book-recommendations

[stray veldt]

there is a "notes and further references" part, did you check that?

finding a single source for so many topics will be hard

[bronze sinew]

Hey guys, just started a class on Vector Calculus and there's no recommended textbook given by my subject co-ordinator, wondering if you guys could perhaps give me some of your top recommendations for Vector Calculus textbooks. For reference, apparently our course is going to be focused on the purer, more proofs focused side of Vector Calculus, and although computations are definitely a part of the class, my lecturer has said that derivations and proofs will be very pronounced in this class.

Just in case that helps to adjust your selections

[zenith oasis]

im finally reading through some textbooks that ive seen recommended online as being the best textbooks for learning some subjects, specifically for real analysis and linear algebra

ive gotta say that reading a well written textbook is eye-opening to how atrocious the textbooks most college courses use

[marble solar]

Apostol calculus volume 2 is pretty good

[grand thistle]

how good is it for diffeq and linalg?

[marble solar]

I don't have my copies on hand right now

I remember it being good

[grand thistle]

oh i see

thanks

[gray gazelle]

Any good books on Galois theory

?

[restive falcon]

what books are you using
and what textbooks did your uni courses use

[runic hatch]

Are there analysis courses that don’t follow parts of the standard texts like rudin/apostol?

[gray gazelle]

I have that Rudin is one of the most challenging or tiring books ever. Is that true?

[runic hatch]

It’s more concise compared to some other analysis texts

[restive falcon]

it also doesn't do differential forms well afaik

[rugged seal]

I'm trying to learn about line integrals via one-forms does anybody know a good textbook? I would prefer one with exercises and solutions if possible

[sage python]

@rugged seal try "Differential Forms and Applications" by Do Carmo

[rugged seal]

thank you i will do that

[warm glen]

what's the opinion here on loomis and sternberg for multivariable analysis

i wanna read it after chapters 1-8 of baby rudin

[gray gazelle]

You don't need real analysis

@gray gazelle

[sick wigeon]

I am having my multivariable analysis course next semester and i don't feel prepared enough for it

Any suggestions?

[cursive orbit]

Rudin is terrible for multivariable

[sick wigeon]

What about spivak

[stoic aurora]

Hey guys, what are some topology books with good set theory intros? I have to read engelking but the introduction pretty much just assumes you know set theory and just spits facts.

[karmic thorn]

What do you seek from a good set theory intro?

I found Munkres chapter 1 to be very thorough

[stoic aurora]

Well, only the stuff necessary for topology, maybe some actual proofs and justifications, preferably under 50-60 pages but not ... 10

munkres does actually look pretty good

[inner token]

I take it y'all love this book

Why do y'all love topography so much

[karmic thorn]

Topography

[hollow drum]

Can anybody recommend a book to learn about concentration of measure?

[flint forge]

no one loves this book

[keen blade]

I want good book recommendations on: formal logic with boolean algebra stuff, conic sections, and graph theory with applications related mostly to computer science

thanks in advance

and ping me when you ansewr please

[prime oak]

would you recommend Harold Simmons introduction to category theory?

[gray gazelle]

Rosen's or Susanna's Discrete Mathematics

usual among CS majors

[keen blade]

thx a bunch

[lime sapphire]

hi, im looking for an introduction to differential equations

[smoky zephyr]

pauls online notes is good for this

it’s a website

https://tutorial.math.lamar.edu/classes/de/de.aspx

[lime sapphire]

oh cool thx

[foggy relic]

Idk abt those but Aluffi is also pretty good for an intro

[restive falcon]

are Hatcher's notes enough for pointset

[flint forge]

riehl is the only valid category theory text

ill die on this hill

[keen blade]

also integration by reduction coz cant find that in stewart or thomas

[gray gazelle]

No. Never read it

[flint forge]

they are enough if all you want to do is AT

[keen blade]

Mathematical Methods for Physics and Engineering saw that book in the references in a wikipedia article about reduction formulae searched it and saw andrew dotson recommending. what's your guys opinion about it

[flint forge]

or like any form of topology that isnt point set

[restive falcon]

cool

[gray gazelle]

Continuum theory?

[flint forge]

its enough if you want to do difftop or AT or knot theory or things of those flavor. "any form" is too strong, of course

[restive falcon]

those are all what i was thinking of

[flint forge]

i figured

[restive falcon]

I'm not too interested in analysis

at least atm

[keen blade]

umm anyone?

[keen blade]

.

[keen blade]

.

😦

the books may contain other topics but like cover the mentioned topics in adequate detail

[fluid bay]

idk what "integration by reduction" is, but the rest of the stuff should be in any discrete math book like Rosen

oh someone already said this

[hallow sundial]

Intro to Mathematical Thinking by Kevin Dublin. good little math book to ground and prepare you for real analysis beyond.

[vital iris]

I'm in the weird position of having learned point set topology from Munkres' text without ever learning first-year/undgergraduate-level real analysis. I'm aware that a lot of the ideas should be repeated (focusing on the standard topology) but I'm conflicted — should I jump into Rudin or is there a better alternative specific to my situation

Thank you so much,
Raman

[dapper root]

You can just skip the topology if you know it

I think you should pick a book based on the analysis content being presented

[sudden kindle]

Whats your favorite class field theory textbook

[dapper root]

Doesn’t Serre have a class field theory book?

Like Local Fields or whatever

I like Serre’s writing in general, but it’s very terse.

[sage python]

I think Cassels Frohlich is supposed to be the book™️

[warm glen]

trying 1 more time 🤠

thoughts?

[slim peak]

In general if people don't answer it's because they don't know the book

[ripe granite]

Neukirch

[sudden kindle]

I might read Neukirch in the future

[grand wren]

When ppl recommend books to other ppl. Have they actually read those books or do they just recommend it because other ppl have recommended it to them?

[sudden kindle]

Varies

[balmy phoenix]

introduction to set theory for someone who is not understanding set theory operations

[dapper root]

I try to differentiate when I’ve read a book and personally recommend it, when someone I know well has recommended it, and when I’m just parroting what seems to be the general consensus

[gray jungle]

im looking for books/resources for number theory and graph theory at the level of a discrete math course (problem sets and lecture notes work too)

[rain hound]

https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/readings/MIT6_042JF10_notes.pdf

[covert oxide]

Any books for IMO preparation? Also functional equations if any 😁

[covert oxide]

Shouldn’t necessarily be books, any free resource online would do

[smoky zephyr]

a bit late, but would this include differential geometry too?

[flint forge]

uhh

should be

[queen island]

Does anyone know any summary-level engineering/math texts? I'm a senior Aerospace engineer, and I have a lot of math and engineering classes under my belt, but I find it hard to find specific information (mostly formulas and problems) from lower-level classes because it's spread out across numerous textbooks. It really seems like there is room for a lot of it to be consolidated into a condensed text. Do such texts exist, and if so, which would you recommend? It should cover math up through PDEs and Linear algebra, all manner of sciences, materials analyses, computer science, fluids, and anything else.

[tulip blade]

😐

Maybe a book like math methods for engineers/physicists

[proper lotus]

If you're looking for just a library, perhaps https://dlmf.nist.gov/

[gray gazelle]

Texts about what specifically

[grand thistle]

what are the prerequisites for hubbard and hubbard's vector calculus, linear algebra and differential forms?

i'm debating on whether to go through apostol

calculus vol. 2

or hubbard and hubbard

also how good is hubbard for analysis?

it says that it can be used for a first course for analysis

it says this tho

[sage python]

I've heard that Hubbard's angle through the material is a bit awkward, compared to e.g. Shifrin

[grand thistle]

hmm

so

would you recommend shifrin then?

im debating between apostol's vol 2 and h/h since they both seem to cover linalg

im assuming from the title shifrin also covers about as much as h/h

[marble solar]

The nice thing about Shifrin is the lectures are available on youtube

By shifrin himself

[grand thistle]

i really want to use apostol, but i also wanna learn the differential forms and intro to manifolds and such that shifrin and hubbard both have

so

im not too sure as of yet

h/h also seems to treat lebesgue integration

idk how good that section is

but it seems important

ive decided to use hubbard and hubbard

but to use apostol for the two chapters on odes

[covert oxide]

.

[real trail]

out of curiosity, does anyone enrolled in uni/college have access to this springer book?
https://link.springer.com/book/10.1007/978-3-642-58604-0

[fluid bay]

yes

[real trail]

thanx

[blissful pollen]

Hey

I recently started reading "Calculus" by Michael spivak and know the basics of calculus

So should I pick a different easier book or is this one fine (just started reading it, so idk bout the difficulty level)

Im currently in high school

[grand thistle]

if u know the basics of calc ur fine

if its too hard, try apostol

[gray gazelle]

I was wondering. Is there a book that talks about topology and game theory

[gray gazelle]

I guess not

Still, does anyone have good sources to learn stuff like topological games

[sage python]

@gray gazelle might not be what you're looking for but

Try "Measure and Category" by Oxtoby

[gray gazelle]

Oh, I heard about Oxtoby

he's the one that studied the similarities between the measure theory and Baire spaces

Baire property being equivalent of equality up to sets of measure zero etc.

[short gate]

Guys, what book do you recommend for self learning rigurous abstract and linear algebra, real analysis and topology? With many exercises

[gray gazelle]

I think this is fine, but did it pass the test of time though?

[runic hatch]

For analysis I'd recommend either Apostol or Rudin; choose whichever one you think has a better style

[dense hamlet]

CLRS Halwa

[gray gazelle]

Good algorithms and data structures book that isn't CLRS?

[solid idol]

Best books on statistics and probability??

[junior merlin]

I like linear algebra done right by axler which I'm going through now, for topology theres mat327's big list of problems

[covert oxide]

Any good functional equations problem set w/ solutions?

[gray jungle]

i really like hoffman/kunze for la
which im assuming you can handle given your request
tho people here seem to prefare freidbergs la or linear algebra done wrong

[gray gazelle]

Are the a very short introduction books good starting points for getting the hang of some concepts math and not?

They're seems to be hundreds all made by different authors. Should I just judge the quality of it based on individual reviews?

[runic hatch]

What sort of introduction books are you looking at?

[gray gazelle]

Any of the a very short introduction books concerning mathematics and other sciences.

[runic hatch]

Can you give examples?

[gray gazelle]

No.

[runic hatch]

Ok

Well I guess in that case you might as well just go by reviews yeah

[gray gazelle]

There's seemingly hundreds to thousands of these books though so I was just wondering the general consensus on how people felt about them. They are Oxford university press so I suppose there is at least a level of quality expected.

[lime sapphire]

The very short introduction books are very general and not meant for study but rather just for looking at the big picture so i doubt you'd learn many math concepts let alone intuitively from them

[marble solar]

I'd say keep pushing through it. Find someone you can talk to about it

Maybe a calculus instructor at your school, someone here on discord, a private tutor

[gray gazelle]

Ah okay so textbooks are better to get introduced to a subject.

[lime sapphire]

yes

[cedar mist]

any good more modern computational geometry books that account for recent computational developments of the past decade or so? Been browsing O’Rourke’s methods for C and de Berg’s algorithms and applications which are both good but also really quite old

[restive falcon]

i would recommend looking at a proper textbook

like stewart, thomas, or spivak

i haven't used them

these are the three that i hear mentioned

stewart and thomas seem to be more like just calculation based

whereas spivak is more similar to regular university maths textbooks

I've heard

spivak calculus should be good

sloth recommended royden's real analysis afterwards if you want to go further

[sage python]

Fwiw idk if Royden is the best book necessarily but something at the level of Royden if that makes sense

Mostly because Royden seems to cover metric spaces and whatnot

So pretty much it does exactly the part of Rudin that isn't redundant with Spivak

[restive falcon]

yo hi sloth

did i summon you

it might be difficult at first

but people here can help

[sage python]

Eventually you'll have to do difficult things so might as well get used to it now 😛

[restive falcon]

#calculus (and #real-complex-analysis later) are the places to go

[smoky zephyr]

what book would you guys recommend for learning more advanced mathematical logic? i already know the basics of it

[dense hamlet]

Don’t go the #foundations route

It’s not good for your soul

[south salmon]

have you read a book on like discrete math? Or is that not what you’re looking for

[smoky zephyr]

i haven’t read a book for discrete math, and i don’t think that’s what i wanted

[south salmon]

I just think that like Rosen gives you intro logic so you can move into proof strategies
but if that’s not what you’re looking for, then I’m not sure

[subtle mango]

+1 for Rosen, you can just skip past the non-proof parts

[fervent lava]

Check this pins for this channel. diligentClerk has a reading list for logic text books.

[rain hound]

I've been reading Graham Priest's book on non-classical logic and it's been pretty good so far

if you would prefer more classical mathematical logic though, honestly I learned it best by working through Terence Tao's analysis textbook, it has lots of good shit, including axiomatic set theory, which is something so many books gloss over

[smoky zephyr]

i didn’t think the pins had that so i didn’t check lol, thanks

[smoky zephyr]

this is on my book list anyways, so thanks for the extra recommendation

[zenith oasis]

I love how aggressive the quotation marks in this book are

(It's Bartle introduction to real analysis

[glacial tartan]

stewarts calculus textbook or spivak's calc textbook

[fluid bay]

these books are not comparable

[remote ginkgo]

in for an answer on this too

didn't keenan crane do something in this space recently?

[hard falcon]

does antyone have any resources on vector questions

[rain hound]

can probably find them to your heart's content in any math methods textbook

[marble solar]

Looking for a good elementary ODE book that's not Boyce & DiPrima or Zille, but roughly covers the same material

Considering Schaum's outline to ODEs

[sage python]

What do you think of Hirsch/Devaney/Smale?

(That's what ODE here used to use, though last couple years I feel profs have been changing it up a bit)

[marble solar]

Oh this

I've heard Smale's et al. is very good

[sage python]

Also the one without Devaney is less chaos memes more LA

[gray gazelle]

Good math book for a road trip?

[restive falcon]

principles of mathematical analysis by walter rudin

seriously I'd recommend "Curves for the mathematically curious" if you don't want a textbook

[hollow shore]

what's it about?

[restive falcon]

some cool parametric curves

[hollow shore]

oh nice :')

[heady ember]

[restive falcon]

certified hood classic

[frosty girder]

[lapis sundial]

Jealous of being able to read on a road trip

[gray gazelle]

You can't?

[hidden rain]

probably motion sickness

feeling nauseous feels crap

[lapis sundial]

yes

[serene falcon]

how is abbotts book for real analysis?

how does it compare to rudin?

[hearty steppe]

You can use it to follow along with Rudin, which it is conveniently designed for IMO

But you don’t simply read PMA, your probably gona end up juggling 3-4 other books, probably one or two of them being algebra books, just to provide leverage to get through it

It’s a very hard read. And I think very few people can simply go thru rudin without supplementary texts

[glad prairie]

abbott is well loved i would say

it's less tough than rudin's book, which is a good thing in this case

[serene falcon]

yeah i’m trying to self learn real analysis, and my calc3 teacher recommended abbott

[surreal phoenix]

it's pretty gaming for self learning (that means it's awesome)

Maybe try Rudin after you're more familiar with analysis, but I wouldn't recommend diving in soon

[smoky zephyr]

well then i know what i’m doing for analysis

[manic seal]

any recommendations for an algebraic stuctures book?

[manic cape]

gallian, artin, jacobson, and dummit and foote

are all good

[foggy relic]

Pugh also recommended

[frosty girder]

u will do apostol

why? coz i said so

[gray gazelle]

I don't like Rudin

[gray gazelle]

Apostol is better

That is why

[restive falcon]

i disagree

it's very slow

and imo doesn't have a style that keeps attention
whereas rudin for example is full speed ahead on the next proof before you know it

that could just be me though

i would recommend browder

he covers a lot more content, and it's overall more concise

[rare patrol]

Hi, do you guys think George F. Simmons covers PDEs well? I'm a beginner in PDEs rn
Should I switch books? I loved it for the ODE part

Would you guys recommend your favs for PDEs

[covert oxide]

Any book on the maths behind image processing or imaging in general?

By imaging I mean image editing eg: exposure, vignette etc

There must be some maths behind it, right?

[fervent lava]

Figured I let people here know another rigorous multivariable calculus book.
It’s called Multivariable Calculus and Differential Geometry by Gerard Walschap.

[fervent lava]

How much physics do you need to know for studying differential equation(That requires a decent linear algebra and real analysis background)?

[dapper root]

Absolutely none

[timber mesa]

[fervent lava]

Thank you.

[timber mesa]

though they have some applications ofc

a few examples come from mechanics

[mystic orbit]

what's some good math history book?

it'd be nice if it focused on the rise of modern mathematics and not too comprehensive

[karmic thorn]

Mathematics and its History, Stillwell

[mystic orbit]

542 pages 💀

will check it out tho

[karmic thorn]

You could probably find more concise survey articles 🤷‍♂️

This one is written like a textbook

So it even has exercises

[mystic orbit]

I heard about infinite powers!

but I don't think it serves my purpose

the main reason I want to read about math history is because I was curious about axioms and how they came to be...etc

and maxj suggested I read a book on math history

[quick hornet]

if you want a textbook specifically on the history of logic, try Grattan-Guinness' The Search for Mathematical Roots

then read Believing the Axioms

i dont know of a less "academic" source, i dont think one exists

since "history of formalist logic" is kind of a niche topic lmao

not the kind of thing that makes for a good pop math book

[restive falcon]

then naturally next should be principles of mathematical analysis by walter rudin

[quick hornet]

but Grattan-Guinness is very very good

we need an emote for "not funny"

taking suggestions

[frosty girder]

we have that

[smoky zephyr]

alison not mentioning rudins book for 24 hours challenge (impossible)

[restive falcon]

sorry 😔

[remote ginkgo]

agree

[mystic orbit]

have you done rudin yet, alison?

[trail yarrow]

What is a good abstract algebra book

i was looking at this https://www.amazon.com/Abstract-Algebra-3rd-David-Dummit/dp/0471433349/ref=pd_bxgy_2/143-8919247-5931369?pd_rd_w=5M11S&pf_rd_p=6b3eefea-7b16-43e9-bc45-2e332cbf99da&pf_rd_r=A4M218Y8VP136QXA9ZQF&pd_rd_r=14338793-1b33-463e-a365-3d1b7b5e1fb1&pd_rd_wg=X7sVf&pd_rd_i=0471433349&psc=1&asin=0471433349&revisionId=&format=4&depth=1

[surreal phoenix]

Concise isn't always a plus, especially so for a beginner

I wouldn't recommend Abbott to someone who's already familiar with proof based maths to some degree, and if that's the kind of person we're talking about, then I agree with you

[marble solar]

I liked Richard Elman's Lectures on Abstract Algebra

[surreal phoenix]

But the person I was replying to said they were still doing calculus, so I wouldn't be doing them any favors by recommending something concise, Abbott is definitely enough work to keep someone new to analysis on their feet

It's a kind introduction, but it's still analysis

[trail yarrow]

alright thank you

[hearty steppe]

Say what now?

You always got recommendations I never heard of

[marble solar]

https://www.math.ucla.edu/~rse/algebra_book.pdf

That's because I got a good education that most people haven't in math

I don't like the part on group actions or orbits here

But the other parts are great

Really helped me in my grad algebra sequence

If I get into a PhD program, I'll be working through this, complex, and real

[restive falcon]

this is at least somewhat subjective

[marble solar]

To say that I got a good education in math in a way most people don't?

I don't think that's subjective

I'm not saying there are no other good ways learning math

But my particular path wasn't a standard one

[restive falcon]

fair enough

[marble solar]

I dunno, why don't you look through it

And see if you're ready

Alrighty, well give it a looksy and see if you like

It's a good algebra text that I like a lot

I learned directly from Elman, but I was too engaged in other things to truly learn like I should have

[manic fox]

me when the aba^-1b^-1

[marble solar]

I'll have to face the fact that I have to learn algebra eventually

The only thing I learned was basically Commutative Rings and Algebraic Curves

Some elliptic stuff as well

I think a week or two will not be sufficient to learn a year's worth of graduate algebra sequence to pass a qualifying exam for a PhD program

I'd probably need ~ 2-3 months with a staggered study schedule

And a good study group

[mellow bison]

are there any books for basic, math-comp level probability/stats?

[marble solar]

I finished my MS. I'm out of school for now

I get to work while I await for decisions on my fate

Supposedly within the next week and a half I'll know what I'm doing

[restive falcon]

this will not be the same sort of algebra

[marble solar]

I dunno, hopefully

[restive falcon]

yes

[marble solar]

It's up for the admissions committee to decide I'm good enough for them

[restive falcon]

this algebra is about ways to combine objects in sets

that satisfy certain properties

gor example addition and multiplication
but also function composition

no you don't need much logic/set theory other than what you'd need in any field

which isn't much

same

[trail yarrow]

he was ur professor?

if so that's like learning econ from krugman

[marble solar]

I had a lot of famous profs. They were usually not as good as other, lesser known profs

[restive falcon]

how so

[marble solar]

Just not as dedicated to teaching

🤷‍♂️

[restive falcon]

advice taken
for if i ever get that far

[trail yarrow]

you wanna be a prof?

[restive falcon]

yes

I'm like 16 now tho

so it's far off

[trail yarrow]

i see

[mellow bison]

.

[restive falcon]

depends

short term is awful

long term is pretty good

also #discussion

[supple ferry]

If anyone want to know more about geometry and mechanics i recommend this book

Above

[quick hornet]

[supple ferry]

Dont sully me

[robust mortar]

Is it outdated though?

[karmic thorn]

[gray gazelle]

I was looking for something easy about mechanics tbf

Landau is too much for me

[manic cape]

Try taking a look at books from Thorton & Marion or Taylor

[gray gazelle]

thanks

[prime oak]

Opinions on Pugh RA?

[glad prairie]

I think pugh is based. It's very explanation and intuition heavy but it can feel like the arguments are not presented rigorously at times

The level of content is the same as rudin, but the presentation is basically opposite

I would say in general that pugh is a good option but that you should keep something else on hand for proofs that dont feel fully rigorous to you

@prime oak

[prime oak]

i see

im planning to use it in conjunction with rudin

[glad prairie]

Thats probably the best usage

I also really like pughs problems and extra sections. They're fun and experimental

[prime oak]

gotcha, ty

[sudden kindle]

Any one used Stein and Shakarchi's Fourier Analysis?

[glad prairie]

Didnt metal

@broken meadow

Ive skimmed it but i havent read it

Like

To learn

[gray gazelle]

is there book or pdf for sat math guide ?

please tag me

[sharp latch]

@gray gazelle Princeton review is a great choice

[livid ermine]

I only read the first two chapters, but I thought those were really really good. Did a very good job motivating the material.

[broken meadow]

yes

i read thru it for a class

[tranquil orbit]

Can anyone recommend a set of books for nunher theory

[tulip blade]

A classical introduction to modern number theory

[sage python]

Counter: A modern introduction to classical number theory

Fite me

[brazen niche]

wouldn't this slows down your thinking

modern people should think in a modern way

I believe it even does harm to highschool students

rather than reading this. Nowadays people would just learn the symplectic geometry, and then classical mechanics

[quick hornet]

this is why you dont post dumb jokes in #book-recommendations

let this be a lesson to future users

(also lol at symplectic geometry)

[brazen niche]

I'm not talking jokes. A student in my highschool learn classical mechanics and geometry in this way in his last year. The joke is that the guy recommended principia

[quick hornet]

...yes

the guy who posted principia was joking

glad you figured that out chief

[brazen niche]

zorich's mathematical analysis is also a good book to mathematical physics students that you can learn freshman analysis and differential geometry at the same time

[gray gazelle]

How do you all afford real textbooks?

I was casually adding textbooks which interested me and I got easily over 500 dollars.

[tepid prairie]

Dover Publications. 😆

[gray gazelle]

It's insane how expensive a lot of textbooks are.

A general biology textbook is 150 dollars.

[tame pivot]

it's even more crazy that the only real difference between most editions is the order of the questions!

[tepid prairie]

The textbook cartel.

[gray gazelle]

Really?

[tame pivot]

from what i've heard from my mom who TA'd, yeah

[gray gazelle]

It would probably be cheaper to just get an ebook and print all the pages.

Spend an afternoon.

[tame pivot]

professors will make you buy their newest edition of textbook despite the content mostly being the same

but you have to do it or else when they assign you questions, you'll be doing the wrong ones

[gray gazelle]

Ah I'm not in college just have a general interest in the subjects.

[tame pivot]

ah yeah

[gray gazelle]

Do colleges help you afford textbooks?

[tame pivot]

tbh very loaded question

it's very dependent on how much financial aid you get

at least, in the US

[gray gazelle]

Yeah I suppose that's true.

https://www.amazon.com/gp/product/1111990360/ref=ox_sc_act_title_3?smid=AK1E2EC2U4ETR&psc=1 How is this for a general college algebra textbook?

https://www.amazon.com/gp/product/0835934535/dp/ Would this be a good combination for a general introduction to algebra?

[tame pivot]

if my assumption that this is high school/lower level algebra, then i'd suggest using something like khan

i dont think textbooks are really necessary until like calc 3/lin alg

[gray gazelle]

Well it's a college level algebra textbook I believe yes?

[tame pivot]

lot of textbooks used in high school have the word "college" in them

since you're looking at a pre-algebra textbook, i assume that this is like algebra 1 algebra 2 level stuff

[gray gazelle]

https://www.amazon.com/gp/product/013446916X/dp/ So this one is highschool as well?

[hearty steppe]

I don’t like how curriculums like this try to enable people to think that learning math is just some simplified streamline process

A lot of students I tutor struggle with “remedial math” such as college algebra and such.

These courses don’t really teach you math but just enable you to memorize formulas and think plugging in simple algebraic manipulations is enough to guide intuition when it’s not. Math is very abstract

[gray gazelle]

You're talking about a separate conversation?

[tame pivot]

it looks so, yeah

[hearty steppe]

And these curriculums are so loaded that it makes the experience of learning math for real, disingenuous

[gray gazelle]

Okay I'll look for one that colleges use and come back.

[tame pivot]

you could say it's 'used in college' but i mean, even the introductory level college algebra you dont need textbooks

[hearty steppe]

Think about how students take two semesters of calculus for nothing.

[tame pivot]

introductory level college algebra is about the same as what most would learn in high school

[gray gazelle]

Oh by the way how can I gain access to college cirriculums? They should be publicly available yes? I want to get some textbooks on mechanical engineering and other subjects but I'm not sure where to find the cirriculums.

[hearty steppe]

Most students*

[tame pivot]

most colleges will publish the required courses for certain majors

and in those courses you can find general outlines of the curriculum

some colleges publish video lectures

[gray gazelle]

Okay so I just need to look up random colleges until I find one that has that available.

[tame pivot]

sure

[hearty steppe]

If you want to learn math, I hope you plan to do more than go through a college algebra class, a precalculus class, and two semesters of elementary calculus because you are not actually learning math yet in those classes

[tame pivot]

imo, when thinking about "what textbook should i use," don't use one just becuase a college uses it

or resources in general

[gray gazelle]

I'm sorry who are you talking to?

[hearty steppe]

Anyone who needs to hear this

[gray gazelle]

Oh of course it's just a general indication that the textbooks have at least enough value to put a student through a degree.

[tame pivot]

right but you're not really planning on a degree, you're just looking for self-studying

so only buy textbooks when you absolutely need to

again, for simple algebra, i recommend online free resources like khan

[hearty steppe]

Did you check the pins for this channel? I know basic math by Lang is mentioned in it. You can follow Paul’s online notes as well

[tame pivot]

^

[gray gazelle]

For what?

[hearty steppe]

If you search Paul’s online notes on Google

[gray gazelle]

I'm well aware of the site I don't see the relevancy of it to this conversation though.

[tame pivot]

the relevancy is that it has what you need for your current level of math

and is a free and great alternative to a $150 textbook

[hearty steppe]

So Paul’s online notes is pretty well structured for most common math courses for college majors

[gray gazelle]

Of course but the college is generally going to try to supply the student with enough information to be able to function well enough in a field concerning their degree.

[hearty steppe]

But again those math courses are watered down for people who aren’t serious about math

[tame pivot]

yeah so worry about buying "college level" textbooks when you get to college

imo? the best textbooks dont have anything about "college" in their titles

ultimately you can buy textbooks for something elementary like algebra 1 and 2 if you insist on doing so

it's just not a great financial decision

when something like khan can provide you more than a textbook can

[gray gazelle]

Interesting I'll avoid textbooks on early algebra then.

[tame pivot]

mhm

i'd suggest if you're super passionate about math, come back and ask for textbook recs when you get to around calculus 2 or 3

there's great textbooks out there for that level of math that online resources can't really replace

[gray gazelle]

I'm asking about college algebra textbooks right now.

[tame pivot]

but for things like algebra, pre-calc, trig, basic calc, etc, khan p much has u covered

[tame pivot]

ye im just saying in the future when you consider textbooks, that's the level you should be thinking about for textbooks

[gray gazelle]

Yes that's what I'm doing right now.

[hearty steppe]

Try knuths concrete mathematics and Lang’s basic math

You’ll learn a lot

[gray gazelle]

So what would be a good college algebra textbook?

[hearty steppe]

Paul’s online notes should be enough for you to work through for that kind of content but if you want to reinforce what you are learning, Lang is the way to go for that level of stuff.

Knuth will help more with a foundation if you need more insight

[gray gazelle]

https://www.amazon.com/Algebra-Graduate-Texts-Mathematics-Serge/dp/038795385X/ref=sr_1_1?crid=18WQG9PRSWOHD&keywords=lang+algebra&qid=1646712065&s=books&sprefix=lang+algebra%2Cstripbooks%2C136&sr=1-1

This textbook?

[hearty steppe]

No

Basic mathematics

[gray gazelle]

I'm sorry?

What algebra textbook were you referring to?

[hearty steppe]

Basic Mathematics https://g.co/kgs/4zKciL

[gray gazelle]

Oh okay so his linear algebra textbook?

[tame pivot]

https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877

[gray gazelle]

Right so his linear algebra college textbook I suppose. Thanks.

[tame pivot]

nooooo

nonono

linear algebra is not simple algebra

[hearty steppe]

We literally linked it for you bro

[tame pivot]

this one

[gray gazelle]

I wasn't asking about simple algebra. I was asking for a college algebra textbook.

[tame pivot]

then why would you link a pre-algebra textbook

[hearty steppe]

College algebra is basically remedial algebra with catch all term “college” thrown into it

[tame pivot]

^

again, "college" in the title doesnt mean anything

it's just a way to attract naive students who dont know how to look for textbooks

they see college and think "oh this is for me!" when there are far better alternatives

[gray gazelle]

Yes I see.

[tame pivot]

if you want to learn college-level algebra, like algebra 1 or 2, use paul's online math notes

[tame pivot]

if you really want to hone in, use "Basic Mathematics" by Serge Lang

not Linear Algebra by Serge Lang

that is not algebra 1 or 2

that is higher level algebra

[gray gazelle]

No it's not basic algebra yes.

Yes okay linear algebra would be the closest thing. Thank you.

[tame pivot]

you can buy it if you'd like

it's a good book

you just wont understand it rn

if your goal is to learn algebra, you will not understand that book by lang

you will, however, understand Basic Mathematics by Lang

[gray gazelle]

I don't appreciate your tone. I asked a question and I was lead to the linear algebra textbook which would be higher algebra in college. Thank you this discussion has spent its usefulness.

[tame pivot]

hey im just being honest

you linked a pre-algebra textbook so i assume you dont know basic algebra

and there's nothing wrong with that, im trying to save you money from buying a textbook that is too high for your level

[gray gazelle]

Oh I had thought this channel was for book recommendations. I didn't ask for you to try to examine my situation and find the best book for me unrelated to my question I asked a fairly simple question which was asking to find a college algebra textbook. That would be Linear algebra so this discussion is quite over I think.

[tame pivot]

sigh

[sick flame]

eh idt its wrong to examine ur level

i mean they are recommending u smth

[gray gazelle]

Something unrelated to my question yes.

[sick flame]

What was ur question again?

[gray gazelle]

It's something extremely irritating but common with individuals that are concerned with academics. I asked for a college algebra textbook.

[sick flame]

Wdym by college algebra

[gray gazelle]

Linear algebra was the answer.

And I was given a book so the discussion around that is over.

[sick flame]

ok

[tame pivot]

for reference, they linked this book and asked if it was a good "college algebra" book^

[gray gazelle]

Yes.

[tame pivot]

they also linked a "pre-algebra" textbook and asked if it was good supplement

[gray gazelle]

Yes.

[tame pivot]

the topic of linear algebra didnt come up until you saw the name "linear algebra" in the title

[sick flame]

if u dont mind answering what grade are u in?

[tame pivot]

if you needed to learn linear algebra, you would know you need to learn linear algebra

and not college algebra

[sick flame]

yea pre algebra is way below linear algebra

[gray gazelle]

What grade I'm in? I'm not in highschool.

[tame pivot]

call me stuck up as an "academic", im trying to save you from spending money to buy a book to open and read that you will not understand

[sick flame]

so elementary school?

preschool?

[gray gazelle]

Very funny.

[sick flame]

;/

[gray gazelle]

Your conception of what I will or will not understand is not relevant to the original question.

[tame pivot]

let me ask you this

do you know what a matrix is?

[gray gazelle]

Why are you asking me this? I don't see the relevancy in the question.

[sick flame]

i still dont get what ur og question was cuz you're everywhere

[gray gazelle]

I was asking for a college textbook on algebra which would be linear algebra.

[tame pivot]

because matrices are prerequisite to entering a linear algebra textbook

[sick flame]

well no duh pre algebra is a really bad review

for linear algebra

[tame pivot]

it's one of the things you're expected to know when going into a book like Lang for Linear Algebra

[gray gazelle]

I do not see the relevancy.

[sick flame]

ok well hf wasting ur time learning linear algebra after pre algebra

🙂

[tame pivot]

oh well, i tried

at least linear algebra by lang will make a nice bookshelf decoration until you can learn it

and when you can learn it, then enjoy

[sick flame]

lmao

[tame pivot]

i've heard it's a really good book for linalg

not so great of a book for learning what a polynomial is

[gray gazelle]

In the future I'll try to specific whether or not I want a book recommendation for a specific subject or an examination of my academic level to try to find prerequisite material for that question.

[sick flame]

or even better 6x=66

[quick hornet]

what a bizarre conversation

[dark valley]

I don't have a good foundation on maths, and I've picked up bits and pieces here and there, but I always feel like there are things I don't know. Is there a good book to go over and learn some basics? (I guess algebra and geometry being the main topics)

I'm currently in calc 2, I'm doing okay, but there's always that feeling that my previews knowledge isn't complete

[flint forge]

khan academy is great for this

start wherever you are confident you know everything

and then just go through and review stuff

[dark valley]

oh okay

[dark valley]

thank you

the difficult part is figuring out what I don't know

what is the path to calculus 2?

in what order should the topics go I guess

[flint forge]

i think khan itself has an outline it recommends

[loud trail]

paul's online notes has pretty good supplemental material

my college uses "college algebra & trigonometry" by lial, hornsby, schneider and daniels for their remedial algebra classes, so you could check that out if you want a lot of practice problems on hand

what could be helpful is if you know which topic you're confused on and search that term for online resources. for example, maybe you have trouble with trigonometric identities or composite functions. the more specific your search term is, the easier it will be to find help online

in terms of "path to calculus 2", it may be best to look up course outlines of remedial algebra classes & calculus 1 so you can have a sort of checklist to go through

[dark valley]

Thank you so much!

[dark valley]

I appreciate the help!

[hollow shore]

Axler's precalc book is also very good

[iron granite]

Resources for Hilbert spaces. I only know some linear algebra and calc 2.

[supple ferry]

How dare you this is thengreatest work by the greatest teacher

omnibus non nisi omnibus

[dapper root]

lmfao

[supple ferry]

τι είναι τόσο αστείο

[sage python]

You want to do real analysis first. In particular basics of metric topology

Also was your calc/LA proof-based?

[gray gazelle]

How good is Halmos' LA?

[coral narwhal]

FDVS or LA problems?

[gray gazelle]

FDVS

[gray jungle]

from what i heard its a good reference and very terse

[gray gazelle]

@gray gazelle dont listen to these guys. You should check Aluffi Algebra Chapter 0. Works out a lot of the higher algebra you seek. Linear and abstract. Make sure to go deep in the preliminary Chapter

[bronze gyro]

does anyone have a book with practice problems and lessons for all of algebra (1, 2, honors-level topics as well)

[gray gazelle]

Thanks!

No problem, good study

[still saddle]

plus one, Aluffi & Artin made me appreciate algebra.

problem selection is also great

[gray gazelle]

Very based

[solar anvil]

does anyone know of any books for learning calculus through a more proof and theoretical based approach, that would be fit for a highschooler?

[mellow bison]

there is spivak though idk if its the right book for what u want

[solar anvil]

yeah I was considering that, but im worried the problems will be way to difficult for me

my current background is math is kind of everywhere, though I can say I have a pretty solid understanding of discrete mathematics, elementary linear algebra, and just calc 1-2 ( not very rigorous )

ive just been dying for a more rigorous understanding of calculus though

as im not satisfied of how im currently learning it

[inner token]

How experienced are you with writing proofs @solar anvil

[brittle breach]

If you have done calculus before,
See if Abbot Understanding analysis strikes your fancy

[inner token]

Fantastic recommendation

[solar anvil]

im decent with them

[solar anvil]

thanks ill check it out

[inner token]

Give Abbot a try. Everything is really well motivated

[mellow bison]

spivak is meant for experienced people right?

not as a way to learn calculus from scratch?

[runic hatch]

yeah it'd be very helpful to know some calc before going into spivak

[grand thistle]

would yall recommend Abbott or Apostol for analysis?

i dont really wanna go baby rudin

i'm thinking of going through it after i finish apostol's calc volume 1 and a combination of hubbard and apostol for multivariable calc, linalg and differential forms

i want to go through an analysis book along with mendelson's intro to topology

after

so i can start like differential topology or diff geo

[supple ferry]

First do geometry before you even touch topology

[gray gazelle]

I skipped freshman analysis. I do topology then real analysis

[supple ferry]

Ok

[gray gazelle]

if you don't have other courses need to take (for example in summer) you can just finish baby rudin in 3 weeks. It just like a dictionary book, although not pedagogical but using this book you can attain the minimum knowledge of mathematical analysis quickly

[supple ferry]

True knowing basic meaning of things can help improve your math skills

[grand thistle]

im looking more towards apostol

since i like his exposition

and he also covers about the same material

but

i guess its more approachable

[grand thistle]

differential geometry? what type do you mean

i mean im pretty sure hubbard and hubbard covers a tiny bit of diff geo at the end, so i think i can just go straight to a diffgeo textbook i have if you think topology will be too difficult

[supple ferry]

Ok then you can go to that book

[grand thistle]

but then in the book's preface it says one of the prereqs is point set topology

thats the general topology covered by mendelson im pretty sure

[grand thistle]

isnt analysis a pre req or at least a co requisite for topology? sorry im not very experienced

[gray gazelle]

not necessary. for example, you can just learn the concept of continuity in topology.

[grand thistle]

oh i see, so you reckon i could jump straight into diff geo after going thorugh vector calc and the topology book then?

[gray gazelle]

usually, your first course in differential geometry is the "differential geometry of curves and surfaces", for this subject, you only need vector cal, linear algebra, and elementary DE

there are a lot of types of differential geometry, including: riemannian, lorentz, symplectic, poisson, contact, complex

[grand thistle]

my book seems to be about riemannian (i think) dg

and it says this

for the prereqs

[gray gazelle]

yeah this agree with my opinion

[gray gazelle]

if you are doing riemannian geometry rigorously. You must need final year level real analysis

this book is for physicists so it will do this in a less-rigour way

usually physicists learn riemannian geometry for doing gr-qc research

[grand thistle]

according to him, this is a halfway point between math and physics differential geometry

which i like, since i want to do physics

so i think ill go with this book after i do the topology book and vector calc/linalg

[gray gazelle]

I am also interested in gr-qc(general relativity and quantum cosmology)

You can also try nakahara if you dont want to learn topology

It has a full chapter dedicated to that

But I would choose to use Wald GR and accompanied by John M Lee's book on riemanian manifolds

+some other prereq stuff

[gray gazelle]

First do topology before you even touch geometry?

[gray gazelle]

in my university students learn topology before diff geo

[grand thistle]

hmm i see, ill look into it

[gray gazelle]

while wald GR is indeed the most hardcore book on GR, it suits theoretical(but not mathematical) physics students

[supple ferry]

Imdid it and I understood topology sorry

[gray gazelle]

correction*
you should first do topology, then do topology, and then do even more topology

learn topology until you start to puke with the amount of topology you've learnt

[gray gazelle]

Does anyone have this book? I need photos of exercises that are in this book so I can solve them. I'm not sure this is the right channel to ask.

[gray gazelle]

anyone here read lang's basic mathematics?

[hollow shore]

I have read the initial chapters

[gray gazelle]

Has anyone here ever read "everything you need to ace x" book series?

Are they credible?

is it worth reading?

[keen flare]

very good I can tell just by looking at the cover

[gray gazelle]

Very funny

Haha

[inner token]

Guess I can sell my library on Amazon and pick that up instead

[gray gazelle]

Look at the reviews and such

It's like school but in pretty book format

[keen flare]

No construction of the reals?

Terrible book

[keen mountain]

does anyone know a good math recap book for high school/college maths?

i'm feeling so lost looking at formulas

oh yeah and a book for what symbols in math are and how the grammar works

[keen flare]

Maybe you should specify what subject? (college maths is not specific enough) Notations differ from different subjects. If you mean the basic symbols like $\forall$ or $\exists$, maybe any intro to proofs book

[hasty eagle]

neko fanboy

[clever ore]

I have another kind of a general question. I always enjoyed the problem solving aspect of mathematics, but I've noticed that when you get deeper into the university tier math, the study material gets a lot less exercisy and starts having a lot more of just reading and even some memorisation.
I don't necessarily have a problem with reading, but I also like exercises and doing nothing but reading can get kind of dreadful.
Is this something that you just need to get used to in math or is it more of a case by case thing, where some things will have amazing study materials available, while for others you just have to make due with what you get?

[gray gazelle]

@clever ore doing exercises is still a good way to learn, just exercises become much harder to solve

[clever ore]

Yeah I've noticed that, and I'm okay with that. But there are some courses and materials where these kinds of practice exercises seem very hard to come by

[runic hatch]

I feel like in some cases it’s just that any good exercises would just straight-up be open problems for some topics

[gray gazelle]

I know. Sometimes you don't need to be an expert in the material you're reading ig

So no need for exercises

[clever ore]

eh

that's not a very satisfying answer but i'll take it I guess lol

[runic hatch]

You can always just play around with the results and see what else you can come up with I guess

Sort of like creating your own exercises

[clever ore]

Right

[runic hatch]

I’ve started doing that myself, mostly along the tune of “what happens if I do this?”

[gray gazelle]

It's also that not everything is computational, so you don't always need exercises to understand a topic

[runic hatch]

Yeah later exercises also tend to take the form of “complete this proof”, or the proofs themselves may be very barebones and need some filling in

[clever ore]

We've had a lot of exercises that ask you to just prove something, those are cool imo

[gray gazelle]

It's hard to say, every math field is different about this I think

I'd expect analytical number theory to be very computational for example

[clever ore]

Guess I'll just accept that it depends on the field and then avoid the fields that are nothing but reading like the plague

[gray gazelle]

I feel like you'll enjoy analysis a lot

[sick wigeon]

I know only basic real analysis and group theory. Will it be useful for me to read category Theory?
I was given quite a number of simple commutative diagrams in the course which made me consider it

If so, then will the book by Harold Simmons be useful?

It 'looked' nice

[flint forge]

I would wait until you have more background

And then I would read riehl

[glad prairie]

definitely a good idea to know some topology first, among other stuff.

[slim peak]

People should stop praise about "Holy Category Theory", this is a powerful theory interesting for its own purpose with many applications (even in some "Applied" sub fields), but this is not an all mighty point of view.

And I join Ryc, having some background in general and metric topology would be better to get into the subject.

[frosty girder]

no construction of reals is the based way to go

the fundamentally correct way to do it

[sick wigeon]

I see ... Alright then 👍

[wicked trout]

How to study from the books? Is it ok plan to solve all the book in order to extract every bit of knowledge from it?

[gray gazelle]

Hey guys, is How to Prove it by Velleman a good book for beginners?

[tame pivot]

sucks imo

read Rosen

[gray gazelle]

What would be the easiest book to follow in terms of proof writing?

[tame pivot]

"Discrete Mathematics and Its Applications" - Rosen

Rosen teaches proofs

[gray gazelle]

I have a hard copy of Velleman.

Why is Velleman bad?

[tame pivot]

Rosen teaches what Velleman teaches in a fraction of the words

[gray gazelle]

But I want to grasp a good understanding.

Like I'm very lost

[tame pivot]

Rosen gives a great understanding, imo velleman talks too much

[gray gazelle]

So Rosen is more organized?

[tame pivot]

there's also resources in the pinned of this channel for Proofs and stuff

yeah

[stray veldt]

just try velleman, see if it works

its very long and the later chapters are bad i think

but at least the first half is decent, just long

[gray gazelle]

Good idea

[stray veldt]

if you want something faster, i wrote a short intro pinned in #proofs-and-logic

if you want something that does actual mathematics, check aluffi's notes

[gray gazelle]

I just downloaded the intro

[gray gazelle]

What would that look like?

[stray veldt]

he does intro proofs in the first half

and then an introduction to topology and some set theory

stuff that every undergrad math should know but there isnt necessarily a class on it

http://www.math.hawaii.edu/~pavel/Aluffi_notes.pdf

[gray gazelle]

Alright. I guess I will start with basic intro proofs.

Thanks for the notes

[gray gazelle]

Is serge lang good book to start math again?

basic mathematics

[rain hound]

Some have had a positive experience with Lang. personally I have not. He’s generally quite terse.

[gray gazelle]

I didn't really finish calculus but im long past highschool

I want to do math self-study and my goal is to learn calculus

I just want to start from algebra/precalc but don't know where to

[rain hound]

For your background, I think khan academy combined with 3blue1brown’s calculus series would be pretty good.

That’s what I did when I needed to start from the beginning and learn everything

[gray gazelle]

I prefer books over videos, and 3b1b is just overview and perspective, not actual course, I've watched all of the videos and I'm pretty sure I don't know calculus

[rain hound]

Oh 3blue1brown is absolutely a supplement you’re right. That’s why you still get the meat from khan academy.

[gray gazelle]

I still would like a book

I don't think I'll do khan academy

[rain hound]

3blue1brown is mainly for the intuition, but to actually grasp the material requires work

Khan academy is just good for all the details in early math. But very well. I’ve heard good things about Sheldon Axler’s precalculus. And for calculus, I greatly enjoyed Silvanus Thompson’s Calculus Made Easy.

Honestly for intro algebra stuff, Leonard Euler’s elements of algebra is actually pretty nice. It’s a bit dated at this point but I’d expect you’ll still get a lot out of it.

[gray gazelle]

ill look into euler's book thank you, right now im leaning more towards lang's basic math tho but ill try euler first

its table of contents just look so good idk why

[hollow shore]

I am using a mix of Axler's PreCalculus and Lang's Basic Mathematics. I think I can shill Axler and certain parts of Lang.

[gray gazelle]

Do I need both or can I learn from either? @hollow shore

[hollow shore]

either would do

I would prefer Axler though

[gray gazelle]

Thank you very much

[slender cargo]

I think this book is often fancied by people higher up in math for showing a more rigorous, proof-oriented view of lower-level math where rigorous arguments and proofs are often less of a thing (or not even a thing at all). If that's the route you want to go in the future, then I think Lang's Basic Mathematics is designed with that in mind. On a related point, calculus is usually studied first in a non-rigorous fashion, where instead you're supposed to learn calculus on a more geometric, intuitive level. There are calculus books that instead teach calculus in a proof-oriented, rigorous way (the exercises are substantially different in those)

[long spoke]

Hey guys I need book on the basics of discreet math and like the math required for computer science

any recommendations

[rain hound]

Book of proof by Richard Hammack, is a pretty nice intro. And concrete mathematics by Donald Knuth will more or less finish everything for you. Also this is pretty good https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/readings/MIT6_042JF10_notes.pdf

[long spoke]

thanks

[umbral yoke]

does someone have a recommendation for a book covering complex manifolds with lots of pictures?

by lots I mean lots

[fallow fern]

Hey everyone, I’m a high school student who’s looking for recommendations for books about differentiation and integration, and would like to know if you guys have any you recommend?

A book with exercises would be a big plus as well

[keen flare]

Obviously

(Kidding)

[sage python]

Feels like beyond dimension 1 you can't really draw many pictures anymore

[marble solar]

Spivak's Calculus is good

[fallow fern]

Hmm, I’ll check it out, thanks!

[fathom osprey]

Any book recommendation for Graph analytics books ?

[tulip blade]

What is graph analysis?

[fathom osprey]

I mean graph analytics sorry

[quick hornet]

you might get better recommendations for that in a CS q&a place

[tulip blade]

Ive never heard of graph analytics

[fathom osprey]

Thank you.

[quick hornet]

i think its the buzzword ML people use for like, systems/network analysis and stuff

[hearty steppe]

Have you gone through Bona’s combinatorics and graph theory yet?

Analytics itself is a buzzword

It just means your working with abstracting information from data sets

[fathom osprey]

Well I get it from my field. Software engineer

And I am working on integrating analysis of graphs into blockchains

[hearty steppe]

That doesn’t matter if you don’t have a rigorous understanding of graph theory.

This is partly why I don’t take the engineer mindset seriously most of the time.

Work through Bona. I started working thru Bona recently. The exercises are gona put you thru hell cuz they’re hard af but that’s how you learn this stuff imo.

I feel like buzzword books are mostly garbage anyway based on personal experience

It’s hard for me to work with graphs personally if the only context I have from them is from a comp sci curriculum based discrete math course which I’m assuming is the knowledge base you have

[gray gazelle]

Im currently struggling in financial mathematics

I need resources for content such as compound interest, simple interest, loan, instalments, annuity

[gray gazelle]

Discrete mathematics and its applications by rosen or book of proof for learning proof writing ?

of Velleman ?

[tulip blade]

@gray gazelle just read the table of contents and see which you think looks more interesting. I wouldnt spend soo much time on an intro to proofs book. Just cover basic set theory/logic, proof techniques, relations &functions. Then start reading whatever is interesting.

[inner token]

@gray gazelle book of proof is what I used and it's free on the internet

I have no complaints

[daring ravine]

Hello friends, looking for some overview books on:

1. Group theory
2. Combinatorics

Any recommendations? Thanks

Also is morris kline calculus a good calc book to start or would you recommend others

[fervent lava]

For combinatorics and graph theory people here have recommended bona a walk through combinatorics.

All non rigorous calculus book have the same contents nowadays, it’s probably best to go through this https://www.whitman.edu/mathematics/multivariable/multivariable.pdf instead of that.

It’s single and multivariable calculus, and it’s not 900 pages.

[gray jungle]

there is a nice pin on abstract algebra books

^

[fervent lava]

Shoot, I thought it said graph theory.

[heady ember]

[daring ravine]

Understandable

Also sorry what would be a more “mathy” (as opposed to phys/application based) calculus text

[brittle breach]

Stein and Shekarchi Fourie analysis

[daring ravine]

Ok i’ll check that out

Also will add that i’m kind of a noob if that makes any difference

[sage python]

That's not what I'd put under the banner of a "Calculus text" lmfao

If you're thinking very introductory Calculus, do Spivak

If you've already had loose/computational calc, do Rudin, Kriz/Pultr, or Browder Real Analysis

[daring ravine]

Basically i’ve done calc i and ii but feel like i don’t have a good enough foundation

[sage python]

Yeah then try one of those three

[daring ravine]

Alright thanks

[sage python]

ANd if it's too much then Spivak

[daring ravine]

Maybe i’ll start there

[fervent lava]

Browder

[marble solar]

I prefer spivak

yes

More exercises, better exposition, crafty problems

Takes its time with ideas moreso than Apostol

Also ostensibly cheaper to get a hardcover copy

paperback of spivak?

Calculus?

I mean if you plan on referencing it for years to come

You should get a hardcover

Is that a question?

I mean just think about it

[safe thunder]

books for an undergrad introduction to algebraic geometry?

[marble solar]

Fulton's introduction to algebraic curves

It's slow by many people's standards here, but I'm a firm believer of concrete examples that take their time developing ideas

[quiet forge]

HUZZAH!

[marble solar]

yUh, people here are too eager to skip more foundational things and jump straight into something like hartshorne or vakil

When in fact most students are nowhere near ready for something of that magnitude

Many graduate students struggle with Hartshorne/Vakil

Another interesting book is Geometry: Euclid & Beyond by Hartshorne

Gives you a historical overview and develops into things like projective geometry

To that end, this book also looks interesting

https://link.springer.com/book/10.1007/978-3-642-17286-1

[patent mango]

Any good books for number theory and graph theory?

[clever ore]

Any recommendations for learning about metaheuristics, or specifically simulated annealing? Books, papers, anything goes.

[gray gazelle]

Can anyone recommend a non-specialist/pop science book about the history and impact of (ordinary) differential equations? I'm looking for something to read the make me excited for a first introduction to ODEs.

[slim peak]

non-specialist/pop science I don't know but the Chapter 1, entitled Introduction (1.1, 1.2 & 1.3 p.1-21) , of Viorel Barbu's book review briefly everything from Physics/Chemistry/Enginering use of ODE to formal elementary computations to solve usual ones

(but be careful, read just chapter 1, the rest will be ....)

Hmmm

[frosty girder]

[manic fox]

hmmm

[crude wyvern]

any intresting books that a year 11 can read

[gray gazelle]

year 11 is what grade?

[gray gazelle]

u mean math books or any books?

[lapis heart]

gcse year

[gray gazelle]

what is that

[lapis heart]

wtf

im saying yr 11 is the year you take GCSE in

[tardy walrus]

Tbh idk what gcse is either

[gray gazelle]

i mean what grade

[tardy walrus]

I know it’s a test

[lapis heart]

ok ignore me then

[gray gazelle]

wtf is gcse

[real sand]

i recommend calculus

[tardy walrus]

Is it last year or year before last year of HS Shuri?

[gray gazelle]

huh? he didn't say a math book?

[lapis heart]

no

its -2

[gray gazelle]

what

[tardy walrus]

Ah okay

[lapis heart]

wait

let me be explicit

[gray gazelle]

u mean grade 7?

[real sand]

calculus isntmaths?

[lapis heart]

2 years before the final year

[real sand]

waait wut

[gray gazelle]

he didnt say he wanted a math book

[crude wyvern]

maths

[gray gazelle]

u mean grade 10

[tardy walrus]

So like
Final year
Semifinal year
Semi semi final year <- GCSE

[crude wyvern]

grade 8+

[gray gazelle]

ohh

[lapis heart]

How would know what I 'mean'

In a system I am not familiar with

[gray gazelle]

go for mathematical circles

[tardy walrus]

They really need to standardize all this

[crude wyvern]

what

[gray gazelle]

or like, higher algebra by hall and knight

that;s pretty good

[tardy walrus]

Or not, idk HS is dumb anyway

[crude wyvern]

English exan system

[gray gazelle]

ok or u can try a cartoon guide to calculus

[lapis heart]

are gcse's even english? I was under the impression they were taken in many countries

[crude wyvern]

dk

[gray gazelle]

idk what gcse even is, but whatev

[crude wyvern]

i think its in most uk countries tbh

[real sand]

let him live

no books at 11

[gray gazelle]

what

[crude wyvern]

nooo i like maths

[real sand]

or calculus

[gray gazelle]

he says he's grade 8

[lapis heart]

wait this is #book-recommendations maybe lets chill on the chat, woops

[crude wyvern]

i already have 3 calculators, 4 books but just revision ones

[real sand]

wwait are u asking for urself?

[crude wyvern]

yeah

[real sand]

oh

[gray gazelle]

higher algebra by hall and knight is ok for grade 8

and it's damn good

[real sand]

i thought u were asking for ur kid

[gray gazelle]

oof

[crude wyvern]

hmm

[real sand]

learn physics

its kind of maths

[gray gazelle]

stop bruh

[real sand]

wot

[lapis heart]

Stop on the chatter - #chill for shtposting

[crude wyvern]

lol like any kid is intrested in maths

[gray gazelle]

he's asking for a good book

[lapis heart]

They want a serious recommendation

[gray gazelle]

i am

[real sand]

then why are u

u said u r 11 yo

wot da

[gray gazelle]

#book-recommendations

not #chill

[real sand]

are u the second einstien ?

[gray gazelle]

bruh stop shitposting

[real sand]

alright

chill

im out

[gray gazelle]

ok where did allen go

[real sand]

i dont even know any books

[lapis heart]

@crude wyvern perhaps tell us what topics you are currently already studying and ppl can help you more (sorry, I can't)

[gray gazelle]

yes that would be better, tho ur probably asking for general math i think

[crude wyvern]

oh i meant like how year 7 or below can be intrested in maths

[crude wyvern]

general or algerbra stuff

maybe geometry

[gray gazelle]

for algebra, try higher algebra by hall and knight

[real sand]

whats ur age

[crude wyvern]

16

[real sand]

ohh

[crude wyvern]

mhm

[real sand]

wait someone used the integer 11

i thought u r 11 yo

ik this aint chill

bye

[lapis heart]

We've already established 'Year ??' describes what is called a 'Grade' elsewhere in the English school system

[gray gazelle]

ok so if he's 16 he's probably grade 11 in the indian school system

u can then try "challenge and thrill of pre-college mathematics"

It's a very good book

[lapis heart]

They are probably looking for something like an introduction to calculus. Not sure what else is introduced at this stage

[crude wyvern]

i meant year 11 not 11 year old

[gray gazelle]

then try "the cartoon guide to calculus"

it's pretty cool

[real sand]

ohh mb

[frosty girder]

i wont really recommend that book to someone who hasnt done any algebra before

[frosty girder]

oh hmm

[frosty girder]

why is every book in your recc so olympiad based

[restive falcon]

year 11 is gcse content

[lapis heart]

whats wrong with an intro to calc then 🤔

[restive falcon]

so the next bit of content is trig and exponentials/logs

[lapis heart]

I'm assuming they're looking for something to transition to A-levels / similar

[restive falcon]

ye

[lapis heart]

eh isn't that done in gcse?

[restive falcon]

no

[lapis heart]

🤔

[restive falcon]

well

[lapis heart]

different boards, different things.

[restive falcon]

proper trig isn't done

[lapis heart]

What is proper? I expect all the identities you need to know to already have been done at gcse, no?

[restive falcon]

no

they don't

do identities

[lapis heart]

🤔 🤔 🤔 🤔 🤔

[restive falcon]

this is not based on exam board

all boards do the same content

[lapis heart]

I vaguely remember having done the sin, cos rules, as well as compound angle formulas

But maybe not so then...

[restive falcon]

you definitely do in like
further maths gcse or equivalent

they changed the gcse spec quite recently