book-recommendations

[torn crypt]

I didn’t get a notification, but I don’t know philosophy (or like it)

[sudden kindle]

Any thoughts on Nicholson Open LAWA

[novel hound]

So, an update regarding Springer. There are some books (softcover) on Springer which are available for discounted price 15.88 EUR. However, the discount would get revoked at the payment step. I placed an order by "advance invoice" method (I was basically trying all payment methods) and emailed customer support that the price was not reflecting the discount and they generated a new discounted invoice for me, for which I then made payment. Just putting this out there in case folks want to claim the discount. Their customer support doesn't reply on weekends though.

I've also asked them how to claim the discount for subsequent orders, waiting on a reply.

[remote sparrow]

what book is this from

[sudden kindle]

Nicholson Open LAWA

[sage python]

So many linear algebra books fr

[quartz agate]

i need a calculus book for the basics

[violet shuttle]

hey i've been recommended that!

[heady ember]

Real men publish open source

[glossy zealot]

Or sell a book for 900 dollars on amazon

[heady ember]

[glossy zealot]

https://www.amazon.com/gp/aw/d/0201002841/ref=dp_ob_neva_mobile

Maybe you get a different price

I got 987 bucks

[oak stag]

cheers

[native cradle]

do people actually pay this much for textbooks?

[delicate valve]

hi

[tribal crow]

pretty much never

[oak stag]

u can always find them cheaper online and/or use them for free depending on the institution u are at

also for these textbooks id always recommend getting second hand

[glossy zealot]

Or they force you to rent/buy a new copy/digital version

Some schools can be nasty

They are like “I will only put problem number and the page number on the homework handout”

Or like “you are automatically charged for this digital version of the textbook that comes with yadayadada” something that is interactive

[raw bay]

i need a rundown on topics/subjects for prereqs on real analysis and stochastic processes actual book recommendations for real analysis and stochastic??

[remote sparrow]

#book-recommendations message

regarding stochastic processes, a non-measure theoretic treatment can be found in grimmett and stirzaker. a measure theoretic treatment can be found in le gall's Measure Theory, Probability, and Stochastic Processes. i recommend having done measure theory first. a good source is axler's Measure, Integration, and Real Analysis. while le gall is self-contained, someone suggested reading billingsley or durrett (two commonly assigned texts for measure-theoretic probability) before reading le gall.

[gray gazelle]

i want a deep history bout maths
its symbols..why they b like dat..
why and how did they think of concepts, like through observations of what..
the general hisyory of how a simple thing (like a) became so complex to smt else like (a-57+*4/54() yk..

i became too specific on the last point but..i hope u get the big picture ..

[remote sparrow]

#book-recommendations message

#book-recommendations message

[raw bay]

so i should do measure theory before trying both real analysis and stochastic processes?

[remote sparrow]

real analysis is a requirement for measure theory

[fresh skiff]

Only requirement? (Beside basic set theory)

[raw bay]

and is there any specific topics or whole subjects needed to understand real analysis, my lecturer just gave me a textbook and said try this :()

is calculus just needed?

[remote sparrow]

for some books on measure theory, yeah. you might need some knowledge of metric spaces (which is covered in several real analysis textbooks, but not all)

[remote sparrow]

yes

[raw bay]

ty

[remote sparrow]

optionally, you may choose to read a book on how to prove things

[raw bay]

any book would do, or u got recommendation?

[remote sparrow]

#book-recommendations message

[fresh skiff]

Ooh. I am using Abbott, but plan is to pick Axler measure theory or stein after Abbott.

[remote sparrow]

alex?

[fresh skiff]

Axler, sorry.

[remote sparrow]

👍

and by stain you mean stein?

[fresh skiff]

Oh yes.
Sorry my spelling is weak.

Will Abbott covers all prerequisites for these both books?

[remote sparrow]

idk about stein, but the first five chapters of axler doesn't require any knowledge of metric spaces

there is a brief section intended to review metric spaces in axler

[sudden kindle]

Axler is goated

[remote sparrow]

I would recommend the following books for coverage of metric spaces:

Real Analysis by Carothers
Introduction to Topology by Gamelin
Metric Spaces by Magnus
Metric Spaces by O'Searcoid
Principles of Mathematical Analysis by Rudin

[sudden kindle]

BUt I could improve some sections

[remote sparrow]

which book

[sudden kindle]

Axler

Ladr

[remote sparrow]

what would you improve

[fresh skiff]

Oh, is there prerequisites for these books too?

[remote sparrow]

basic real analysis

[fresh skiff]

From basic you mean first course in analysis?

[remote sparrow]

well rudin is itself an introductory real analysis textbook for honors students too

[fresh skiff]

Like Abbott

[remote sparrow]

maybe i should say analysis on the real line

[remote sparrow]

@sudden kindle

[fresh skiff]

Heard a lot about baby Rudin

[sudden kindle]

I feel like the spectral theorem applications were lacking

For such an important theorem on linear algebra its not clear why we care from Axler's book

I feel like a lot of books start off really strong in the begining, in terms of quality, and then drop off near the end

Maybe its writer's fatigue

[grand relic]

or reader's one

[dense loom]

Baby Rudin is 90% real analysis, but it has also a chapter on multivariables functions (just to give you a taste of papa Rudin)

[glossy zealot]

I found this super duper comprehensive and advanced “Basic” real analysis book today (with metric spaces)

https://link.springer.com/book/10.1007/978-1-4939-1841-6

It is Basic Real Analysis by Houshang H.Sohrab

If you wanna get super serious and hardcore, try this hell mode

[fresh skiff]

Is it really that much horrible ?

[manic sinew]

Does anyone have any recommendations for an analysis book after Abbott's Understanding Analysis?

[remote sparrow]

#book-recommendations message

skip gamelin

[earnest wolf]

btw how is his book on CA?

complex analysis that is

[remote sparrow]

great! there's lots of helpful motivation

[glossy zealot]

It has too many things in it

[fresh skiff]

Oh, haven't took a look of the book. Lemme do it (curiousity)

[honest scroll]

Hello. I am looking for a book about valuation theory and p adic analysis. Prefrebly if it talks about complete fields , hensel's lemma and henselization. Any recommendation ?

[hallow oriole]

it's my fav series of all time i love everything about it i cannot recommend it enough

book 1 is mid but book 2 past is really good

book 6 has some pacing issues but is still amazing

book 5 and book 7 are in my opinion some of the best of all time

[violet shuttle]

...there's more than one book?

[hallow oriole]

total wordcount is a bit over 3000000 words

length is seven books + extra chapters (lore)

https://practicalguidetoevil.wordpress.com/

read it right now!!

[violet shuttle]

oh "book"

it's webfic, that length is like slightly longer than one webfic book

[hallow oriole]

ohhhh fair fair

read it anyways

[violet shuttle]

it's honestly been a while since i've read longform fiction

[dim sierra]

fr the magic tree house hits different

[glad rampart]

What’s it about

I’m a sucker for longform web based fiction

[hallow oriole]

i suck at writing big-ass recommendations so here's a copy paste of one from reddit with spoilers edited out and some things i especially like added in:

What's it about?

APGTE is the story of Catherine Foundling, who decides to join up the Evil™ empire currently occupying her homeland, because she believes real change can be wrought from within the system, not tearing it down. Because dying in a doomed rebellion might be heroic but accomplishes little except death. And even if you succeed, you just replaced shitty evil kings with shitty incompetent aristocracy. Things.. escalate from there.

So, why should you give it a shot?

The biggest draw for me is the genre-savviness. This is a world that basically runs on tropes. The usual things like the cornered hero finding strength at the last moment, the all powerful villain just doing something stupid causing their downfall, the hero randomly stumbling into just the ancient artifact that they need to win the plot. The sort of things we've all run across reading fantasy, the tropes we've learned to know and love and hate. Well, in this story, the protagonist (and a few others) have learned to try to game this system, to stack the narrative odds in their favor. This makes for a very different feel to the story, almost a meta-ness.

The competence porn. The practicality. The practical in the name isn't just for show, it is what drives Catherine's actions a lot of the time. Wars are not won by speeches and bravado, but by solid planning and logistics. Killing one set of bad rulers to replace them with another won't fundamentally improve the lot of the everyday folk. It results in a protaognist that is focused on getting shit done, and boy does she get a lot of shit done

Character development. Over the course of the story, Catherine, the protagonist, goes from your typical brash teenager who think any problem can be solved by being good enough at killing stuff, to a veteran who realises that to do the sort of wide ranging and long lasting changes to the world she wants, military might is just not enough. You have to work with people not just scare them into obediance (though sometimes you do have to do a bit of the latter too). Catherine's companions also undergo their own journeys, and thanks to the massive length, the author is able to do it all very gradually and naturally, so there's rarely big turning points, but by the end the Catherine we end up with is barely recognisable from the one at the start. The evolution of her and other characters and the relationships between them was super satisfying to read.

[glad rampart]

Sounds fun

[hallow oriole]

it also has a lot of like

intricate political discourse of the nation-states inside the story

and tons of pretty songs and poems and whatnot

it's so good

[glad rampart]

I’ll check it out

[rigid forge]

Now I am going to ruin my nights by reading because I am too curious how the author handles building the world in this three million word guide, thanks.

[hallow oriole]

yessssssss

[glad rampart]

Wtc exposed my love for meta narrative shenanigans to myself

[violet shuttle]

there's a acx book review

i mean it's in the book review contest

they haven't chosen winners yet

https://www.astralcodexten.com/p/choose-book-review-finalists-2024

I like The Game at Carousel

[remote sparrow]

you should play The Last Sovereign @hallow oriole

be warned, the game is NSFW

[hallow oriole]

great review, i like that they compared it to unsong! unsong is my second fav book, it's so good

[hallow oriole]

it's good but i dropped it a few months ago bc it was a bit boring i'll pick it back up when it's completed, probably

but yeah practical guide to evil is top tier and nothing compares

i love the protagonists, antagonists, foils, villains, politics, wars, fights, lore, everything

the little blurbs at the top are also often hilarious

i think the correct word is epigraph

[remote sparrow]

yes

[violet shuttle]

i have been recommended unsong too

[dusk panther]

Where do I get an online good copy of spivak's calculus (4th ed) that isn't just a bunch of poorly shot images or through some optical reader?

[gusty orbit]

Has anyone here heard of the book of Mortari (logic)? Do you know if it's good for beginners?

[gentle arrow]

any cookbook ODE textbook recs?

nvm i forgot math lamar exists

[strange owl]

Just wondering does AoPs' Precalculus book teach all of this for those of you who know?

[tribal crow]

teach all of what?

[strange owl]

It won't let me send a picture

[tribal crow]

er, do you want to write the list out then?

[strange owl]

sure

[tribal crow]

I don't have much familiarity with the AoPS books unfortunately, @glad rampart might be a better person to ask

[strange owl]

Algebra & Geometry Review
2 Functions Review
3 Introduction to Trigonometry
4 Graphs of Trig Functions
5 Inverse Trig Functions
6 Angle Addition Formulas
7 Double & Half Angle Formulas
8 Trigonometric Equations
9 Parametric Equations
10 Polar Coordinates
11 Polar Graphing
13 Laws of Sines and Cosines
14 Complex Numbers
15 Polar Form of Complex Numbers
16 Exponential Form of Complex Numbers
17 Roots of Unity
18 Complex Number Geometry I19 Complex Number Geometry II
20 Vectors in 2D
21 More Vectors in 2D
22 Projections in 2D
23 Vector Geometry
25 Matrices in 2D
26 Matrices as Transformations in 2D
27 Inverse Matrices in 2D
28 Determinants in 2D
29 3D Coordinates
30 Vectors in 3D
31 Cross Product
32 Planes in 3D
33 Projections in 3D
34 Matrices in 3D
35 Determinants in 3D

dont mind the numbers

[strange owl]

Oh ok thank you

[grand fossil]

Hi guys

does any of you learn Maths for machine learning?

[glad rampart]

I think it mostly teaches the first half of that list

[strange owl]

Thank you

so no polar coordinates and polar graphing?

[glad rampart]

It has a table of contents you can look at

https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/precalculus/toc.pdf

[strange owl]

Thank you very much

[glad rampart]

Np

[tender river]

looks fine, lots of practice problems each chapter. will make for a great revision

how did you even come across this

[narrow relic]

The book I learned analysis from, Methods of Real Analysis by Goldberg, I found from a few recommendations on stackexchange. There are some really random books out there.

[glossy zealot]

I came across a syllabus by chance

This book was under the additional material section

It looks new to me so I made a quick search

Found out it is loaded with content and problems

[fresh skiff]

How is the book "From calculus to analysis"?

I took an overview. The author has started from decimal representation of numbers.

[dusk panther]

is no one familiar with a online book store that sells spivak's ecopy?

[lime vessel]

Google books has it

[dusk panther]

says "no ebook available"

[lime vessel]

Oh

[dusk panther]

nvm, the preview seems to work fine

i dunno where i can buy this though

[remote crescent]

Does anyone have any recommendations for start up in the math, basic books until advanced math

[cobalt badger]

Hey, I'm looking for mathematical logic textbook recommendations (something that talks about the peano axioms specifically, among other topics)

[gray gazelle]

what are good books for calc and la?

@prime dune

[prime dune]

My experience with Calc and La textbooks are in the more theoretical sense than the calculation/application sense

Like how “calculus” differs from “analysis”

So it depends

[gray gazelle]

yeah

idrc about computation

[prime dune]

Like I am going from Jacobson Basic Algebra and Abbot real analysis right now

[gray gazelle]

im generally pretty good at computation after like 5 questions

[prime dune]

Which are more theoretical and the former covers a lot of LA concepts just because they are rather vital to later Abstract Alg

[gray gazelle]

yeah uh

[prime dune]

If you want some analysis, Abbott is a causal read and I recommend it

[gray gazelle]

ok

[prime dune]

For algebra definitely Dummit & Foote or Artin

[gray gazelle]

but whats like a comprehensive textbook for like limits to diffeqs

[prime dune]

Jacobson is good concept wise but the exercises require some deep mathematical maturity

[gray gazelle]

gotta actually learn it

[prime dune]

Unsure, limits are like the actual crux of analysis

[gray gazelle]

ik

[prime dune]

Idk a reference for DE’s tbh

@gray gazelle I would start with Abbott to gain some mathematical thinking

[gray gazelle]

ok

[tender river]

we went from calculus to jacobson real quick

[maiden glen]

looking for good universal algebra books

[remote sparrow]

Calculus was independently published by Publish or Perish press, the author's publishing company. it is now owned by the Hindustan Book Agency. afaik, there are no official ebooks. however, i have seen some very high quality scans. keep going through them. consider downloading a djvu file instead of a pdf.

[remote sparrow]

#book-recommendations message

[cobalt badger]

thanks!

[maiden glen]

^

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-319-11478-1

https://bookstore.ams.org/view?ProductCode=CHEL/383.H

https://bookstore.ams.org/view?ProductCode=SURV/268

https://bookstore.ams.org/view?ProductCode=SURV/269

i heard these were good

[naive veldt]

burris samkapanavar. as far as i know it is freely available on the internet

[naive veldt]

second it, great book

[hearty steppe]

Anyone heard of this? https://archive.org/details/JohnDeweyLogicTheTheoryOfInquiry/mode/1up

[crimson leaf]

Also available on his site https://math.berkeley.edu/~gbergman/245/

[maiden glen]

I can always count on you can't I

[maiden glen]

Thank you

[naive veldt]

a little off topic, but recently I read in the Stanford Encyclopedia that the name for the notion of categoricity in model theory was suggested by dewey, which is quite surprising

[rigid forge]

Are there any good books on discussing how programming languages are built? (different type systems and their proofs, design choices, optimizations etc)

I am not really looking to build a language myself, but rather understand the inner workings.

[vital bane]

Formal languages would be a good starting point I think

I'm not very familiar with it, but I think programming language theory is built on formal languages and formal grammar

[maiden halo]

I don't know, but you might check this thread and/or subreddit: https://www.reddit.com/r/ProgrammingLanguages/comments/28uq4r/programming_language_design_theory_book/

[vital bane]

I was recommended the cinderalla book for the former "Introduction to Automata Theory, Languages, and Computation"

[rigid forge]

thanks

[digital geyser]

hey guys, im an irish med student who is kinda interested into getting into maths and basic physics again. Its been 3 years since ive done anything remotely related to either but when i did do them i got what is comparable to a 5 in AP stats, calculus and physics 1,2 and C however it took my heart and soul to get those grades back then. Is there somewhere you would recommend to pick as a point to get back into studying these as a kinda hobby or any tips etc.

[remote sparrow]

you should probably not bother relearning from the same kinds of class materials for AP stats, which is algebra-based

it will be more instructive to pick up books on probability and statistics which use calculus

same deal for physics 1 and 2, which are also algebra-based

as for calculus and physics C, your old textbooks should serve you fine if you still have them

[digital geyser]

so is calc like the bread and butter of "proper" maths, like should i jump in starting with that, ive probs forgotten a shocking amount and dont have any old notes or any reference material

[vague dagger]

what do you mean by "proper" maths

like math major level courses? analysis, algebra?

[violet shuttle]

Kallenberg ftw

[digital geyser]

idk, i have 0 exposure to maths outside of school classes and dont even know where to start so just looking for yard stick

[remote sparrow]

they just want to relearn some old material as a hobby

[digital geyser]

well hes saying to not bother with algebra based and go to calc so im assuming theres something behind that reason

[remote sparrow]

calculus is simply very useful for scientific applications. you will also be able to derive some theorems in probability and statistics. arguably, however, some calculus courses aren't "real math" since generally you aren't reading or writing proofs in those classes.

[digital geyser]

im not so much looking to become some maths wizz but just to kinda truck along for fun as i miss the challenge and satisfaction of the grind paying off. I am developing an interest in space etc and the thought of understanding some of the cool physics there would be nice but thats quite a while away lol

[slender cargo]

What are you interested in? At a higher level math has been described as a "great tapestry" by one professor. Meaning, there is a lot of foundational material that one can learn to understand math more deeply. Calculus is just a step into that world (an important step though).

[digital geyser]

i suppose astrophysics but like thats a real uninformed desire hahaah

[slender cargo]

Oh, physics. If you want to learn some physics in your spare time, then maybe check out Roger Penrose's Road to Reality. It's this 1000-page book that, if you read through it entirely, will get you to the frontiers of modern physics in a mathematically rigorous fashion (supposedly, I have not read it myself).

[violet shuttle]

no terrible

i hear that's a popsci book

[slender cargo]

He tries to teach you all the math along the way. I have my doubts that you can learn all the math from that one book, but it can serve as a blueprint.

And when things get confusing, you can pick up a book to learn the material more deeply.

[violet shuttle]

why not recommend some math and then likee goldstein + shankar + griffiths electromagnetism + jacksons electromagnetism + etc

[violet shuttle]

maybe i have heard incorrectly about that book

[slender cargo]

This person is a med student who just wants to learn this stuff on the side for fun.

[violet shuttle]

so?

[slender cargo]

And the book I suggested was recommended by John Baez.

[slender cargo]

Suggesting a whole physics curriculum, which includes multiple books, while being a med student, does not sound like a fun suggestion to me for someone who wants to dip their toes in physics/math in their spare time. They don't even know where to start yet.

[violet shuttle]

oh okay

[slender cargo]

That's just me though.

[violet shuttle]

i always found books like that inviting but i get that i am weird

[remote sparrow]

There is no royal road to science, and only those who do not dread the fatiguing climb of its steep paths have a chance of gaining its luminous summits.

• Karl Marx

[slender cargo]

I find them inviting too (which is why I'm now studying this stuff full time)

[remote sparrow]

if you want to whet your appetite by all means read a pop physics book

[violet shuttle]

whenever i want to learn about another subject i grab a textbook in it

like, say, organic chemistry

[remote sparrow]

but to really learn something you need to sit down with a textbook

[slender cargo]

I don't think Roger Penrose's book is a pop sci book. It's detailed with actual physics and math

It's just not a good classroom book

Here's a whole list of math and physics books if you want:
https://math.ucr.edu/home/baez/books.html

The book I suggested is mentioned here as a good road map

[digital geyser]

i suppose ill give the penrose book a go and use other websites videos etc to help

thank you v much

[slender cargo]

I should have actually just linked that website to you first. I think it's a great resource.

Some of the books on there are a bit dated, so if you are interested in a more particular subject in math/physics then maybe ask here again

[digital geyser]

will do thanks a mill

[cobalt badger]

This has been my philosophy recently

Just picking up a textbook in any subject I'm even remotely interested in learning about even if I don't necessarily plan to pursue it as a major/career

[junior isle]

Cool quote

[gleaming void]

do you guys have any recommendations for books I should read before attempting baby rudin?

[dim sierra]

if it’s your first time doing analysis you should read abbott

[narrow relic]

A professor I respected a lot liked the book, but he had already learned all that math before he read it.

[slender cargo]

Yeah, if you're going through a standard curriculum for math then I think you learn all the math in that book

He wrote that book to reach layman audiences and teach them the needed math and physics, which... is ambitious, to say the least.

[narrow relic]

Right. It just annoyed me when I looked at it.

[bright basin]

Hello , Could anyone recommend any sources or books related to the equation of a circle that include difficult problems?

[covert mauve]

What's usually the recommended textbook around here for someone starting out with physics? (assuming you have no prior or very little experience)

[remote sparrow]

like calculus books, they are all very similar

just pick up an old edition of any one of them and you should be good to go

[covert mauve]

well, i am not very familiar with any of the authors

i dont know which one i should read

cant pick when i dont know any of the choices

[remote sparrow]

https://www.amazon.com/University-Physics-Modern-15th/dp/0135159555

here is one choice

[deep moat]

Any introductory books for national math olympiads or any competitions?

Been reading aops interm. algebra lately. Along with its volume I and II problem solving books

[vast jackal]

why tf kids now want to do oly

[deep moat]

I do it for the fun and the pain

unlike some people who just joins and get bragging rights

[remote sparrow]

young people like being on discord, people that are interested in math are more likely to want to join a math discord, so kids that are interested in doing math olympiads are overrepresented

[deep moat]

my point being

I only joined the server to ask for books and learn more

and be able to solve oly problems

[terse garnet]

Hi

can i do calc if i only know soh cah toa

trig

[remote sparrow]

hopefully you also know algebra

all you need is algebra and trig to do calculus

[terse garnet]

Yes I know algebra very well

Just dont know trig

alot

[swift mountain]

U need to know trig identies and angles

Easiest way to find trig values is through 30 60 90 triangle

[gray gazelle]

Back in my days we used taylor series….

[slate quarry]

Hi, I have list of topics for which I would like to find an undergrad level textbook: Truth tables, Tautologies, Propositional calculus, First-order logic, Axiom of choice, Compactness theorem, Zorn's lemma, Schröder–Bernstein theorem. So if anyone knows what textbook (or what kind of textbook) I should check out, please let me know. Thanks in advance.

[remote sparrow]

#book-recommendations message

#book-recommendations message

[broken comet]

NSM HSC Extension 1 and 2 is very good for high school students

Very much recommend

https://www.pearson.com/en-au/schools/secondary/mathematics/new-senior-mathematics/

[quartz agate]

i want a book about calculus introduction and stuff

[marsh ingot]

Apostol, Spivak

[knotty egret]

Does anyone have a list of exercises one ought to do from Commutative Algebra by Atiyah and Macdonald

[steel cloud]

To cover module theory from Aluffi, do I need to cover the first category section ?

[slate quarry]

Thank you very much ❤️ . I'll check those out.

[cold musk]

Does anyone know any books for linear algebra?

I'm looking for a book that is rigorous in its proofs and is detailed in its explanations

Please ping if you have a good choice : )

[remote sparrow]

which aluffi

oh i guess not Algebra: Notes from the Underground since you mentioned the category section

[idle widget]

An interesting maths book!

[narrow relic]

Ziemer's Modern Real Analysis: 2nd edition has some of those topics, it's written really well.

[narrow relic]

What is your linear algebra background?
There are books that a lot of people here will recommend, you can search for linear algebra.

[trail hemlock]

currenly doing jech's set theory book, and im 2 chapters in. these practice problems are way to easy 💀 . should i switch to big jech for more coverage, or is it better to do it in order?

i looked ahead, the practive problems dont improve 😭 😔

[twin heron]

hi :) does anyone know any book for optimization / operations research? The one I'm supposed to read is Taha but I cannot comprehend it 😫 if u know another one, please please tell me, thanks :))

[remote sparrow]

you can't do part II of jech's Set Theory without prior knowledge of logic

[trail hemlock]

😔

part 1 doesnt do any logic tho

[gray gazelle]

Does anyone know a book that focuses on word problems and how to solve them step-by-step for beginners? I often get confused doing word problem and I would really aprecciate it if someone recommends me a good book to improve this aspect!!

[violet shuttle]

...an entire book?

[narrow relic]

I have not worked through this in-depth so take my "recommendation" with a huge grain of salt.
Foundations of Optimization by Osman Guler has all of the major topics from my limited knowledge, but it's written in a very general style which I like.

[twin heron]

thank you !!

[narrow relic]

You're welcome. There's a more slightly "out-there" book, but I don't know enough about optimization to tell you if it's good or not (it's called Classical And Modern Optimization by Guillaume Carlier).

[twin heron]

i'll look them both, thanks again :)

[narrow relic]

You're welcome, and please come back and let me know what you think.

[fresh skiff]

I was checking Lang's analysis book. His introduces topics quickly

[tribal crow]

average Lang book:

[fierce hedge]

I was working through the algebra book by Silverman, it's a good book but the problems are not that good quality. I know I can try DnF but do I have any other option - basically looking for a book with fewer but good quality problems. A problem solving approach book will also be good. There's few such books for analysis but I couldn't find any such books for algebra. Lemme know if anyone has any recommendations.

I guess there's also University problem sets if nothing else works.

[remote sparrow]

https://www.amazon.com/Basic-Abstract-Algebra-Undergraduates-Mathematics/dp/0486453561

you can also look at UCLA qual problems

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

https://ww3.math.ucla.edu/past-qualifying-exams/

https://www.johnabeachy.com/

you can look at the study guide for beachy and blair's Abstract Algebra

[fierce hedge]

Oh I forgot about this book. Yeah this should work. Thanks

[remote sparrow]

Algebra: Notes from the Underground has solutions to some exercises in the back

you worked through knapp but didn't like it, but for any others curious about it, most of the problems have long hints or solution outlines

[fierce hedge]

It's not that I didn't like it, more like the group didn't like it. Plus Knapp is a bit too efficient maybe even so for someone who is not a first time reader.

I also wish it had problems inbetween the topics like Rotman does rather than everything at the end. You know what, I'll try some questions and let you know if they're good @remote sparrow

[fresh skiff]

Any recommendation for reference books for Axler measure theory?

[sturdy shore]

folland - analysis I guess

tho the way axler covers some topics is unique, like defining integrals using lower lebesgue sums

never seen that anywhere else

[fresh skiff]

Ooh. Ig folland is famous one. I also heard about Cohn, and L.schilling

How are these two?

[daring lake]

Schilling also does martingales, I read couple chapters of it and thought it was pretty decent

[fresh skiff]

Also the prerequisites are only one semester real analysis or any other subject too?

[sage python]

Wait this feels homotopic to the usual definition

Where you say oh take the sup of sum a_i mu(A_i)

Over simple functions sum a_i chi_{A_i} ≤ f

[daring lake]

Yeah, should be enough for Schilling

[glossy zealot]

For axler you can find the supplemental materials for his book on his websites

I only read chapter 2 of axler. You should be fine if you have studied sequences of functions + having some topology in your first course

[fresh skiff]

Oh I see. I know some topology on real line and general space too; (but Not proof base)

Actually got a chance to buy book. I have Axler, so thinking to buy some reference book. So tha after real analysis I pick these books. That's why asking for reference.

[heady ember]

[heady ember]

People normally read Kunen's set theory text before big Jech, due to the difficulty, so I doubt that's a good idea.

[trail hemlock]

gotcha

[trail hemlock]

the hints are basically the answers 💔💔

[heady ember]

... just don't look at them?

[trail hemlock]

they r written right next to the problem (hint: blah blah blah)

but like idk

[heady ember]

Use a piece of paper to cover them up

I do that with all of FIS' hints

Or, if you're working digitally, scribble a box on top.

[trail hemlock]

i just jot down the problem

and try my best not to look

[heady ember]

This was what I did for Rudin's exercises

and proofs

[trail hemlock]

yeah i copied then onto a paper before i looked at em

more tactile better for learning i guess

[sturdy shore]

it is
you won't care if you already know the subject, but the differences can confuse a beginner

[hearty steppe]

How does Terry Tao’s books compare to his blog? I am enjoying going through these blog posts so far

I am aware his analysis books are somewhat popular but I’m digging the exposition in the blog… I’m not sure if he spent time to present it to a broader audience as opposed to his books

https://terrytao.wordpress.com/2009/01/01/245b-notes-0-a-quick-review-of-measure-and-integration-theory/

https://terrytao.wordpress.com/2010/01/01/254a-notes-0-a-review-of-probability-theory/

[remote sparrow]

#book-recommendations message

[orchid canyon]

Book Recomendations related to math, or just books

[covert mauve]

who is calculus on manifolds intended for? is it a multivariable successor to his normal calculus book?

[gray gazelle]

people who have a solid linear algebra and basic calculus/analysis backing who want to learn the multivariable calculus they need to get to manifolds quickly

sorry higher

:3

[tribal crow]

ahaha

I was about to copy paste and credit you

[covert mauve]

so not exactly the direct successor, then. thanks!

[gray gazelle]

you need some linear algebra to be able to go from his calculus book to his calculus on manifolds book

though you could go directly from his calculus on manifolds book to his 5 volume series on differential geometry

[tribal crow]

I wonder if anybody has actually read that series front to back

[covert mauve]

what linear algebra book is usually recommended as an introduction?

[gray gazelle]

the book by friedberg and the other two guys is good

[tribal crow]

FIS

[gray gazelle]

axler's book is al;so good

axler's book is slightly controversial for having a weird presentation of determinants but he's rectified this in the newest edition

the newest edition of axler's book covers multilinear algebra

which you need in manifold theory to talk about tensors, differential forms, etc.

(spivak's treatment of this stuff sucks ass btw)

[tribal crow]

[covert mauve]

going to be honest, i had no idea multilinear algebra was a thing.

but sounds cool

[junior isle]

If I've read o good chunk of lang's linear algebra (until chap7) a while back, what would be a good book to review and learn more? Is hoffman suitable?

[junior isle]

Whats fis

[gray gazelle]

friedberg insel spence

[junior isle]

ic

[remote sparrow]

by lang's linear algebra book, do you mean Introduction to Linear Algebra or Linear Algebra?

[junior isle]

Linear algebra

[remote sparrow]

hoffman is good for review. you can also look at Advanced Linear Algebra by roman. abstract algebra books that cover modules would also be good if you've learned some algebra

[junior isle]

I don't really know any algebra, just know some definitions. The one by roman seems interesting, but isn't that a graduate level text?

[remote sparrow]

that's the intended audience

[sturdy shore]

do you want to learn algebra?

if so, I'd recommend giving artin a try, it's an algebra book that also covers linear algebra along the way

also, roman is pretty advanced

[junior isle]

Yes

[junior isle]

Actually that'd be really nice

Thanks, I'll take a look at them

[sturdy shore]

it's artin - algebra

[boreal widget]

what do you guys think about AOPS books

[deep nebula]

there seem to be a lot of pathways you can pick after the standard high school stuff, is there a good resource that goes over some of the popular ones and how they interact?

[dim sierra]

They’re pretty good

[dim sierra]

“A Concise Intro to Pure Mathematics”

It’s basically a transition to proof based math type thing

And it includes bits of abstract algebra, analysis, etc

[heady ember]

I'd say just pick a topic you're interested in and ask for book/resource recs

[past dust]

What book do you guys recommend for linear algebra ? I have heard Elementry linear algebra by Howard Anton is a decent one

[formal bronze]

Hoffman and Kunze

[wild grail]

Depends on your level and what style you prefer Hoffman and Kunze or Linear Algebra Done Right are the popular options

Hoffman and Kunze is the Rudin of linear

[heady ember]

FIS is good, especially if you have lower mathematical maturity

[past dust]

Thanks

[past dust]

this ? https://www.amazon.com/Linear-Algebra-4th-Stephen-Friedberg/dp/0130084514

[heady ember]

There's a 5th ed, but the 4th is probably fine as well

[wild grail]

Chapter 0 by Aluffi

[narrow relic]

BTW what was your impression of the Lang book Linear Algebra? I'm in Chapter 5.

[junior isle]

I liked it up until that chapter

I thought chapter 6 wasn't great and 7 was meh

[narrow relic]

Okay I see! Good to know, thanks.

[gray gazelle]

What are people’s favorite Springer books?

[short ferry]

https://tutorial.math.lamar.edu/

FREE

[tribal crow]

what criteria do we consider?

just general vibes?

[gray gazelle]

pretty much

[short ferry]

GUYS MATH IS FREE

[gray gazelle]

I get to choose a Springer book for free, so I’m looking for recommendations

[short ferry]

NO NEED TO PAY

[tribal crow]

in that case, I don’t think I have seen enough Springer books to give a good recommendation lol

[dim sierra]

what are you interested in?

[gray gazelle]

algebra/number theory

[dim sierra]

what level r u at in those subjects

[gray gazelle]

I’ve read parts of herstein’s topics in algebra, and have done elementary number theory at the level of Ireland & Rosen’s book

[dim sierra]

I’ve heard people use this book for algebraic NT https://link.springer.com/book/10.1007/978-3-662-03983-0 (I think it might be as a reference)

[gray gazelle]

Thanks

[dim sierra]

https://link.springer.com/book/10.1007/978-3-319-90233-3 also have heard good things about this book

and https://link.springer.com/book/10.1007/978-3-319-07545-7

But you prolly wanna go for the first one

cuz its the most expensive and u’ll probs buy it in the end

[agile shoal]

This and khan academy.org will make a new Einstein

[short ferry]

this is a w

bro it helps alot dawg

[agile shoal]

I already knew about it from a comment on a vdeo

[short ferry]

say less brother

haha

[agile shoal]

The math scorer

Was it u

Who post it

[short ferry]

a machine learning engineer

on instagram

i checked his linked brother

[agile shoal]

Send video

[short ferry]

bet

g

@studymlwithme

on ig

i found that big dawg

[agile shoal]

What grade r u

[short ferry]

im in college dawg

[agile shoal]

Oh

😂😂☠

[short ferry]

done with first year

[agile shoal]

I am in 11th

[short ferry]

thats tuff 1 more year

ur done

[agile shoal]

I hate English p2

🙏☠

[short ferry]

u already know calc and stufF?

[agile shoal]

Nah

[short ferry]

ofc us black ppl hate english but not all

lmao

[short ferry]

u have to bro

i did that mistake

[agile shoal]

I am trying to do so

But can't manage my time

[short ferry]

after i get there i regret then i started learning before i take classes for next semester

in order to understand the subject before i get there

[short ferry]

i get it

we have time bro is just we dont wanna have time for serious stuff lol but i worked on it

[agile shoal]

Literally school takes 8 hours of my day and u have 6 hours at home 1h to workout 1 hour for stretch and like 3 hours to do other stuff then I would be left with like 20min to study☠😂

[short ferry]

dang it used to be me

in hs

same thing

homeworks

and stuff

[agile shoal]

Nah they don't give hw

[short ferry]

in college at least u have break

in between

[agile shoal]

I be doing nothing at school

[short ferry]

homeworks due sunday

only

[agile shoal]

Nope

[short ferry]

for me yes

[agile shoal]

Since the start of the year I didn’t get no hw

[short ferry]

not everyone

[short ferry]

i mean college

[agile shoal]

Oh

[short ferry]

im doing cs major

too many math

[agile shoal]

Nah u cooked

[short ferry]

i tryna catch up before i get knocked the fuk off

lmao

i barely sleep cuz i tryna make it dawg

[agile shoal]

Ask vmm to assist u idk if je would accept

The guy us 16

[short ferry]

its aight

16?

[agile shoal]

He finished everything in math

[short ferry]

wow

wtf

nah

[agile shoal]

Ikr

[short ferry]

💀

[agile shoal]

Crazy

[short ferry]

at 16 i was hooping

getting fs

[agile shoal]

SAMEEE

[short ferry]

and ds

[agile shoal]

I am still doing so

[short ferry]

he knew it since kid

it depends on the parents

like asian parents they teach their kid important stuff

[agile shoal]

My parents are chill

[short ferry]

i have 12 year old Asian kid in my cs class\

[agile shoal]

😂

They don't give af

[short ferry]

12 year old know better than me

in my college cs calss

class*

[agile shoal]

OH

😭😭

Blud ur done

[short ferry]

yes he helped me on hw

to

lmao

[short ferry]

haha

[agile shoal]

Did u finish calc

[short ferry]

u know our parents

lol

[short ferry]

first year im taking calc in fall

i took pre calc

cuz i came from ghana yk

[agile shoal]

What was ur %

In hs

[short ferry]

haha

i cant remember

i finsihed last year

[agile shoal]

Mine would be like 80s

[short ferry]

wow

[agile shoal]

No way I am locking in 90

[short ferry]

in college i being going to war

with my grade

either A or B

[agile shoal]

College if u get 50% ur a genius

[short ferry]

i have As rn but im waiting for my english teacher to grade 3 essays

since semester begin

she didnt grade

[agile shoal]

I just can't with the essays no more

I hate em

[short ferry]

now we finished first semester today

and still not graded

😭

[short ferry]

ikr

[remote sparrow]

please move this conversation to #discussion as this is no longer about books

[short ferry]

ok

thanks

appreciete

@agile shoal nice speaking to u bro

[agile shoal]

OK so which link do u use for math

[short ferry]

https://tutorial.math.lamar.edu/

[short ferry]

sorry

[agile shoal]

Is that only it

[short ferry]

we are done

thanks for letting us know

[remote sparrow]

knapp's Basic Algebra and Advanced Algebra are pretty expensive new from springer. maybe you'll want to read lang's Algebra at some point

if you can get one book for free, might as well go for something expensive

[remote sparrow]

@gray gazelle https://link.springer.com/book/9780817645335

apparently you can buy both knapps as a set

buying both individually would be $300

as a set it's $220

[fresh skiff]

I have seen Knapp has books on analysis too

Basic real analysis~

Is it basic one? With no prerequisite or just 1st course in analysis?

[remote sparrow]

@sturdy shore

[sturdy shore]

you need a 1st course for it

[fresh skiff]

Oh. Are you using this book?

[sturdy shore]

first half of baby rudin kind of thing

no

I used a bit of it before

[fresh skiff]

Hopefully Abbott will be enough

[sturdy shore]

enough

[fresh skiff]

I see. Thank you.
But Abbott is not that much easy book as I expected

[sturdy shore]

certainly not easy

but friendly

[fresh skiff]

Oo. I use to think friendly means easy book

[sturdy shore]

I'd say friendly moreso means "doesn't make you think you are an idiot" kind of thing

plus overall language

examples

etc

but you can have these and still be hard

[gray gazelle]

How legible is Lang lol

[muted tusk]

Hey I'm going to be a undergraduate Introduction Abstract Algebra course this fall and wanted to know any tips for self-studying/getting an idea of what the course entails. I just wanted to ask if there was any good resources or online courses to go through to get an idea of the subject content. Currently I was thinking of looking through this Modern Algebra Course.
https://www.youtube.com/playlist?list=PLwV-9DG53NDxU337smpTwm6sef4x-SCLv

[remote sparrow]

you'll have to fill in many gaps yourself. there's this guy named george bergman that wrote a companion to lang's Algebra along with some handouts.

https://math.berkeley.edu/~gbergman/.C.to.L/

https://math.berkeley.edu/~gbergman/grad.hndts/

https://tableschairsandbeermugsmathemagician.blogspot.com/search?updated-max=2017-05-14T23:24:00-07:00

this guy called the mathemagician used to be active on mathstackexchange

he has a couple of poorly designed websites

web design was not his strong suit

but i found the content of his posts good

he wrote reviews of some algebra books

[earnest wolf]

cute

[remote sparrow]

https://www.youtube.com/playlist?list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5

this one follows artin

https://www.youtube.com/playlist?list=PLmU0FIlJY-Mn3Pt-r5zQ_-Ar8mAnBZTf2

this one follows gallian

https://www.youtube.com/playlist?list=PLBY4G2o7DhF0JCgapYKrqibGaJuvV4Gkb

another following gallian

https://www.youtube.com/playlist?list=PLVMgvCDIRy1y4JFpnpzEQZ0gRwr-sPTpw

[remote sparrow]

getting a book is always best though.

#book-recommendations message

consider one of these

[muted tusk]

Which book do you recommend to go self-study as an introduction for undergraduate abstract algebra? Just took Real Analysis and I'm looking to mainly just go over the concepts to prepare since I'm going to be taking the actual course in the fall.

[remote sparrow]

is it just a one semester-long class or a year-long sequence?

[muted tusk]

Semester class

[remote sparrow]

http://abstract.ups.edu/

judson is free online

it's also available as a cheap paperback

pinter is not free but is also very cheap

[gray gazelle]

Influence by Robert Cialdini

[narrow relic]

He has some good recommendations, although I don't think I ever ended up reading any of the books he recommended, I just looked at them and some of them were cool.

[formal bronze]

Dummit and Foote

[quartz agate]

Guys i want a begginers book for calculus if someone has i would be gratefull

[trail hemlock]

thomas and stewart's calculus are both good introductions

there is also the less traditioanlly recommended "calculus: a physical and intuitive approach" by klein which is both very beginner friendly, and fairly cheap

in terms of resoures, this is a great one: https://schtschenok.github.io/calculus-made-easy/

anything on this list is considered good for an intro

https://www.amazon.com/shop/themathsorcerer/list/SKD9TCJQOZAI

[old lintel]

what's a good book for studying math proofs

[trail hemlock]

depends on your level of maturity

i personally liked jay cumming's proofs: a long form textbook

how to prove it by vellman, and book of proof by hammack are also good

[modern ruin]

which ones

i shouldn’t have pinged you over this i am just making a stupid joke

[quartz agate]

thanks

[rough lagoon]

Hello there! I need to get back to a high school level in Math, any good book recommendations for that?

[trail hemlock]

any algebra 2 skills workbook you can find will prob be good

https://www.walmart.com/ip/McGraw-Hill-Education-Algebra-II-Review-and-Workbook-Paperback-9781260128888/172567664

[frank fractal]

is there any e-book available to study delay differential equations? I already have decent knowledge of ordinary differential equations.

[hollow drum]

Is there a linear algebra book that might discuss block matrices, or in other words matrices that come with some partitioning of columns and rows?

[rigid flint]

Anyone know of books about integration techniques that aren’t u-sub or IBP?

[short ferry]

https://tutorial.math.lamar.edu/

goodluck

thank me later

[trail hemlock]

https://a.co/d/0Mh9t5T

[deep nebula]

whats a good introductory book to type theory? (please mention the prereqs, aswell)

[jagged badge]

any graph theory books that covers both algorithms as well as theory?

[remote vortex]

Wilson's book mentions some algorithms

I think it's a fairly good starting point for graph theory

[remote sparrow]

https://www.lix.polytechnique.fr/Labo/Samuel.Mimram/teaching/INF551/course.pdf

i was recommended this book

Although most of the material is self-contained, the reader is supposed to be already acquainted with logic and programming.

also scroll down pins

there's a logic reading list by diligentclerk

[fleet veldt]

what're the recommended books for ODE, PDE, CALC(1,2,3 combined if possible) and discrete math? (for discrete math i mean on undergrad level for stem? talking about the basics like sets, relations, functions, combinatorics, probabilities, graphs and trees and whatever else)

[deep nebula]

thanks!

[jagged badge]

wilson's graph theory in ameerica, the first 100 years?

or intro to graph theory

[hallow oriole]

this book isn't my favorite for the record

#book-recommendations message

are my recs

[rigid flint]

Yeah that’s the book I initially looked at, but it costs nearly 50 dollars, and I couldn’t find online versions of it ;(

[trail hemlock]

i think there is an ebook coming out

you know what that means ...

[silk fiber]

Any good starter books for algebraic number theory and algebraic for an undergrad student without expierience in number theory?

[gray gazelle]

First 5 chapters of Ireland and Rosen for an algebraic approach to elementary NT, then Marcus’ Number Fields

[slender cargo]

Axler's LADR book has some nice colors, but I don't think they help with readability. That is all.

[deep nebula]

I dont remember getting an answer to this question yesterday, but how exactly do the different math topics relate to each other?

you have: linear algebra, calculus, differential equations, abstract algebra, category theory, algebraic geometry, differential geometry, hyperbolic geometry, manifold theory, lambda calculus, set theory, homological algebra, real/complex analysis, measure theory, harmonic analysis, functional analysis, topology, algebraic topology, number theory, and all the stuff from combinatorics and stats i dont even know about.

i know mathematics has no true linear path of studying, but how am I supposed to know what the purpose of such subfields is and how they relate to each other?

its extremely confusing, and while i know about most of the fields i have mentioned, there are many i dont know about, and i cant find any resource that documents them.

[violet shuttle]

everything is linear algebra

[deep nebula]

who let the programmer out (/s)

[violet shuttle]

? no, i see it a lot more in mathematics

most programmers don't know linear algebra, i don't think.

most programmers don't do scientific computing

[deep nebula]

its used a horrendously lot in the bases

[deep nebula]

saying everything is linear algebra isnt really helpful, though. even if they branch off it, where do they do that? why? for what reason?

[violet shuttle]

oh my bad lol i'll elaborate

linear algebra is the "nice" case

differential calculus, after all, is just approximating functions via linear ones so that you can do linear algebra

abstract algebra is of course more general than linear algebra, but i find it helpful to take the intuitions from linear algebra. sure, general modules aren't as nice, but, you can still kinda think of them as vector spaces

..."manifold theory"

lambda calculus is computer science stuff.

functional analysis literally is about vector spaces

most homologys in practice that i've seen are modules

algebraic topology, for example, with its singular homology, uses modules

number theory can be split into "analytic number theory" and "algebraic number theory"

algebraic number theory is like ideal class group and bla bla

probability theory and statistics are a bit different

set theory at an advanced level, along with logic and stuff form "foundations" stuff

i note that you don't have representation theory

[deep nebula]

i dont even know what that is

[violet shuttle]

so suppose you have a group

a representation is a homomorhpism into GL(V)

and thus is a way to represent the group via matrices

there are also representations of algebras and etc.

[deep nebula]

i think i get it, i havent really done much group stuff yet

[violet shuttle]

you should definitely do some algebra

[deep nebula]

any good books you'd recommend?

[violet shuttle]

I have heard good things about dummit and foote for beginners

I personally like Lang's algebra

[deep nebula]

i thought thats a reference book

and not really something you study from

[violet shuttle]

I don't know why you'd think people don't learn from it!

[deep nebula]

reddit and quora have created a certain stereotype about many books in my mind that i cant get rid of

[violet shuttle]

reddit and quora, when i checked years ago, said it was fine soooooo

[deep nebula]

i will give both a read and see which one i can read

[violet shuttle]

that is indeed the better way to do it yes

[rigid flint]

Hopefully 🙏

[junior isle]

How???

[violet shuttle]

... it's a homomorphism into GL

[fleet veldt]

what're the recommended books for ODE, CALC (1,2,3 combined if possible) and discrete math? (for discrete math i mean on undergrad level for stem, talking about the basics like sets, relations, functions, combinatorics, probabilities, graphs and trees and whatever else)

[manic brook]

does anyone have recommendations for a graduate level abstract algebra text suitable for self study? In particular, I have read Dummit and Foote chapters 1-13 (excluding 6, 11, and 12) but I don't think I have a particularly strong grasp on those topics. Additionally, I'm looking for a book that is readable and hopefully doesn't have too many errors for self-study (neither of which conditions Lang fits, from what I have heard) and has an solution manuel that I can find somewhere to check my understanding. Something from a categorical perspective would probably be best, as I have a decent background in category theory.

[junior isle]

For discrete math i like book of proof. For calc1,2,3 id recommend thomas calculus

[fierce hedge]

For categorical perspective Aluffi is the popular recommendation

Most graduate textbooks won't have a solution manual so there's that. Notable exceptions are Knapp and Robert Ash's book

[frozen minnow]

everybody gangsta until you can't find the basis

[gray gazelle]

Guys, recommend me a book to understand the essence of matrices, determinants, functions, etc
Basically all algebra

[formal bronze]

One book cannot cover 'all algebra'

[gray gazelle]

That sounds like a linear algebra book

[formal bronze]

Yes, I would suggest Hoffman and Kunze for linear algebra

[rain wren]

artin's algebra

atlho I wouldn't really call functions apart of algebra

it's basic definition to all of math lmao

[modern ruin]

aluffi has what you want probably

algebra: chapter 0 (not notes from the underground)

[rain wren]

yea, aluffi sounds like it fits

[wild grail]

Lang?

[rain wren]

altho I disagree with the way you're trying to consolidate that knowledge

[wild grail]

Standard graduate text

Aluffi is cool in principal

for an undergraduate perusal of category theory

but it's only qualification for being a graduate level algebra book is being apart of the GTM series

[rain wren]

I think if you have decent grasp on a piece of mathematics, the best way to strengthen your understanding is to do more problems

of which aluffi is a poor source

[wild grail]

they're too vague

[rain wren]

nah, the later chapters are very much graduate level

like 5 and onwards iirc

[wild grail]

I have a reason to open my copy lol

let me check

The last chapter

homological algebra isn't a standard undergrad topic

the rest of it is

[dapper root]

What

Semi direct products are not undergrad fare

Structure theorem of modules over a PID are not undergrad fare

[wild grail]

for groups? absolutely

[dapper root]

It definitely is not lol

[wild grail]

was literally in my first abstract algebra class

[dapper root]

Idk what kinda undergrad courses you’re taking

[rain wren]

I thought doing LA on modules at all was at the very least upper undergrad

[dapper root]

It isn’t taught in virtually all undergrad algebra classes

Just because you did differently doesn’t make it standard lol

[wild grail]

huh, I figured the linear, abstract algebra and analysis/topology sequences are the same pretty much anywhere

[remote sparrow]

knapp's Basic Algebra and Advanced Algebra have detailed hints (some even bordering on solution sketches) to most of the exercises in the back

you can also look at rotman's Advanced Modern Algebra

the second and third editions are very different

rotman wanted the third edition to be more pedagogically oriented

the second edition is more intended to be a reference

the third edition is split into two volumes, while the second edition is one large tome

https://www.amazon.com/Basic-Abstract-Algebra-Undergraduates-Mathematics/dp/0486453561

you can also look at this

[rain wren]

knapp is terrible tho

his basic algebra at least, I dunno about his advanced

[remote sparrow]

because?

[rain wren]

I dunno, I just don't feel like his writing style is the most lucid out there, and a lot of students I was helping didn't like it

like, everyone from ereh's algebra reading group thought it was terrible

[remote sparrow]

were they students that had never read an algebra book?

because the individual i was making the recommendation to has already read a substantial portion of dummit and foote

[rain wren]

hmm, some have

but fair point

I had read an algebra book too tho and I thought the writing wasn't that good so

I should make a brezis tier list

[narrow relic]

It's helpful to hear these kinds of things. Sometimes when I'm curious about other books I like to hear what other people thought of the style.
That Knapp book looked good content-wise from browsing it, but having never worked through any of it I can't really tell if it's worth sinking any time into without these kinds of first-hand stories.

[rain wren]

in all honesty I think the best option for OP is lang, as stupid as that might sound

coz if I were in their place I'd mainly just grind problems

and lang seems to be a good source of those

[slender cargo]

Feel like this is the best piece of advice. Depends though on why they want to strengthen their grasp of the material - i.e. qualifying exams?

Just want a categorical approach to the material?

[velvet gyro]

What is your take on Hardy and Wright vs Ireland and Rosen? I’m most interested in expository style, I’m somewhat aware of the differences in the covered topics

[gray gazelle]

Haven’t read Hardy and Wright, but I’ll say that, while I & R’s exercises are excellent, their exposition is (a) terse and (b) full of minor errors

So you’ll want to work through the proofs on your own and keep the errata in a second tab

[velvet gyro]

I see, (b) doesn’t sound encouraging. Would you have another recommendation for something that covers the topics in I&R, but that’s a bit less dense in the way you’ve mentioned?

[manic brook]

do u know of like an online solution archive?

i feel like thers gotta have been somebody mad enough to collect the solutions for all the problems somewhere

[subtle fractal]

can anyone recommend a book that covers calculus 1 (preferably one that's straight to the point)

[wild grail]

What level of detail are you looking for @subtle fractal

[remote sparrow]

there doesn't seem to be any exercises in hardy and wright

#book-recommendations message

here's some other books for number theory

[subtle fractal]

eh something quick I could use for competitions not a lot of explaining if that makes sense (just so i get a general feeling)

[rain wren]

no sorry

I'm not much of an algebraist tbh

nor am I fun of solution manuals for that matter

I much preper getting hints and guidance from this server

[wild grail]

Been awhile but I remember we were assigned OpenStax, which wasn't bad, but I liked Marsden and Tromba more

[remote sparrow]

https://math.berkeley.edu/~gbergman/.C.to.L/

there's a companion that could help with reading lang

don't think there are any solutions

knapp or ash are your best bets for something with solutions

[gray gazelle]

Does anyone know of any good calculus books that contain helpful visuals? Reading a bunch of words doesn't really click that well for me.

Something that goes through the math but follows along with visuals showing what the math is actually doing geometrically.

[earnest wolf]

guys, does anyone know of any 'guides'/books I can read to build my crypto for fun?
like idk, I was contemplating learning haskell and so why not to try to learn it by doing xD

I just need a systematic source of info ig
Like there are so many fun parts that will pop up for sure: distributed algorithms and a bit of cryptography to mention a few

/not interested in any kind of profit – just fun/

just discovered Cardano is written in haskell lol

[unborn jackal]

Could anyone who has used hoffman kunze for lin alg tell me which topics weren't covered/skipped?

[violet shuttle]

i know someone named ireland

[jagged badge]

does anybody have a combinatorics for idiots book recommendation?

[dapper root]

Lmfao

[unborn jackal]

combinatorics book for highschool olympiads maybe?

idk

[late plinth]

im a big fan of extremal combinatorics by jukna

it's p approachable imo if u r somewhat comfortable w proofs

[remote sparrow]

maybe not for idiots, but bona's A Walk Through Combinatorics has solutions to all the non-supplementary exercises within the text

[wild grail]

As someone who likes Haskell, I'm genuinely curious why anyone would want to learn Haskell. I wrote some code for class in Haskell, I would suggest against doing any sort of "practical" project, especially anything that uses external APIs. Maybe start with something simpler, like a parser? It's good at being a parser. Check out Bartoz Milewski and Tsoding they have cool Haskell videos.

[jagged badge]

ok maybe i shouldn't have memed, what about just a first combinatorics book lmao

[strange sentinel]

Not sure how well this fits your purposes, but it is a good book with approximately 0 prereqs besides mathematical maturity https://www.ms.uky.edu/~sohum/putnam/enu_comb_stanley.pdf

[earnest wolf]

why someone would want to learn Haskell

cuz it seems to be fun 🙂

obv not for jobs lol

[violet shuttle]

for the xmonad tiling manager obviously

paul graham attributes part of his success in one of his startups or something to using lisp

[trail hemlock]

is "Advanced Calculus: A geometric approach" a good standalone book or good as supplament

its pretty thick

i wanna focus on rigour and theory but ofc i wanna learn computations

[slender cargo]

Just a tangent but if I were self-studying I would use Edwards Advanced Calculus: A Differential Forms Approach. That book looks fun and has full solutions in the back.

[trail hemlock]

i alr purchased the book :(

[slender cargo]

I was generously gifted this book by a retiring professor, so I imagine it's good enough.

[trail hemlock]

that sounds so cool

[slender cargo]

(It is quite thick, yes)

[trail hemlock]

i was planning to use hubbard and hubbard

honestly i should stop fixating on teh book and just do it smh

[slender cargo]

If you don't know linear algebra, that seems like a fun way to go.

[trail hemlock]

i just want a book thats rigerous and not computational

i glanced at advanced calc and it seems pretty well suited

[slender cargo]

I'll be taking multivariable calculus for a course next term. We will be using Edwards Advanced Calculus of Several Variables.

[trail hemlock]

i will take a look at this, thank you!

[slender cargo]

My feeling is that you want some computational practice with that subject.

[trail hemlock]

i am taking a class on multivar next year, so i will prob get all teh computations i need there

[slender cargo]

Did you learn linear algebra yet?

[trail hemlock]

very computationally

[slender cargo]

I feel like that should come first

[trail hemlock]

i just picked up the first book i could find

it was a long time ago

[slender cargo]

Probably should go through a rigorous approach for linear algebra first? Otherwise go for something like Shifrin or Hubbard Hubbard

I'm going through Axler LADR this summer. You could join me! lol

[unborn jackal]

which semester are you in?

[slender cargo]

Sorry I went on a tangent. I'm not sure if rigorous linear algebra is actually needed. I feel like if you already bought the advanced calculus book though, it'll be just fine?

[trail hemlock]

i was gonna do lang actually but seems fun

[trail hemlock]

yes sir

TopDreg my savior

[slender cargo]

I don't know anything about Lang's book but I believe Axler's book is the most popular book that is used at universities (that or FIS).

But again, something about this server and Lang...

[trail hemlock]

loll

[left cloud]

do not the lang

[slender cargo]

Lang Linear Algebra specifically

[tribal crow]

fwiw, only a few people consistenly recommend Lang

it's not that many

[slender cargo]

They are very vocal though!

[tribal crow]

yes, I agree with that

[unborn jackal]

loud minority

[slender cargo]

Axler provides the book for free online if you're curious.

[trail hemlock]

i think all the books are online for free iirc

[slender cargo]

Yeah all of his are (legally)

[trail hemlock]

wowzers!!

ok ill add it to the list

really hoping to at least begin measure theory this summer

but zorn will appear under my bed and beat me to death with a copy of rudin if I rush.

[slender cargo]

Feel like you're a far ways away from that?

[trail hemlock]

i mean im nearly done with rudin

[slender cargo]

Could go check out Linear Algebra, Abstract Algebra, Topology, Multivariable Real Analysis then like you mentioned

[trail hemlock]

i feel like folland isnt too heavy on the prereqs

[slender cargo]

Math students don't usually get to measure theory before going through those topics first

[trail hemlock]

ok i will def

i will prob use tao 2 for multivar real cuz rudin is just so shit

[slender cargo]

Oh. I don't know why you're asking about Callahan then

Just go through Tao 2

[trail hemlock]

will do

i love tao's analysis series

maybe as much as rudin

[slender cargo]

But yeah, maybe look at other subjects also. Gotta study more than just analysis

[trail hemlock]

true lol

[slender cargo]

If I were self studying I would check out the crazy experimental books lol

[trail hemlock]

but analysis is so fun

all the other subjects dont seem so fun

other than set theory

jech is pretty nice

[slender cargo]

Abstract Algebra is fun. You get to see math you know through a new language

[trail hemlock]

ok i will def check it out after linalg

next school year will begin dummit and foote

[slender cargo]

(also it's considered essnetial)

[trail hemlock]

but thats for the future

[slender cargo]

Oh, for a class?

[trail hemlock]

no

[slender cargo]

oh just self study

[trail hemlock]

my school doesnt offer anything after multicalc

sadly

[slender cargo]

is this high school or community college?

[trail hemlock]

hs

[slender cargo]

That is a very nice high school

[trail hemlock]

in 10th grade rn

basically a grandpa 💀 👴

[slender cargo]

Since you have the time (you're way ahead) then linear algebra + multivar calculus should be the goal, yeah

[trail hemlock]

gotcha

i will prob work on that in parallel with rudin

will never ditch my pookie

[slender cargo]

Oh you're still going through Rudin?

Just linear algebra for now then

er

[trail hemlock]

on like ch5 rn

[slender cargo]

I guess it doesn't matter too much

[trail hemlock]

ch 9 is the end of single var rudin

and ill pick up tao 2

[slender cargo]

I think he assumes linear algebra for his book

Maybe work through a linear algebra book concurrently with Rudin right now

[trail hemlock]

yeah good idea

[slender cargo]

If you're not accustomed to linear algebra then I've heard Friedberg Insel Spence is good. That seems to be a popular choice at universities.

[remote sparrow]

it mainly focuses on the 2d and 3d cases, but that doesn't mean it's nonrigorous

hubbard and hubbard is good

if you have never encountered linear algebra, axler doesn't cover gaussian elimination

hoffman/kunze and my other linear algebra recommendations do: #book-recommendations message

[remote sparrow]

i don't see stokes' theorem in tao ii

it only gets up to fubini's theorem

[narrow relic]

I've worked through about 5 chapters of Lang's Linear Algebra and recommend it. I will be doing more.

[slender cargo]

I have not worked through any of it, so I shouldn't really give an opinion either way. It just doesn't seem like a popular choice at universities, but Lang is well known for his work in algebra.

[narrow relic]

It's not popular but who cares. It's solid. You have to know a few things, but he covers those in his earlier book Introduction to Linear Algebra and anyone who has taken a "first course" in linear algebra knows them. There's a Columbia professor who wrote a fantastic supplement to the Lang Linear Algebra book: https://www.math.columbia.edu/department/pinkham/LangCommentary.pdf

[slender cargo]

I'll take a look at it. You've got me curious now.

[narrow relic]

At the Lang book or at that LangCommentary.pdf?

[slender cargo]

The Lang book

[narrow relic]

Have you studied any linear algebra before? (I got the sense you have from skimming your convo earlier)

[slender cargo]

Only the elementary stuff. I am currently working through Axler's book over this summer before I start my M.S. program.

So I'm no authority on this stuff at all.

[narrow relic]

Oh, cool, you're like the perfect audience for Lang then.
Here's a syllabus I've been following, with recommended homework problems:
https://math.ou.edu/~forester/5373F09/
https://math.ou.edu/~forester/5373F09/homework.html

[slender cargo]

Oh god... haha. I'll consider it then.

[narrow relic]

Now, let me tell you one more thing

I recommend reading LangCommentary.pdf Chapter 1, before beginning Lang Chapter 1. And, LangCommentary.pdf Chapter 2 before beginning Lang Chapter 4.

[slender cargo]

Chances are I'll stick to Axler since I like that it's easy to check my work with how popular it is, but I'll look into it.

[narrow relic]

Oh sure, I'm just sharing my knowledge 🙂

[late plinth]

Axler is acc so nice
Eventually going from lay to Axler was acc such a breath of fresh air
Lay -> Strang -> Axler

[slender cargo]

Yep I'm really liking the book so far

I think I can get through it in 3 months

[maiden glen]

I need a good elementary algebra book, every one I've read or looked at is too generic. I need something better, something that gives me the knowledge I thrist for, I need something vast and broad; really allowing me the concrete foundations I need to improve my problem solving methods and open the way to formal algebraic fields

I want it lengthy, abundant, great.

I seek the perfect book

[glad rampart]

Art of problem solving intro to algebra?

[formal bronze]

Dummit and Foote is a great introductory text on algebra

[modest prairie]

guys

is hall and knight good for algebra?

i'm thinking of getting intermediate and higher algebra

since i'm already familiar with 95% of the content in elementary algebra

[safe horizon]

is it normal to feel immense boredom while reading through the first chapter of abbott?

how screwed would I be if I skipped the construction of the reals and went straight into sequences

[remote vortex]

Try Rudin instead, you might find it more stimulating

[shadow river]

hey luckily you can construct the reals using rational sequences

lol I dunno what abbot does, cuts?

[safe horizon]

uhh, the axiom of completeness it seems? but he does provide an exercise where he gives you the definition of a cut and asks to show that it's equivalent to AoC

[remote vortex]

"luckily"

Yeah, Abbott uses the axiomatic definitions of reals, but proves that such an object exists, by constructing it using Dedekind cuts

[shadow river]

ahh

[safe horizon]

https://tenor.com/view/the-me-the-when-math-me-when-math-me-when-when-when-when-math-the-math-the-it-the-math-gif-25968629

I feel like this gif

[lusty escarp]

As far as I remember, it does not go deep into construction of reals. If you read rudin you will see how technical that construction is. Just read it, it will not take much time.

[shadow river]

my first exposure was just completion of metric spaces using cauchy sequences, but in hindsight cuts are really elegant

[remote vortex]

The Cauchy sequences have the advantage of generalizing more broadly, but the cuts are much less fiddly

[shadow river]

but yeah, it can be dry and can probably skip to chapter 2 (just looking through the table of contents), but it's the sort of stuff you should know eventually