book-recommendations

[formal bronze]

Right, I sort of just assumed that they wanted recommendations for linear/abstract algebra.

[neon tiger]

.

[mystic orbit]

How tf are those bad marks?

[neon tiger]

Well I get above 90 percent usually

[mystic orbit]

No, being more interested in math than in other subjects isn't bad

[neon tiger]

But it is affecting the other subjects

[heady ember]

In what way is it affecting other subjects

[neon tiger]

Bad marks?

[mystic orbit]

I don't give 2 shits about stuff that I'm not interested in tbh

[heady ember]

Yeah but how is that directly related? Like do you spend so much time on math that you don't have any to spare for other subjects?

[neon tiger]

Ye that

[mystic orbit]

As long as I'm getting passing marks, i don't spend an ounce more of effort on them lmao

[heady ember]

I wish I could

[heady ember]

Hmm how much time do you spend on math?

On average

[paper plover]

asian

[mystic orbit]

We could do without the racial stereotypes

[heady ember]

Also, at this point its getting a lil' off topic I think

[neon tiger]

technically yes but not south east asian

[quick hornet]

Fuck off

Anyway, please use #book-recommendations to recommend books

[neon tiger]

ye so algebra books for olympiads

[mystic orbit]

Sry

[neon tiger]

high school

[neon tiger]

wish i could do that but im expected to be a topper

[gray gazelle]

Hi, I need a math book that will explain algebra for beginners.

[paper plover]

david burton

[gray gazelle]

Can you show a picture?

[paper plover]

uhhhh

wait

[gray gazelle]

?

[paper plover]

whoops

sorry

forgot

im sorry i mixed up the names

but this is the book i was referring to

[onyx wren]

nice!

my favorite book

[languid plinth]

Lang Algebra

[gray gazelle]

Could you send me a picture?

[mystic orbit]

Don't use lang to learn algebra

[languid plinth]

dont use lang to learn anything

he writes books to pay off his mortgage

all of them were written in less than 2 weeks

[mystic orbit]

Also, please specify whether you mean abstract algebra or HS algebra

[gray gazelle]

HS algebra

[languid plinth]

any textbook would probably be fine ig

[mystic orbit]

In that case, DEFINITELY don't use lang lol

[gray gazelle]

Where should I find them.

[mystic orbit]

And you should prolly just use Khan academy

[languid plinth]

DO NOT USE lib gen BUY IT ON AMAZON OR GO TO JAIL

[gray gazelle]

Thanks

[mystic orbit]

Sigh

This is a partnered discord server

Endorsement of piracy is prohibited

[gray gazelle]

What should I learn after HS algebra on khan academy.

[languid plinth]

anything u want

depends on ur interests

[gray gazelle]

More math

Linear algebra and Abstract algebra?

[mystic orbit]

Please delete this message before you're banned by one of the mods

[languid plinth]

ig u could learn analysis or that

[gray gazelle]

what is analysis?

[restive falcon]

the study of certain kinds of "nice" functions on spaces with both topological and algebraic structure

i think is the most general way you could put it

[rich sun]

with bornological structure

the notion of boundedness

[delicate shore]

I enjoyed The Trial by Franz Kafka

[gray gazelle]

Are you a fellow bornological space enthusiast?

[rich sun]

I have come across them in The Convenient Setting of Global Analysis by Kriegl and Michor.

when I tried to study smooth mappings between manifolds

[gray gazelle]

Prelude to calculus by sheldon axler maybe

[icy knot]

Guess I should throw his linear algebra book in the garbage

[gray gazelle]

On second thought after seeing its rating of 2.66 maybe not

[tawdry orbit]

I am interested in learning calculus, rigorously. Which between G.H. Hardy’s a course of pure mathematics, Tao’s Analysis, or Spivak’s calculus better to use? I know spivak’s considered a difficult text.

[mossy flume]

are you interested in learning calculus, or real analysis?

these mean different things, depending on what your level of mathematical maturity is (i.e. have you already taken calculus and maybe an introduction to proofs course?)

[tawdry orbit]

I have taken a calculus course. Calculus 1.

[remote sparrow]

how about you give me the book instead

[tawdry orbit]

I don’t want to get into a different text to learn introduction to proofs. That would take too much time, I think. Would any of those books teach me proofs at the same time as their named material?

[remote sparrow]

you're in an awkward position

some of the calc 1 material would be redundant in spivak, but i guess you can use it

you won't learn calculus from hardy or tao

apostol is good too

hardy is analysis

hubbard and hubbard is good for multivariable calculus

[tawdry orbit]

Yeah, I don’t want to spend months or weeks reading a 400 page “intro to proofs book” just to read an analysis book.

[tawdry orbit]

Hi, what do you mean by this? Spivak doesn’t use calculus 1?

Thanks.

I saw someone say it was the other way around.

[spare ridge]

lol nice functions

[night nebula]

Anybody have any recommendations for books on number theory, set theory, logic, etc.? I am not worried about anything being too advanced (most books no doubt will be, but I like the challege). Thank you

I'm honestly interested in anything that isn't geometry, graph theory, topology, or similar fields that do stuff with shapes

[remote sparrow]

number theory, try burton or dudley's books. set theory you can try enderton (montalban's lectures optional) or hrbacek and jech. logic you can use enderton paired with montalban's online lectures or try a new book by mileti.

[night nebula]

Thanks for the recommendations, I'll take a look!

[sturdy shore]

I now shill goldrei's books for both set theory and logic, pedagogically better than enderton imo

from what I've skimmed at least

[remote sparrow]

lems, you should try mileti. i need the reviews

a draft copy is available online for free if you don't wanna drop money on a physical copy

[sturdy shore]

I'll just wait for more than a draft copy, in no rush

[remote sparrow]

the physical copy is available rn

https://www.amazon.com/Modern-Mathematical-Logic-Cambridge-Textbooks/dp/1108833144

[sturdy shore]

it seems pretty good from what I've read of the notes, better than enderton at least imo (also more self-contained wrt set theory and cardinals) but it is also slightly more advanced than goldrei

but also I'm no logic expert so I hope people don't take what I say too seriously

just had to check out many for my course this term

[lean pagoda]

I'll shill Levy Basic Set Theory for an "intermediate" text - something a bit more mature than Enderton or others but still not requiring any knowledge of model theory.
My favorite introductory set theory text is by Ebbinghaus but unfortunately it's the only text of his that hasn't been translated into English (despite it even getting a new edition just last year)

[remote sparrow]

hmm, a dover

nice

https://www.maa.org/press/maa-reviews/basic-set-theory

here's the MAA review for levy's Basic Set Theory

i'll put it on my amazon wish list

[severe falcon]

I think Abbott’s intro analysis book would be ideal for you. It includes aspects of proof-writing and it’s very readable.

Also if you’ve never written proofs before, you can find lots of relatively succinct online resources to get familiar with different proof techniques, for example this one: https://math.berkeley.edu/~hutching/teach/proofs.pdf

Once you can comfortably do the exercises in there you’re ready to learn analysis. Definitely don’t skip the exercises!

[tawdry orbit]

Thanks! I’ll definitely try that out.

[remote sparrow]

just know you won't solve many computational problems like with spivak or apostol

like calculating derivatives or integrals

if you use abbott

given you still need to learn calc 2 and 3

tangentially, dover should buy the rights to apostol

[lean pagoda]

Oh jeez that review sounds pretty harsh
But I think students with a background in (basic) first-order logic might appreciate the careful (almost pedantic) treatment of the basics in the first half of the book

[remote sparrow]

neverbloom do you happen to have any recommendations for modal logic

or know someone that might

https://www.reddit.com/r/logic/comments/6c8knr/book_recommendations_for_modal_logic/

[fierce hedge]

One of the mods had a logic reading list are there no modal logic books in the list?

[remote sparrow]

i've only seen this

[remote sparrow]

diligentclerk wrote they have nothing to offer for modal logic

[sturdy shore]

the teach yourself logic guy might have some

[remote sparrow]

yeah but his list is sorta geared to philosophers

nothing wrong with that

[fierce hedge]

Not diligentClark, I think it was Loc... something something

[remote sparrow]

lochverstarker?

[fierce hedge]

yeah

[lean pagoda]

i know very little modal logic but i did end up looking for some books at one point and after having to go through hundreds of philosophy texts found two, gimme a sec

[remote sparrow]

benthem's Modal Logic for Open Minds seems like it might fit the bill, but do let me know

[lean pagoda]

is that the guy from the amsterdam school

[fierce hedge]

I think this is the list, I do see model theory

[remote sparrow]

yeah

[lean pagoda]

yea but it looked more like a philosophical text, no?

[remote sparrow]

it's probably the only book i remember since it's free online

[lean pagoda]

but funny you mention that because out of the two texts i saved for later one of them is from one of his students

modal logic by de rijke

looks promising, with a heavy focus on computer science though

the one other that seemed very promising was Tools and Techniques in Modal Logic by Kracht

[remote sparrow]

interesting, thanks

if anyone with more expertise would like to look at the r/logic post i linked above, i would appreciate that too. there are some more recs for modal logic for the mathematically and computer-science inclined.

[lean pagoda]

only one i can talk about in that list is the Huth & Ryan book

didnt even think about how it technically contains some modal logic but its absolutely not a book about logic for the sake of learning logic

its a great book in its own right but its targeted at computer science students (and not the ones working on the foundations of computer science)

talks about various applications of logic in computer science (model checking, agents, whatever)

well written book but the logic content is very surface level (it could probably be used for a 2nd year course for computer science students)

[turbid mural]

any recommended set theory books ?

[heady ember]

At what level

[turbid mural]

undergrad

[heady ember]

Naive or axiomatic

[turbid mural]

both

[heady ember]

So you want one for each?

[turbid mural]

yes

[heady ember]

I have never done naive set theory myself (well, other than a little in school) but people here normally rec Halmos

[minor knot]

Paul Halmos?

[heady ember]

I like Enderton for basic axiomatic set theory, rather friendly compared to others. Practically not much mathematical maturity required. Its the first real math book I started doing and hopefully am going to complete.

But if you have more mathematical maturity, you can use Jech's undergrad set theory book

[heady ember]

Yeah iirc

[willow pecan]

One does not need a whole book for naive set theory

[turbid mural]

i will try to find enterton's

[heady ember]

Ok

[sturdy shore]

halmos's book is like 100 pages I believe

[willow pecan]

What is there to say for 100 pages about naive set theory?

[sturdy shore]

and the name naive set theory is a bit misleading, he still goes over the zfc axioms and stuff it's just done a bit more informally and the obvious goal is to get non-foundations people comfortable with ordinals, cardinals, zorn's lemma, transfinite constructions etc

not really how we use the term naive set theory today

[willow pecan]

Oh so that’s like a brief intro logic book then

[sturdy shore]

more like intro set theory, but sort of yes

[turbid mural]

ah

[willow pecan]

The point stands that one does not need a book for naive set theory

[turbid mural]

would you recommend the book by felix hausdorff

[unique ice]

I'm reading Concrete Mathematics by Knuth, Graham, Patashnik.
I'm on page 63, grinding the exercises. I don't recommend it, in fact I hate it, but I will finish the book.

[remote slate]

please recommend me a good book on first course boolean algebra

[formal bronze]

Try 'Introduction to Boolean Algebras' by Paul Halmos. Great book, I am currently going through it and I find it quite well-written.

[remote slate]

can you tell me how is this one?

https://www.amazon.in/Boolean-Algebra-Dover-Books-Mathematics/dp/0486458946/ref=asc_df_0486458946/?tag=googleshopdes-21&linkCode=df0&hvadid=619458958682&hvpos=&hvnetw=g&hvrand=449059957897491991&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9050502&hvtargid=pla-524460029171&psc=1

[formal bronze]

Unfortunately, I am not familiar with this book, sorry.

[remote slate]

ok

[turbid mural]

would you recommend topology by james munkres for point set topology ?

[heady ember]

I have heard some people here say that it focuses too much on less important stuff at times

[sage python]

Yeah that's correct imo

The thing about point-set topology is this

Different generalizations of point-set creep in at different times in math

[fierce hedge]

Is there a proper alternative to munkres though?

[sage python]

If you've done real analysis at the level of Rudin, you know about topology of metric spaces. Your main examples being normed spaces, some basic function spaces like C(K) where K is a compact metric space, and submanifolds of R^n

[sage python]

Two big things you lose when going from metric spaces to general topological spaces are encoded come from the loss of two types of axioms for topological spaces:
(1) Separation axioms - the most important one is the Hausdorff axiom, which is equivalent to the idea that limits are unique.
(2) Countability axioms - the most important idea here is whether the topology of the space can be understood using sequences (is a set closed iff it contains all limits of sequences?) as opposed to nets or filters.

There are examples of spaces which don't satisfy these properties, but understanding/motivating them involves more background than many point-set students have. For example, you lose Hausdorfness when taking Zariski topology in algebraic geometry, or dealing with group actions on spaces. You lose sequentiality often when dealing with functional analysis: weak topology on Banach spaces, spaces of test functions/distributions, etc.

So we have a conundrum. We wanna teach students about non-metric spaces, and give them examples, but the standard examples are things that are hard to understand/appreciate with their background. Munkres' solution is to present a bunch of examples that don't matter. Imo this fails to motivate the ideas and just makes the subject more boring

Honestly my preference is to just not spend that that much time on point-set topology and just pick it up as you go. Folland's Real Analysis has a chapter on the stuff, which is just before it actually uses it to do functional analysis. I learned it from chapter 1 of Bredon's Topology and Geometry (60 pages instead of hundreds). Hatcher's point-set notes are also good for this.

If you want a dedicated book, I recommend Lee's Introduction to Topological Manifolds. Focuses on what's important more

[fierce hedge]

But how would someone know what's more important. Tbh, what's the big goal of topology? When we say topology do we generally mean point set topology?
What are we trying to study? continuous functions in a more general setups with less structure?

[sage python]

I mean someone studying doesn't know what is/isn't important, hence why I prefer other books that focus on the important stuff

And... the framework of general topology exists mostly in service of other areas of math

So yeah you're trying to understand the general notion of continuity

[gray gazelle]

Does anyone have the solutions of the books how to prove it by vellemen

Where can I find the solutions of this book

[sage python]

If a mathematician studies topology, they probably are interested in understanding interesting/geometric examples of spaces (especially manifolds), and what "separates" it from geometry is that you're studying spaces up to homeomorphism or diffeomorphism, and not considering extra structure such as distance and angle

[sage kelp]

https://www.inchmeal.io/htpi/index.html

[gray gazelle]

Tyy brother 😭😭

[thorn cloak]

Is Calculus two by Flanigan a good book for learning multi variable for the first time?

That’s the book my class is using but I was wondering if it would be a good idea to get another supplementary book

[tawdry orbit]

What do you mean?

[remote sparrow]

as in calculating derivatives or integrals, which i stated directly below the message you replied to. there are also some application chapters in apostol. you know, problems where you aren't asked to prove/disprove or give an example of something with some property.

[tawdry orbit]

Ok, thanks.

[bitter path]

Any recommendations on a rigorous calculus textbook (or an introductory real analysis book)? I've completed calc 3 but haven't taken a formal proof course yet. I have some exposure to logic and proofs but also not comfortable with writing proofs yet

[remote sparrow]

abbott Understanding Analysis

or cumming's Real Analysis: A Long-Form Mathematics Textbook

[crimson leaf]

Tao Analysis I or Schroder Mathematical Analysis

Abbott also good

[bitter path]

great, thanks for the recommendations! 🙂

[grave thorn]

Rudin

[gray gazelle]

Apostol's calculus is good

it's rigorous calculus, but not analysis

i've heard people usually recommend it after completing calc 1-3 from a book like stewart.

[dire stone]

i got this linear algebra book, Linear Algebra Done Right, a while ago and was wondering if it was any good? also, if anyone knows, theogony-like epics about greco-roman mythology

[crimson leaf]

LADR is good minus anything it says about determinants, check the pins

[dire stone]

yeah, i was worried about that given the back says it "takes an unorthodox approach" and i typically like orthodox approaches, thanks!

[mossy flume]

What is the approach to determinants in LADR?

[remote sparrow]

https://math.stackexchange.com/questions/1472978/is-linear-algebra-done-right-3rd-edition-good-for-a-beginner

https://www.maa.org/press/maa-reviews/linear-algebra-done-right

https://www.maa.org/press/maa-reviews/linear-algebra-done-right-0

some other reviews of ladr

[foggy relic]

none

bad book

[mossy flume]

Hmmmm

Interesting

I like the FIS approach of doing the axiomatic approach of the determinant

In that it's the unique multilinear alternating function which maps the identity to 1

[sturdy shore]

it "discusses" determinants in its last chapter and defines the determinant as the product of eigenvalues

I think it is a bad book if it's the only resource you will use to learn linear algebra

but I do stand by the opinion that its approach is pretty cool if you pair it with a book like H&K that is more algebraic in nature

[sturdy shore]

this is also the halmos way, pretty cool imo

[foggy relic]

why do you need axler if you're doing H&K

[sturdy shore]

they have very different approaches to the subject and knowing both is beneficial

axler comes from the halmos school where his way of teaching linear algebra is meant to be as coordinate free as possible, and the intent is to get students ready for infinite dimensions where a lot of the tools you have for finite dimensions are no longer available

most important one being a basis to work with

[remote sparrow]

both halmos and axler are functional analysts right

[sturdy shore]

roughly yes, and I believe halmos was axler's advisor's advisor? but don't quote me on that

[remote sparrow]

"roughly yes, and I believe halmos was axler's advisor's advisor?"

• lems

[sturdy shore]

yeah seems to be true

axler's advisor was Sarason, whose advisor was Halmos

[sturdy shore]

roughly yes was a reply to the functional analysis part, as in they both did/do work in fields related to func. analysis

[sage python]

Halmos + HK > Axler + HK

[night prairie]

Any recommendations for a real analysis problem workbook? Something like Berkeley Problems in Mathematics.

[sturdy shore]

I agree with that

[remote sparrow]

https://4chan-science.fandom.com/wiki/Mathematics#Problem_books

[night prairie]

oh jeez, the list is overwhelming but some books on that list definitely seem better organized than the berkeley book

[night prairie]

Does anyone know where I can find solutions to questions in Pugh?

[heavy kraken]

can someone recommend me a book for basic math's

[remote sparrow]

can you tell us what you're thinking of when you say "basic" math?

[fierce hedge]

Is that the same Sarason who wrote a complex analysis book my proff kept quoting?

[sturdy shore]

never heard of it but I doubt there are many mathematicians with surname Sarason

so probably

I'll check this out actually, maybe similar to Halmos' books

it is similar to Halmos in style

many many subsections, short 150 pages

[formal bronze]

What is your mathematical background?

[spare ridge]

what is FIS

[mossy flume]

Linalg text

[spare ridge]

i see

[mossy flume]

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

I like this alot

used it for my lin alg class

[heady ember]

Friedberg

Oh but just keep in mind that iirc the 4th ed has a missing chapter

[molten mason]

I came in this channel after specifically googling around for a Linear Algebra textbook to study on my own and saw "LADR" on Amazon. Glad to see other people in this channel talking about this exact text lol

[dapper root]

Honestly

LADR, Spivak, and Rudin are the most discussed books here

LADR might be #1

[heady ember]

Ah yes reminds me of Dami commenting on LADR

(Iirc he's talking about the parts on determinants and/or characteristic polynomials)

[molten mason]

I'm a super part-time math major, just finished Calc II, won't have time for an official course in the Spring due to work. Wanting to start Linear Algebra on my free time.

I think my university uses Linear Algebra, 4th edition Friedberg but I would have to doublecheck, which I saw Spamakin share a little bit ago

[dapper root]

Yeah, Dami loves to talk about how stupid the definition of characteristic polynomial is

[molten mason]

The chapter on Jordan canonical forms is removed, how important is that for the study of LA?

[willow pecan]

I would argue not very

Others would argue very

[heady ember]

I'm not the right person to ask lol, at least for now.

[crimson leaf]

Idk when I asked my prof he said you can worry about that when you need it

[willow pecan]

Yeah I never learned it

I've also never needed it

[molten mason]

Those answers sound more reassuring

Thanks

[sturdy shore]

well, I think the JCF is fairly useful conceptually

helped me understand the structure of linear maps better

[sturdy shore]

but this is right

[onyx wren]

central importance

[gray gazelle]

true but also funny how our opinion changes depending on what we are currently doing

[willow pecan]

Well

I will claim that JCF will never be relevant to me

[gray gazelle]

I'd say JCF is important if only for the completion sake

I never saw the proof and I think it's long and irrelevant (at least from what the lecturer were telling us), but it's still useful to know it exists

we learned how to compute such things in university

[gray gazelle]

it's not a bad recommendation though

[rugged oriole]

If we finish school maths (like yr12 maths in aus) what maths do we learn after that?

[willow pecan]

Are you asking for a book recommendation

[rugged oriole]

Ye bro what’s the best calculus book?

[pliant stream]

There is no so called best

[rugged oriole]

Then what’s the accurate word?

Most proficient?

[vital bane]

spivak is pretty good

[gray gazelle]

Spivak I feel requires a lil bith of prior calc knowledge like a question requires you to know about the power rule beforehand

[vital bane]

it asks you to do questions needing the power rule before introducing the power rule?

[rugged oriole]

What book is great for people who want to learn numerical analysis?

Like I want to learn it

[gray gazelle]

1.iv on chapter 5 limits, this is before chapter 9 derivatives

[vital bane]

it introduces all the rules in chapter 9

[willow pecan]

Where do you need the power rule

[gray gazelle]

1.iv chapter 5 I've checked the answer book it just says apply the power rule

[willow pecan]

Ok but you don't need to

You can compute that as a limit

[willow pecan]

What type of numerical analysis?

[gray gazelle]

How that's the definition of the power rule solving 1.iv is literally proving the power rule

[willow pecan]

?

[broken meadow]

You can use the binomial theorem

Write x-y as h

and the rest is yours

[gray gazelle]

I suppose but this is question 1

[broken meadow]

And

[white laurel]

Try applying this bad boy on it\newline $x^n - y^n = (x-y) \cdot (x^{n-1} + x^{n-2}y + ..... + xy^{n-2} + y^{n-1})$

[hasty eagle]

edwardborn

[white laurel]

vi was somehow easier than this one so there's most likely something I've overlooked

Oh well

[white laurel]

Ye

It's kind of silly cuz l'hopital gives the same answer but is 10 times easier to do

[vast cave]

Can someone recommend a textbook to self study a second course in real analysis? Preferably not too terse with a lot of exercises

[foggy relic]

browder

[willow pecan]

What do you want in your second course

Analysis on R^n?

[foggy relic]

or wait do you want measure theory?

[willow pecan]

Measure theory?

Something different?

[vast cave]

The last course I took covered Heine borel and integration on Rn

I want to pick up from there

I would also want something that explains Baire category theorem

[gray gazelle]

Hey! What's the best book for IB AA HL maths?

[brittle breach]

there is Munkres analysis on manifolds,

stein shakarchi fourier analysis is another direction

[deft citrus]

Anyone have any recommendations for learning pdes?

[icy knot]

Either Haberman or Asmar. Others will suggest Strauss, Taylor, or Evans

I'm trying to learn them also.

[sturdy shore]

quite a large difference between haberman/strauss and evans

and evans is also quite different from taylor

in difficulty

[remote sparrow]

try zachmanoglou

https://www.maa.org/press/maa-reviews/introduction-to-partial-differential-equations-with-applications

[sage python]

What's your comparison of those books lems? Maybe it's time someone other than me to have long detailed reviews that get pinned here

[sturdy shore]

oh my knowledge is far from adequate for that, I just know the difficulty level they each correspond to

haberman/strauss are standard introductory undergrad texts, general focus on R/R^2/R^3 no measure theory a lot of separation of variables stuff (and fourier series)

evans requires a solid grasp on multivariable analysis for its first part, then goes into sobolev spaces for which you'll need measure theory and functional analysis obviously

I know of taylor the least but on top of evans prerequisites he also seems to use quite a lot of differential geometry

[severe falcon]

what’s your background like/what aspects of PDE do you want to learn?

[deft citrus]

I essentially want to learn what Dirichlets Problem is and how and when to apply it @severe falcon

[willow pecan]

Strauss then

[deft citrus]

sorry what is Strauss?

[deft citrus]

ah ok thanks

I haven’t taken lin Alg yet so prolly gonna struggle

but I’ll give it a shot

[deft citrus]

Does Strauss talk about Dirichlets problem?

[remote sparrow]

an author of a partial differential equations book for undergraduates

[sturdy shore]

yeah you will

[sturdy shore]

the "dirichlet problem" is the most obvious way you can pose a PDE problem, any textbook on PDEs will talk about it

very likely in chapter 1

[crimson leaf]

Isn't the Dirichlet problem in Artin chapter 1?

As an exercise

[sturdy shore]

seems to be a discrete version of the dirichlet problem for laplace

which btw I forgot people also use "dirichlet problem" to talk about laplace specifically

you can see strauss talking about the original dirichlet problem in chapter 6

[willow pecan]

Strauss will talk a lot about the dirichlet problem

[sudden kindle]

Material derivative

[deft citrus]

thank u guys

[zenith lintel]

any large resource for computational geometry-trigonometry problems (oly types)?

[uncut zealot]

Calculus would be useful for the complex analysis book.

And the diffeq book

Otherwise, knowing how to write a mathematical proof would be useful for most of those, but that's about it.

Learn LA before the other subjects though.

[zenith lintel]

someone on this?

[sullen raptor]

Can anybody recommend me books to use for self-studying after I finish this one? Something that builds on this.

[fierce hedge]

<@&268886789983436800> spam account

[quick hornet]

Thanks

[safe apex]

Hi, someone can suggest me some book about mathematical logic and math foundation?

[remote sparrow]

math sorcerer reviewed saracino very favorably

[remote sparrow]

look in pinned

[remote sparrow]

check peter smith's blog. he has recommendations on logic and set theory. also check diligentclerk's pinned message.

[sullen raptor]

What am I supposed to look at?

[remote sparrow]

the algebra recommendations

[sullen raptor]

aaa ok

[remote sparrow]

enderton's set theory is good. enderton's mathematical logic is regarded as pretty tough but it could be doable if you pair it with montalban's lectures (who also has lectures for enderton's set theory, but most would say the level he writes at in that book is easier than his logic book). you could also try a new book by mileti.

for an alternative to enderton's set theory, try hrbacek and jech's set theory book.

[tawdry orbit]

I’m reading spivak’s calculus now, and i like his prose. It’s very well written. Another book that left a similar impression on me is “An introduction to mathematical reasoning” by Boris Iglewicz. I know it’s a weird question, but what are some math books that have nice writing?

A course of pure mathematics by G.H. Hardy was another one with nice writing.

[arctic ruin]

any book recommendations for math foundation (high school math and singaporean math books) and for applied math?

[night prairie]

are there any books which can teach linear algebra and abstract algebra at the same time?

[mossy flume]

Probably not because they sort of approach the subject in different ways

[sturdy shore]

uh

[mossy flume]

linear algebra texts go into a super deep dive on vector spaces

[sturdy shore]

artin?

lol

[mossy flume]

it does?

[sturdy shore]

yes

fairly famous for that

[mossy flume]

I thought artin assumed lin alg

[sturdy shore]

no

[mossy flume]

huh I must be misremembering

[mossy flume]

anyways most introductory algebra btexts (guess not Artin) don't go into as deep a dive into the various structures like groups, rings, and fields

[night prairie]

yeah I was looking for a book which might cover stuff up to some basic galois theory but also cover what you would learn from Hoffman and Kunze

for example you wanna learn both things but buy only 1 book

[sage python]

Probably Artin or Knapp

[hearty parcel]

Art of War by Sun Tzu

[zenith lintel]

PEOPLE PLEASE! any large resource for computational geometry-trigonometry problems (olympiad types)?
(resent)

[formal bronze]

In which olympiads are computational geometry problems asked?

[stiff sentinel]

what are ur opinions about munkres vs hubbard for calculus on manifolds?

any other alternatives that are better?

[gray gazelle]

the book by munkres on manifolds is not very good

in my opinion

it's extremely verbose, spends a lot of time on unimportant material, and has poor exercises

it's good if supplemented with another book like hubbard, but on its own it doesn't hold up

[sand crescent]

i felt the same for loring tu

[gray gazelle]

spivak's calculus on manifolds is the classic here

terse ass book, but you won't find better exercises elsewhere

it gets right to the point and doesn't waste time

folland's advanced calculus is also good for the multivariable calculus stuff, but it doesn't go to deep into the manifolds aspect

the ideal pairing imo is spivak + folland

[stiff sentinel]

Hmm i see

I'm already familiar with most of the multivariable stuff given in these books

[fierce hedge]

How is shrifin's multivariable mathematics?

[still umbra]

it doesn't help much with your intuition though

I think spivak is good if you supplement it with watching the occasional lecture online

[gray gazelle]

Is Tao’s Analysis I considered a book for a first course?

Books for linear algebra (pls quite basic I am just in highschool, be merciful and tell me easy ones. But I am in senior year so I would love some on like first year linear algebra as well)
Any book ideas ?

[heady ember]

Look in pinned btw

[gray jungle]

roman I think Introduction to linear algebra by gilbert strange is quite accessible , with lovely video courses available.

[gray gazelle]

Thanks 💞💞

[gray gazelle]

I got the pdf yes 💝

Thank you ^°^

Are the questions in it hard but not very hard for me tho ?

[gray gazelle]

can't comment

[gray gazelle]

i said to pair it with folland for a reason

wrong reply but whatever

do you have any such lectures in mind?

online video lectures for a math student at the level of spivak's CoM

[vital bane]

shiffrin has a bunch of lectures (his multivariable calc book covers some of the things spivak's CoM covers)

they're both calc in R^n (but spivak has a bit more stuff i think)

https://youtube.com/playlist?list=PL5I-Eyk8l9FHdJUd9UujGcvumjCFPHbrd&si=EnSIkaIECMiOmarE

like the last dozen videos of it

[foggy relic]

Browder does some stuff on manifolds as well

like generalized stokes

[gray gazelle]

i think my days of recommending spivak are over

if it gets me pinged so much

it is time to retire this channel

[vital bane]

[night prairie]

Does Aluffi leave out anything that I would normally see in D&F up to material on fields and basic galois theory?

it looks complete in this sense but I just want to make sure

[finite heath]

Does anyone have a pdf version of A First Course in Noncommutative Rings by T Y Lam?

[fallow cypress]

You can't ask for illegal copies of books here, sorry

[lapis sundial]

If you want to ask for illegal copies of books, use a different channel

jk

just don't

[remote sparrow]

try zorich's mathematical analysis

[fallow cypress]

how the garcía girls lost their accents is such a beautiful book

[lapis sundial]

yeah, they ended up just being the garcia girls instead

[remote sparrow]

Settlers by J. Sakai is pretty good. It can be read here: https://readsettlers.org/ or purchased as a paperback. A good interview with Sakai that clarifies some points in the text is here: https://kersplebedeb.com/posts/raceburn/.

[gray gazelle]

Fun fact: I don’t like reading

But I recommend “The God Equation” by Michio Kaku

[fallow cypress]

boooo

[brittle breach]

https://personal.math.ubc.ca/~jychen/m223/Book.pdf , this is the closes to that approach that I know of

[sage python]

This doesn't do any abstract algebra it seems

[real veldt]

Any recommendations for a rigorous undergrad abstract algebra book?

[still umbra]

Dummit and foote

[sand crescent]

check pins

[remote sparrow]

a book of abstract algebra by charles pinter is good. so is judson

[stiff sentinel]

I'll check it out. I used his book for analysis 1 and it seemed decent

Thanks

[remote sparrow]

pretty sure zorich does multivariable analysis in greater generality too

than say, spivak

also @stiff sentinel consider submitting a review of Zorich to MetalNinja27 in DMs

[stiff sentinel]

Okay

[remote sparrow]

read instructions in #books

[faint nebula]

Wholesome book

It's got pictures but it's a good read

Now you have to read from right to left. Idk it's a quirky feature

Now the name might throw you off but don't worry that's intentional

It's called Berserk

[fierce hedge]

You mean holesome

[faint nebula]

Exactly. Thanks numbpy. A true life saver

[crude sage]

Has anyone read Bartle and Sherbert? How is it in terms of motivation, rigour, clarity, or difficulty?

[fierce hedge]

We had used it as textbook for intro maths class. My friend used it cover to cover and mostly enjoyed it. Easier compared to most analysis textbooks, beginner friendly

[remote sparrow]

abbott wrote it was one of his inspirations

it's a pretty standard text for lower level unis

could also be used for intro analysis

[crude sage]

Wait, so is it comparable to spivak in terms of the material?

[remote sparrow]

no

calculus is not covered, it's assumed

[crude sage]

I see, thanks

Someone actually told me it's "the best math book ever written" so I had to see

[fierce hedge]

"the best math book ever written" is definitely a stretch but it's beginner friendly

[crude sage]

I was surprised too

[fierce hedge]

That said, it does really help in building proving skills as suggested by my friend.

He did his summer project doing all exercises from half the book if I remember correctly

[crude sage]

Oh neat

[spice spade]

Hello, I've heard mixed things Engel's Problem Solving Strategies. On one hand there are people who say it's one of the best books for olympiad preparation, however, I've seen a few people mention how there are a lot of mistakes in the solutions presented. Does anyone know of an alternative or even just a list of corrections? Thanks

[hasty turret]

Well it's a good book for learning the "principles"

You can use those principles in literally any other book

[alpine rover]

what's the most beginner-friendly introductory abstract algebra book that is easy to read and that one can read for pleasure?

[sudden dock]

Is there any good book with in-detail chapter on "Sequences and Progressions or Series"? high school level.

[formal bronze]

What topics do you want the resource to cover? Are you looking for something on limits and convergence?

[sudden dock]

I need it to cover ap gp, agp hp, misc series and rms>am inequalities @formal bronze

[tropic jasper]

oh books

i love books

[amber olive]

i've read it, had it for my real analysis class. honestly, I found it really hard to comprehend, and i really wish it had more examples so that the concept would be clearer. as someone who had absolutely 0 experience with analysis it was tough, i'd often refer to solutions online to understand the content. this is just my opinion though T_T

[molten mason]

I'm looking at Linear Algebra 5th edition (Friedberg) on Amazon and I see that while the hardcover is $175, the paperback is only $32.

Am I correct in assuming this is the international version? Is there any difference in this version?

[fierce hedge]

Usually, international editions omit the last chapter and have slightly inferior page quality. For last chapter, you can check the preview if it is available or see the number of pages the book has compared to a soft copy.

[molten mason]

Ah good idea, interestingly the paperback has 8 more pages. I did find near that where it says the paperback is the international economy edition.

[fierce hedge]

For reference, my copy of Friedberg has around 610 pages and it's an economy edition.

And it has all the 7 chapters

[heady ember]

What edition is that

Just curious

[fierce hedge]

5th edition

[heady ember]

Oh nice

[turbid mural]

what books would you recommend for algbraic topology

[gray gazelle]

Yo guys

I'm in HS, and I'm interested in doing maths beyond what we do in school

was wondering if anyone had a suitable recommendation that isn't beyond my capacity, but also isn't something that I'll cover in HS

I'm completing GCSEs/IGCSE for reference of my math level

[heady ember]

GIve us more context?

Are you familiar with proofs?

[gray gazelle]

Nope

[heady ember]

What have you learnt? E.g.: Linear Algebra

[gray gazelle]

Ah I see, ok give me a minute I'll share the syllabus of the course I'm soon going to complete

[gray gazelle]

I'm in 11th grade so I haven't started final 2 years of HS

[heady ember]

Have you learnt anything else outside your syllabus?

[gray gazelle]

Nope

other than probability

[heady ember]

Do you have a rough idea of what you're interested in learning? E.g.: LA or anal

[gray gazelle]

Logic based math I guess

I really enjoyed probability

even though we didn't do much on it

I also enjoyed permutations and combinations

[tawny copper]

you can do problems on combinatorics

[gray gazelle]

Ah I see is there like a book I could use to get better at it

I enjoy just doing problems from a textbook

[tawny copper]

I don't know a lot of them, but I like Bóna's, a walk through combinatorics

[heady ember]

"logic based math" is really vague. But either ways, here are some topics you can check out:
1.Intro to proofs (loch has a summary pinned in #proofs-and-logic )
2. Linear algebra (look in pinned)
3. (Real) analysis - Dami suggests either Browder or Schroder, which are more friendly texts. Be warned, real analysis is not an easy topic. E.g.: Some proofs might require like 10 pages literally lol

[gray gazelle]

Thank you

[tawny copper]

Look up the math olympiad server https://discord.gg/3sbwZdh for problem recommendations

[gray gazelle]

Thank you

[gray gazelle]

o didn't know this existed

[tawny copper]

What proof requires 10 pages in introductory analysis? xD

[heady ember]

Or if you're weird like me lmao you can see if you're interested in axiomatic set theory. I'm studying Enderton's Elements of Set Theory right now. However, unless you're sure you want to study axiomatic set theory for its own sake, you're probably better off with something else first.

[tawny copper]

Enderton is pretty friendly

[heady ember]

I have heard that, so just giving that as a warning. Though, I haven't done real anal myself yet . Soon™️

[heady ember]

Yeah agree

[gray gazelle]

this is what I'll soon be starting for the next 2 years in HS, and in the IB I also need to do 4000 word essay on something outside of what is taught so I was wondering if proofs might be a good idea to start with then

And it's something I could also write a lot about

[tawny copper]

Okay I think the most involved proof in introductory analysis I have seen is the Stone-Weierstrass theorem, its some pages, yes. (Not that I know a lot of analysis anyway)

But what you will be mainly facing its definitions and new concepts all the time

[heady ember]

Yeah there are a lotta defs and theorems in real analysis

[gray gazelle]

Well based on the fact that you mentioned there are proofs in real analysis I guess it'll be best to start with intro to proofs, thank you

[heady ember]

If you want a gentler intro then yeah that's probably the way to go I guess

[grand thistle]

construction of reals

yeah and stone weierstrass

[glacial crypt]

How to Prove It by Daniel J Velleman

[glacial crypt]

mfw its one whole chapter

[crude sage]

Good to know, thanks

[plush arrow]

Is there a follow up to A Mathematician's Lament

?

[tawny copper]

yes

It has many nice problems with full solutions

some will be challenging tho, but don't desist

(the pdf is available online btw)

[remote sparrow]

For linear algebra, click here: #book-recommendations message
For real analysis, you can try using Abbott, Cummings, or Schroeder. Actually @heady ember is not correct that Dami recommended Browder for beginners.
You can do intro to proofs or discrete math. Click here for suggestions: #book-recommendations message
If you've haven't had multivariable calculus, you can try using Shifrin's or Hubbard and Hubbard's book.
If you want to try elementary number theory, you can read either Burton or Dudley's books.
If you want to try combinatorics, you can use Bona's A Walk Through Combinatorics.

[remote sparrow]

math sorcerer reviewed saracino's and beachy and blair's books very favorably

[sage python]

Yeah Schroder is the one that I peg as gentle, even to the point where I wouldn't be surprised if a Calc 1 student (aka no background in proofs or calculus) could use it

Browder is basically Baby Rudin cup Spivak Calc on Manifolds but better

[unique ice]

non-math book recommendations too?

[wheat cargo]

@violet shuttle do u have any books that are similar in content to spivak's calculus on manifolds but are slightly less terse?

[violet shuttle]

Does it count if it has way more than spivak?

"Introduction to Smooth Manifolds" is very unterse, but also covers a whole lot

[wheat cargo]

well i suppose it would, but as long as i can approach it with my current background

[violet shuttle]

Lee's other book, "Introduction to Riemannian Manifolds", is similar but covers Riemannian Manifolds

i don't know your background

[wheat cargo]

yeah typoing this right now

[violet shuttle]

Lee's Smooth Manifolds only really take multivariable calculus, linear algebra, and mathematical maturity

[wheat cargo]

that background is ug algebra, real analysis (baby rudin ch. 1-7), linear algebra (axler)

[wheat cargo]

ok cool that works for me

[violet shuttle]

note that i do really mean "mathematical maturity"

it's much more well and in depthly explained than baby rudin, but it is harder

[wheat cargo]

assuming that i have a fairly good understanding of the content mentioned above, do u think it is a good book for me?

[violet shuttle]

i truly do not know

maybe?

maybe not?

[wheat cargo]

well ill just try it out

see what happens

ty

[violet shuttle]

yeah, that makes sense to me

[fluid bay]

A lot of the content of spivak’s Calc on manifolds is in the appendix of lee’s ism. I wouldn’t say the actual content of the books intersects very much

Albeit I preferred the exposition in the appendix of lee over spivak

[gray gazelle]

Thank you for the list! I'll check these out

[sturdy shore]

I believe that book also uses a nontrivial amount of topology

[violet shuttle]

oh, shit, forgot about that

how did i forget about topology...

[remote sparrow]

what about bottomology

[gray gazelle]

[lapis sundial]

Classic joke

[sturdy shore]

so classic it has mold on it tbh

[heady ember]

Just use Lee's first book, intro to topological manifolds, for the required topoplogy

[vital bane]

first time im hearing about bottomology

[fallow cypress]

I did that, it was nice

[heady ember]

Nice

Still have so much to grind before I can even start reading Lee

[fallow cypress]

tbh I don't think there's really much background required

[heady ember]

Hmm really? I need to finish Linear Alg (e.g.: Friedberg), real anal (e.g. Schroder), and some algebra (e.g.: Basic Algebra I by Jacobson) first right

[fallow cypress]

you can

I guess knowing topology wouldn't help you much at this stage

I can't think of a reason why you couldn't learn it in principle though

(This is not that I'm telling you to read it, you should finish reading whatever you're reading now first lol)

[heady ember]

Lmao

I see

[glacial crypt]

Can LADR really not be used as a "first course" for self-study?

[fallow cypress]

I wouldn't recommend it

I like Treil's Linear Algebra Done Wrong

[glacial crypt]

Oh that looks quite nice actually

should probably print this out

[fallow cypress]

LADR is nice as a second semester imo

Goes through the same stuff but more theoretically with fewer concrete examples

It's very elegant too

The only annoying thing is how it handles determinants, but if you're going through linear algebra for the second time when you read LADR, it shouldn't be too bad

[remote sparrow]

#book-recommendations message

https://www.youtube.com/watch?v=Zsib22FFie8

cheap workbooks

[lunar sinew]

Hello everyone, please suggest me a good resource/s to cover the following topics, I'm almost newbie to math, and need to study for my grad. Thanks.

1. Matrices
2. Determinants
3. Mathematical Induction
4. Sequence and Series
5. Complex Numbers
6. Equations
7. Inequalities
8. Differential Calculus
9. Integration
10. Vectors
11. Three Dimensional Geometry

[heady ember]

Looks like highschool stuff so probably Khan Academy

You can also look at loch's intro to proofs pinned in #proofs-and-logic for induction stuff

[sullen spruce]

rd sharma class 11 mathematics

[hasty turret]

I wouldn't trust Rd Sharma for anything tbh

[sullen spruce]

why is that

his books are reliable for high-school atleast

considering they're in high-school

[gray gazelle]

The cover page of those books looks made with MS Paint tho 🤣

[minor knot]

He keeps complaining about the Indian system and is pessimistic, lol

[blazing canopy]

Wow that is a lot to cover in one year of high school mathematics

[vital bane]

This isnt a textbook, this is a problems book so a single chapter is split up into 2 or 3 that's why it seems like a lot

[gray gazelle]

You are pessimistic?

[fierce hedge]

If that is RD Sharma then no, they are actual chapters. The whole book is like 800+ pages

[hasty turret]

No,I am being realistic. RD Sharma isn't good for learning math

[fierce hedge]

I have used RD Sharma and it's an ok book but there might be better ones

[gray gazelle]

Usually in the Indian books for highschool
None of that is rigourous so it's hard, and a lot but not that hard for it to be unrealistic.
It's just unrigorous which one might say is good or bad
Individual opinion it, I personally don't it like that

[gray gazelle]

I mean, everybody thinks they are realistic tbh

¯⁠\⁠_⁠(⁠ツ⁠)⁠_⁠/⁠¯

[acoustic ridge]

Is there any site where I can read math and science ebooks without the pdf viewer?

[gray gazelle]

sounds too comfortable to be true

[pure swallow]

Agreed, dont use it

[eager pollen]

Agreed. 100%.
It's just to prepare for school exams... u can't actually learn math there

[eager pollen]

Pick up math textbooks of those topics instead of exam focus prep books I'd say...

[lime sapphire]

i personally don't think thats the best advice if sirius doesn't have a lot of time

[eager pollen]

Well... he didn't really mention he doesn't have much time

[eager pollen]

You may follow any undergrad math fresher course, most of these topics are covered there

[lime sapphire]

if it's only about a year then its best you stick with prep books that are designed for your exam style as many different books can become quite redundant

[eager pollen]

I am assuming he wants to learn em in a pure form instead of learning problem solving oriented books which include fast cheap tricks

[lime sapphire]

oh look something resembling a single book with many different topics

[remote sparrow]

@eager pollen ODE, you can use Morris, Tenenbaum, and Pollard's ODE book. For a book that emphasizes qualitative and graphical analyses over analytic solutions, you can try Blanchard, Devaney, and Hall's book. You can pair your reading of this book with Bill Kinney's lectures, which discusses linear algebra as well. Neither of these books cover boundary value problems, a pretty simple class of PDEs, although Kinney covers them in a couple of the final lectures. A book that does cover boundary value problems would be Elementary Differential Equations with Boundary Value Problems by Boyce and DiPrima. I don't know much about dedicated PDE books that only use calc 1-3 and linear algebra. I would imagine Strauss doesn't fit the bill. I think this video could help you, though: https://www.youtube.com/watch?v=-yksoVsb47s. Generally further theoretical study of differential equations, both ordinary and partial, is less about trying to find a closed form solution and more about studying existence, uniqueness, well-posedness, etc, however.

[meager parcel]

Not entirely sure if that’s what you mean but the PDF viewer is built into your browser most likely

Maybe try downloading the file

[rapid flame]

my favorite book just arrived

[gray gazelle]

Thoughts on the free e-book Abstract Algebra: Theory and Applications by Thomas W. Judson? I ask being a good way in already. Nice being free but is there a must have paid-for book on abstract algebra out there?

[remote sparrow]

pinter's abstract algebra book

knapp is free online btw, and according to the mathemagician it's apparently dummit and foote done right

the margins suck though

i guess lang

rotman's second edition i heard is good

third edition has mixed reviews

both are reviewed by MAA

jacobson is cheap

[gray gazelle]

Big Chungus of physics

1300 pages of thickness

[mossy flume]

D&F done right?

Sounds interesting

[remote sparrow]

https://www.math.stonybrook.edu/~aknapp/download.html

you can see for yourself here

[mossy flume]

Found it but wdym D&F done right

[remote sparrow]

pretty sure mathemagician wrote that on his blog

[remote sparrow]

http://tableschairsandbeermugsmathemagician.blogspot.com/2015/08/normal-0-false-false-false-en-us-x-none.html?m=1

[alpine rover]

thank you saracino is good

[cursive orbit]

holy shit that website is hard to read

[sudden kindle]

Saracino is the best intro algebra textbook for undergrads

I have no problems with D&F

I think its a good choice for algebra courses

[gray gazelle]

Thank you

[remote sparrow]

thoughts on judson or pinter?

[sudden kindle]

No thoughts

Havnt used them

[mossy flume]

I agree with the post he wrote about D&F being amazing and extremely dry

God it is dry

[loud cradle]

D&F sucks all the joy out of algebra, yet it has a wealth of good examples and exercises

[sage python]

Yeah D&F is fine as a reference, though it should at least introduce categorical language

Extremely clear, but very boring to read

[foggy relic]

Lang is a good reference and fun to read

[vital bane]

the true big chungus of physics is MTW gravitation

1340 something page book on graduate GR

[pale slate]

anyone have suggestion for beginner theory to calculus books?

[loud cradle]

spivak would be the standard suggestion

[pale slate]

o ok thx

[cobalt arrow]

Depends on what you’re looking for but Apostol is also great. Spivak’s Calculus on Manifolds is what I’d recommend after (just a personal preference, though)

[pale slate]

thx for the suggestions

ill look into the two books

[cobalt arrow]

Apostol is a two-volume set. I think it’s just a plain name, like Calculus or something. It has good examples and exercises without getting bogged down in doing the same thing a dozen times in the exercises (I can’t say I’ve worked through all of them but each one I’ve done has had a distinct feel to it which is what I want in a book).

[eager pollen]

The real math legend is the one who actually reads all the books lmao

[remote sparrow]

have you already learned calculus? if so, then spivak and apostol would be redundant in some places. something like abbott, cummings, schroeder, or tao would work for you instead.

[molten mason]

Any personal opinion on those last 4 that you mentioned?

[heady ember]

Schroder
dami would agree

[gray jungle]

Most of my friends said D&F style of giving a lot of examples was extremely helpful.

Me and a study partner were both using artins book and i thought it was ok but i had to suppliment the book with other references to fully grasp some ideas , so i can definitely see how D&F is the better choice for learning a first course in AA.

Same for exercises, artin has some neat exercises but it often wasn't enough so we had to go to D&F and random psets.

I would definitely recommend D&F if someone told me he is doing a first course in AA.

[main void]

Does anybody here have a reference for alpha-densities (and integration of densities) on manifolds? The only reference I could find was “Manifolds, Tensor Analysis and Applications” of Abraham but it doesn’t quite cover it

[gray gazelle]

which book will be the best if i want to study "Game Theory" (e-book or physical)

[lunar sinew]

@heady ember @eager pollen @lime sapphire Thank you guys. I will take the exam in June.

[sudden dock]

Any good book to self study Sequences and Series in depth? looking for topics (A.P, G.P, H.P, A.G.P, AM>GM>HM). Right now I know nothing about it

[pale slate]

thank u, I'll look into the books after I get more familiar with the inner workings of calculus. Most of the videos I watched about calculus is from 3blue1brown because I won't formally learn calculus at school for a couple of years

[crude sage]

What are the prereqs for Bona's A Walk Through Combinatorics? I'm trying to read it and I seem to be missing some geometry/number theory background, but I'm not sure if that's important

[gray gazelle]

murakami hard boiled wonderland

[sage python]

Vector analysis by Janich

[remote sparrow]

calculus and the ability to read and write proofs

although i think calculus is used mainly in generating functions and analysis of algorithm complexity

scattered throughout the text are mainly just the idea of limits and how certain stuff is asymptotically close to another thing

heavy calculus like derivatives and integrals are pretty infrequent tbh

[remote sparrow]

spivak and apostol are good then. if it gets too challenging, you can try reading an intro to proofs book. or you can do something like elementary number theory, combinatorics, or linear algebra.

[eager pollen]

Bro what exam are u taking?

[loud cradle]

Yeah, the examples in D&F are good and plentiful, and so are the exercises. It's definitely worth owning but I just find the exposition itself very dry and boring. Unfortunately I don't have a good alternative to recommend as my undergrad algebra instructor used his own notes

[remote sparrow]

pinter and judson are good

[crude sage]

Oh wow I did not expect that, thanks!

[split mica]

geronimo stilton

[pale slate]

o ok thx

[fallow cypress]

I love D&F

[fallow cypress]

the picture of dorian gray is so relentlessly funny

[tawdry orbit]

Great book, with great writing.

[gray gazelle]

@remote sparrow where are you frm ?

[remote sparrow]

america

[glacial crypt]

gallian has a lot of examples too

[crimson leaf]

I strongly disliked Gallian

[marble solar]

Richard Elman's Lectures on Abstract Algebra

Not as dry

But good luck through the orbits section

[mossy flume]

Anyone have a recommended resource for group extensions and composition series (solvable groups, nilpotent groups, etc) at the level of a first graduate course in Algebra?
I am reviewing my profs notes and I really am not getting any level of intuition from his notes and am hoping some sort of better resource exists

[loud cradle]

Elman was in fact my undergrad algebra prof!

[marble solar]

He was also mine

What a coinky-dink it's almost like we both went to LA

[loud cradle]

haha

in my case many moons ago, before he had any PDF notes

[marble solar]

Mine was a few years back now

[loud cradle]

he may be my all time favorite math prof

[marble solar]

I loved his linear algebra class, but his algebra class was not so great for me

[loud cradle]

i didn't have him for LA but I would like to have

i had some friends who went to grad school there and said his graduate algebra was insanely fast paced, they didn't seem so thrilled 😁

[marble solar]

Yeah, I took him for 110H

He tried to do too much to fast for me

I had his academic brother William Murray for algebraic curves

Very similar style, but better at teaching in almost every facet

[loud cradle]

my only complaint was that i later had to break the habit of using his notation ⊲⊲ for a characteristic subgroup, i had no idea it was not standard and seems to have been his own notation

[marble solar]

and I know how great Elman could be

I've been spoiled rotten by fantastic professors

[loud cradle]

much better than the alternative for sure.. can't really complain about most of mine either

[marble solar]

Anyways, check out his algebra book

He put a lot of love into it

[loud cradle]

taking a look at it now, it's great to see written notes, and these appear to be at least somewhat expanded compared with his lectures (I doubt he'd have time to cover this whole thing in one year)

[marble solar]

I dipped out after the B part

[loud cradle]

876 pages!

C was fun and somewhat relaxed as there were no exams, just 50 problems that he handed out near the start of the quarter

[marble solar]

He got to part 5 in C

[loud cradle]

you had to do like 40(?) of them to get an A

[marble solar]

Yeah, and 41 for an A+

Due at the end of the term

[loud cradle]

yea that sounds right

[marble solar]

I had a time conflict: it was either C or riemannian geometry

I wasn't having fun in algebra so I took riemannian geometry from petersen instead

[loud cradle]

i recall the 2nd AH midterm was take-home and took many hours as I was still getting my footing in algebra, but I managed to get a 100 on it, I was so damn proud

even though i was still really shaky on quotient groups and a few other topics

[marble solar]

I found out in the 110H sequence that I fundamentally cannot solve problems the way an algebraist would

[loud cradle]

on most of the HW's there were at least a couple of problems that I would have to chew on for a few days before I could even think about how to start them

[marble solar]

I was taking grad complex at the same time, and I'd always just use weird analysis results to get out of doing any algebra

[loud cradle]

haha

i took one quarter (I think?) of grad complex from gamelin

[marble solar]

Gamelin was retired before I got there

I primarily had Garnett and Tao teach me analysis

(mostly Garnett)

[loud cradle]

gamelin was fun, iirc there were no exams and you had to pick some number of problems from each chapter and turn them in at the end of the term

and he encouraged you to adorn your submission with anecdotes, biographies, poems, whatever, just to make it more interesting reading for him

ah i was there just before Tao joined

[marble solar]

That was many moons ago then!

[loud cradle]

yep!

[marble solar]

I learned undergrad complex from David Gieseker

He couldn't decide on a book

So he switched half-way thru the course

He also drooled in class while teaching

[loud cradle]

i seem to recall that i skipped undergrad complex and just did the graduate version? but i might be misremembering

[marble solar]

Gieseker just retired, Elman is going to soon

[loud cradle]

end of an era for that generation.. i guess elman must have been born in the 40s because I recall him telling me that a strong motivation for him to go to grad school was to avoid the vietnam draft

i guess it could have been early 50s depending on what stage of the war that was, it did drag on for years

[marble solar]

I went to community college before LA, and my professor there went to vietnam first

Then went to Berkeley for Math

He was there at the same time as Elman, but as far as I know they didn't meet

[loud cradle]

damn, i can't imagine what it's like to try to study math or anything that requires a ton of focus after just coming back from getting shot at

[marble solar]

It's crazy how small the math community is

[dense mantle]

what do people like as a second book in harmonic analysis?

I've seen most of pereyra + ward and would like to keep going with it

[loud cradle]

katznelson is nice, if you know measure theoretic real analysis

[dense mantle]

yeah that's probably worth mentioning

I've got a semester of measure theory/ RA (95% of folland) and semester of functional (mixture of texts)

[loud cradle]

that should be adequate background for katznelson

[dense mantle]

yes this book looks like an education

thank you

[gray gazelle]

Anyone read “Mathematics for Human Flourishing” by Francis Su? I really enjoyed “Letters to a Young Mathematician” by Ian Stewart and have been looking around for similar things.

[narrow fiber]

are you familiar with deitmar-echterhoff

I say this because it (Principles) comes off of a gentler first course (Intro) and largely resembles Folland's harmonic analysis text except a little more laid-back in exposition, at least to me

[dense mantle]

I am not

have not looked deeply into harmonic analysis before

[narrow fiber]

it's a lovely book, I definitely recommend it

[dense mantle]

i see i see... thank you

[grand thistle]

any texts similar to spivak’s physics for mathematicians and hall’s quantum theory for mathematicians that presents e&m at an introductory level from a mathematical pov?

[narrow fiber]

i've heard good things about garrity's e&m for mathematicians but haven't personally read through it

wow i wish i had these much earlier on lol

hoffman & kunze was my intro and it was not a gentle one

also roman gets bizarre

[grand thistle]

ooh cool thanks

[gray gazelle]

Can someone recommend me a good book on Graph theory

[chrome yacht]

maybe Graphs and Digraphs by Chartrand,Zhang?

[sage python]

Thanks for connecting I just noticed some typos, should be better now

[gray gazelle]

Thanks, I'll check it out

[foggy relic]

Landau+Lifshitz the Classical Theory of Fields

Hot take: Roman > Halmos > Hoffman Kunze

[sullen spruce]

you must have a reason for being this bold

[errant solstice]

Does three volume set of Fundamentals of Mathematics by H. Behnke is good for getting started with math for self-learning?

[spare ridge]

bruh he said introductory

[foggy relic]

but he also said mathematical POV

[lapis sundial]

Are there any nice sources for problems on (baby) functional analysis?

Like on the level of the banach space techniques in papa Rudin or smth

[severe falcon]

I like the problems in Bressan’s intro to functional analysis

[lapis sundial]

oh cool I might give that a whirl thanks

Hadn't heard of that book actually

[severe falcon]

oop i think it’s called lecture notes in functional analysis, he taught my functional class so I’m a bit biased lol. he’s a great expositor tho

[crimson leaf]

introduction to graph theory by douglas west

[lunar sinew]

Graduating (CS)

[proven junco]

differential geometry book

[narrow fiber]

this is definitely a take

[cursive orbit]

one of the takes of all time

[dapper root]

Cat with a hat on

What will he do?

[remote sparrow]

is he the department chair at cal state long beach? or is it someone else with the same name

[grand ingot]

I'm looking for a book (online) with lot of solved questions of integration (calc 1 & 2);

basically I learn easily by looking at how they're solved (ton of questions)

not interested in chit chat book

[mossy flume]

reposting this

[remote sparrow]

https://www.youtube.com/watch?v=Zsib22FFie8

oh online

well, i guess you could get this online in certain places

[remote sparrow]

https://personal.math.ubc.ca/~CLP/

click the relevant books

then click on the problem books

#book-recommendations message

additional calculus resources ^

[marble solar]

That's him!

That's where I did my MS

(fully funded too!)

[remote sparrow]

oh cool

[crimson leaf]

What's a good intro to harmonics

[severe falcon]

stein and shakarchi Fourier Analysis

[woven sparrow]

What's a good book on set theory? I'd like to get into ZFC axioms, functions, binary and equivalence relations, and constructing the naturals, integers, rationals, and reals. If the book has exercises that would be great. Also PDF preferred if possible.

[heady ember]

Enderton's Elements of Set Theory is a friendly introduction that does not require much in the way of mathematical maturity.

Jech's undergrad set theory book is also an introductory one but needs a bit more mathematical maturity.

All of the things you mentioned are covered by Chapter 5 of Enderton. After that its cardinals and ordinals

[narrow fiber]

Oh man I remember trying to get through Jech's big book

My intro to set theory was Kaplansky but he does it from a naive set theory perspective however well-written

[sturdy shore]

I recommend goldrei's book, imo best and friendliest intro to set theory

[fallow cypress]

there's also the big open source logic textbook

great resource

[narrow fiber]

oh that resource is wonderful

have to sit down and go through it thoroughly one of these days

[remote sparrow]

i've heard the open logic project books are too easy for math students though

and generally geared to philosophy students

https://openlogicproject.org/

here's the website if anyone's interested

they also have set theory books

[grand thistle]

good (concise) resources for learning optimization? like lagrange multipliers, duality and all that

i'm aware of boyd's text

but it's a bit too long and complete

i need kind of a straight to the point and simple text, preferably one that is introductory and doesn't require that much math background (probably just some multivariable calc, analysis and linear algebra), so doesn't assume like calculus of variations or something

[crimson leaf]

Introduction to Optimization by Zak and Chong is what the course I'll be in next semester will be using

[grand thistle]

cool ill check it out

[gray gazelle]

How do u get them online? Ive been trying to find them for months

[hollow shore]

check the pins in #calculus

[grand ingot]

broken link

[unborn inlet]

hi

which book should I use for Olympiad prepration [INDIA, IOQM type of olympiad]

[gray gazelle]

Need books on Linear algebra

[heady ember]

Look in pinned

[mental canyon]

Any good text books regarding these topics

The first section deals with events, the axioms of probability, conditional probability and independence. The second introduces discrete random variables including distributions, expectation and variance. Joint distributions are covered briefly

[sudden dock]

https://artofproblemsolving.com/wiki/index.php/Olympiad_books

#old-network

[molten mason]

There's also PDF online

[grand ingot]

hello today

I'm looking for pdf to understand vector fields

I'm basically looking for vector analysis to understand physics better

electric, magnetic, gravitational field etc

so i thought it might good ideas to under them from the maths point of view
like understanding how purely vector files

work

[karmic thorn]

Are you familiar with calculus and linear algebra?

[leaden cliff]

Hi please can anyone record textbooks for epsilon definition under limits

[brittle breach]

abbot understanding analysis

[gray jungle]

not a textbook but my old professor wrote some nice lecture notes regarding epsilon delta arguments during my freshman course, which i still have if you are interested.

[leaden cliff]

Yes I’m interested thanks.

[gray jungle]

I sent it in dms

[remote sparrow]

#book-recommendations message

[clever mica]

Hi. Any recommendations on abstract data types(data structures) or proofs(especially interested in proofing algorithms)? That may sound like CS stuff but I'm interested in those topics from mathematical perspective

[sage python]

Dam SourDrop tryna compete with my linear algebra book review huh

[indigo mesa]

Team Dami!

[versed quiver]

it’s not a whole book on the subject but the start of griffiths electrodynamics provides a decent introduction to vector fields for use in undergraduate physics. a classic book on the subject that physics students tend to use is “div grad curl and all of that” or something similar-sounding

if you want to learn about vector fields properly then you’ll be looking at books in differential geometry but physics students can tend to find that difficult in my experience. it’s definitely worth having a look at though if you can. i like the book titled “manifolds, tensors and forms” but i forgot the author

[mental canyon]

Any good text books for these topics
events, the axioms of probability, conditional probability and independence. discrete random variables including distributions, expectation and variance.

[remote sparrow]

blitzstein and hwang's book

[wise spindle]

Any other recommendations? I’ve looked at this one and it’s a bit more complex than what I am currently studying in probability

[remote sparrow]

is your class algebra- or calculus-based?

[slim rose]

What’s a good book to transition from competition math to Olympiad (aime to usa(j)mo), like an intro to Olympiad math. (Self study)

[wise spindle]

Neither it’s a probability class. Intro to probability

[remote sparrow]

do you use algebra or calculus in that class

blitzstein and hwang is one of the easier books i know of

obviously it's too complicated if you're just using algebra of the solving equations variety

like solve for x if we have the equation x^2 + 2x + 1 = 0

that's what i mean by asking whether your class is algebra- or calculus-based

as in what prerequisite math class does it need

[remote sparrow]

hubbard and hubbard or shifrin's book are good choices

hubbard and hubbard also has chapters dedicated to discussing electromagnetism

[wise spindle]

Pre requisite is just an Alevel in maths in the UK. It’s a level 4 undergraduate course

[orchid mortar]

Honestly I don't think you can get simpler than Blitzstein

[remote sparrow]

i don't live in the uk

so idk what constitutes A-level math

[orchid mortar]

There's also this
https://services.math.duke.edu/~rtd/EP4A/EP4A.html

[remote sparrow]

surely you can at least tell me whether your class uses calculus or not

do you see any integrals?

derivatives?

Any of these symbols: $\frac{d}{dx}$ $\int$?

[hasty eagle]

Sour Drop

[remote sparrow]

limits?

[heady ember]

Pretty sure there is calc in AL

I don't live in the UK but my country's O-Levels already covers some of calc 1

[molten mason]

A level math goes up to calculus

[rancid abyss]

do you have any videos or book recommendations that help ease my way into maths

[oblique dove]

what do you guys think of the pre-requisites of Diestel's graph thoery?

[slim rose]

Any suggestions?

[narrow fiber]

does anyone have recommendations for intro books on dynamical systems? I'd be totally new to the subject I've just been curious about it

[oblique dove]

at that point i’d say look at topic based books such as EGMO, MONT, etc…

[sage python]

What's your existing background, and do you have a particular angle on dynamics you enjoy

[narrow fiber]

I'd especially appreciate a number theory angle - idk exactly what background would pertain to dynamics but to throw out some books I'd say I'm at the level of across various topics that may relate: Folland for analysis, Lee for smooth manifold stuff, Hatcher for AT, Milne for algebraic number theory and some CFT (still studying the latter). I'm also into Lie groups & algebras and I've heard there's an avenue there that connects to dynamical systems

[sage python]

Maybe try Einsiedler and Ward

Ergodic Theory with a view toward Number Theory

[narrow fiber]

Awesome thank you I'll check it out

[wise spindle]

We have done calculus; integration differentiation etc. but not limits

[sage python]

Wat

[signal charm]

i mean the definition of the derivative is literally a limit

how can you even use derivatives without properly defining them

[orchid mortar]

Probably via formulas, like Cavalieri's quadrature formula, remembering integral of sine is minus cosine, etc.

[night knot]

the A-Level math syllabus has this thing where they mention the idea of a limit, at least on the textbooks, but don't really test you on it

[solid wadi]

Hello! I am looking for a book on Constructive Logic and Type Theory for a generic equivalent of a college student. Something that can help getting into Type Theory and Formal Proof: An Introduction by Rob Nederpelt and Herman Geuvers, which is an awesome book but a bit too steep.

[heady ember]

Check out Clerk's recs in pinned

[grand ingot]

have done calc 1

partial fractions etc

[karmic thorn]

Hmm, see the Calculus III part of Paul's Online Math Notes

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

It's good for a first look into the subject, although I think multivariable calculus might make much more sense after going through a class on linear algebra (or at least learning it in parallel).

[solid wadi]

@solemn rover   It seems you have an error?

It is not hard to see that in a proof there may be circuitous or roundabout
reasoning; even redundant reasoning. For example, we may assume A, and go
on to prove A; by this we establish that A =⇒ B. Now we give a direct proof
of B. By modus ponens we conclude B. This is a perfectly legitimate proof of
B, but it is circuitous: we could have started by proving A directly instead of
assuming it, and then continued on to prove B. The circuitous proof introduces
a new application of both the introduction and elimination rules for implication.

It seems you meant to say «… we may assume A, and go on to prove B; by this we establish that A ⇒ B. Now we give a direct proof of A. …».

[solid wadi]

All of those books are too hard.

[heady ember]

Perhaps you can try asking in #foundations

[novel trail]

I have about a month to learn some complex analysis. I’m familiar with multivariable calc I’m looking for a book or resource that has a decently high pace, I don’t really have hours to spend on understanding proofs. Something with exercises would be a bonus, but I don’t mind hunting for those myself

[karmic thorn]

What topics do you want to cover?

Pete L. Clark has a decent set of lecture notes on introductory complex analysis, and they're pretty compact (~90 pages iirc)

[novel trail]

Fairly introductory material iirc from the last time I took a look at it

• Function theory of complex variable: differentiability, Cauchy-Riemann equations.
• Complex line integrals, Cauchy integral formula.

[karmic thorn]

I'm sure those notes have everything you mentioned

And more, which you can gloss over

It also has exercises

[novel trail]

From a quick google, do you mean this? http://alpha.math.uga.edu/~pete/complex_analysis_supplemental.pdf

[karmic thorn]

Yes!

Here

[novel trail]

Perfect, I’ll take a look. Thanks. As topics advance I find it harder and harder to find good material that doesn’t go way too deep into the weeds

[karmic thorn]

The course he taught apparently used a complex analysis text by Beck, which is also (legally) available online for free

https://matthbeck.github.io/complex.html

[gray gazelle]

I know this is a random question

I am trying to buy "Calculus" by Jon Rogawski, because I really like the book and I can't stand reading PDFs.

However I am living in Italy, and it's normal that such books are not existing in our shops. Does someone have experience with buying foreign books in Europe?

[sand crescent]

i have some cute notes from my undergrad >.< it has a more algebraic flavor of complex analysis i could send them if you wanna give it a try. (they aren't fully complete, but i think they still manage to give a slightly different perspective from many other introductory notes)

around 90ish pages as well

[novel trail]

Definitely would love to have them, it does seem most take a very geometric approach, maybe an algebraic version might work better for me given my linear algebra knowledge is pretty stale

[gray gazelle]

How do u even make notes for maths tho ? What do u write in it ?