagoon]

Like how a lot of math breakthroughs are made because someone has a work problem to solve

[sage python]

What's a work problem? Like a job? Work in physics?

[gray gazelle]

What kind of math breakthroughs do u mean too 🤔

[sage python]

(Maybe give an instance that you know of so I have a better idea what's what)

[wicked lagoon]

Yes, mathematical breakthroughs done by people, and an in-depth context of the history around the people, and the job issues they're trying to solve.

Not mathematicians, doing exploratory math, but mathematical ideas created as ad-hoc solutions to work problems.

I think Napier established logarithms because he wanted to get more rent money?

[sage python]

I see

I guess applied math is the closest thing to a "thread" here

[wicked lagoon]

Yeah, computer graphics I'm sure is a big field for this one

[gray gazelle]

Would they really be the ones making the mathematicla breakthroughs tho

[torn crypt]

What’s a good book/reference for forcing?

[wicked lagoon]

I watched an hour long doc on types of splines used in art software and font creation and had a much better grasp of the content than when I was looking through a math dictionary and making sense of the same concept.

[remote sparrow]

https://www.amazon.com/Set-Theory-Thomas-Jech/dp/3540440852

https://www.amazon.com/Set-Theory-Studies-Logic-Mathematical/dp/1848900503

[torn crypt]

👍 I’ll toss em in the archive

[crimson leaf]

Idk I think watching videos can give you the impression you grasp the content when you don't. Like I doubt this video went over divided differences, n-widths, polynomials, etc.. which are all considered foundational to splines afaik. Also I wouldn't use a math dictionary to learn math that seems like a very bad way to do it just picking books on things you find interesting have the pre reqs for should be fine

[wicked lagoon]

I'm not saying I have a degree in splines now, I'm saying I had a lot more success in understanding elements of splines than in past attempts to learn about them. For example, I had no ideas about anything related to parametric and geometric continuity, the series of n-continuities, how derivatives fit into that idea, tools used to work with splines like curvature combs, and different definitions for several different types of splines popularly used in graphics programs like bezier curves.

[south dust]

Any book recommendation for jee exam india

[heady ember]

Good ol' Jech lol

[heady ember]

Shouldn't you ask that in foundations

[remote sparrow]

no

[sudden vale]

How does Lee's Riemannian Manifolds compare to Do Carmo's Riemannian Geometry if I want to study Riemannian Geometry (curvature)? I am undergoing a course in Differential Geometry right now where we follow Lee's Introduction to Smooth Manifolds

[scarlet pumice]

Hi, can someone recommend me some books to keep up to the math required in engineering? My math level is probably year 10/11 igcse right now. Currently in my bachelor of commerce degree and thinking of changing to engineering.

[chrome yacht]

kreyszig's advanced engineering mathematics

[gray gazelle]

Hi, which book wpuld you recommend for a course on noncommutative algebra? These three are in the recommended literature, but you can also suggest any other if you think is better:

1. B. Farb, R.K. Dennis: Noncommutative Algebra, Springer, 2012.

2. T. Y. Lam: A first course in noncommutative rings, Springer, 1991.

3. T. Y. Lam: Lectures on modules and rings, Springer, 1999.

One that im also considering is
4) Brešar: Introduction to Noncommutatige Algebra

(as I really liked his abstract algebra introduction)

[silk sigil]

What is the equivalent of baby Rudin for abstract algebra?

I guess "equivalent" implies that it is a respected, classic work which handles the basics

[grand thistle]

like

lang maybe

[mystic orbit]

respected

[mystic orbit]

dummit and foote?

personally I like artin

I've heard D&F is quite dry

[fierce hedge]

Probably Jacobson

[sudden vale]

^

[sage python]

If you already are familiar with Lee, stay with it as a follow-up. Friends of mine who read do Carmo don't like it

[silk sigil]

Do you prefer it over Lang?

[crimson leaf]

Have you studied any abstract algebra?

[silk sigil]

I have, I took a course which covered groups through fields, but as usual, one course isn't enough to build insight, so I would like to study the basics again and read a classic along the way

[crimson leaf]

You should try both of them see what you like. I like Lang so far but it's a time investment he's keep it brief and expects you to do a lot of the work which is nice but some people may not like

[dire gorge]

What are some good book recommendations to read if you've seen my message?

[pliant stream]

@dire gorge how are we supposed to know what your message is..

[tender river]

#chill message

As I prepare to enter grade 10, I'm determined to elevate my math skills to new heights. While I currently don't feel entirely confident in my math abilities, I'm eager to change that. My aim is to become adept at mental math, tackle challenging problems well above my current level, and build a solid foundation for advanced learning.

I'm reaching out to this community for guides, resources, and tips that can help me achieve my goal. I'm particularly interested in eventually delving into calculus ahead of schedule. If you have any recommendations – whether it's strategies for enhancing mental math, book suggestions, online courses, or other resources – I'd be grateful for your insights.

My aspiration is to not just catch up but to forge ahead, and excel in math beyond what's expected at my level. Thank you for your time and any support you can provide. I'm excited to learn from your experiences and knowledge as I work towards my goal.

this was the message

[finite gale]

Not really sure what they have in mind with regards to "mental math"

[wraith edge]

maybe algebraic manipulation + computer like calculation
or
math problem solving intuition

[dire gorge]

is mental math important?

Nowadays.

Because I've been hearing mixed answers.

I've also been told to read a lot so I am wondering what books are reccommend?

[chrome yacht]

books for calculus? or mental math?

[dire gorge]

Both.

And books that genreally for math/

[fallow cypress]

you should be able to do stuff like 5+6

but doing stuff like 37*29 in your head? no it's not important

[empty junco]

1073

[hasty eagle]

Result:

1073

[dusky anvil]

i mean it depends

if ur going to do mathcounts and tournaments, you would prolly need to be good at it since they are usually no calc

but just for HS ur fine i think

maybe for sat a but more

[finite gale]

For most people, I don't think there's any need to put any extra time into improving mental math

A standard middle school education should suffice

[dusky anvil]

ong

[chrome yacht]

stewart calculus: early transcendentals

[lapis heart]

Half the time you get it wrong anyways when you're older

[finite gale]

I've definitely seen profs stand at the board for a bit to write down a wrong answer and get corrected by students

[gray gazelle]

Hello, are you a college student?

[gray gazelle]

some don't admit their mistakes

[flat jackal]

does anyone have a good copy for the vector calculus book by Jane sane colley 6th edition

I’ve got the pdf for it but it takes really long to go to the next page on my laptop

so idk if it’s a pdf problem or my laptop

[wraith edge]

why cant i just start reading "graduate texts for mathematics" books as an undergrad?

[finite gale]

you can

no one's stopping you

[wraith edge]

what are the most difficult parts in doing so

[finite gale]

certain ones are harder than others

there are some that are very very approachable for undergrads

[wraith edge]

ex: algebra by lang

[finite gale]

what about lang?

[wraith edge]

is it approachable lets say i want to read first two chapters

[mystic orbit]

like aluffi!

[finite gale]

i think lang is best read as a second course in algebra

[mystic orbit]

don't read lang lol

[wraith edge]

but i like him

[finite gale]

or at least after you've covered the basic topics once

[wraith edge]

i read his linear algebra till like ch4 or 5

[finite gale]

otherwise it can be a bit fast

[mystic orbit]

lang's algebra is mainly used as a reference

not for a first exposure

[wraith edge]

what do you recommend

[mystic orbit]

artin

[finite gale]

how much algebra have you learned?

there's also a list of algebra texts to consider somewhere in pinned messages of this channel

[wraith edge]

i want something similar to lang

[finite gale]

there are many much better options for a first course

[mystic orbit]

[finite gale]

in what ways "similar" do you want

[mystic orbit]

why are you so fixated on lang lol

[wraith edge]

pretty consice and doesnt have too many words

[mystic orbit]

that's not something you should be looking for

[tender river]

hungerford is pretty concise

[finite gale]

well you can try to read lang if you want, but i don't think it's a great idea for a first course lol

[wraith edge]

idk i get super unmotivated when i see examples or stories

[finite gale]

uhhh

[mystic orbit]

stories? lol

[finite gale]

examples are much of the motivation

[tender river]

idk about stories but id die to see more examples

[finite gale]

it's ok, reading the preface is not for everyone i guess

[wraith edge]

i mean good examples are good but examples like

evaluate this

or calculate that and stuff

[wraith edge]

i mainly read the first sentence then skip the pre face

[finite gale]

if you can't calculate anything, what's the point

even if you don't want to do say all the exercises of computing things, it's usually nice to at least to see things a couple times

[wraith edge]

i mean i can do it not just when the author has a half page on doing it

maybe i havent seen enough books so i am misunderstanding how they actually are

[finite gale]

what have you read so far (for context)?

in general

[mystic orbit]

you won't find that in an abstract algebra book

at least not in the sense of calculating integrals or evaluating functions

[wraith edge]

apart from my uni math(which is engineering) serge lang LA 4~5 chapters and 1,2 chapters of topology and deifferential geomtry books i dont remember the name

[mystic orbit]

where you're basically just trying to find an algorithms that works

[finite gale]

you can find things like compute all subgroups of S5 or something

[wraith edge]

but they are very introductory books

[finite gale]

i remember we did that in lecture for a class i think

[mystic orbit]

if you've done LA already artin might not serve you as well

tho it's still a good reference if you just skip the content you already know

[mystic orbit]

[keen orbit]

what is a very good book to self study classical mechanics

[wraith edge]

ok yeah seems good, i will just need to skip the first chapter and some others, thanks

[gray gazelle]

Still no recommendations?

[mystic orbit]

oh you're going with artin?

nice

if you've only done engineering the rest of the book might all be new content for the record

[gray gazelle]

can anyone recommend mildly complex quantum mechanics books? or quantum physics too

[silent jolt]

better book than this: https://www.amazon.co.uk/dp/1292289686?ref_=cm_sw_r_cp_ud_dp_V8D1JCDDXRZ8WW73SMW7 looking for something between U.K. A Level and first year U.K. uni level

@ me if response pls

[remote sparrow]

what does "mildly complex" mean

[gray gazelle]

okay lol. I know quantum mechanics/ physics in and of itself is complex, but I meant the type of style the book is written in, maybe more understandable. it doesn't have to be too simplified, mid/highly complex language is fine.

[remote sparrow]

do you know linear algebra already

[gray gazelle]

ehhh a little yeah. I'm going for more like the scientific concepts of quantum mechanics/ physics

yk what i mean?

[remote sparrow]

no, not really. griffiths is a pretty commonly used introduction to qm

there isn't really any way out of doing some math

[gray gazelle]

yea, so I meant- do you know stuff like the LHC? That obviously operates and was built on a foundation of a lot of mathematics but I'm looking for the conceptual ( or theoretical I'm not sure) parts of all of it. if you don't get it then it is okay.

[gray gazelle]

yea, but that isn't relevant to my point.

forget about the physics part, just mechanics

[wispy bison]

have you looked in #books-old

[rich sun]

Goldstein

[keen orbit]

Is it better than the one by John taylor

[rich sun]

Idk, haven't read Taylor

[keen orbit]

Oh ok

I'll download the one by Goldstein and check tysm is there any other book so that I can have multiple choices

[keen orbit]

Oh I read the prerequisites in the preface it requires advanced calculus tensors and other stuff Idk these ik multivariable calculus and I am starting linear algebra

I am studying alone i am not in university yet

[blazing canopy]

I would focus on linear algebra then, it's really important for everything

[keen orbit]

Ok I am studying linear algebra from shilov's book

[spring pendant]

has anyone read :

https://www.amazon.com/Axiom-Choice-Dover-Books-Mathematics/dp/0486466248/ref=sr_1_4?qid=1692087601&refinements=p_27%3AThomas+Jech&s=books&sr=1-4&text=Thomas+Jech

im needing something light to get lost in for September (some holiday scheduled)

[deep field]

is knapp harder than dummit foote?

[fierce hedge]

nope

It's definitely faster than dnf

[deep field]

oh okay thanks

would it be 'possible' to use knapp as an introduction to algebra. like i don't mean easy or pleasant one, just in terms of being technically possible

[karmic thorn]

Possibly yes, but I'd hesitate if you're learning the material on your own for the first time

It makes much more sense as a primary textbook for an advanced undergrad/starting grad algebra course sequence that has to cover several foundational topics

[deep field]

okay, maybe i should study gallian/fraleigh first

[karmic thorn]

Judson's Abstract Algebra: Theory and Applications is another text that I've come to appreciate for that

Freely available online, with printable and EPUB versions too

Otherwise, either of the texts you mention are fine too

[fierce hedge]

Just as chaigen said, I'd highly recommend Judson especially if this is your first rigorous maths subject.

[gray gazelle]

Can someone please recommend a good textbook for noncommutative algebra? Maybe Lam or Brešar? Why?

[modern tree]

hi

pls give me some trigonometry formula

[stuck zephyr]

I don't think this belongs to book recommendations

[modern tree]

bruh this server is so stupid

[stuck zephyr]

No isn't

[modern tree]

no one is helping me

everyone is ignoring me

[stuck zephyr]

With what

What do you need help with

[modern tree]

with math problems

[stuck zephyr]

#❓how-to-get-help

[modern tree]

they have said they are not going to help me

[stuck zephyr]

You must capping for that

[modern tree]

@loud cradle this is the guy who are not helping me

[stuck zephyr]

Some people will help you but they aren't doing your hw or helping you over test

[modern tree]

pls report him

pls report him

[modern tree]

but thery are geting paid for this

[loud cradle]

i am too busy spending my wages

[stuck zephyr]

Can you link the message

[modern tree]

bruh y are u doing this?

[loud cradle]

why are you taking this nonsnse to #book-recommendations , no one here is gonna calculate the square root of 786887 for you either

[loud cradle]

context: #help-3 message

[modern tree]

but u are from helper team so u have to help me it dosent matter what im asking

[loud cradle]

that is very false

[modern tree]

so who are gonna help me ?

@everyone

[stuck zephyr]

Got it

[stuck zephyr]

!volunteers

[hybrid sparrow]

Helpers are just people volunteering their time to help you. Be polite.

[stuck zephyr]

Also I agree with bungo

You seems trolling

[modern tree]

he is ur friend that why

[stuck zephyr]

No?

[finite gale]

#chill

[modern tree]

who is gonna help me ?

[stuck zephyr]

^

[modern tree]

my english is bad i struggle to understand

[finite gale]

in any case, this isn't the right channel..

[fast mulch]

Why dont I have access to general

[fierce hedge]

umm... there is no general channel though

[pine tundra]

Go to channels & roles and there you can tick "follow general"

[fast mulch]

Nah I found the problem 😂

I had hide social channels... xd

[grim plume]

Are there any similar books to "Vector Calculus, Linear Algebra, and Differential Forms" by Hubbard & Hubbard? i.e. one that combines calculus with linear algebra and includes proofs. I'd like a physical textbook but I can't find Hubbard & Hubbard for less than ~£90 anywhere

[remote sparrow]

https://matrixeditions.com/orders.html

it's not less than $90 but buying from their website is substantially cheaper than buying anywhere else

oh wait you said pounds

[grim plume]

Ty although I checked and it's $98 + $42 shipping to the UK which comes out at roughly £110 not accounting for the cost of converting currency, which is still too expensive for me. If there isn't a good alternative that's more affordable I'll probably just make do with a pdf

[remote sparrow]

hmm it is cheaper than 90 pounds but idk about shipping

[grim plume]

Yeah "Flat rate envelope" seems to be the cheapest shipping option for Europe and it's $42 Edit: "UPS mail innovations" is $37

[remote sparrow]

https://www.amazon.com/Multivariable-Mathematics-Algebra-Calculus-Manifolds/dp/8126574372/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=&sr=

there's an international edition of shifrin available as a paperback for a price well below 90 pounds

https://www.amazon.com/Vector-Calculus-4th-Susan-Colley/dp/0321780655/ref=sr_1_1?crid=24508646RWUZC&keywords=vector+calculus+colley&qid=1692126709&s=books&sprefix=vector+calculus+colle%2Cstripbooks%2C153&sr=1-1

[slender cargo]

I've heard good things about this book: https://www.amazon.com/Calculus-Analysis-Euclidean-Undergraduate-Mathematics/dp/3319493124

[remote sparrow]

colley has some used copies that are in good condition with a price of less than 90 pounds

but i don't recall if it teaches linear algebra

[slender cargo]

ah you might be right. it seems to do "just enough" in the linear algebra section

[remote sparrow]

i see

i'm looking at US amazon but the price should be similar for UK amazon wrt int'l ed. shifrin

which is a paperback, but it fits your budget

[grim plume]

My bad, I should clarify my budget is more like £50, but I couldn't find Hubbard & Hubbard for less than £90. Ty both for the suggestions, I'll check them out

[slender cargo]

whoops I meant to say "you're right" 😆

[silent locust]

Is there a best calculus book containing proofs,derivations and lots of problems

[remote sparrow]

spivak or apostol

[shrewd kraken]

Hey guys

asking about books here

but not math

has anyone read the 3 museketeers?

no spoilers

im planning on reading it in a few weeks

and i want to know if i should read 20 years after next or man in the iron mask

what is the right order?

and are there other books?

im assuming the order is:

3 musketeers

20 years after

man in the iron mask

thats the publication order iirc

but im pretty sure man in the iron mask takes place 10 years after, no?

[valid monolith]

I'd read it in order. Though probably doesn't mattee if you read 20 years or iron mask first

[shrewd kraken]

aight cus i need to read 3 musketeers and man in the iron mask

thanks

[valid monolith]

Yeah i don't think 20 years is a prerequisite for iron mask if that's what you were asking

https://www.online-literature.com/forums/showthread.php?42241-Advice-on-reading-Dumas

Turns out i was wrong?

[shrewd kraken]

screw it

ill read them fast

i need to write a paper on man in the iron mask and three musketeers

like 3-4 pages each

and like i have the whole semester to write one, and maybe 5 weeks for the other

i have time

eng 101 doesnt require me to read any books

[valid monolith]

Yeah i was wondering if it was for that reason

[shrewd kraken]

they are also classics

but i do hate the french

[valid monolith]

Not saying it is a good thing to do, but i passed hs readings with grades above 15 on my essays on each required reading and i didn't actually read the books. So you might be fine... The most useful thing is, if you already have a topic in mind, look for quotes to support your argument

[valid monolith]

Oh ik, was just you said you had to read them

[shrewd kraken]

im going to also read the great train robbery, fathers and sons, and maybe all's quiet on the western front?

i get to pick 2 others apart from the Dumas

The cheeses and the worms looks good

and theres the great cat massacre...

im going to read most of these eventually, but idk which would be best for a paper

[valid monolith]

... If you have time, and like reading (even if you don't give it a try, specially because idk if thr other two you get to pick are from a list or can be whatever), might as well read them

[valid monolith]

I am only familiar with fathers and sons and all quiet on the western front. I think probably the one which would be easiest for a paper is all quiet on the western front due to the subject matter

[shrewd kraken]

I can probably read it right before we discuss world war 1

[valid monolith]

Though the message from fathers and sons is also not that complicated, just isn't comparatively as obvious. Again i only know those two, so probably my comment on this isn't worth that much

[valid monolith]

Ww1 literature?

[shrewd kraken]

i assume thats what All's Quiet on the Western Front is about?

[valid monolith]

Oh i was asking if you will be adressing ww1 literature in class, i didn't realize the books you mentioned were directly related to the class, if that makes sense

[shrewd kraken]

they really aren't

i read hunchback of notre dame and murder in the cathedral already

and they aren't extremely related to the class

its a lot better htna reading something like

mornings on horseback

thats strictly biographical

[valid monolith]

Lmao you would hate something like diary of anne frank

[shrewd kraken]

i uh

didn't enjoy it?

i didnt read the whole thing

i just skimmed it

[steep lance]

Hey does anyone know of any good complex variables/analysis books? I really enjoy learning more about the branch, but was never the best at choosing specific books.

[finite gale]

#book-recommendations message

[wind osprey]

Hey so ive been planning on starting to self study the big concepts in algebra. I was wondering if I should just follow one books approach or use a couple of books

for reference i was thinking of following Artin's algebra book and supplementing some sections like the vector space chapter with other books

[steep lance]

You're the best, thanks!

[finite gale]

:3c

[finite gale]

This seems like a good plan, generally stick to one book and supplement with others as needed if you get stuck or need other ways of trying to understand something

[gray gazelle]

can anyone recommend a beginner book for the algorithms of a rubix cube?

[torn crypt]

I wouldn’t think you would find a whole book on that? Just look up the algorithms

[teal vale]

Does anyone know a book that you need alot of thought and research behind reading it

*before

And its got like

Alot of information details or stuff

[wispy bison]

why do you want such a book?

[golden salmon]

There are two nice scattering theory books I'm aware of:

• Volume 3: Scattering Theory by Reed and Simon
• Scattering Theory by Taylor

I am interested in both the physics and the maths side of things on this topic. Can anyone do a compare and contrast between them?

[inland elm]

a physics professor recommended "scattering theory of waves and particles" by newton as well
this was recommended to me as a math student, so i think that it could also be a good one on the math-end of things

[golden salmon]

Thanks! I'll check that out

[gray gazelle]

probably to represent a more advanced book

[rain wren]

hartshorne? lol

[heady ember]

Jech's graduate set theory book

Yeah but Wolfram421 was asking for a book "that you need alot of thought and research before reading it", which jech probably qualifies as, no?

[deep summit]

Any Compact reference book for set theory ?

[crimson leaf]

What subject

[torn crypt]

Enderton, or learn it as you go if you mean sets to use in, like, algebra and such

[deep summit]

Containing all theorems and proofs aswell, nothing left for excersizes

[torn crypt]

Ok that’s a much taller order

[deep summit]

I want a reference book, not a course book to solve problems and stuff

[crimson leaf]

Well most books that are considered references don't even do that

[remote ridge]

Hello, everyone,I studied Group&Ring theory using Algebra by Hungerford.Is it good to study Field&Module Theory using it?

[empty junco]

sure it can't be that bad

[remote ridge]

I have Dummit one but I think it's too wordy.I am tired of reading it

[deep summit]

that book has a lot of content right

[fallow timber]

anyone have a good recommendation for measure theory? all ive done is analysis 1, is that enough?

@ me if you answer please

[finite gale]

What is analysis 1 to you?

You should be reasonably comfortable with real analysis

[fallow timber]

single variable real analysis (through reimann integration)

i read through abbott chapter 7 if that helps

[pliant stream]

it would help to know about changing the order of limits

i'd read that too

[finite thorn]

Anyone know a good book on Game Theory (better if I can find a pdf online for it, math books tend to be prohibitively expensive to import)

[thin storm]

Hey does anyone know of any good complex variables/analysis books? I really enjoy learning more about the branch, but was never the best at choosing specific books.

@RiverRunner
Hey does anyone know of any good complex variables/analysis books? I really enjoy learning more about the branch, but was never the best at choosing specific books.

most likely to :3c — Ontem às 23:07
⁠book-recommendations⁠

darling — Ontem às 23:08
Hey so ive been planning on starting to self study the big concepts in algebra. I was wondering if I should just follow one books approach or use a couple of books
[23:10]
for reference i was thinking of following Artin's algebra book and supplementing some sections like the vector space chapter with other books

@most likely to :3c
⁠book-recommendations⁠

RiverRunner — Ontem às 23:15
You're the best, thanks!

most likely to :3c — Ontem às 23:27
:3c

@wind osprey
for reference i was thinking of following Artin's algebra book and supplementing some sections like the vector space chapter with other books

most likely to :3c — Ontem às 23:28
This seems like a good plan, generally stick to one book and supplement with others as needed if you get stuck or need other ways of trying to understand something
16 de agosto de 2023

arez — Hoje às 07:32
can anyone recommend a beginner book for the algorithms of a rubix cube?

Dragonslayer Sharp — Hoje às 08:55
I wouldn’t think you would find a whole book on that? Just look up the algorithms

Wolfram421 — Hoje às 09:47
Does anyone know a book that you need alot of thought and research behind reading it
[09:47]
*before
[09:47]
And its got like
[09:48]
Alot of information details or stuff

@teal vale
Does anyone know a book that you need alot of thought and research behind reading it

even order group => solvable — Hoje às 09:55
why do you want such a book?

1

[tender river]

What?

[tardy oasis]

what

[fallow cypress]

I don't know what your intention was, but don't do this.

[narrow relic]

I've never heard of Lang's Undergraduate Algebra. Interesting.

[gray gazelle]

someone has book recommendations for the basic of economics

??

[pliant stream]

Yes anything by kreps

[remote sparrow]

for those that bought a hardcover of friedberg insel spence, how was the binding? can anyone send a picture

[spring pendant]

Applied Math Book Rec (AI, ABC corp, applied math / modern history book) :

Head in the Clouds

Chapter example: "Strategies for a Culturally Illiterate World"

the book details the invention of the internet (heavy math / statistic use) and offers a nice bridge for the math literate to explain the realities of math and living with not math literate communities (globally)

[restive hawk]

What is a good book for elementary number theory? Looking for more introductory in case I missed anything

[haughty trail]

try search it up on github

[coral prawn]

?

[haughty trail]

the e-book about the topics

theres plenty of them

[coral prawn]

What topic? Are you replying to ttrrryyaaaa

[haughty trail]

yea

@restive hawk

I search up a lot of e-books on github but eventually I need a youtube explanation about it

[coral prawn]

but he's asking for a book recommendation, not any e book on github which may or may not be reliable/covers the "usual" content

[haughty trail]

well ok

[restive hawk]

ok

[clever orchid]

"An illustrated theory of numbers" by Martin Weissman

[restive hawk]

ty

[remote ridge]

Hello,is there any good book of elementary number theory?

I am using elementary number theory by Jones

[heady ember]

Silverman is a rec I have heard here numerous times, so might be worth checking it out

[sleek canyon]

im in high school and im looking to do some supercurricular, and just wondered what the best maths books are out there that would be okay for me to understand?

ive read fermats last theorem

[heady ember]

You should probably state what you're interested it. Or at least your knowledge level

[coral prawn]

and there's no "best" math book, really

[empty junco]

yes there is

I'm writing it rn

[coral prawn]

[spring pendant]

When Genius Failed is one of the best summer reading list books out there for the application of math by the best math people making money

It’s about one of the first quantitative algorithmic high frequency hedge funds called Long Term Capital Management

Written for a popular audience most math fans interested in finance Pre internet will enjoy

.
.
Suitable for high school

[sleek canyon]

knowledge level is pre university and honestly, i think i enjoy all areas of maths ive done so far, but to name a few i enjoyed the basics of calculus ive done, i liked mechanics, especially collisions as well

i also enjoyed learning about different distributions in statistics

[restive falcon]

how much of maths/fm a level have you done (assuming that's what you're doing)

[sleek canyon]

just the y12 course so far

[restive falcon]

further maths too?

[sleek canyon]

yes

[restive falcon]

hm

[rain wren]

hubbard!

you should do hubbard's vector calculus, linear algebra and differential forms

the only prereq is the equivalent of ap calc bc

[sleek canyon]

oh thank you that sounds really interesting

[empty junco]

how did you know

[rain wren]

imo hubbard is one of the best intros to rigorous mathematics out there

[spring pendant]

Fundamentals of Engineering Drawing 1943 published by PH by Warren J Luz. Purdue University

Is great for applying calculus and geometry and learning math via drawing … it presents all machines a person could create including complex motors and gives you the math equations to engineer the parts

[restive falcon]

they're below that level

[rain wren]

especially for those that aren't super sold out on math and are still exploring other stem fields

[rain wren]

meh, she'll be fine

I didn't know calc bc either

[restive falcon]

Michael Artin's "Algebra" is good

[sleek canyon]

thank you, ill look into it :)

[rain wren]

I knew you'd say that

[sleek canyon]

me?

[rain wren]

that's what I'd recc too if someone is hard set on math tbh

[sleek canyon]

lol

[tender river]

artin?

[rain wren]

that or some ranal book

[restive falcon]

yep

[sleek canyon]

thank you

[restive falcon]

do you like matrices

[sleek canyon]

yes

[restive falcon]

then yes absolutely

artin is the way to go

[sleek canyon]

ok thank you!!

[coral prawn]

what even is calc bc

[rain wren]

it's like calc ab

• taylor series memes or some shit

plus... other stuff

I don't remember

[restive falcon]

btw if you don't know what radians are it would be a very good decision to learn that asap
mathematics above school level does not use degrees

[empty junco]

I forgot degrees were a thing

[rain wren]

it's been a while since I've heard about degrees

[rain wren]

same

[restive falcon]

i think engineers use them

[empty junco]

no

[upbeat vine]

its also used for temperature

but redundant over there

[empty junco]

otherwise how can they say sin(x)=x

[restive falcon]

oh yeah

[coral prawn]

[sleek canyon]

ah yes i have basic knowledge of radians, thank you

[deep field]

are there any multivar calculus books that have detailed explanations on what jacobian matrix is

but that does not got overboard like hubbard?

[restive falcon]

referring to "mechanics" in a maths context and the fact that they mentioned pure, mech and stats as the stuff they were doing
"supercurricular" sealed it

[rain wren]

what makes you think they went overboard?

[deep field]

i mean it could be my lack of effort but i felt that the book was too 'rigorous' for my objective

like i was trying to get a picture of how jacobian matrices work and where did they come from

[coral prawn]

well if it's too rigorous for u maybe an applications book would suite you better

yayy it's rigorous!

[deep field]

imo hubbard has enough material to constitue a multivariable analysis course

it even had proof on generalized stokes theorem from what i've seen

[coral prawn]

damn that's so cool wtf 😭

[deep field]

also the book will take me like 1 year if i wanted to learn everything from there

[whole canyon]

any good book recomendations for probability?

[deep field]

which type of probablity?

i'd recommend blitzen and hwang for non-measure theortic

for measure thoery based , i'm not in position to answer

[whole canyon]

any book that covers all topics in-depth?

[coral prawn]

there are too many topics in probability

for a single book to cover "in depth".

[whole canyon]

thats the prob....

[fierce hedge]

I was very confused till I realised you were talking about trig degrees not academic ones

[rain wren]

not even close

hubbard is like

almost 4 courses worth of material

[deep field]

linear algebra, multivariable analysis, multivaraible calculus, differential geometry

am i right?

anyways i've decided to keep on using hubbard/hubbard

just need to put in more effort

[rain wren]

I don't know exactly

[deep field]

like its grab bag of materials

[rain wren]

there's smatterings of a wide veriety of topics

like optimization and numerical analysis as well but not too much

[rain wren]

I could expalin that like

rn

lol

[deep field]

the author said in preface that the course is for studnets who 'have gotten 5 at ap clac bc)

[rain wren]

you know what the total derivative is, right?

[deep field]

actually i've found a youtubevideo

that explained things nicely

yep i know what total derivative is

[rain wren]

yea, so basically that's a linear operator

and it turns out that, if the total derivative exists, the matrix that represents it in the standard basis is exactly the jacobian matrix

and since you can calculate the jacobian with just calculus stuff you can therefore calculate the total derivative

the key fact to note here is the difference between a linear operator and the matrix that represents it since they're not the same

[coral prawn]

........

[rain wren]

meimei, hubbard is HUGE

it's like

almost a thousand pages or some shit

[deep field]

the video kinda explained things like you did

anyways thanks

and yeah hubbard is extremely huge

[rain wren]

[deep field]

and dense

i was surprised by its sheer scale

the author said taht the only prerequisite was '5 on ap calc bc'

but i think that a person with only that experience would require significat effort

[coral prawn]

800+, I have physical copy, totally by legal means

[deep field]

to self-study hubbard

[coral prawn]

gonna um, read it, after I finish spivak

[deep field]

spivaks calculus?

[rain wren]

hubbard is hardly dense by math texts standards lel

[coral prawn]

yes, not to be confused with CoM

[deep field]

i should've studied caculus with that in the first time

not with stewart

[rain wren]

it's prolly the most chatty math text I've ever read

[deep field]

not that stewart is bad or anything

[coral prawn]

stewart to me....

[rain wren]

aside from veleman ig but that doesn't count

[deep field]

i was comparing it to other calculus book, of course it is less dense than books like lang's algebra

[coral prawn]

the first chapter made me say "no" cuz it felt lacking in rigour and the exercises... oh god they were SO SPAMMY

[heady ember]

> Lang's algebra

[rain wren]

oh makes sense

[deep field]

this may sound stupid but i tried to learn algebra for the first time with lang's algebra

instant regret

[heady ember]

[coral prawn]

😭

[heady ember]

That has the same energy as learning set theory for the very first time using grad Jech

[deep field]

dunno if i was brave or stupid at that time

[heady ember]

If you want some nice alg recs see pinned btw

[rain wren]

[deep field]

now i'm using gallian occasionaly supplemenitng with dummit foote

[heady ember]

nice

[rain wren]

yea, gallian is gud

[deep field]

dunno dummit has better explanations imo

[heady ember]

I bought jacobson and I'm gonna read it after lin alg + anal

[deep field]

gallian is still better introductory book

[coral prawn]

or, ignorant and arrogant

[rain wren]

now I dip

later nerds

[deep field]

bye seeya

my professor loves lang's algebra tho

he recommends undergrad students to read it if possible

[median saffron]

What books do you guys recommend for calc 2

[finite gale]

Stewart if computational

[median saffron]

What’s the difference between that and non computational

[sage python]

If you're doing theory, the theme is that you're spending more time on proving all the facts you learn

[median saffron]

oh

That doesn’t sound very fun

[sage python]

You'll still do computations, but your homework won't be just "calculate this integral"

Proofs here aren't like the 2 column bullshit you see in 9th grade geometry, fear not

I personally enjoy the conceptual side more than the calculations

[median saffron]

yeah I think I would as well

Is there a book that includes like practical applications of it not just the calculation side

[finite gale]

What do you mean by practical applications

[median saffron]

hmmm

[finite gale]

Because that just sounds like computations

[median saffron]

[sage python]

Those two tend to go hand in hand but are not synonymous

[finite gale]

The practical applications you are in high school or what not is what i was assuming, though maybe you meant something else

[rain wren]

schroder I believe

@gentle arrow can you confirm?

[sage python]

Calculation just means you tell people techniques to calculate integrals and have them do it, but a priori you're not explicitly referencing anything in stuff like physics

Schroder does include some applications here and there but isn't the flavor that water beam is looking for

Water beam doesn't seem to want much proofs

[median saffron]

i want one as like supplementary and self study purposes

[sage python]

Bad call, they want applications and don't want proofs lmfao

[gentle arrow]

schroder does not include many applications

i think they want stewart if they want applications

[sage python]

Like they'll want something for which, say

[median saffron]

well i mean im not opposed to like proofs i just dont want the majority of the book to be about that yk

[gentle arrow]

considering its also calc 2

[sage python]

The ODEs bit includes applications of them

Like oh this ODE comes from physics, here's even the physical derivation

[gentle arrow]

yeah i think you want stewart if you want an application-based calc 2 book

with little proofs

[coral prawn]

ye

[sage python]

Hmm, I know Stewart is good at computaton but does it have much by way of applications?

(Also it is kinda expensive)

[coral prawn]

well it does have those yes

some

[gentle arrow]

there was a section on physics applications

[coral prawn]

oh right that too

[gentle arrow]

like fluid pressure stuff with pools

[sage python]

I will say the way we teach calculus 2 here there isn't as much room to talk about applications except in the ODEs part

[median saffron]

haha yeah i saw online the pricing

[gentle arrow]

also dami i got a copy of hartshorne and i got baited by its preface
it told me that a basic grad level algebra course should be enough but

I GOT BAITED...

i am keeping the book though it is a very nice book

[rain wren]

https://tenor.com/view/laughing-dying-gif-24782560

[gentle arrow]

gonna read it in like 2 years or something

[rain wren]

oh this account doesn't have embed perms

L

[sage python]

The flow is basically:

• Advanced integration topics (parts, trigonometric substitutions, partial fraction decomposition, improper integration)
• ODEs
• Sequences and Series
• Taylor series
• Basic 3D geometry

[gentle arrow]

the ODE section was pretty nice

they do have polar stuff

[sage python]

We don't bother with that

It might be in the book

[gentle arrow]

it is

[sage python]

Honestly it doesn't make sense imo to include it in a calculus class

[finite gale]

Why is basic 3d geo tacked on at the end?

[sage python]

It's fundamentally a multivariable calculus concept

[gentle arrow]

calc 3

my copy of stewart has calc 3

i am not going to read it

[median saffron]

is this for stewarts only

[gentle arrow]

because i am going to learn it from schroder and then a dedicated diffgeo book

[sage python]

Our class references Stewart

But as you can see it skips some stuff

But yeah point is, if you look at those topics... you already have the physical motivations for integration in calc 1 (assuming your class is trying to tie into applications)

So the advanced integration stuff doesn't have so many natural applications to present that you didn't already present earlier. ODEs are gonna be the big applied bit here

Sequences/series/Taylor series... Physicists do like to Taylor expand

[gentle arrow]

those damn physicists and engineers approximating sin(x)=x

[median saffron]

alright

do most calc 2 books include odes

[sage python]

But I don't know if their usage of it feels like a dedicated "application of the topic" the way thinking about second derivative as acceleration is

It's just, oh we know these functions come up for their own reasons, using Taylor expansion is kewl

[sage python]

I wouldn't know. I only really interacted with Stewart and the proof-based books, especially Spivak

[median saffron]

i heard spivak is quite the rigorous book

[gentle arrow]

it is

[finite gale]

You can also reasonably learn calc 2 from Paul notes online

[sage python]

It's pretty rigorous though the more time goes on the more I feel like its organization is a bit too screwy

[gentle arrow]

schroder

[sage python]

The flow of Spivak is like

[finite gale]

But I would say that they are more of a supplement to say Stewart

[gentle arrow]

become theory pilled

[coral prawn]

https://tenor.com/view/laughing-dying-gif-24782560

[coral prawn]

ok fair

that one is a bit whack

but!

Aside from that spivak = !!!

[coral prawn]

it's like half calculus half introductory analysis

[tender river]

calculus is applications

read a physics or an engineering mechanics book if you want applications for specific stuff

[sage python]

Spivak_irl

• Axioms of an ordered field ("Properties of Numbers" or whatever they call it)
• Induction
• Incredibly screwy (idk if you can even call it rigorous) chit chat about "functions" and "graphs"
• Delta-epsilon and continuity
• Try to prove intermediate and extreme value theorem. Fail at this task and realize you need a new axiom of R if you want them to be true
• Suprema and finally actually proving those theorems
• Differentiation
• Integration and FTC
• The most bullshit definition of angles and trig functions ever
• Some cutesy shit about pi being irrational and planetary motion???????? (I guess we wanna pretend to be applied)
• Exponential and logarithm
• More integration techniques (not sure why you didn't just do this stuff right away tbh)
• Taylor polynomials
• Sequences and series (arguably should've been done close to the beginning)
• Uniform convergence/power series
• Complex numbers/functions/power series (I guess? (we didn't bother covering this stuff so idk))
• Epilogue: existence/uniqueness of R

[empty junco]

what he do

[rain wren]

wtf is a bullshit definition of angles?

how tf do you screw up the definition of angles lmfaooo

[finite gale]

Iirc defining trig function in terms of some integral

Though I don't remember the details

[empty junco]

define angles now

[empty junco]

meh that's

fair

[rain wren]

draw circle with a center at the head of the angle

[empty junco]

lmaoooo

[coral prawn]

mmmmhm

it was um

[median saffron]

National geographic calculus 2

[rain wren]

the arc length is your angle

[coral prawn]

basic properties of numbers

[sage python]

Yeah I know the intuition there but as a matter of definition it's so fucky

[rain wren]

omg cos

[sage python]

Like part of the point of Spivak is that you're learning to say things right lol

[rain wren]

lololololol

[coral prawn]

Try to prove intermediate and extreme value theorem. Fail at this task and realize you need a new axiom of R if you want them to be true

😭

[sage python]

I told you

In the moment when my class hit this part our professor tried to explain all this and we were just looking at each other like

[rain wren]

that's fucked up

[sage python]

Is this mf on crack?

[coral prawn]

isn't that the... alternate def of cos

[sage python]

I mean any technically correct definition is an alternate definition of cosine

[coral prawn]

that's why I love spivak it just kills you over

[sage python]

But also w h y

[rain wren]

omggg

[coral prawn]

w h y n o t?

[rain wren]

that's hilarious

[coral prawn]

I mean tbh if udc abt it just skip it tbh

[finite gale]

Who did you have lol

[sage python]

Like you spend all this time giving some pretend rigorous take on angles to try and give intuition

And then define sin(x) = sqrt(1-cos^2(x))

What are you even doing my man

I had Sebastian Hurtado

[coral prawn]

ok.... fair

😭

[gentle arrow]

schroder_irl

• establishes what R is, gives you a couple axioms, and comforts you into proofs
• sequences of real numbers/cauchy sequence stuff
• epsilon delta/continuity
• EVT/IVT
• differentiation/MVT
• integration/FTC
• series
• set theory/countability
• the most brilliant things i have seen in my life
• measure theory in R
• some approximation stuff (STINKY)
• bunch of abstract stuff
• topology
• more abstract stuff
• applications

[coral prawn]

well overall to me the extra stuff was moistly interesting random BS facts- tho I've yet to rlly complete it soooo

we'll see

[torn crypt]

rudin_irl
•let delta be f(epsilon)
•qed

[sage python]

Throwing in set theory/countability that late is... like I get it in a way

You don't really need it until you hit measure theory

But I feel like it disrupts the flow somehow

Also topology so late

[tender river]

be like garling and tao

[finite gale]

I think fefferman gave us a problem using the definition on a homework, it was strange

[coral prawn]

sounds perfect for me :3

[gentle arrow]

i think i can skip the topology chapter when i get to it

[tender river]

do fkton of set theory in the beginning

[gentle arrow]

if im being honest

[sage python]

I know what it's trying to do but it just feels strange to me somehow

If I were trying to do something like this my flow would be this

[coral prawn]

pog

[gentle arrow]

if schroder was more motivating like tao

it would be the greatest intro analysis book in existence

[sage python]

Okay so thing is what part of me would wanna do is build things up in a certain way where I frontload a bit of algebra

[coral prawn]

dami abt to write his own anal book fr

[gentle arrow]

let me in

its stein and shakarchi all over again

[tender river]

like garling

[gentle arrow]

i actually kinda want to write a textbook

it seems interesting

[coral prawn]

https://tenor.com/view/good-morning-do-it-gif-24435329

[lime vessel]

You can learn a lot of things from reading a textbook
You can learn even more from writing a textbook

[finite gale]

I had a friend who did a post bac as essentially a professional textbook writer

[gentle arrow]

i mean im thinking of writing kickass intro calc notes

[coral prawn]

kickass

[gentle arrow]

(i am going to write it similarly to hatchers point set topology notes)

[lime vessel]

Spent two weeks writing notes for an algebra tasting course
Did not regret

[tardy oasis]

how does algebra taste? I've never tried it

[gentle arrow]

barbed wire

[lime vessel]

Chewy and charred with a hint of cactus

[coral prawn]

[tardy oasis]

my favorite 😋

[heady ember]

Enderton is the best math book I have completed

[timber ember]

Reccomend some books about logic (i'm a beginner) 🙏

[coral prawn]

you completed it alr? damn

👏

[dusk wind]

imagine reading a book from 10 years ago

[mystic orbit]

Very few math books from 10 years ago are actually good

[coral prawn]

more or less than?

[mystic orbit]

Being too new is actually negative in my eyes coz it got less time to be thoroughly reviewed whereas old books withstood the test of time

Which is one hell of an indicator of quality

[coral prawn]

ah, so less than 10 years

well 90% of the book reccs I see here seem to be at least 10 + years old so

[stray veldt]

people dont usually go around reading math books about stuff they already know

so people recommend books that were used in their classes

and profs use what they learned with

[loud cradle]

also, you'd think that people wouldn't keep writing new books about subjects that have been covered to death.. but then again we're talking about math publishing

[sage python]

Oh lmfao I forgot I started writing a somewhat spicy take on how to do intro to conceptual calculus/analysis

[finite gale]

Where'd it go then

[clever orchid]

Wanna learn LA ? Consider Finite dim vector spaces by paul halmos

[sage python]

I pasted it in some notes

[stray veldt]

i dont think a good LA book exists actually

someone should write one

[coral prawn]

and make it free

[sage python]

Shilov feels like something of a meme but alright, Halmos is also good but dated and painful notation, also I think the order it does things in is strange

Hoffman-Kunze is fairly different from Halmos but I think the same comments apply

[stray veldt]

if im writing a book, its free

[sage python]

Friedberg-Insel-Spence is probably the "modern pick" and prob what I'd generically recommend people but somehow it rubs me the wrong way

[stray veldt]

free as in freedom

i have to mention that i have nonstandard requirements for linear algebra though

so probably there are ok books, just not for me

[sage python]

I'd do things quite differently from most in linear algebra

I'd do some hand computations but really I'd push for computer stuff more

Interplay as much as possible the matrix and vector space stuff instead of just doing one then the other, e.g. Gram-Schmidt as QR factorization

And try to include cool topics. Coding theory, Markov chains and Perron-Frobenius, circulant matrices, Vandermonde matrices, singular value decomposition and low ran approximation, maybe even Heisenberg Uncertainty

I say it's a meme because of the determinants first bit mostly lol

[karmic thorn]

A lot of new linear algebra books are experimenting with such topics I've noticed

[dusk wind]

well I go for rule of thumb of 'within 5 years'

[karmic thorn]

I've seen a couple of books by AMS

"Linear Algebra in Action" is one I can recall

Another is "Dynamical Systems and Linear Algebra"

[dusk wind]

old enough to be tried and tested but not too old to become improved on

tbh at this point all books should now be open source so nothing ever gets regurgitated/clickbait

[sage python]

True but imagine one which covers the full theory like Jordan form, and these topics. I don't know too many of these

[dusk wind]

why not keep the cycle of fresh knowledge going? You wouldn't want to read some Algebra text from the 1900's (unless it was relevant to something you were researching)

[mystic orbit]

What're your requirements for an LA book?

Also, sup loch

Long time no see

[dusk wind]

this needs to stop lol we should only be using the 'best' or most current books, so many students give up on math due to rehashed content

like, there should not be any such book released seriously (commercially) with no answer key

[sage python]

This is questionable

It helps self-studiers but it's bad for professors' ability to assign problems

[dusk wind]

let's just outsource that too

[finite gale]

It's also a ton of work to write out answer keys like that

[sage python]

Also being modern can be nice for sure, insofar as newer books can look at the older books and say "Oh I think this is a defect in the presentation lemme fix", and sometimes we change how we think about things at super large time scales (e.g. our understanding of basic algebra evolved much since 1900)

Thing is

We don't think about group theory fundamentally differently than we did in... 1980

[dusk wind]

not anymore with AI, and they don't have to do the whole book, maybe just half

[sage python]

So in that regard I don't really buy what you're saying

[loud cradle]

and what if say 11 years ago someone wrote an absolute masterpiece on some subject, you're gonna reject it because it's "old" and read probably an inferior newer book?

[dusk wind]

if it hasn't been topped then it's an ancient goliath

[loud cradle]

an ancient troll maybe

[dusk wind]

yea authors set us up for this probably

[stray veldt]

first half probably like most, but i dont really care about doing anything in R;
i would put focus on being more general (work with algebraically closed fields instead of just C
and then do a lot of stuff in char > 0 and work with finite fields in general
then put more focus on geometric aspects and do a chapter on projective geometry

[stray veldt]

imagine not being a discussion user

[mystic orbit]

it's not my fault discussion went to shit

¯_(ツ)_/¯

[mystic orbit]

sheesh

I don't know any of the latter stuff lmao

[stray veldt]

skill issue

[mystic orbit]

chrew

I should do more LA

[timber ember]

. 🫠

[torn crypt]

What kind of logic and what kind of beginner

As in, background and what do you intend to put it towards?

[timber ember]

Beginner in the sense that i know quite literally nothing about logic

i've watched some videos about propositional logic on yt

[torn crypt]

Introduction to mathematical logic, by Elliott Mendelson, may be suitable?

@timber ember

[timber ember]

I'll read it,thx

[torn crypt]

Or, maybe mathematical logic, by Ebbinghaus, Flum, Thomas, as an alternative to compare against

from Elliott's

so it has things to help

Elliott I'm not convinced about on some notation, but some of the diagrams and such might be nice

and it has some interesting topics

[remote sparrow]

hubbard is only 600+ pages

not counting the appendices

[torn crypt]

borrowing from Ultra's reading list

[remote sparrow]

which you should skip if you're reading this as a course taken immediately after calculus. although if you're reading this as a book on analysis, those appendices are required.

[timber ember]

What about "The Logic Book" by Merrie Bergmann,James moore and Jack Nelson ?

[torn crypt]

No idea

[remote sparrow]

this book is aimed at philosophy students, not those with some math background

[timber ember]

Aight

[torn crypt]

I think so

No I'm schizo

it was Clerk

(What’s ur rec for model texts)

What would you recommend instead

I see I see

Any model theory notes to recommend in particular

[rigid barn]

Hoffman-Kunze

[rigid barn]

As an H-K enjoyer, nothing you said about Halmost applies to H-K.

Only 2 possible critiques might be levelled at it: the rational/Jordan canonical form derivation is kind of wacky and awkward and they don't cover multilinear algebra (not properly, anyway).

[sage python]

I guess I should've said typesetting instead of notation actually, that's what I meant. And it's a little bit dated somehow

[rigid barn]

I ADORE that Addison-Wesley typesetting. It's simply beautiful to me.

[sage python]

I will ban you irl

[rigid barn]

I hate the modern AMS typesetting. E.g. looking at the 2nd vs 3rd editions of Cox's x2+ny2 is literal SOVL vs soulless

[sage python]

Anyway for me the whole dated shtick/funny order amounts to the fact that it does its matrix pushing shenanigans before talking about vector spaces

[rigid barn]

IDK how to describe it, it's like there's too much empty space in the characters.

[sage python]

I guess history etc etc

[rigid barn]

That is a bit old-fashioned, sure, but it also serves as good motivation imo.

[sage python]

But... I feel like it's nicer to talk about vector spaces and linear maps coordinate-free first

Just aesthetically

[fickle whale]

I agree with dami???

[rigid barn]

And they do, all they do is in the beginning is talk a little about linear systems to motivate the entire subject.

[sage python]

Thing is the idea of linearity is imo motivated by the geometry as well, and I feel like I remember that chapter being clunky because you couldn't use vector space terminology

I had this summer "apprentice REU" where we did some linear algebra. Then my analysis class had us teach ourselves from Hoffman-Kunze and do a bunch of problems

[rigid barn]

I mean, I'm looking at that chapter and it's the length of 2-3 lectures tops, first week basically. Just introducing row reduction and invertible matrices before diving into the abstract machinery.

[sage python]

First week we were given a metric fuckton of problems from HK chapter 1 and in the moment I remember feeling like

Holy shit

I wish I could say "linear independence" right now

It was quite annoying

[rigid barn]

So you're a trauma victim and that's why you hate HK, I see.

[sage python]

I didn't say I hate it lol

I just said the order of topics is something I'd change

[rigid barn]

I picked it up subliminally, you didn't have to. I'm good with people like that.

7th sense, you know

(my 6th does something else)

[sage python]

For a long time that was the book I'd suggest to people lol

[rigid barn]

I'm joking bro, you don't have to justify yourself

[sage python]

Mostly because I knew that and Axler, and Axler's book becomes a pile of shit once it hits characteristic polynomials 😛

[rigid barn]

I can't believe I used to like it.

When I read HK it was one of those "I was blind, but now I see" moments.

[sage python]

But yeah everything after the first chapter was mostly fine? I think the treatment of determinants was cute in the moment but in hindsight I think a systematic treatment of multilinear algebra would've been good

[rigid barn]

Their determinant chapter is just :chef's kiss:

[sage python]

Chapter 3 second half was a bit tricky I guess, I remember finding double duals tricky in the moment

And then we went to our analysis prof asking about it in office hours and he started talking about weak convergence

We leave and we're just like... still not sure what this double dual stuff is all about tbh

[rigid barn]

That's what happens when you ask an analyst a linalg question lol

[sage python]

Yeah lol he did not want to teach linear algebra

Hence why he just made us learn it by ourselves

Also as I recall HK doesn't do quotient spaces

I remember second quarter of analysis, one of our pset problems was to prove that commuting matrices are simultaneously triangularizable over C, in particular prove the base case

[rigid barn]

Yes, but you don't really need them in the first year.

[sage python]

And we were thinking alright I guess we have to copy HK's conductor stuff down?

A few of us go to office hours and our prof is like, just use quotient spaces!

[rigid barn]

Did they really do it with conductors? I checked, the conductor stuff was for diagonalisability (which admittedly is a bit weird, yeah), but for commutation it's just a basic argument.

[sage python]

Then on the midterm one problem was to show that 3x3 matrices are triangularizable

And when we get it back our prof said "The people in office hours should've told the rest of you about quotient spaces, but you can do this very hands on. And don't come to me talking about conductors, this is linear algebra not Amtrak."

[rigid barn]

All 3x3 matrices over any field? Doesn't make sense.

[sage python]

Over C

[rigid barn]

Ah.

Since I got you here, I've got a suggestion on your algebra list.

You should take a look at Isaacs and add it to the list, if you like it.

It's a fantastic book

[sage python]

Ah you saw my lists lmfao

[rigid barn]

They're quoted here constantly so I peeked. Narasimhan was an interesting suggestion, I'm looking into it.

[sage python]

Updated the algebra one a bit, indicating that Isaacs and Rotman are frequently brought up

And mentioning my omittance of stuff like Gallian

[rigid barn]

Gallian and Fraleigh are trash, I hate these bloated American McGraw-style textbooks, make me think of Stewart's Calculus.

Alright, fellas, I need you to bring out your big guns: I'm looking to dip my toe in algebraic geometry, any suggestions? I've got a good amount of the kind of commutative algebra involved (localisations, integrality, DDs, valuations, general field stuff, etc.).

I was thinking of going through Fulton's curves book for the basics since it's so short, then seeing where that takes me.

[sage python]

Fulton's alright, but I think if you're mature enough you can get to sheaves and whatnot a bit sooner

Gathmann's got some notes. If you want something a bit longer and probably harder try Kempf

[rigid barn]

I don't see the fun in that, it's just machinery afaik.

I want some actual results tbh.

[sage python]

Bad take. The full power comes in when you see cohomology

[rigid barn]

Well idk anything, just my initial impression.

[sage python]

But also it's how you think of varieties in a similar light to smooth manifolds rather than just doing things in a makeshift manner with affine/projective varieties

@steel viper used Kempf and can talk about it a bit

[rigid barn]

Yeah, but a priori idk affine/projective varieties, doesn't it make sense to learn them first?

[sage python]

I didn't say don't learn them first, I said makeshift

The better way to think about things imo is that you start with affine varieties

And then understand how to patch them together ("locally ringed spaces", play the role of charts in diffgeo), and think about "regular functions" correctly

And have projective varieties as your big examples of varieties patched by charts, and you study them in good detail

[steel viper]

i mean if it was "just" machinery then no one would use them, no?

It exists for a purpose

i liked kempf and think it is good but it is not the best at getting you good at like

getting your hands dirty with explicitly examples

[rigid barn]

Ofc, what I mean is such texts (the way I understand it) spend a LONG ass time building up the sheaf machinery to kill things stone dead.

E.g. Vakil's 800 page notes.

[steel viper]

kempf is like 150 pages

That is not an appropriate image to send here

[rigid barn]

People meme in pretty much all the channels.

[rigid barn]

I'll look into it.

[steel viper]

[lapis sundial]

There is something different about that meme which I know you are aware of

[quick hornet]

the problem is the racial slur.

[rigid barn]

OK, so what are some good ones besides Kempf? I was looking into Kunz.

[mystic orbit]

new pfp

[abstract hollow]

I'm looking for a well simplified book about analysis for my first year in college, is there any recommendations?

[fickle whale]

Yeah I'm looking fantastic

[mystic orbit]

abbott

[abstract hollow]

Thanks seems helpful

[abstract hollow]

Thanks 🤗

[manic brook]

could anyone lmk the neccesary pre-reqs for self-studying Symmetric functions and hall polynomials by I.G. McDonald?

[safe barn]

I want to study the properties of hyper operators are there any books that could help me do so?

[deep summit]

Where can i find book which has all purr geometry proofs

Pure synthetic

Like Cevas theorem and concyclic properties etc

[mystic orbit]

I wield a few, yes

Tho not as much as others

[pallid crater]

@sly beacon

[grand thistle]

egmo

evan chen

[restive falcon]

egg mo

[fallow timber]

?

@ me if you answer

[subtle mango]

idk what analysis 1 entails, but you kinda need sequences and series and whatnot

in this channel, theres a pinned recommendation list by dami

[coral prawn]

Henry read Abbot's understanding Analysis. Maybe a content page would make it better for ya'll

[rigid barn]

Take a look at Schilling's "Measures, Integrals, and Martingales", all you really need to know is the Riemann integral and its shortcomings.

[mystic orbit]

royden is very good

folland is fantastic if you could get through all the technical overhead

which could be a slog

it also get's progressively harder to read as the more and more details of the proofs are left to the reader

I also like stein and shakarchi a lot

but I wouldn't recommend it if you want the measure theory for other things like probability or ergodic theory

coz it only does the measure theory on the real line and leaves the abstract theory till way later

royden does that too

bad

it's a good reference

I wouldn't recc it to anyone for self-study

folland is also a good reference but it's a lot better than rudin for self-study

[mystic orbit]

note: if you go with folland once you reach section 3.4 you should do chapter 3 of SS instead

it's the only part I've read off of SS and I like it a lot

btw analysis 1 is all you need for measure theory so you should be good

[fallow timber]

thanks for the recs, i might check out folland as it seems thorough

whats the "technical overhead"?

[mystic orbit]

it constructs the lebesgue measure with utmost generality

[fallow timber]

sounds fun

[mystic orbit]

it's not

I don't know if it's with utmost generality tbh

but it is pretty general

it doesn't even construct the lebesgue measure

it constructs the lebesgue stieljie measure

[fallow timber]

me when folland defines how to integrate a set with no additional structure

[mystic orbit]

of which the lebesgue measure is a special case

anywho, if you can survive through 1.5 you'll be gud

[heady ember]

Have you looked at dami's recs

[fallow timber]

i already got a few from darq but ill check those out too

[heady ember]

[fallow timber]

seems to imply folland is good as well

[vast cave]

Measure integration real analysis by Sheldon axler

It's available for free on Axler's website

[tired smelt]

Hi, I am looking for a book in functional analysis. Does anybody know some kind of book that is similar to Sidney A. Morris Topology Without Tears? It is pretty easy to follow so I hope that there might exist same book on functional analysis.

Though I think I might need book with more exercises. Because my book just got only few and others don't even have any

[gentle arrow]

axler also puts a cat in his measure theory book

on page 44

its name is moon

[tight geyser]

Hi! I'm self studying Real Analysis using Understanding Analysis by Abbott. Everything was going fine until I got to subsequences and Bolzano-Weierstrass Theorem. Should I put more effort into it or use the book by Ross instead? It seems to be much easier.

[fallow cypress]

folland <3

it's so nice and clean

[fallow cypress]

Easier isn't necessarily better, struggle is normal while studying mathematics

It's ultimately up to you, but it's worth pinpointing exactly what you're struggling with and asking questions about it

Feel free to ask analysis related questions in #real-complex-analysis

[fallow timber]

personally i really enjoyed abbott, but i do agree it gets a bit tough at that point and could benefit from some more examples. imo just stick with it, its a great book

[river forge]

Hello! Does anybody know an interesting book that explains the use of advanced maths in "real" life? So like, how it was even discovered and for what?

[stray veldt]

i dont think most "advanced math" was discovered in the context of real life

not in the way you are asking

usage depends a lot on the specific math, though hmm

simon singh wrote some books on codes

there are a few books on the history of analysis, which was in part developed for use in physics

amir alexander wrote a book "infinitesimal", david bressoud "calculus reordered"; though neither go really into use, its more historical/philosophical