book-recommendations

[molten gulch]

where did you end off

like within hs maths

[gray gazelle]

passed a bit of time, last thing that I remember is equation of first grade... and I'm ashamed of this

my end log term goals is to learn the same math that know ppl after finished the university of computer science

[eternal jasper]

Hi, can someone recommend some books for calculus? They may have some basics plus advanced stuff

[gray gazelle]

good idea, I'll follow this path, thanks for the suggestions

[molten gulch]

stewart or thomas' calculus

[eternal jasper]

thanks, i'll look them up

[sonic zealot]

Calculus I, course name: "differential and integral calculus with proofs".

not computation like high school but not spivak analysis level. any suggestions please? ive heard of stewart but open to other notes/recommendations

[open merlin]

Calculus With Applications by Lax & Terrell, maybe?
I haven't read it, but this review makes it sound like it fits the bill:

The book is written at a level more advanced than the standards calculus texts and one less advanced than the standard real analysis textbook. You will need a solid understanding of proofs, as they are typically taught in discrete mathematics, to work through the book.

[sonic zealot]

thank you! will take a look

[remote sparrow]

velleman is good too

https://www.amazon.com/Calculus-Rigorous-Course-Aurora-Originals/dp/0486809366

@median saffron

[manic carbon]

Hello!

does anyone know a good book on Relational Algebra and Relational Calculus for SQL?

[molten gulch]

Silberschatz, Korth, and Sudarshan - Database System Concepts
Garcia-Molina, Ullman, and Widom - Database Systems

Should cover relational stuff and databases

[trail hemlock]

I like Apostol's calculus for this. if its "with proofs" but you want an easier text, Apostol's text is probably the best. There are also Lang's A First Course in Calculus

[remote sparrow]

@narrow fiber did you ever look at any other references for probability besides ch. 10 of folland and shiryaev

[median saffron]

Ya I can confirm there are a good mix of exercises with proofs and what not and it’s not too overwhelming

[narrow fiber]

Yes i like legall a lot

https://link.springer.com/book/10.1007/978-3-031-14205-5

[vocal egret]

do y'all recommend I buy Lang's book after Thomas' book?

[tribal crow]

I don't know which Lang book you're referring to, or what Thomas' book is

[remote sparrow]

on calculus? no reason to

[vocal egret]

Do you recommend I spend it on "Book of Proof" instead?

For proof writing

[remote sparrow]

sure why not

you could also arrange to have it printed at lulu

takes moderate technical skill but it might end up cheaper

[tender cobalt]

I like Thomas Calculus

[mystic orbit]

Sorry, I cannot

Giving a faithful review would require me to read a significant portion of the book to check out the quality and the clarity of the exposition and

I wouldn't even be able to make sure the ordering/selection is good

Since I don't know enough about the subject to have an opinion haha

[knotty gust]

Guys im in 10th grade in Germany, I take part in Math olympiad regularly and fare pretty well, but im really interested in physics Olympiad. My teacher said that the 10th class is a perfect time to start learning for the physics olympiad, so me and my friends took part in the first round, but it turns out im really trash at physics. I dont have a good foundation on anything really. Despite starting the same time as my friends, they did much better than me. I do get A's in class, but for some reason i feel like i know nothing here. Any book recommendations for me to get better in physics olympiad?

[subtle violet]

ngl the only le gall i was aware of was the one about stochastic calc

[knotty gust]

what is HRK?

[grizzled solar]

Valentine Crow and Mr. Death

Sounds a little like a kid book but it has a serious aura

[tender cobalt]

Fundamentals of Physics by Halliday, Resnick, Walker

[grave badger]

Guys do u have any book suggestions regarding time management?

Pls I need some book to improve myself

[knotty gust]

Atomic Habits - James Clear is a great way to start

[grave badger]

Yeah it's a really good book, my dad suggested it too. 🙂

[finite marten]

I read a book recently (I don't know the name, it's French) and it talks about the infinite and stuff, it's really nice

[heady ember]

Kanamori?

[distant rampart]

I reccomend highly Eragon. Great book. Plot starts off a little shaky at first, but you will learn to understand it. Long book averaging about 500-600 pages per book. Yw!

[signal zenith]

I lovvvveee this series

[distant rampart]

Ik it’s so good

[remote sparrow]

that's fine, thanks for answering

[glad rampart]

im looking for an introductory physics book, i know basically nothing about physics and would like to know some things

[molten gulch]

Halliday and resnick

[glad rampart]

thanks

[glad rampart]

i have a friend who knows a bit about physics and can help me get through some of the initial learning pains

which i am def having lol

[open merlin]

Angela Collier's got a video called "how to teach yourself physics" with a bunch of books she recommends
(Although, the point of the video is kinda "Don't buy a big stack of books actually" so idk :P )

[glad rampart]

difficult is fine

i am having a bit of trouble with the terminology theyre using but im sure ill get used to it

[remote sparrow]

walter lewin's physics lectures are good

[glad rampart]

i prefer text based stuff if i can help it

[fresh skiff]

Is probability 1 (or 2 as well) by albert shiryaev is suitable for undergraduates as well?

[remote sparrow]

the first chapter goes over probability theory without measure theory. chapters 2 and 3 develop measure theory and measure-theoretic probability side-by-side. it wouldn't hurt to already know some measure theory somewhere else, though, as shiryaev has a reputation for being a harder book.

i'm a bit sad some of the figures and tables are so low quality though

actually it just seems to be that one page. i don't think it'd be too hard to replace it with a better diagram

https://old.maa.org/press/maa-reviews/probability-1-0

https://old.maa.org/press/maa-reviews/probability-2

@fresh skiff

https://old.maa.org/press/maa-reviews/problems-in-probability-0

[fresh skiff]

oh cool, but the issue is that idk basic probability theory

why this table is not very much clear. I think his 3rd edition is digital now

[remote sparrow]

there are some faded words

it's readable but i have high standards

especially since i'm planning to have these books printed

faded text hurts it as a reference

https://old.maa.org/press/maa-reviews/probability-a-graduate-course

this book has full solutions

it doesn't cover as much and it's slower-paced

[fresh skiff]

oh cool so you are planning to study probability theory

[remote sparrow]

some time in the future i guess

[remote sparrow]

https://stat110.net

[fresh skiff]

I see, I am studying measure theory. But saw that probability and MT are closely related

[remote sparrow]

best place to pick up the basic intuitive notions of probability

everything there is free

[fresh skiff]

so thought to study both

i mean study probability theory using MT

[fresh skiff]

oh thats cool.

[fresh skiff]

and this could be readable after first course in Probability and MT right?

[remote sparrow]

yes

actually allan gut develops measure theory within

a lot of probability texts are self-contained with respect to the measure theory needed (of course it's a bit less general but it suffices)

you can skim those chapters if you like

[fresh skiff]

yeah sure

oh nvm i misread lol

[remote sparrow]

https://old.maa.org/press/maa-reviews/probability-theory-and-examples-0
https://old.maa.org/press/maa-reviews/probability-theory-and-examples

this is a standard text

along with the third edition of billingsley

[fresh skiff]

so usually probability theory books develop measure theory inside. But less in general

is there some good textbook which develop measure theory as in one part and probability in second part?

[remote sparrow]

Probability and Measure by billingsley and Probability and Measure Theory by ash and doleans-dade

[fresh skiff]

i am abit of confused, which text could server better as second course on probabilty via measure theory

[remote sparrow]

second course on measure-theoretic probability?

wdym by that

everything i sent are standard introductions to measure-theoretic probability

[fresh skiff]

oh got it, so everything you have sent require like some MT and basic of probability right?

[remote sparrow]

besides https://stat110.net

only requires calculus, no measure theory is used

measure-theoretic probability texts often develop measure theory and probability in tandem

durrett sorta reviews the requisite measure theory but i'd say it's better if you've already learned it elsewhere

[fresh skiff]

gotcha, thank you so much for making everything so clear

[remote sparrow]

@fresh skiff

https://old.maa.org/press/maa-reviews/a-second-course-in-probability

https://www.amazon.com/Probability-Martingales-Cambridge-Mathematical-Textbooks/dp/0521406056

these are good supplementary texts

Introduction to Probability Models by ross and Probability and Random Processes by grimmett and stirzaker are also good supplements (ross is not measure-theoretic, while grimmett and stirzaker doesn't do measure theory until very late)

[spring bridge]

so i'm in highschool (in my country 11th grade) and i have A level maths and want to learn more about something my level, what do i read?

[remote sparrow]

i do recommend learning how to think about probability intuitively before doing measure-theoretic probability

just blitzstein and hwang (stat110) is good

[remote sparrow]

https://www.amazon.com/First-Look-Rigorous-Probability-Theory/dp/9812703713

i heard this was good, though maybe a bit simple

[remote sparrow]

rosenthal might be most suitable for advanced undergraduates

https://www.amazon.com/FIRST-LOOK-AT-STOCHASTIC-PROCESSES/dp/9811207909

there's a more recent follow-up

[slender wasp]

what's a good abstract algebra book for intro to composition series, Jordan Holder, solvable groups stuff. Dummit and foote is very short (3 pages) and Keith Conrad's notes get into advanced stuff too quickly (30 pages). I need something in between the two with examples and some straightforward exercises.

[vocal egret]

Decided to buy Lipschutz's probability (SI edition, blue cover). idk if this is enough for self study

[grave badger]

Hey

Do u guyzz have any suggestions for non fictional books mainly based on mathematics?

[timber mesa]

you mean like, not textbooks but essays, biographies and such

stuff like Villani's A Birth of a Theorem ig

which is a telling of the process that led to his Fields Medal-winning work

[grave badger]

Yes

[timber mesa]

or one of my favorites Where Mathematics Comes From (by Lakoff and Núñez), which aims to explain the tenets of mathematical practice through recent advances in cognitive science

[grave badger]

This sounds good

how many pages does it have?

[timber mesa]

Villani's book is short, less than 200 iirc

[grave badger]

great

[timber mesa]

this one is deffo longer and more dense it's more of an academic text

[grave badger]

nah

i dont need academic texts

i want something that explains the world from the eyes of mathematics

[timber mesa]

with regard to this matter an old prof of mine recs Conversations on Mind, Matter, and Mathematics by Jean-Pierre Changeux and Alain Connes

hm

[timber mesa]

this one is similar in the sense that it's also an exchange between a neuroscientist and a mathematician

in the form of an interview though iirc

[grave badger]

k

i'll see

thanks

[timber mesa]

np

[timber mesa]

I'm not sure what I could recommend that is like this though sadly

[grave badger]

np bro

[timber mesa]

what are you trying to get at, something related to mathematical modelling or something more about e.g. foundations of physics or something

not that I'm an expert on either but to get an idea of what you're imagining

[grave badger]

I've read The Brief History of Time-Stephen Hawkings

I want something that talks abt how everything is based on mathematics

[timber mesa]

icic

[grave badger]

yeah

my frnds r so ded that they have 0 knowledge regarding maths and physics

llol

[remote sparrow]

https://www.amazon.com/Proof-Pudding-Changing-Nature-Mathematical/dp/0387489088

[grave badger]

k ill try thanks 🙂

[gray gazelle]

Which books should I get for self-studying undergraduate math? Is there a roadmap or similar for self-studying math like there is for programming? I'd like to have a quality book or two for every subject I encounter.

[remote sparrow]

where are you already in your mathematics education

also, you can look at the catalogs of a few different universities to get an idea of what the core curriculum is

[gray gazelle]

I finished high school and haven't had any contact with math since. I will look at the catalogs, thanks for the suggestion!

[prime oak]

hi, has anyone here read schilling's 'measures, integrals and martingales'

is it a good first intro to measure theory

[remote sparrow]

@fossil nest @gray jungle

it has a full solutions manual available for free online

[gray jungle]

yes, its a very solid book, it takes a bit of a probabilistic angle unlike the other mt books, but its quite friendly with really good exposure and exercises.

[spark jay]

Any book suggestions for basic conic sections

[tired glen]

anyone suggest me some book on number theory and also give the link of synopsis of elementary results in pure and applied mathematics

[spark jay]

Elementary number theory by David m Burton

[tired glen]

kk thnk

[ionic warren]

Any recommendations for SAT math?

[gray gazelle]

do ppl study for SAT math?

[ionic warren]

I’m struggling to get 750 and above

[gray gazelle]

just asking

[ionic warren]

I do study from time to time

The maximum I got is 720 but anything above 750 I couldn’t do it

[gray gazelle]

oh i always thoguht ppl never study

cuz it was so easy for indian students

but

what about the english

things in SAT

[ionic warren]

I also study for that. I found that part a bit more difficult

[gray gazelle]

damn ok

[gray gazelle]

lol

yall write 8 SATs?

my mom is killing me when i asked her for writing one sat

PSATs?

just syaing bro lol

nto for us lol

in india

they dont

do SAT

and all

i only trying to do sat

because

i wanna

do RSI

by MIT

who tf is that

WHAT

bro

i

dont understand lol

oh

i didnt

kniow

cuz im south India

yeah but

im in 11th rn

idk if i can focus on 12 th and sat

LMFAO

BRO

lund

means

bad word i think

OH LMAO

i wanna go to MIT

(im delusional)

i have 98/100 board scores

in science

real

but

we have JEE

lol

damn bro

any suggestions

for olympiuads

tha ti can do

in 11th?

im so

plain

like my background is very plain

I only do MUNS

thats all

by SOF?

IMO

by SOF?

that olympiad?

because that is dead easy

lol k

oh then i am talking about differen tolympiad lol

bro IOQM

RMO

INMO

and IMO

this one?

lol k

[kind fossil]

nah bro they ask from putside the textbook

[signal kettle]

BITS PILANI they consider SAT for non resedential indians and stuff only hv to give BITSAT to get into BITS

[signal kettle]

is there a more detailed book with more theory in it

[crude plover]

My algebra is absolutely abysmal. Any book recommendations to strenghen my algebra? Mostly looking for something like college algebra level (advanced hs early college level)

[gray gazelle]

Hi! I want to learn about linear algebra (first year in the university, I am studying telecomunications engineering), what books or courses can you recommend me?

[gilded olive]

Linear Algebra by Friedberg Insel and Spence is what my uni followed in first year

it is very suitable for self-studying

[thorn cloak]

khan academy and lots of practice problems !

[torpid ice]

Scythe by Neal Shusterman

[rugged silo]

Im looking to self-study real analysis. Any recommendations?

[oak flower]

Understanding analysis by Abott, is quite pleasant.

[graceful moon]

Abbot, Ross and Tao all have nice introductory analysis books that are great for self study

[rugged silo]

thanks!

[gray gazelle]

Another vote for abbott

[plain barn]

any recommendations for a book on advanced set theory? like, that talks about ordinals and stuff
I don't want to learn it "for" any other area btw I just want to know these advanced set theory stuff

(as a note: my knowledge on set theory basically goes as far as what is learned in munkres' topology's first chapter)

[molten gulch]

Jech's set theory book comes to mind

[heady ember]

If Jech is too hard, Kunen is well-liked.

[plain barn]

ty

[plain barn]

ty

[foggy quest]

https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[foggy quest]

https://www.math.brown.edu/streil/papers/LADW/LADW.html and https://mtaylor.web.unc.edu/notes/linear-algebra-notes/ are good.

[stark turret]

does anyone know the 50ish page linear algebra book from like the 60’s? i’ve heard about it a few times but i can’t find any other information on it

[remote sparrow]

if you have never had any prior exposure to mathematical logic, a better source would be Introduction to Set Theory by hrbacek and jech

[spark jay]

Well you want to study nt for ? Olympiad or university

Anyone has any book recommendations for conic sections

[old elk]

Hi guys, someone could recommend me an introductory book to algebraic topology, I would really appreciate it.

[pallid quail]

this^

[old elk]

which one?

[old elk]

??

[pallid quail]

i need that reccs too

[heady ember]

#book-recommendations message

[autumn bane]

This can help learn differential geometry..?

[remote sparrow]

no

[drowsy nacelle]

There are 2 jechs btw

I think one is called intro to set theory and the other one is just set theory

[gray gazelle]

Thanks! What are the differents between the books Linear Algebra Done Wrong and Linear Algebra Done Right?

[drowsy nacelle]

But both are like axiomatic set theory thr way you’re saying

[open merlin]

LADR is a more abstract 2nd course in lin alg for math majors, roughly speaking

[fresh skiff]

I got it. I am just kinda very busy with final exams (assignments, tests). I will follow this course whenever I will get time after exams
Thank you Sour Drop

[fresh skiff]

I see. Well I am not really much interested in probability stuff. But for the sake of knowledge of probability I will touch it if time allows.

[molten gulch]

@old elk @pallid quail #book-recommendations message here's some alg top books

[drifting echo]

Can I have introduction to linear algebra by Gilbert Strang

[plain barn]

Depends on what you mean by mathemstical logic

Ym like, predicate logic?

Cus if you're talking about it in general yeah I have a lot of exposure

But not predicate logic

[delicate jacinth]

Which textbook would you all recommend if I wanted to self study ap calc bc.

[shadow river]

Kunen Foundations of Mathematics is good (his book Set Theory as well as Jech's Set Theory are also good but much more advanced), or Enderton's Set Theory book

Foundations is good because it also covers the required first order logic/proof theory

[signal zenith]

MA Armstrong Basic Topology

The pinned AT rec is pretty good but those books are all graduate level and quite a lot harder than Armstrong

So if you find them too hard I would check out Armstrong

[plain barn]

oh interesting

I may look this one up since I don't formally know a lot about first order logic

[shadow river]

actually look up Antonio Montalbon on Youtube, he has 2 full courses of lectures, one for first order logic, and the second for set theory following Enderton, it's really great

it should definitely get you up to speed to read more advanced set theory

[plain barn]

I don't really like watching lectures but ty for the reccomendation anyways

[shadow river]

ahh all good

then yeah, Enderton or Foundations of Math are great

[gray gazelle]

is A primer of abstract algebra by Robert Ash a good beginner proof book? (just finished calc 1 about to go into calc 2) ?

[north summit]

@gray gazelle Don't know about that book, but i learned the basics with a book devoted to writing proofs called book of proof by Richard Hammack. https://www.people.vcu.edu/~rhammack/BookOfProof/

[foggy quest]

not much difference.

[willow merlin]

which book covers projection operators in linear algebra and linear transformations over polynomial spaces

[teal prairie]

To me this looks like a book for a beginner who wants to dive into pure math. The focus is not totally on teaching proofs to a beginner, in fact, I can see a total beginner to proofs struggling with this book. If your goal is simply learning how to do proofs to move on to calc 2, I wouldn't say this is the most appropriate book.

[gray gazelle]

I will say it’s not just calc 2 it’s math in general plus I’m a physics major

Idk if that helps

[royal stone]

Oo can I recommend a book? If so imma recommend, what if (1&2) Randall Monroe and how to lose the time war by max Gladstone and amal el-mohtar

[inner quartz]

I want to recommend a book for intro to analysis. It does what spivak calculus does but without too much words in a formal and concise way. It’s the best way to describe it

The book is mathematical analysis function of one variable mariano giaquinta giuseppe modica

And it’s has another book for multivariable too that does the same thing

mathematical analysis introduction to functions several variable mariano giaquinta giuseppe modica

Which spivak doesn’t have. Hopefully someone checks it out

[broken pecan]

anyone knows a relatively comprehensive book on multigrid methods?

[river fog]

i feel like i can kinda-sorta do the following topics, but it'd be nice to have a set of book problems/worksheet or two/etc that has a ton of central questions/answers so that i can just grind for a bit to get a better arithmetic intuition.

• matrix-vector multiplication
• matrix multiplication
• gram-schmidt
• qr factorization
• finding projections

anyone know any good resources?

[dense gorge]

Hey i am in 7th sem in iit anyone here who belogs to same ??

[north summit]

can someone recommend me a geometry book that uses linear algebra

[fresh skiff]

Can I ask why?

[gray gazelle]

anyone know of

college physics books

with no bs and straight to stuff?

this book i have is just full of pictures and stuff like hell

so many nonsense

this is like absolute dog water

[near geode]

whaaat serway and jewett is a banger

[gray gazelle]

oh man

lol

[near geode]

I have the fifth edition of one of theirs on my shelf rn haha

[gray gazelle]

xdddd

[near geode]

surely some specific topic book will be more to the point

[abstract copper]

These are more typically suited towards those who aren't majoring in physics

[gray gazelle]

i want like introductory physics book with calculus

[abstract copper]

It provides the 'basic'

[gray gazelle]

as it says

"engineering"

[near geode]

for my first year I used that exact book

in physics

[gray gazelle]

are u physics major?

[near geode]

yeees

[gray gazelle]

:O

[near geode]

struggling one at that

[abstract copper]

'Introductory physics book' is a vague term. What topic do you wish to study? Classical mechanics? Electrodynamics?

[near geode]

have all my exams next week

[gray gazelle]

like how the normal colllege physics goes, some what of all topics

u know

[near geode]

Serway and Jewett is good for that man - I would check out the principles of physics or something similar from a lib to see if it's nicer or something

[gray gazelle]

well may be serway really is the way to go

[near geode]

are you an engineer?

[abstract copper]

Yeah I think Serway fits that description

[gray gazelle]

im not in college yet

[near geode]

ah

yes

S+J

What are you planning on doing?

[gray gazelle]

well i have interest in cs, maths, and physics im doing maths all the time

thinking to get into physics too now

[abstract copper]

My recommendation is go for a book that is directed towards a certain topic.

[gray gazelle]

are they more rigrous

[abstract copper]

Taylor's classical mechanics is generally accepted as a first introduction to classical mechanics.

[gray gazelle]

yeah im aware of them but i thought its preq to read college physics before that

lmao

[abstract copper]

Just calculus

I'm pretty sure calculus is also introduced in that book

[gray gazelle]

i am doing calculus so thats fine

[near geode]

If you've taken a physics course (sliding blocks, whatever) in HS, then serway and jewett will take you through 1st year physics (most of it), and then it's specialized

[gray gazelle]

yeah i have done those

basic problems

[near geode]

I had no calculus experience in my first year of college and I got cooked (am still getting cooked), so you're a lot better off

[gray gazelle]

free body diagrams

friction

[near geode]

Yeaaaah

that stuff

[gray gazelle]

gravity

yeah

[near geode]

If you like reading then read Feynman's books! Bit of a general reccomendation but they're good and make the field seem a bit more fun I think

[gray gazelle]

nice

cool will read the s + j

tho it feels less rigorous

lmao

🙏🏻

thank you guys

[swift sierra]

University Physics Young & Freedman is nice if you want a general book for a physics major

But like others mentioned, for each topic, you should look at individual books that go more in depth

[north summit]

What do I stand to gain from this book? Is the material useful?

https://a.co/d/9eH5hwk

[remote sparrow]

any good textbooks for learning french?

[remote sparrow]

what's wrong with pictures in a physics textbook? it's a science textbook; there should be pictures of models.

[median sequoia]

Im looking for a book on functional analysis that has problems and is cheaper in comparison to other textbooks

[gray gazelle]

Well I mean it kinda gets overwhelmed for me idk if its cuz of some disorder or what

😭😭😭

Tho I don’t have any problems with the theory and text itself

Graphs and stuff is also fine

[loud cradle]

tbf, current physics textbooks have a lot of fluff including tons of unnecessary pictures
compare e.g. Halliday Resnick today vs editions from the 60s-70s-80s

[sand path]

Color is nice

[gray gazelle]

you better join French discord server, you will find one that parterned with discord in the discord discover

[earnest notch]

Are there any recommended books for trigonometry, especially for studying physics and complex geometry?

[near geode]

Has anyone read Mathematical Methods for Physics and Engineering by Riley Hobson & Bence? Is it good?

[near geode]

ok it seems to have been reccomended in ehre a lot so surely it's good

[plucky socket]

I did read it around 20 pgs and it was good.

we have it in our library

[gray gazelle]

Do any have soft copy of Ars Conjectandi by Jacob Bernoulli translated in English??

[gray gazelle]

yeah those are gems

but material is old

which is sad

[chrome tide]

Guys help please I registered in ap Calculus BC my sophomore year and I need to self study now I already got a very good Calculus background. What is the better prep book to use Ap calculus barons 2025(cover both bc and ab and is 570 pages) or the princton ap calculus bc (only for bc and is 770 pages)

[chrome tide]

Thanks. It is just that it has less pages and is for bc and ab that got me a bit u know.

And it doesn't have a specific section for parametric but everyone told me taht barons is better so I am gonna go for it. U saved me time I have been thinking about this for a weak

They are the same price at my Amazon (sale)

So should I just buy 2025 then ?

Alright dude thanks you very much for your help 🙏 🙂 👍

One more thing 2025 has less pages for some reason lol 😆

Like we talking 200 pages diffrent

Thanks alot like alot

Is it a mistake that I only took one ao sophomore year (I am trying to admission for better unis) I feel like I did a mistake and I should like register for more but bc is a tough class

Thanks alot I thought I could just get a feel for AP through a course that is easy for me in this case calc because I covered alot of it in uni level then I would go crazy for senior and jenior

But who ever you are thanks very much I have been thinking for a mounth

I hope haravard accepts u full ride dude

[quaint wagon]

Hi guys,

Can you recommend some books/online courses/notes etc for functional analysis as a complete beginner?

This is my mathematical background:

I have taken courses in Real Analysis (following Bartle and Sherbert); recently I started revising from Rudin and I am about to complete chapter 6 ( I intend to do till ch 8)

I have done Linear Algebra ( I am revising from a book by S Kumaresan and doing exercises from Friedberg)

I have done Topology (upto ch 3 ) from Munkres (but mostly theory and not many exercises)

I am quite aware that this kind of background is very raw, however I am to undertake a self study program in functional analysis for 6-8 months so I think I can cover any gap in this time

[mellow wren]

probably read Folland for the very basics

to get used to stuff like measure theory

then a good one is probably Reed Simons
A lot of people swear by that book

it's a bit older though

[daring lake]

Kreyzig

[pliant wadi]

I want to explore the intersection of Galois theory and Algebraic topology. Any recs for this specifically?

[grim ore]

I am not yet familiar with the intersection as i will be taking a course in it next fall, but funny enough its called Intersection Theory in Algebraic Geometry if that narrows your focus

Idk any book for it tho so if someone wants to chip in

[pliant wadi]

WHAT

Lmfao

[grim ore]

yeah lmaoo

[pliant wadi]

Intersection theory

Wow

[grim ore]

it has to deal with polynomial equations in relation to cohomologies which is basically taking manifolds from topology

that’s the extent that i know of it

[pliant wadi]

Oh I see

[grim ore]

math people are sooo creative

[pliant wadi]

"Who let mathematicians name things? Mathematicians."

[grim ore]

i do see fulton as a i guess standard book for it and he’s been good for other AG books so take that as you will

on the other hand with more of a modern take, i look at the cambridge releases; so i see they do Fulton and Eisenbud too

https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Algebraic Geometry/Intersection-Theory_Cela.pdf

[pliant wadi]

Oh Fulton ik

[pliant wadi]

Thanks I'll check these out

[swift sierra]

Kreyzig’s Introductory Functional Analysis is very nice for your background

It also has hints or partial solutions for many of the exercises in the back of the book, which would help for self study

[foggy relic]

how do you know what you're taking next fall lmao

[grim ore]

We decided what courses are being offered next fall in the math department and i will just work my schedule around them

I only attended the ag subdepartment meeting tho for the course choosing

Outside from that I will be taking grad alg and grad real

[foggy relic]

very cool

[foggy quest]

The Functional Analysis appendix from https://link.springer.com/book/10.1007/978-3-031-33859-5 is good. In my experience, functional analysis is a subject that you should study when you need to use it, not just for the sake of learning it. That may be why Taylor gave such a detailed treatment of functional analysis in his PDE book.

[broken depot]

@abstract trellis @verbal ibex Hi, the foundations channel seemed pretty active, so I came here. I saw the convo in the category channel about universal algebra books. I'm interested in learning, i took a look at the contents and it seems that universal algebra is a form of model theory for algebra. what are your views on how universal algebra stands in relation to operad theory and props, and to topos theory?

[verbal ibex]

I will be honest i am not even in university yet and i learned UA because of a funny coincidence, really.

It is true though that it is sort of model theory for algebra, though model theory does also use universal algebra (it is often described as universal algebra + logic, hehe)

[broken depot]

oh ok thanks

[verbal ibex]

I believe at the heart of (pure) universal algebra it really is just the study of classifying and giving properties to sets of axioms (which translate nicely to certain classes of algebras due to Birkhoff)

[surreal token]

Any book recomendations on precalc?

[molten gulch]

stewart's precalc

[sand path]

Axler Precalc is good

[gray gazelle]

I'm looking for a book that covers all of highschool level math without calculus.

[sand path]

Basic Mathematics by Serge Lang

[gray gazelle]

That's exactly the one I thought might be it! Thx

[night salmon]

stewart vs spivak for learning calculus on my own?

[trail hemlock]

uh well what is your end goal

stewart is really computational, and spivak is basically an intro or segue into real analysis

[night salmon]

well i guess im more into applied math than pure math, eg physics, engineering, computer science, but im approaching calculus currently just as an interest, learning ahead

i dont really want to go into stuff like number theory and all that

[trail hemlock]

hmm

well i used spivak as my intro, and i think its rly nice

u can try spivak and supplement each chapter with problems from stewart for a mix of problems

[night salmon]

if it gives any context, you can think of me as an IB Math AA HL or AP Calculus BC student in terms of math level

[trail hemlock]

yeah i mean both books are written as introductions, but spivak is generally considered pretty difficult

if ur approaching as an interest, u can read the first chapter and see if its for you

spivak has a few computational problems, and you can also just use stewart for more computation practice

[still panther]

im pretty interested in improving my speed with computational linear algebra, can someone recommend a practice problem book? dont need theory, just like a book with a thousand problems of the "multiply two matrices" kind

[quaint wagon]

Thank you

[quaint wagon]

Thank you

[random estuary]

What books would you recommend for someone who knows very little about differntiation and integration and wants to broaden their understanding of it?

[molten gulch]

stewart's calculus
thomas' calculus

really any calculus textbook

[violet solstice]

dose anyone know a good book of measure theory ?

[molten gulch]

• Folland
• Cohn
• Axler

[violet solstice]

ty

[open merlin]

#book-recommendations message

Axler's MIRA looks nice too, but I haven't touched measure theory yet

[violet solstice]

ty

[gray jungle]

do you have any specific goals in learning MT?

[heady ember]

Hi James

[gray jungle]

some books are biased in how they present it

[gray jungle]

allo

[violet solstice]

i need to get better at it so i can pass my exam in january

[gray jungle]

Id say "Real analysis for graduate students" by bass is probably what you want then

[heady ember]

bassed take

[vocal egret]

Desperate for some resources for olympiads rn. Is AOPS a good one?

Currently owning "The Art and craft Of Problem Solving" and "Problem-Solving Strategies"

Thx for the info :3

[mystic orbit]

if you want something advanced you can try out the art and craft of problem solving

[vocal egret]

I got stuck with some parts of the book tho. It's more like a dictionary of methods that I don't know where or how to understand it. it does extend the book choices :3

[gray gazelle]

art and craft of problem solving 👀

[vocal egret]

I forgot I owned that book 😦

[royal remnant]

So... I want to understand how "Ordinals" and infinities work. Are there any good books or resources for that?

[obsidian blade]

I've heard Naïve set theory by Halmos is good / standard

but also that it's old and not necessarily easy

[trail hemlock]

hi darq

[royal remnant]

Oh.

Why is it not easy? Is it due to notation or explanation?

[obsidian blade]

I don't remember

I didn't learn from it, just a review I heard

but Wikipedia says it tries to be minimal about how much it cares to prove everything from axioms and stuff

which makes the stuff you want to learn easier

[royal remnant]

I see

[obsidian blade]

I'd start, if it's completely unreadable I'd find something else

[night salmon]

you guys should add a pinned message for calculus book recommendations

[rich sun]

we had channels #books #books-old why were they archived?

[drowsy nacelle]

what are the names of those?

i cant see em

[umbral field]

it was not very maintained. all existing reviews were moved to the website https://mathematics.gg/books

[umbral field]

you can view archived channels with the archivist role, obtainable in id:customize

[rich sun]

books and books-old

[drowsy nacelle]

oh thanks

[mystic orbit]

hello!

[mellow surge]

does anyone have recommendations for textbooks on discrete optimization

[heady ember]

Depends on what level are at. For undergrad level set theory (which includes ordinals and cardinals), Enderton's Elements of Set Theory or Hrbacek and Jech are well-liked; the latter requires some mathematicial maturity. Kunen's foundations of mathematics is another choice.

Let us know when you reach Kanamori

[trail hemlock]

jech is nice imo

[heady ember]

Baby jech right

[trail hemlock]

yesh

[heady ember]

Tfw big Jech is nice and wholesome

[royal remnant]

I'll try that.

Enderton's Elements of Set Theory
Hrbacek and Jech

[remote sparrow]

https://www.youtube.com/playlist?list=PLjJhPCaCziSQyON7NLc8Ac8ibdm6_iDQf

this playlist follows enderton

https://ocw.metu.edu.tr/course/view.php?id=270

this course follows hrbacek and jech

[royal remnant]

Is Hammack good as well?

https://www.people.vcu.edu/~rhammack/BookOfProof/

[remote sparrow]

nothing about ordinals i don't think

if you are struggling with general proof techniques it's good though

[royal remnant]

Doot recommended me this because I need to brush up on basic fundemental set theory

I'm missing these, according to Hammack

[remote sparrow]

if it helps sure

[royal remnant]

yes

[cerulean wind]

could anyone recommend a book on learning theory (PAC learning, VC dimension)?

[stable flicker]

Sadly, seems like current literature still refers to the 30-year old
https://direct.mit.edu/books/monograph/2604/An-Introduction-to-Computational-Learning-Theory

There are textbooks that introduce this early and use it
https://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning/
https://cs.nyu.edu/~mohri/mlbook/

There are books that dedicate a single chapter to it, which is probably not sufficient for what you are looking for

You might want to refer to (recent) lecture notes that use the Kearns book as a reference, since they would be more modern and give more modern perspective

[cerulean wind]

thank you! i will look into this

[cerulean wind]

and this seems like a good idea!

[dim pendant]

Hey guys, what are some math books you like which are motivated by tough questions, in which the math begins at a reasonable level and builds up to very deep content?

The primary example I'm thinking of is Cox's "Primes of the form x²+ny²"

It simply asks which primes are of that form, and within its pages, develops from some basic number theory to class field theory

[gray gazelle]

hey guys book recommendations starting with math oly

[autumn frigate]

Does anybody have the solutions manual for Calculus for Business Economics Life Sciences and Social Sciences Barnett Raymond A.; Ziegler Michael R.; Byleen Karl E

13th edition

[ionic osprey]

https://link.springer.com/book/10.1007/1-4020-2187-9 lol

from the preface, "I had given to Moscow High School children in 1963–1964 a (half year long) course of lectures, containing the topological proof of the Abel theorem."

[cerulean wind]

khan academy + schaum's or homework helpers

alternatively precalculus books / khan academy's precalc section give a good enough intro to trig

[signal zenith]

Average Russian high school

[gray gazelle]

[molten gulch]

I need to find the original paper, but it's about hodge theory, complex geometry, and infinite categorifications of lie algebras

[dim pendant]

Nice find.

[thorn cloak]

Any good books intro books for logic that are like higherish level? Not like intro to proofs but mathematical logic. I have copies of a course in mathematical logic by srivastava and a course in mathemetical logic for mathematicians by yu but they seem to be a bit advanced (im not sure what a prereq in logic would like like)?

[remote sparrow]

#book-recommendations message

[random fable]

can you guys recommend me books on algorithm analysis? or algorithms in general?

[remote sparrow]

clrs is a good book for algorithms

https://aofa.cs.princeton.edu/home/

i think sedgewick and flajolet is a standard book for analysis of algorithms

you can also peek at knuth's taocp volumes from time to time

[hollow shore]

https://jeffe.cs.illinois.edu/teaching/algorithms/

[novel shoal]

yeah my first algorithm book, i recommand it but maybe before reading it ppl should have a linear algebra, calculus and probability done

[fossil hemlock]

can anyone recommend me a few books for infinitary model theory?

[remote sparrow]

@torn crypt @harsh patrol

[torn crypt]

Why

But uh,

Marker’s
Keisler’s
Dickmann’s
Barwise’s

Are my go-to names

Depending on what exactly you wanna do, I might say a specific choice is better

[fossil hemlock]

atm I'm looking for stuff abt categoricity (mostly on L ω1,ω)

[torn crypt]

Ok, if it’s omega1, omega and categoricity stuff I’d propose Marker, Keisler, Baldwin, and Vasey

Namely the first two for their infinitary model theory books, Baldwin’s categoricity, and Vasey’s thesis has some related information especially in regards to some eventual categoricity stuff but in a very AEC-pilled framework

[fossil hemlock]

thank you
would you recommend either of Marker or Keisler over the other one or are they pretty similar

[torn crypt]

I’d recommend you cross reference because marker feels more modern and with a lot of good stuff, but he is very very typo heavy

And I forget what all is in Keisler lol

[fossil hemlock]

ah ok
thanks

[fossil hemlock]

oh lol ok

[torn crypt]

Like, the ToC etc and I don’t have it on hand to check

[remote sparrow]

fyi chang and keisler is available as a dover

[torn crypt]

This is a different Keisler book but good to know

[remote sparrow]

https://bookstore.ams.org/amstext-54/

@marble solar maybe the strauss killer

@molten mason @willow pecan

[blazing holly]

I know this is a channel for book recs but notetaking tools must go alongside it so thats what I wanna ask
Does anyone have recommendations for pencils/pens? Maybe even good paper/notebooks

[trail hemlock]

pilot g2 0.7mm black w/ printer paper & camscanner to scan important shit is what I use

[jaunty parcel]

For pens I am obsessed with Uniball's click gel for it is the smoothest pen I've ever used. I do not recommend pencils because we need to sharp them. I think that investing once in a Kuru Toga mechanical pencil is great because it automatically rotates the lead keeping the head pointy. I am never concerned of paper or notebook, cuz I draw in some software or scan everything which I write on paper, I use Google Drive's scan feature.

[real veldt]

Unfortunately, a lot that they said resonates with my personal experience 😭

Way too much separation of variables

[glossy zealot]

I recommend pentel energel too. There are a lot of options, just choose the one you can find at a local store

For papers I used to use Rhodia paper pad and it was very good

[tardy wolf]

https://dl.acm.org/journal/csur

That's a publication avenue only for CS surveys

is anyone aware of a similar one but for Math or Logic?

[gray gazelle]

echopraxia

good book

[thorn cloak]

i started to skim through this and i like this so much more than strauss wow

[pulsar lantern]

Bulletin of the AMS for math

[remote sparrow]

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

[remote sparrow]

@drowsy nacelle @tribal crow @vital bane

[drowsy nacelle]

Interesting

Yeah that is pretty true

[tribal crow]

what’s this?

PDE book?

[gray gazelle]

Hello guys any good books to start reading?

[velvet cove]

Hello , can anyone give me the list of O levels and A levels textbooks/books on subject of mathematics??

[mossy flume]

what sort of math are you looking for?

[signal mountain]

for o levels/gcses you might get one textbook that covers the whole thing, for alevels probably one per year for each of maths and further maths

i dont know of any particular ones, any will be fine

[trail hemlock]

@remote sparrow hi, sorry for the ping 😓 . i know you used lulu to print out some books, and I had a quick question. i formatted my pdf into a5 paper, and the cover looks like this. is this alright?

[normal crystal]

does Lulu really let you print that🤔

[trail hemlock]

fuck if i know

wait yeah thast prob not a good idea

[remote sparrow]

umm looks ok

aren't you gonna put anything on the spine

[remote sparrow]

not sure about "let" but i don't think they care if you make it private access and only print for personal use

[remote sparrow]

yes

[trail hemlock]

um this might sound dumb but ... what does margin mean?

[normal crystal]

but what is the point of this
is the print quality/binding better?

[trail hemlock]

its significantly cheaper

[remote sparrow]

cheaper for similar quality to springer POD

[remote sparrow]

i originally thought, aside from covers, that the body text wouldn't print inside of those margins but i guess they'll adjust the file to full bleed

mind those inner margins tho

you don't want to open a book and have the body text too close to the spine

[trail hemlock]

oh rip

[remote sparrow]

nah it's fine

[trail hemlock]

final question, does this look alright?

[remote sparrow]

i would only put the author's last name on the spine

i also like to put the advertising blurb on the back of the book

[thorn cloak]

i wish there was a way to make the covers look like the old mcgraw hill ones. They use like a weird mateiral or something tho so i dont think its possible in lulu

[gray gazelle]

Oh, I already have some Ideas, ty bro dw

[remote sparrow]

maybe leather or vinyl?

[vocal egret]

is thomas' calculus sufficient for div, grad and curl?

[molten gulch]

yes, once up to the multivariable section

[remote sparrow]

oh btw

if you aren't done yet

[vocal egret]

thx for the info ;3

[remote sparrow]

make sure you extend the pictures on the covers all the way to the corners and edges

i'd also advise getting multiple book projects done...if you're buying them one at a time, shipping adds up

if you buy in bulk, you can save on shipping

[trail hemlock]

hmm, ok

this is what the final product ended up looking like (i accidentally selected the wrong book size and had to restart)

[remote sparrow]

what's the spine and back cover look like

[remote sparrow]

notice how the colors extend all the way out

otherwise you'll see white margins on your cover

[trail hemlock]

oohhh

[heady ember]

@trail hemlock Are you printing a book out on lulu, like Sour Drop has?

[tall herald]

logic is so fire, cannot reccomend enough for prospering math students

i honestly believe logic (real logic, sentential proofs, none of that set theory or probability stuff) should be taught before students learn any math

it’s valuable af cuz all math is is a set of rules or axioms that you apply in different ways, and logic with its rules is the exact same but more raw

[hollow shore]

I think a Discrete Math course does a cursory glance over Logic

which is concurrently taken with Real Analysis and Linear Algebra

[tall herald]

the discrete math course i took didn’t get past set theory, truth tables, probability and game theory

which is good but not at all what im talking abt here

omg wait were u referencing a book

u capatalized it

i look silly

[hollow shore]

oh you mean like a sufficiently thorough course on Logic?

[tall herald]

Yeah, but honestly you can learn it yourself really quick

A full college class is fine but for whatever reason math degrees avoid including philosophy

[hollow shore]

now that you say that, I remember I was going through this https://people.umass.edu/phil110h/text.htm

[heady ember]

Implying that set theory isnt part of 'real logic'

[tall herald]

I’d reccomend

1. Just learn the major operators

2. Learn how the game works, premises and conclusions and QED n all that

3. Learn the basic 8 rules of inference, do 20 practice problems on them (GTP will generate it for you)

4. Learn the 6(?) replacement rules, do 20 problems

5. Learn conditional proofs and indirect proofs

And that’s honestly all you really need

To understand logic

And you get all the forementioned benefits

[hollow shore]

Hm okay

[tall herald]

You know what i mean

Set theory is valuable for like

Stats

But I think we can agree predicate logic is the broader one

[hollow shore]

You mean Naive Set Theory or Axiomatic Set Theory?

[tall herald]

They call it naive set theory???

The jokes write themselves

Naw but generally people are contentious about set theory since you kind of have to employ numbers to teach it

[heady ember]

Basic/naive set theory is fundamental for all proof-based math.

[tall herald]

You mean the vienn diagrams and whatnot?

[heady ember]

Set theory is more than just Venn diagrams.

[hollow shore]

wait lemme pull up a screenshot

[tall herald]

Oh, I was wrong about what naive set theory was

Apologies

My school did not teach set theory well it seems

[hollow shore]

welp I can't send images here

[tall herald]

Thought you were talking about the benign “find what the sample space is!!!” stuff

[hollow shore]

#math-discussion message

[gray gazelle]

Guys can anyone recommend a good book on logic (propositional, first order predicate, …)

[heady ember]

Basic logical reasoning is part of a discrete math/naive set theory/intro to proofs course

[heady ember]

#book-recommendations message

[hollow shore]

yo grass can you talk about the subtleties between naive and axiomatic set theory in #math-discussion ?

[tall herald]

For predicate alone: Intro to Logic, matheson

[heady ember]

That's just about whether axioms are formally introduced to you or whether you're implicitly using those principles (without seeing them formally).

[tall herald]

It’s free I will send you a pdf

[hollow shore]

I think my understanding is mostly blackboxed. Like I do kinda get it but maybe there is a conceptual leap.

[trail hemlock]

yeah

[tall herald]

always found this to be interesting, ironically a lot on the lsat

[heady ember]

Cool

[tall herald]

there’s an entire branch of lsat logic that talks about the application of axioms (and just general lsat specific logic) on the test

it has its own operators, inference/replacement rules, etc

[modest owl]

sock pfp

very kewl

[zinc zodiac]

any book for real analysis?

[trail hemlock]

#book-recommendations message

rudin is good, though very terse

abbott and tao are more gentle, and also very good

[vocal egret]

do you recommend Kreyzig Advanced Engineering Mathematics if someone already did Thomas' calculus?

I feel like sth like vector calculus knowledge would be beneficial, but eh idk

kd sksmdkdmsk

[vital bane]

interesting, but i'm not sure if catering to all audiences is a good thing

[vital bane]

Understanding Analysis by Stephen Abbott

best intro book ever

[zinc zodiac]

is it allowed in the server to ask for pdfs of the books? 💀

[daring lake]

Kreyzig does PDEs and stuff too. But the audience is generally engineering students who don't care about the technicalities.

[daring lake]

no

[zinc zodiac]

alr

[molten gulch]

absolutely not

[trail hemlock]

yeah the sever can get banned for that

:(

[vital bane]

No but you can find it online easily

[pulsar lantern]

This book has good topics, is written for someone with only your background, and is generally well liked, but it may be hard going without having done a bit more math or some applications of it elsewhere. But it only gives an introduction to each of the topics and is not a substitute for more complete treatments of linear algebra and vector calculus, which may be better to seek out instead.

[vocal egret]

Thx for the tips :3

Do you recommend "div grads and curls", along with differential equation book? They seem neat for what I plan to do in uni

[pulsar lantern]

I am only familiar with that book by name and that physics students like it. My preferred vector calculus book is probably Hubbard & Hubbard "Vector Calculus, Linear Algebra and Differential Forms," but that is a bigger more involved book. For introduction to ODE for engineering applications, I think MIT OCW's 18.03 is good

[vocal egret]

Thanks! I'll try to check the books you mentioned, they seem more co plete than the ones I have thought off

Thx for the recos and infos :3

[vital bane]

I recommend this http://www.damtp.cam.ac.uk/user/tong/vc.html

[vocal egret]

Gonna try it out rn, thx!

[hearty steppe]

Did anyone read this yet around here? https://arxiv.org/abs/2301.07494

[rose heron]

I was wondering what are some effective websites or textbooks for Ordinary Differential Equations? I'm currently taking the second class in the sequence for Linear Algebra and like using Georgia Tech's Linear Algebra website as a reference. My University uses the Virginia Noonburg ODE textbook: Differential Equations: From Calculus to Dynamical Systems. This is my second time retaking ODE's and I don't like this textbook that much because the examples within and the writing style I can't really grasp. Thanks again.

[grim ore]

Would anyone be able to recommend any prereqs building up to Huybretchs Complex Geometry

I got my answer, but in case anyone wants to know I was recommneded Griffths-Harris which builds up to Huybretchs

[molten gulch]

I've heard that the first few chapters of griffiths and harris are a good idea

[molten gulch]

oop I didn't see this sorry >.<

[grim ore]

nws but thank you!

[remote sparrow]

can you tell us what's supposed to be covered in this second course?

[rose heron]

Here is the Course Schedule and Course Description:

Schedule: Subject to change based on the overall comprehension of students and possibly other factors.
Week 1 – 2 (with Quiz 1): 1.1-1.3, 2.1; Basic concepts, terminology, and classification of ODEs, modeling
with ODEs, separable ODEs.
Week 2 – 4 (with Exam 1 and Quiz 2): 2.2-2.5.3, integrating factor method, existence and uniqueness theo-
rem, first-order ODEs.
Week 4 – 5 (with Exam 2): 2.7, 3.1-3.2; phase-line and bifurcation, second-order ODEs (homogeneous), har-
monic oscillator.
Week 5 – 7 (with Quiz 3): 3.3, 3.4.1, 3.4, 3.7.2; second-order ODEs (non-homogeneous), forced spring-mass
systems, phase-portrait.
Week 7 – 9 (with Exam 3): 4.1, 4.2, 4.3, 4.4; system of first-order ODEs, review of eigenvalues and eigenvec-
tors.
Week 10: 5.1-5.2 if time permits; qualitative study of systems of first-order ODEs; review for the Final Exam.
Optional materials if time permits: 2.5.1&2, 2.6.1., 3.4.2, 3.6.

Course Description: This course is an introduction to ordinary differential equations (ODEs). We cover
a series of elementary and important techniques in solving several types of ODEs, including first-order and
second-order equations, first order systems (primarily linear), as well as their qualitative properties, appli-
cation and modeling in other area of mathematics, physics, engineering, and biology. Students learn how to
use their calculus knowledge in a comprehensive way, as well as in connection with essential skills from linear
algebra, in solving ODEs.

Don't worry about the Linear Algebra stuff. The first class in the Linear Algebra sequence is a pre-req for the ODE class but the second class is not.

[trail hemlock]

anyone who used lulu, this book is sized 6.14 in x 9.21 in, is this fine?

[remote sparrow]

boyce and diprima and paul's online math notes are good for weeks 1-9. strogatz is best for week 10 stuff but boyce does it too

[remote sparrow]

show some pages inside the covers

i don't believe that warning message should be too big a deal though

[dim pendant]

Has anyone here studied Number Theory from Andre Weil's "Basic Number Theory"?

[trail hemlock]

alr placed the order kekw

[heady ember]

Hi whitehair

[trail hemlock]

i did premium black and white cuz i got scared the latex wouldnt render properly 💀

hi bush

[remote sparrow]

not necessary

at least in my experience

[trail hemlock]

it was like 5 bucks extra but

rip 😭

[remote sparrow]

🤷‍♂️

well what can you do

i mean you can email them to cancel ur order if you really want

[trail hemlock]

yeah i think it will be fine

[remote sparrow]

what book is that

[trail hemlock]

lee's introduction to toplogicla manifodls

[heady ember]

Manifold typos, I see.

You should read Wee's Introduction to Typo Manifolds

They're quite a weese (wise) author.

Puns go brrrt

[carmine river]

Looking for a good book on discrete mathematics (preferably online but I can go to a bookstore to look for one)

[rose heron]

Thank You!

[dim pendant]

Search recommendations on reddit. Most courses don't really go far into anything, so it's very easy to write a passable book on the subject. Anything you can find by name and author would suffice.

Also, since you're looking for any book, I'm guessing you may not actually be doing this for a class. If not, go ahead and skip it. As long as you can write proofs, a study of discrete math is just a delay to your math career, unless you fall in love with something like graph theory

[carmine river]

Oh...

Ok yea I'm just studying this on my own free time haha

What do you recommend I study then

[heady ember]

Try Halmos' Naive Set Theory for intro discrete math --- i.e. first year stuff. But most books are free digitally if you know where to look anyways.

[carmine river]

Ok

[heady ember]

Halmos is well-liked for its beginner-friendliness.

[carmine river]

Also I'm kinda looking for stuff that I won't learn in uni, so I'm not just repeating it when I go to uni

[heady ember]

Just skip the classes instead

[heady ember]

But you can also just jump straight into (proof-based) linear algebra or intro analysis.

[carmine river]

Ooo ok

[heady ember]

Yes I mean when you get to uni.

[carmine river]

Lol yea I got it a bit late

[heady ember]

But not every uni allows for that (skipping intro classes for more advanced ones).

[carmine river]

Ohhh

Oh wow I can do that??

[orchid lynx]

Is there any book that touches the entire undergrad math curriculum on a high level?

For context, I did my undergrad in CS, so I do have some math background

[vocal egret]

do y'all recommend I buy a college algebra book to revision my algebra courses for CS in uni?

[orchid lynx]

if your algebra was solid in high school, you shouldn't need any extra prep for college algebra courses for CS; it should mostly be a breeze.

[vocal egret]

Thx for the reply :3. I'll try to find a suitable precalculus book instead then

[spiral spear]

What's the best book for math

Or calculus

[gentle arrow]

there is no "best book for math"

no one book covers everything

if such a book existed it'd be tens, if not hundreds of thousands of pages long

if you want a book for calculus uhhhh

stewart if you're an engineer/scientist, spivak if you're a mathematician

[heady ember]

Instead of reading Spivak, some would argue for heading directly into Abbott or the like, if one is already going to gun for Spivak.

[tender cobalt]

what's a good differential equations book with nice balance of rigor/theory + applications

[tender cobalt]

Thomas' calculus is a little bit more rigorous than stewart

Its a nice midway between stewart and spivak

[vital bane]

one could argue a set theory book covers everything, set theory is the basis for all of math, the rest of the fields of math is left as an exercise for the reader @heady ember

[signal zenith]

Maybe Evan Chen’s “the napkin” is what you’re looking for

[cursive orbit]

all the math you missed but need to know or some title like that

[signal zenith]

The title to that one is “All the math you missed but need to know for graduate school” I think

[orchid lynx]

Oh yeah, I've heard of that one; have you read it?

[orchid lynx]

But isn't that for math majors transitioning to postgraduate math studies?

Like won't it be a little too complex for non-math majors?

[signal zenith]

Not sure, I haven’t read it

Check out The Napkin by Evan Chen it’s reasonably accessible

[burnt spoke]

hey peeps ... well im a high school student but am very much interested in learning calculus in more depth ...so please give me any recommendations .........

[shadow river]

in more depth would usually mean starting to prove results you learn in calculus, especially learning how to prove things involving limits. Normally this would be part of "introduction to analysis", there are lots of books out there on the subject and a ton of content on Youtube on starting doing proof based calculus/analysis

[torn blade]

im trying to self study real analysis but i got bodied by baby rudin (lol), any alternatives? it doesnt need to be for total beginners (starting with sequences would be ok for me tbh) just not rudin level

[dapper root]

I used, and really liked undergrad Folland, but this is also a really eclectic choice I think

I think more standard responses are like, Tao

[torn blade]

i see the pinned message btw but im having some decision paralysis on which one

[torn blade]

thx

[dapper root]

there's one other one but I forget which one, I think that one has more readig groups using it among ppl in this server

[torn blade]

when people say "abbott" for RA do they mean understanding analysis

[dim sierra]

Yes

I love that book highly recommend it

[vital bane]

Understanding Analysis by Stephen Abbott is the perfect book for you (and for everyone)

[vital bane]

indeed

absolutely beautiful exposition

[torn blade]

it looks really good

[dim pendant]

If you're going to university to study pure math, identify what you're most interested in right now, choose something you're less interested in, and study that. I think that a lot of people new to math are very interested in topics in algebra, analysis, topology, and geometry, etc. If this is you, you could look into axiomatic set theory, combinatorics, you could start learning number theory, so that if you know calculus, you could study analytic number theory. If you know calculus right now, ODEs and PDEs will open areas of analysis.

I personally recommend not learning stuff you don't plan on learning. Just pick something you like, learn more about it, find something that looks really super duper interesting, and chase that.

[dim pendant]

Some of them allow you to test out of courses, e.g. you could take the final exam for calculus 2 to skip it. I actually simply pleaded a case to skip calculus 1. It all depends on their specific structure. You might only be able to skip the first 3 or 4 math courses. You might be able to skip out of most of your degree. It depends.

[dim sierra]

It’s amazing. Very gentle, and he begins each chapter with motivating examples and ends each chapter with an epilogue, discussing how you might explore those ideas further. .And he writes so clearly too

[vital bane]

and the exercises are so good, like I love how he introduces some new concepts via exercises

Abbott is easy to read, but it doesn't hold your hand, it expects you to get better as you progress through the book, leaving more and more proofs to you!

[thin swan]

Ok I got this book "Plane Euclidean Geometry Theory and Problems". Its aimed at people with math school knowledge up to age 16.
But formulated in a way for math olympiad problem solving. Im wondering how long would it take to complete the book.
Ive got knowledge up to trigonometry and circle thereoms. But my problem solving isnt that great, not enough to solve olympiad problems (theres 157 problem pages)

[mellow wren]

It takes you however long it takes you

You should never rush yourself when learning math

Take your time to master everything

[thin swan]

I want to give myself a realistic deadline

Like a goal to motivate

[mellow wren]

Maybe rather set a goal of a number of exercises to do per day then

So you can have time to think about each problem

[thin swan]

Thanks

[foggy quest]

https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/ is good

[sharp goblet]

is there any classification of mathematical intuitions?
(like symmetry, distance , continuity)
and is there any text about examples of this in different scenarios, but focusing in the intuition rather than the formal implementation of it?

[vital bane]

That's a pretty subjective thing

I don't think you can classify that

[storm sage]

Hey can anyone recommend a good problem book for topology?

I'm mostly interested in proofs

I don't really want the classic american treatment of giving a thousand calculatory questions to make sure the reader understood the subject and then disappoint with one easy proof oriented question

[sharp goblet]

yeah, maybe it is too general, now I think I could get a better answer asking about a more particular topic.
but why subjective?

[vital bane]

The two default books in this server are "Introduction to Topological Manifolds" by Lee

and...

[vital bane]

it's subjective because what exactly people mean by "intuition" can differ from person to person

we can't exactly peer into someone's mind when they're thinking about some mathematical concept

[sharp goblet]

yes, I should have to explain it and so on, I should ask in a particular topic, so the explanation can be more accurate

thanks, I will do (but no here lol)

[sharp goblet]

my own idea of intuition

[storm sage]

idk, munkres doesnt really seem to have that amazing proof problems in it, but ill give it another shot

I mean I really want hard proofs that build problem solving

[vital bane]

If you're looking for just problems, then click on the "Big list of problems" link on this website https://www.math.toronto.edu/ivan/mat327/?resources

[storm sage]

This is exactly what I was looking for, thank you very much 😄

[drowsy night]

Anyone got suggestions for a book on combi? I’m gonna try EGMO for geo, mont for NT

I rlly struggle with combi btw

[pulsar lantern]

You need be more specific about the kind of combinatorics unless you mean for math competition problems

[floral lantern]

If you want an open source book, Lebl's Basic Analysis book is pretty good (it was written for the UIUC analysis class and has been used in MIT's class as well) https://www.jirka.org/ra/

[formal parcel]

Anyone have any good math history books? I know nothing of the key great mathematicians who created all the stuff we know today and I’d love to learn more about how math was developed.

[heady ember]

Neam spittin facts out here, for a change

[torn blade]

best introductory representation theory books?

[drowsy night]

yeah for competitions

i find it really hard to translate the word problem into an actual equation with choose or factorial

[dim sierra]

A good intro is Stillwell’s book

[sudden kindle]

Havnt read this yet but I'm exited about
An Invitation to Representation Theory" by R. Michael Howe

@torn blade

Its a new book

Undergrad text

[torn blade]

cant pirate it then :(

[molten gulch]

if your uni has springer access, you might be able to get access for free

[torn blade]

oh mine does great

[foggy relic]

my intro real analysis class used this

it's a bad book

don't use it

[torn blade]

does this look like a good book to you btw?

.

[sudden kindle]

Error opening file

[torn blade]

whoops forgot u might not have access

[bold falcon]

another vote for Abbot - Understanding Analysis

Also there's some decent youtube vids that go along with it.

[magic moth]

https://youtube.com/playlist?list=PLBh2i93oe2qujVx3lY57ViMrbXqE8y0OG&si=IK-VQnMFSq1Ogez9

[tropic nacelle]

dark version?

[magic moth]

Yeah

Its just a change in the color palette

Night mode if u will

[carmine river]

ooo

[carmine river]

oooooooo ok

so pick stuff im weak at and learn that first

ngl the reason i studied discrete maths was cuz i thought it would be in my maths course

yk... since it had "math" in its name

[dim pendant]

discrete math could more productively be called "useful math for scientists", some have even opted to call it "math for computer scientists"

It's really just a bunch of topics which are simple enough at the beginner level to teach anyone with motivation

[carmine river]

yeaaaa that's also why i liked it

i feel like i could've started learning it and 5 and it wouldn't be a problem

like i didn't need a ton of background knowledge

[dim pendant]

but yeah, I mean in reality you should study what you want to study

just know that if you're into the "hot topic math" (analysis, algebra, topology, etc.) then discrete math won't help much

[carmine river]

i see isee

[dim pendant]

it's just going to get you familiar with proofs and thinking mathematically

[carmine river]

btw is geometry important in uni

[dim pendant]

but you can do that in a basic number theory or analysis or lin alg class

[carmine river]

yeee i like that

[carmine river]

i see

[carmine river]

i detest geometry

[dim pendant]

sorta?

[carmine river]

absolutely hate it

what kind of geometry do you learn in uni

[dim pendant]

which part about geometry did you actually dislike

[carmine river]

if a diagram is complicated i cant see crap

i studied a bit of olympic mathematics, and i had a really hard time seeing anything at all

im actually ok with geometry in regular mathematics

[dim pendant]

Idk why some people disagree with this perspective, but I like to think that doing advanced math feels like doing geometry

you don't stare at pictures with angles and lines, really, no

but you have basic facts you need to just know, and you have to piece things together to uncover new results

proofs simply work this way

but there aren't usually pictures to look at, unless you want to draw

[carmine river]

hmm

[dim pendant]

so you won't "do more geometry" in uni

but it will be difficult in a similar way

a lot of complex components that you need to work through

[carmine river]

im ok with that

[dim pendant]

it's just that you're not talking about shapes as often

[carmine river]

ye im practically shape-blind

[dim pendant]

anyway, being able to think geometrically helps in calculus

but you can pass calculus and be successful in math without being a pro at geometry

although a good mathematician should be able to relearn geometry and do reasonably well lol

[carmine river]

does uni have geometry as in shapes

[dim pendant]

yes but it's optional

[carmine river]

oh

[dim pendant]

you can take courses in discrete geometry, polytopes, etc.

but you don't have to

[carmine river]

could you point me in the general direction of a book/online course

[dim pendant]

you can even study Euclidean geometry lelz

[carmine river]

i just wanna know what it looks like

[carmine river]

oooooo that sounds interesting

[dim pendant]

(Euclidean geometry is basically high school geometry, but at uni you study it in a more enlightening way)

[dim pendant]

what what looks like

[carmine river]

what uni geometry looks like

[carmine river]

yes

good

high school geometry has been very discouraging

[dim pendant]

there are different types of geometry because in advanced mathematics, geometry can mean different things

do you know calculus

[carmine river]

of course

[dim pendant]

https://en.wikipedia.org/wiki/Projective_geometry
https://en.wikipedia.org/wiki/Elliptic_curve
https://www.amazon.com/Elliptic-Tales-Curves-Counting-Number/dp/0691151199

[carmine river]

mmm ok

ellipses

im ok with that

[dim pendant]

nah it's a totally different deal

[carmine river]

oh

[dim pendant]

elliptic curves are basically a sort of polynomial curve which exists in space where you can do stuff "at infinity"

so certain ideas you have about geometry fail there

but it's totally different from what geometry was like in high school

I recommend that book in the third link

[carmine river]

ooo okok

[dim pendant]

you can use the first two links to get an idea of what you'd be dealing with

it starts with basic calculus and algebra and takes you all the way up to algebraic geometry

you learn some group theory, some field theory, some algebraic number theory

[carmine river]

mmm ok

btw i estimate i have 10 months until my uni intake starts

[dim pendant]

you could totally study that book in its entirety in just a few weeks

I read half of it in a couple hours

the exercises weren't too difficult either

[carmine river]

oh wow

lmaooo ok den

so what else should i do for the remaining 10 months

[dim pendant]

as for what actual coordinate-like geometry is like in uni, I have no idea. I didn't study any of it

[dim pendant]

explore math, look into stuff and see what sounds cool

[carmine river]

okie

[dim pendant]

also this is a great youtube channel for scouting new stuff to learn

https://www.youtube.com/@Aleph0

i recommend you watch literally every video on the channel

[carmine river]

lmaooo

ok

[tender cobalt]

the goated channel

[dim pendant]

fr

[tender cobalt]

after watching the channel, I am much more interested in pure maths than applications 😅

[dim pendant]

lmfaoo

applied math for more immediate job opportunities, pure math to love your job 🔥

[ashen matrix]

Can u recommend a book for class 6