book-recommendations

[signal mountain]

you dont have to do every problem in a book

[rose hazel]

I dont necessarily have to, yes. but i felt like the entire book was made around being read throughout a course of mathematical proofs ad logic. (hard to explain this)

i think you could say i am not a big fan of the writing style, if that makes sense.

[signal mountain]

fair enough

[plain belfry]

is there a slightly easier counterpart to arnolds ode book? i want a good geometric treatment of ode's and i have looked at his book but atleast the first chapter feels a bit too mature for me, im not sure if its just the old-ish notation or whatever.

[bronze star]

Hi, does anyone has a good book/course recommendation for matrix differential calculus ? Basically, I am working on getting derivatives of Jacobians and Hessian matrices with respect to some other variable. I think I am kind of stuck with usual scalar / vector techniques that do not work well in higher dimensions

[rigid flint]

Anyone have any good books on calc 3? I’m especially interested in learning jacobian matrices.

[covert mauve]

Hello everyone, posting on behalf of someone else (no discord account), but they are looking for a short introduction to single-variable calculus, any suggestions? I tried to recommend them Spivak, but they are not big fans of the size of the book.

[tribal crow]

Spivak is on the smaller side of calculus books though

most calculus books I've seen are 1000+ pages, and Spivak is less than 700

[covert mauve]

I cant exactly decide the other person's preference, unfortunately. 700 pages is still apparently too long for them.

I dont know of any older calculus books i could recommend, but i hear they are usually shorter.

[rain hound]

Calculus Made Easy by Silvanus Thompson. Freely available (legally!) on project gutenberg

[digital galleon]

does herstein refer to topics in algebra or abstract algebra? i am looking for a good resource on GT

[full cairn]

Vector Calculus, Linear Algebra and Differential Forms seem to have a pretty good introduction to the Jacobian, but I'm not sure it covers all of calc 3. Otherwise there's Vector Calculus by Colley, seems to be decent too

[sage python]

Topics in Algebra

[digital galleon]

thank you

[hoary wagon]

Textbooks (labeled appropriately):
Algebra 1: https://bim.easyaccessmaterials.com/index.php?level=11.00
Geometry: https://bim.easyaccessmaterials.com/index.php?level=12.00
Algebra 2: https://bim.easyaccessmaterials.com/index.php?level=13.00

Free to use and access, anything you can learn in a class is in these textbooks. Really great resource.

[foggy quest]

Notes for undergraduates and graduate+: https://mtaylor.web.unc.edu/notes/

[foggy quest]

https://mtaylor.web.unc.edu/notes/math-524-second-semester-ode/

[normal crystal]

do you know if the version on his web page is the exact same as the 2nd edition published?

[plain belfry]

Thanks!

[cursive orbit]

I have never seen someone so dedicated to one author in my life

[hollow shore]

So you want more practice problems?

there are problems books out there with partial to full solutions

just google say "abstract algebra problem books" and see which one you like

you can replace abstract algebra with the subject that you are currently struggling with

if you feel like some terms and definitions are not familiar, you can refer to the lecture notes or books

[wet sentinel]

what are some good books about point set topology

[remote sparrow]

munkres, willard, gamelin and greene

[wet sentinel]

are they all the same content ?

[remote sparrow]

similar enough that they can be used interchangeably for a course

[wet sentinel]

oh ok tysm

[proper depot]

Any good books for pre under grad but after secondary? That mainly involves problem solving, would be good if it had linear algebra, complex numbers, calculus,DE's, matrices

[buoyant halo]

Does anyone have any recommendations of some super "grindy"/computational PDEs textbook?

[proven lantern]

Anyone seen 5th edition of Royden? Seems like with the update it is harder than folland?

[gray jungle]

what was changed in the 5th edition? royden is one of the friendliest books for what it does

[remote sparrow]

i would hope most of the errors would be fixed by now...

the fourth edition was error-ridden judging by the errata sheet

[gray gazelle]

could anyone recommend me aa textbooks?

[molten gulch]

AA? Abstract algebra?

[mossy flume]

At what level, do you know any abstract algebra?

[gray gazelle]

mhm

jacobson?

[covert mauve]

Good evening everyone, so my friend did not end up liking "Calculus Made Easy", but is looking for a single-variable calculus book with a similar length, any recommendations?

[gray gazelle]

undergrad

[mossy flume]

I like Artin as a first algebra text

[molten gulch]

seconding artin

[gray gazelle]

artin must be a good book

[mossy flume]

It is

Better than Dummit and Foote

I’ve also heard good things about Aluffi but never looked at it too close

[molten gulch]

aluffi is cool from what our late undergrad friends at uni have said

[rain hound]

Aluffi is the best second abstract algebra book

The best first book is Judson (also freely available!)

[mossy flume]

Never looked at Judson

[wet sentinel]

what about the one by james dugundji

[fresh skiff]

I will go through ch1 of Aluffi (for cat theory)

[molten gulch]

chapter 1 of chapter 0

[livid lintel]

Are there any other books on reverse mathematics that have the same style as 'Reverse Mathematics: Proofs from the Inside Out'?

[gray gazelle]

thank yall for the recommendations :3

[analog lava]

looking for a textbook in group theory that is at the level of like

general qualifying exams

a graduate level group theory textbook

do i just redo dummit and foote?

[gray gazelle]

if you want plenty of problems to practice for quals, these notes may be of interest: https://www.cis.upenn.edu/~jean/algebra.pdf

[foggy quest]

You can compare. I noticed the indexes are slightly different, but the table of contents look the same.

[remote sparrow]

probably good too

[analog lava]

ty! this will surely help

[brazen viper]

Can someone recommend a good introductory book on discrete maths ?

[pliant saddle]

and on topology to me?

[full cairn]

Discrete Mathematics and its Applications by Rosen is good

[brazen viper]

is it free ?

[molten gulch]

no

[brazen viper]

alright

Thanks

[full cairn]

The standard book is Munkres, but personally I prefer Intro to Topological Manifolds by Lee

[pliant saddle]

how can I access it? is it online?

[molten gulch]

if your uni has a springer subscription, you may be able to get lee's book for free or reduced price

[brazen viper]

Yeah LMFAO thanks 😭

[pliant saddle]

im... not.. on uni yet 👉 👈

[full cairn]

Topology without Tears is free, I didn't like that book so much tho, but some people like it

[pliant saddle]

errr I did check that one but I don't think it's working on me

not that it's bad but more of... it's expecting some prior knowlegde

[full cairn]

You need to be familiar with set theory and proofs yeah, but that goes for any topology book. What did you find difficult?

[calm kernel]

Who have nice source to study Physics,Math before going to Uni

I want you to show me them.Bc my future profession require them a lot and I wanna study it before going to Uni.It will be bad if I just watch videos with person explaining, and falling asleep bc of their voice.Soooo...uhmmmm and math with all "directions"

[pliant saddle]

My set theory knowledge is not very developed yet

I'll look to it first then

sigh trying to learn alone is so hard

[full cairn]

There's also this youtube series: https://www.youtube.com/playlist?list=PLd8NbPjkXPliJunBhtDNMuFsnZPeHpm-0

it conveys the intuition much better than topology without tears

just make sure you do lots of exercises, don't just watch videos

[torn bane]

guys, i need some resources in optimization thery and/or in operational reseach. someone can help?

[normal crystal]

if you want truly free, you can look at the options listed here
https://textbooks.aimath.org/textbooks/approved-textbooks/

[brazen viper]

Thank you so much

[trail hemlock]

?

[fresh skiff]

Yeah

Aluffi's book is for second course in abstract algebra

But I am just going though ch1, that is set theory and category theory

[molten mason]

There's also his Notes From the Underground which is first course

[dapper root]

I used Aluffi as first course

[molten gulch]

holy cracked

[molten mason]

I never knew this emoji existed wtf

[fresh skiff]

cool

[fresh skiff]

fr?

can you please elaborate how ws your experience?

And I have only background of Real anal, and learing LA currently. Is it sufficient?

[dapper root]

I did it as part of a study group. It worked for me

[fresh skiff]

oh I see, I am currently using aluffi for category theory

maybe I use it as refernce when I start algebra

[heady ember]

How many topics are you studying simultaneously

[fresh skiff]

Like 3
Real analysis, Ch1 of Aluffi, Introduction to Topological manifold.
But I spend like 2 days on LA too and I will study Cat theory like 2 − 3 days. But studying Manifold and real analysis continuously

[heady ember]

Rudin
Aluffi
Lee
LA
Meow theory
Seems like 5

[analog plinth]

Can someone suggest some good book for real analysis im struggling a lot in it.

[livid lintel]

Did you try baby rudin?

[daring wave]

If they're struggling with analysis, I doubt baby Rudin would help

The standard intro book is Abbott's.

[livid lintel]

Oh

[rugged lance]

Taos two books Good entry

Focus on the foundations

[fresh skiff]

Wait. I am studying cat theory from Aluffi
And I am not doing LA frequently.

• Rudin

• Cat theory (Aluffi) and LA (both not frequently)

• Lee

I will be slow soon
I have mid exams from 9th September (1 week)

[royal bone]

i am searching for a math book from a USA 🇺🇸 public school, say 8th or 9th grade . is anything like it available online ?

[analog plinth]

nope

[analog plinth]

alright

also if someone sees this pls help me in #help-9

[molten mason]

!noadvert

[hybrid sparrow]

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.

[dull raptor]

Tao

Pugh

Some people like Cummings?

idk

Rudin is a shit book

Idk why anyone recommends it

[remote vortex]

Rudin is an excellent book but a very questionable learning resource.

Abbott is a good friendly introduction

[dull raptor]

Ok for reference

But horrible for learning

Pugh is 100x better in that regard

[remote vortex]

True, but if you're wondering why people recommend it: it's because it is an excellent book if you're already familiar with the material, so a lot of people focus on the greatness, forgetting how inaccessible it is for the uninitiated.

[brave burrow]

Tao and Abbott, which is better for real anal if you are a beginner? 🧐

[remote vortex]

I haven't read Tao but Abbott is very solid

[analog plinth]

💀 sry wasnt aware

wasnt receiving any help since 9 hrs so thought maybe..

[tender cobalt]

is Mathematical Methods for Physics and Engineering a good book

for covering many general applied mathematics in one book?

(want to self study)

[signal zenith]

I learned RA from Rudin for the first time and it was very difficult but very rewarding

in particular I think he treats topology/metric spaces much better than most other RA books

I also much prefer the metric space approach vs the sequence approach a lot of other RA books use

I disagree that it's a shit book

[remote vortex]

As I said, it's an excellent book, but it can be very unapproachable for someone who hasn't had much experience reading advanced mathematical texts, because it's very concise.

Which means that the reader has to fill in a lot of blanks on their own, which not everyone is prepared to do.

[cursive orbit]

rudin is an excellent book for problems

[remote vortex]

Especially because real analysis is often the first rigorous course people take.

[signal zenith]

Rudin was my second ever proof based math course

first being discrete math

which barely counts

At least for me I thought it was very worthwhile

[remote vortex]

And as you say, it was very difficult.

[signal zenith]

sure, but that's not a bad thing

[remote vortex]

That really depends, some people bounce off the difficulty.

[signal zenith]

challenging yourself is a great way to learn

[cursive orbit]

yea u gotta make classes more difficult so less ppl enroll

[remote vortex]

Or even if they do, it takes them twice as much as it would from a gentler book

[signal zenith]

it's so joever lol

[signal zenith]

and they learn it twice as in depth

[tribal crow]

if I had learned real analysis from Rudin, I'm convinced I would've quit math

[remote vortex]

That's a very broad statement; there is some nuance and degrees to it

More or less same; in my first year I really didn't enjoy Rudin and used a different book for my real analysis reading.

And I'd say I have done reasonably fine as a mathematician, although admittedly I was a mediocre one.

So maybe if I was forced to read Rudin and just give up in the first year, it would have been a net positive.

[cursive orbit]

I feel like rudin + lectures is way better than Rudin self study

[mossy flume]

when u took that course

were you reading out of Rudin and doing all your learning from Rudin?

or did you have lectures and office hours from a professor

[signal zenith]

Reading and lectures. I didn't attend office hours

[mossy flume]

because that's a very different story

[signal zenith]

maybe I wouldn't recommend it for self study but it's a great book

even for learning

Actually I still think I would recommend it for self study

I ended up self studying most of my studying in that class

[mossy flume]

yea which is exactly the point that was made here: great book but inaccessible for the uninitiated

[signal zenith]

because I got significantly behind the lectures and caught up primarily by reading

[remote vortex]

In conclusion, Rudin is a land of contrasts.

Definitely not a book to recommend without reservations, but I've heard of some Rudin success stories

[signal zenith]

In particular, I like Rudin's treatment of connectedness and compactness, most other RA books shove it to the last chapter or an appendix and do everything via sequences

connectedness and compactness is extremely valuable in almost every other field of math

[remote vortex]

There's a fine argument in favour of doing metric topology as a separate course.

[signal zenith]

I mean it is weird to me to do RA without metric topology

that's my point

it's not only useful for other courses

but

it makes the theory of RA way cleaner

anyway insert "the rudin glazing is crazy 💀" here

I am #1 rudin glazer tho

[rotund torrent]

someone knows a book with a lot of integral to resolve in it ?

[cursive orbit]

metric topology as a whole semester course would be crazy

[remote vortex]

That's how it's done at my uni

[signal zenith]

brehh

[remote vortex]

Not everyone is as quick on mathematical uptake as the people in this discord

[molten gulch]

Nahin - Inside Interesting Integrals

Make sure you're good at calculus tho

[signal zenith]

ok but there just straight up isn't that much content to cover lol

i mean it makes sense if it's like combined with general point set

[cursive orbit]

the main problem would be if that course is a prerequisite to, say, general topology and further topology classes

[rotund torrent]

thanks exactly what i was looking for!

[remote vortex]

Metrics; open sets, closed sets, convergence, limit points/adherent points/interior points, closure/interior/boundary, continuity, compactness, connectedness, completeness (including Banach Fixed Point theorem and Baire theorem), product spaces, there's enough for a full semester if you're teaching average students.

And our students are very average

For a talented and ambitious audience you can certainly get this done in half a semester or even less, yes

[fresh skiff]

its demotivating exercises
I really want to ask for hints for each problem lmao

[signal zenith]

ok fair enough. There's extra topics in there that I hadn't thought of like Banach Fixed point/baire category theorem

I do still think that RA should be taught with metric topology as opposed to sequences but that's just my opinion

and I'm a topologist not an analyst so obviously a biased one

[fresh skiff]

idk if it is sutable for first encounter

[tribal crow]

[remote vortex]

I mean, you should certainly introduce topological notions such as openness/closedness/compactness/completeness during RA, but it's fine to do it without invoking the general theory of metric spaces; just work explicitly with the Euclidean metric on R

[tribal crow]

Not everyone is as quick on mathematical uptake as the people in this discord

but I exist

[cursive orbit]

but I guess the argument is all of this is about 20 pages in Rudin, and a semester of real analysis without metric topology covers 100 or more pages worth of Rudin

[remote vortex]

My argument is that two pages of Rudin can be hard to cover in just 2 hours of lecture and 2 hours of exercises

[signal zenith]

ok see this is something I struggled with too, but IMO it was about a mindset shift where I eventually really didn't mind asking for help all the time. This is maybe a more #math-pedagogy discussion than a textbook discussion but I think that it is better to do challenging problems you need a lot of help with than do mainly problems you can solve on your own. Ofc a good mix is good but at least me personally it was very helpful to learn not to feel bad when asking for help on a problem

bc I very frequently do need to ask ppl for hints and stuff even today

[cursive orbit]

the exercises in Rudin are it's biggest feature

[signal zenith]

I don't think it hurts ur learning to do that but idk

[cursive orbit]

they are challenging and should probably be supplemented with more routine exercises, but they teach you a lot

[fresh skiff]

ah thank you for this feedback

idk why i am dumb enough to not find few easy problems in exercise set

[signal zenith]

np. I have read a bunch of stuff on the internet like "don't get help until you've spent 3 hours on your own" or whatever but at least for me personally that was not good advice.

[cursive orbit]

the vast majority of rudin exercises are quite hard

but that is good

[remote vortex]

That which doesn't kill you, leaves you stronger ||and that which does kill you, leaves you dead||

[signal zenith]

Like yeah probably don't get help the first time you look at a problem, but you can usually tell when you are stuck/have no ideas, and that isn't determined by how long I've looked at the problem but by what I'm thinking when I do look at it

[remote vortex]

(also citation very much needed on the first part)

[signal zenith]

so giving a general time rule of like "be stuck for [x] minutes" is bad advice

[fresh skiff]

^

[signal zenith]

I think better advice for hard problems is like

start your psets early in the week (so way before the deadline), and if you get stuck 1] take a break and work on some other psets 2] look for advice in office hours/in person if you can.

In person advice is nice bc you can leave the pset just ruminating in the back of your mind and sometimes you do randomly get unstuck in the shower or something and that's a nice feeling. But you're also not sitting at your desk for 4 hours banging your head into the table bc you're not supposed to ask for help

[fresh skiff]

so what could I do if I stuck? Like nowadays I stuck on one problem in CH5. I found a proof that need one justification to prove the entire statemtn but someone here told me this method would not work

I am jsut think, if I am stuck then I can read previous exercises or sections to build confidence

[signal zenith]

basically I think the best advice for getting unstuck if you truly have no ideas on what to do is to just do something else

[fresh skiff]

or do some other problems from the same exercise set

[signal zenith]

whether that's another math subject or some other subject

let the ideas sit in your mind for a bit, and also feel free to just ask for help - in person is better but online is fine too

especially if I haven't done many exercises from a section yet I am more comfortable going for help quicker

cause I find I tend to learn a lot by example and practice and its only once I've done a couple problems from the section that I really start getting ideas on how to solve tough ones

[fresh skiff]

I got it. so the thing is that instead of spending bunch of hours on single problem, do some other problems or maybe read other book then come back to the problem

[signal zenith]

yes

exactly

and also feel free to ask for help

dont do like glorifying suffering culture where you bang your head against a problem with no ideas for 3 hours

if you are done with your other work and still have no ideas, you shouldn't feel guilty abt just asking either online or in office hours

regardless of how much time you've spent

[fresh skiff]

got it. Thank you so much for these advices

I will try to follow them !!

[signal zenith]

np. gl!

[remote sparrow]

because rudin is a popular book, there are a few solutions manuals for it online

[fresh skiff]

yeah I have pdf (solution manual too). But i don't look the solution untill i prove

[hoary wagon]

I gotcha: Big Ideas Math is a resource a lot of schools use in the USA! Here is the link to their free textbook site. Here are some books:
Grade 8, Modeling Real Life: https://bim.easyaccessmaterials.com/index.php?level=9.00
Grade 8 Virginia: https://bim.easyaccessmaterials.com/index.php?level=9.00
Grade 8 (Recommended) Bridge 2 Success:https://bim.easyaccessmaterials.com/index.php?level=9.50
Oklahoma Pre Algebra: https://bim.easyaccessmaterials.com/index.php?level=9.00
Grade 9 (Highly recommended) Algebra 1, Common Core: https://bim.easyaccessmaterials.com/index.php?level=11.00

If any of these links are wrong, there is a dropdown in the top left and you can search through it.
Happy reading 🙂 !

[ancient copper]

Hey I am searching for comprehensive books for the AIME (trying to get better at all topics :3) you guys got any good recommendations?

[dull raptor]

Analysis pedagogy has grown tremendously since the 1950s

Pugh is 100x better covering the same topics

Rudin is only good for its exercises and referencing back for people who’ve already learned analysis

Hence shit book

[marble solar]

Rudin isn't a shit book, by any means. It's just not suited for novices to self-study from. Pugh isn't 100x better at the same topics, but Pugh does go more in-depth in certain ways

It's not clear that Pugh going more in depth is better. Sometimes a brief treatment to get to the good stuff as fast as possible is preferred

Pugh is better suited for self-study. Rudin is better suited for a classroom environment, as the professor can pick & choose what to go over

[dull raptor]

I’ve angered the Rudin hard ons

I still think it has no place in undergrad analysis

Once you get 2-3 semesters of analysis down you should be moving on to RCA or some Measure Theory

[sullen raptor]

Aight so yall are talking about how Rudin is a hard read. So you wouldn’t recommend for someone relatively new to analysis to self-study Rudin? I find it along with online lectures alright but if yall recommend anything else that might be more suitable then I’m down. I just like Rudin’s approach on compactness and metric spaces

[rugged lance]

i dont like the baby rudin book the real and complex is much better although more hardcore

[dull raptor]

I also am not a huge fan of Abott either

It suffers the opposite drawbacks of Rudin

[dull raptor]

Tao

[daring wave]

If you're okay with Rudin, why change? It's just that it's not a good book for introduction to real analysis cause it's probably the first course students are introduced to `higher' math

[jagged axle]

Te Jing

[rugged lance]

well tao is good but our prof states it would focus very much on the foundation thatswhy it is a great supplement

[sullen raptor]

does it cover lebesgue theory as well? I heard he also made a book specifically for measure theory

[rugged lance]

yeah the second volume ig

[jagged axle]

no

[sullen raptor]

true, I might change since it could be easier for me perhaps. I’m still kinda at the start so switching now would be more appropriate

[daring wave]

A good intro to measure theory is Axler's imo, it's really friendly

[sullen raptor]

but I still find it quite enjoyable

[dull raptor]

Axler good

[sullen raptor]

is it similar to linear algebra done right in terms of writing style and problems. yk, general vibe?

[dull raptor]

sort of

[sullen raptor]

I presume that’s the same axler

[daring wave]

The thing that is the same is the typesetting

[sullen raptor]

that’s very nice then

i liked the typesetting

[marble solar]

If you read the pre-face, Rudin agrees with you

[dull raptor]

sure, but the context of all these discussions is if it is a good book for undergrad RA

[sullen raptor]

I’m curious about that as well

[dull raptor]

which it is not

And once you get through undergraduate RA, you move on

[marble solar]

For advanced students, I think it is a great book to learn analysis from

[dull raptor]

Maybe for Math 55 type students

But that represents 1% of undergraduate math students

[marble solar]

So, there was a curriculum change in math. There used to be an "advanced calculus" class that was designed as a bridge to Analysis

This was prior to the 70s? Which is about when Rudin wrote his PMA

[dull raptor]

Rudin wrote in 50s iirc

[marble solar]

It fell out of flavor, so it was designed for people that had two semesters of this advanced calculus, but before they went into measure/integration theory

Some schools still have "Advanced Calculus" classes

[marble solar]

Not even Math 55 students, it's the standard text at Cal for math majors to learn analysis

[dull raptor]

Pretty sure that’s Pugh

Berkeley students use Pugh

Pugh wrote the book for the Berkley curriculum

[marble solar]

Seems it varies a lot on the instructor

https://math.berkeley.edu/~mjgoodman/teaching/104F22/Syllabus.pdf

For instance this syllabus doesn't even include Pugh, nor have Rudin as the main text

UCLA uses Rudin for the Honors sequence

But Terry Tao's book for the regular sequence

(Ironically Tao wrote it as his notes for the honors sequence)

[dull raptor]

I’ve heard ok things about Ross

Imo I think it’s because of tradition

[marble solar]

https://people.math.wisc.edu/~chr/104.S12/

[dull raptor]

Profs used Rudin and don’t feel inclined to change

[marble solar]

This syllabus cites Pugh & rudin as optional reading, but not the main book

[dull raptor]

Even if there is something pedagogical better

[marble solar]

So I guess we both stand corrected

[dull raptor]

yeah

I believe Math 55 uses Spivak

But it’s not really a RA course

MIT uses Lebl that I know for sure

From the open course ware

[marble solar]

Again this varies a lot from place to place

and Prof. to Prof

[cursive orbit]

I mean Pugh is very obviously inspired by Rudin

[dull raptor]

yeah he states it as reference

[cursive orbit]

yeah but like the topics covered are essentially the same

idk ppl either overrate or overhate rudin

[dull raptor]

yes I know

[cursive orbit]

either way from my experience there are way more people using Rudin than Pugh at Berkeley

[dull raptor]

hmmm all the Berkley kids I talked to used Pugh

Some even used Ross for 104

Rudin was mostly a reference

[cursive orbit]

Abbott and Ross are more common than Pugh

then only prof using Pugh this semester seems to be Pugh himself

but that is for honors 104

[dull raptor]

Is Ross good

never heard much

[cursive orbit]

I don't like it

[dull raptor]

a lot of statisticians recommended bartle

idk

[cursive orbit]

I think for Berkeley, 104 should teach metric spaces

[dull raptor]

yeah

[heady ember]

Sbased

[cursive orbit]

since most people take 202a or 105 after 104 and you want to know metric spaces b4 either of those

[dull raptor]

202a is essentially measure?

or no

[cursive orbit]

202a is half point-set and half measure

[dull raptor]

interesting

I’m just a statistics major but I think I’m gonna take the topology sequence this winter

Measure in spring

not at Berkley btw

But I think I have to pass an analysis qual to get into measure at my school🤦‍♂️

[remote sparrow]

by "statisticians" you mean the people on the statistics discord?

[dull raptor]

one of them and a PhD friend

[remote sparrow]

there's this guy, clarinetist, that hates abbott with a passion and constantly shills bartle

[dull raptor]

Yeah Clarinetist lol

[remote sparrow]

i don't think it's wrong to recommend bartle but it doesn't seem accurate to label abbott as "nonrigorous"

[dull raptor]

Good guy

sold me a couple books

just for shipping costs

[woeful rock]

¿Is there exist a "Robert G. Bartle, Introduction to Real Analysis" sequel for multivariable? (Not necessarily from the same author, my question is more about like a spiritual successor with the same king of redaction and formalism)

[remote sparrow]

Advanced Calculus by buck, Advanced Calculus of Several Variables by edwards, and Multivariable Mathematics by shifrin may suit your needs

Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by hubbard and hubbard is on the same level as shifrin but stylistically doesn't resemble bartle

[loud cradle]

depending on what topics you want, you could try Bartle's earlier book: "The Elements of Real Analysis" - it covers differentiation and integration in R^n but not curves/surfaces/manifolds

[dull raptor]

A lot of people like Shifrin

Maybe Spivak

[narrow relic]

You could have a look at Wade's An Introduction to Analysis, 4th edition

[heady ember]

Does he have you wading through the details?

[stoic sage]

@burnt sorrel thanks for the info. You wouldn't happen to know anyone to guide? FYI, the writer of "Love and Math" is probably too busy, LOL.

[burnt sorrel]

uhh

What was this about?

Can you reply to the original message cuz I'm not sure I remember

[stoic sage]

If you know anyone interested in it you could sent me a tell. I wouldn't be surprised if that's the case.

[burnt sorrel]

oh right

I mean for this kind of stuff it's uni profs basically

[stoic sage]

sorry technical difficulties

yeah

[burnt sorrel]

for langlands it'll be very much the "top" unis and not (usually) your typical uni

[stoic sage]

yeah, and I'd hate to spam email, I'm not sure what University Math Programs ediquite is currently, at least in the US.

any idea?

[burnt sorrel]

and tbh i don't know if you'll get a positive response

like this is usually something people do in grad school

[stoic sage]

Also, I'm "off" today, so I may get going, good to talk @burnt sorrel , yes, understandable, I'm communicating a little with my local university on another proof, but not even sure where that's going. Yeah, I've been studying grad+ math roughtly 6-20 years (20 if you take the proof I started on)

[stray veldt]

i mean langlands is a pretty wide area

but yeah, if you want to learn about the langlands program, your only option is to get a degree in mathematics and then do a phd in the subject

[stoic sage]

anyway, you all have a good one, I'll check a little later, @stray veldt , yeah, understandable, at least to get respect, amature-mathematicians have historically been important, but often overlooked, later all!

[stray veldt]

this is the worst math subject to be an amateur in

[burnt sorrel]

yeah

[stray veldt]

even grad students who spent 5+ years fulltime learning this (after a very good math degree) struggle

its not uncommon to graduate grad school with only a single publication or so

[burnt sorrel]

You can spend the rest of yojr life reading/learning, and you'd probs only be in the 80s

So you need to know what to learn and what to skip

[stray veldt]

but yeah, starting to learn some of the background is possible, there is probably a roadmap in some mathoverflow post

but to get anywhere where you can make progress, you will need an advisor

and i dont think a random university prof will advise you unless they get something out of it

[foggy quest]

is it over for this field then? Nobody can contribute anymore ...

[burnt sorrel]

No

Fundamentally, a lot of research papers don't really lead anywhere

so reading everything is definitely not thr way to go

[strange tree]

A friend got a reply from Furstenberg, and I also got a reply from somebody at Oxford. Mathematicians tend to respond emails afaik

[burnt sorrel]

also, the same argument can be made about every area of maths anyways

[stray veldt]

langlands is one of the larger fields of active research in mathematics

[gray jungle]

Has anyone read "Nonlinear Dispersive Equations: Local and Global Analysis" by Terrence Tao?

I'm wondering if its worth reading since i'm not too familiar with dispersive PDEs, my background is ch1-6 of Evans, solid distribution theory and fourier analysis, so i think its accessible?

[stray veldt]

getting replies is easy, most mathematicians are very happy to talk about math

but if you need actual advising, thats a lot of work

[burnt sorrel]

(idk about larger in general, cuz it is very much overrepresented at the top, cuz the modal mathematician does some form of PDEs I think)

[burnt sorrel]

yeah, they'd be happy to chat for an hour. Advising someone into Langlands stuff is like meeting once a week for several years.

also an average maths prof gets enough useless emails anyways, so another email isn't that big of a deal in the grand scheme of things

[stray veldt]

PDEs is larger probably

but number theory is historically pretty big

and most number theorists are doing langlands or langlands-adjacent things it seems today

its about as large as something without real world applications (and thus financing) can become

[burnt sorrel]

might depend on country i think

[stray veldt]

im talking internationally here

well, probably eurocentric

but academia is eurocentric...

[burnt sorrel]

I mean I'm in the UK rn lol. But my impression is that here Langlands is mostly in London, Oxford and Cambridge?

maybe Bristol and Sheffield? Whereas AG seems much bigger here

[stray veldt]

AG is weird example?

considering langlands makes statements about algebrogeometric objects

and heavily uses tools from the field

so someone working in AG could very well be langlands-adjacent

[burnt sorrel]

I suppose

But I'm mostly referring to people working on stuff like birational geo, mirror symmetry, Calabi-Yau and stuff like that

so a bit more distant from the Langlands stuff

[stray veldt]

well ok, its just my impression

maybe im wrong 😛

you could probably do a meta analysis wrt funding...

[burnt sorrel]

well I think it probs depends on your perspective lol

i did my UG at Cambridge, where it seemed like everyone was doing geometric group theory, mirror symmetry or langlands lol

[burnt sorrel]

I mean mirror symmetry also gets a huge amount of funding, compared to the number of people working in the area lol

[stoic sage]

Anyone, if this is the section, have any networking ideas or book recommendations? Networking in the sense of people / specifically math people?

It’s been difficult for me personally, don’t know if anyone else has.

FYI, PhD for me isn’t totally out possibly, perhaps unlikely, not sure yet. More likely, masters, but we’ll see, afa official degrees.

[ancient copper]

Anyone got any book recommendations for the AIME or AMC competitions? I’m trying to get better at all topics in the competitions.

[gritty gale]

do u need the specific books or just the material they cover

https://www.physicsandmathstutor.com/maths-revision/a-level-edexcel/ this can help

btw ur school library almost certainly has a few copies of the relevant textbooks

unless ur school is sknit

*skint

which it might be

fucking what

jfc

some fucking library they've got

actually dm me i wanna try somethign rq

ive never heard of a library that charges people who return books on time

i knew austerity had been harsh but that's a fucking piss take

https://www.symbolab.com/solver @heady beacon this might also help, but try not to use it as a crutch

[ancient copper]

I’ve seen the books but they don’t have intermediate number theory or geometry

[shy silo]

my university library doesn't charge people at all

sometimes I get annoyed with all the

"you have to renew this book 🤓 " so I just ignore them and just return the books whenever I'm done with them

[marsh ingot]

There is a discount on AMS right now? I was looking some books

Also, do you recommend soft or hard cover?

[remote sparrow]

soft covers are easier to open and lighter to hold in your hands for long periods of time. because binding quality is significantly lower than before, books don't often lay flat, so a hardcover is a bit of a disadvantage

that said, hardcovers obviously stand up to wear and tear on the covers better

and they don't cost that much more than softcovers to make

or at least, they're priced usually just a few dollars above softcovers

[marsh ingot]

I see, all the books I have are softcovers and are very comfortable to read so I was looking for it. In the end Im gonna read it so much and very often so I will go for softcover

I saw a discount for Lee Intro to complex manifolds

[gritty gale]

tbh it's as much a matter of personal taste as anything

[rose hazel]

after analysis, are there any books I could use to quickly cover the computational side of calculus? (unfortunately, my understanding is quite rigid, and i'd like to participate in some olympaids)

[marsh ingot]

The difference between soft and hard cover is around 30 dollars for the book I said

[remote sparrow]

stewart

[scarlet prawn]

anyone have the answer key to this book:

calculus for AP by stewart kokosa

[gritty gale]

(pictured)

[scarlet prawn]

ty! lol

[rose hazel]

Sir, when i said quickly, i meant the opposite of 1.3k pages.

[loud cradle]

this might be what you're looking for?

225 pages excluding the appendices

[rose hazel]

i believe that's the original edition of the book by Serge Lang, which isn't really all that into hard computational problems.

[astral river]

Any recommendations for rigorous theoretical background on the study of sobolev spaces and their applications to weak formulations of BVPs? Thanks in advance

[cursive orbit]

Perhaps consult part 2 of Evans

[astral river]

Thanks. Was actually going to look at that today

[astral river]

Is there any chance you could speak to whether functional analysis by brezis is any good? Was considering buying it too

[cursive orbit]

I have not read it, but I'd imagine it also covers sobolev spaces and BVPs

[astral river]

It does, but not sure how robust it is. I'll be doing a little research today, so will currently be using evans, dunford and schwartz, and some various tangential texts

Will buy brezis and find out when it is delivered

Thanks again

[cursive orbit]

well you can surely look at the book online beofre you buy it

[remote sparrow]

if you're done with real analysis, you'd presumably know all the theory

you can just skim over the sections and skip to the problems

[astral river]

Can see contents in google books, but not the relevant chapters

[cursive orbit]

can you not access it through your university?

[astral river]

Actually, I probably can. I just don't make a habit of that, since I prefer hard copies, so I sometimes forget it's an option

But I think my university has access to all the springer stuff

Looks like it has a lot of citations, anyway

Oh. Got full pdf with university access haha

[cobalt maple]

Anyone know of a good book with plenty of both easy and hard problems to supplement my reading of Milnor's "Topology from the differentiable viewpoint"?

[astral river]

Guillemin and Pollack have a good book called Differential Topology, which is quite popular, and may or may not have what you want. That said, I haven't read milnor, and I'm somewhat new to differential topology, myself

I know the spivak 5 volume set on differential geometry is full of great exercises, but it may be from somewhat of a different perspective, and there are some people who tend to avoid it, due to its various peculiarities

but my favourite books as a beginner to the subject are smooth manifolds by Lee, and volume 1 of the spivak set

[nova lotus]

Are there any books which build up algebraic topology through problems

Like theory through problems and subdivision of problems kind of books

[astral river]

Not sure, but I am aware Algebraic Topology by Allen Hatcher is pretty robust

[steel cloud]

What is a prerequisite for Measure theory ? And book ?

[astral river]

I wouldn't say there are any strict prerequisites for measure theory, other than understanding very basic set terminology. It does help to know some topology, though, since there are similarities

[molten gulch]

Wouldn't RA also be helpful

[astral river]

There are a lot of books to learn measure theory. "Real and Complex Analysis", by Walter Rudin is a classic, and very robust, but can be intense for a first text

[astral river]

I'd say it is, yes

[astral river]

"Real Analysis" by Folland is a more approachable book with a few more applications

[molten gulch]

Proof writing and set theory: Velleman's How to prove it, Hammack's Book of Proof, etc...
Real Analysis: Abbott's Understanding Analysis, Rudin's Principles of Mathematical Analysis, Tao's Analysis I and II
Measure Theory: Folland's Real Analysis, Cohn's Measure Theory, Rudin's Real and Complex Analysis, Tao's Measure Theory, Axler's Measure Theory (available for free online too)

[astral river]

Real analysis is more or less synonymous with measure theory from an analytical perspective. Real Analysis used to be the study of the real numbers, but now describes more or less the analysis which is not complex analysis. It often describes measure theory, because measures are often real, and are the natural abstract framework for higher level analysis

[molten gulch]

ahhhhh

okay that makes sense

by RA we were more implying rudin, abbott, tao, etc... levels of basic analysis and proof writing skill

[vital bane]

tall calculus when

[astral river]

Fair enough. I would agree that that is pretty important to have an understanding of measure theory. The learning curve was somewhat steep when I first learned it

[steel cloud]

Tao II 😭

[astral river]

I think the folland real analysis is a very good start for measure theory, since it strikes a decent balance between rigour, mathematical maturity, and approachability. Rudin's real and complex analysis is a masterpiece, but requires either a lot of perseverance or talent. It is a wonderful book, but better for a second read

[steel cloud]

Which book should I pick ?

[astral river]

I would personally recommend folland

[steel cloud]

Okay

[molten gulch]

Folland

[astral river]

Rudin's principles of mathematical analysis is a good book, and may provide a good introduction to helpful skills, but its treatment of measure theory is limited, and is only a very short introduction in the back of the book

[steel cloud]

Okay

Thank you

[astral river]

But Rudin is terse and requires mathematical maturity, which I always find better on a second read

[astral river]

Happy to help

[vital bane]

There is also Axler's measure theory book

freely available online on Axler's website as well

[molten gulch]

we mentioned that in our post

[astral river]

It is not bad, but I personally prefer Folland. The Axler one is arguably more easy-going, but I find folland to be a better reference, and the exercises are a bit more enlightening to me

But it's ultimately a matter of preference

I would say folland is a very good first book on measure theory for a student who is really interested in it

Axler might be better to ease into it if you're having trouble understanding it at first

[fresh skiff]

Folland as first book for MT
I would prefer axler.

[foggy quest]

Folland's book is good. For probability theory, Durrett's PTE is good: https://services.math.duke.edu/~rtd/PTE/PTE5_011119.pdf

[cursive orbit]

folland as a first book is pretty reasonable given a good background in undergrad real analysis

[fresh skiff]

is there a way to know, we have enough/good background in UG RA?

[remote vortex]

Yeah, recommending Folland over Axler comes with much fewer caveats than recommending Rudin over Abbott

I'd still recommend Axler over Folland to the median student, but there's less of a gap

Also just get both books and if you find Axler too boring, switch to Folland; or if you find Folland too concise, switch to Axler

It's not like you have to commit to one book on pain of pain

[cursive orbit]

one good proxy if you learned RA in school is if you a good grade

[remote vortex]

Or if you can solve most of the exercises in a book like Abbott or Rudin

[cursive orbit]

I certainly think solving most of the exercises in Rudin is a pretty high bar

[fresh skiff]

I have learnt RA in uni, but bcz of low quality of education of my area and lack of math prof, the TA who taught us RA, didn't focus on proofs but only example

[remote vortex]

Fair

[fresh skiff]

I think, I can do most problems from each exercise set of abbott. But not sure abbott Rudin, I guess i can do like 50% or 35% of exercises (upto chapter 5)

[remote vortex]

So let's say if you can solve most exercises in Abbott and if you can easily follow most proofs in Rudin 😄

[light fern]

Does anyone have any recommendations for a book for real analysis (self study)?

[cold acorn]

@fathom wharf In response to your message request, no - I don’t. However, you can ask for recommendations in this channel (or search the messages here - I’m sure there’s some good results somewhere)

[molten gulch]

Abbott's Understanding Analysis

[willow merlin]

which book explains vector algebra with a geometric intuitive approach

[foggy quest]

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

[steel cloud]

Okay thank you

[still notch]

Does anyone have any textbook recommendations that is rigorous with the proofs for differential equations? My university has recommended "Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems, John Wiley & Sons, Inc" however I am not too sure about this book.

[still notch]

*a book that one would probably get a hard copy of and keep as well (can be used as reference in case something is forgotten)

[remote sparrow]

https://www.amazon.com/Theory-Ordinary-Differential-Equations-Coddington/dp/0898747554/

out of print though

more of a reference than something to study

[still notch]

Oh I see thanks. Yeah this will be my first (formal) exposure to diff eqs and I just wanna make sure I’m not going in with a bad start

[still notch]

Would there be a different book that is more available in print/readily available?

[flat ermine]

yo has anyone here actually learnt Algebraic Topo through Hatcher in their undergrad?

just curious

[mellow wren]

I took an alg top class that followed hatcher in my first year of UG

[foggy quest]

https://mtaylor.web.unc.edu/notes/math-524-second-semester-ode/

[burnt sorrel]

Ye, ch 1 in a first course, 2 and 3 in a second course

[flat ermine]

First year of undergrad? Gosh dang man

Isn’t that like a graduate level of text lol may I ask which uni taught you that in first year?

[flat ermine]

May I ask how you found the book itself as a learning material?

[mellow wren]

I took the graduate class at UCSD

they're pretty liberal there letting UGs to take grad classes

[burnt sorrel]

I liked it

But I am also very geometrically-minded

i.e. the target audience of the book

[flat ermine]

I see

[flat ermine]

Dang wow im guessing you had some prereqs to be able to take a whole grad course in first year lol

[mellow wren]

it was a bit weird
I had learnt some basic abstract algebra and topology before I got there so I was able to follow
But I technically got into the uni as a physics student so my prereqs were technically all over the place
But the one year I was there it very much solidified me as a mathematician
Tho I had to leave after less than a year due to some personal issues

[flat ermine]

That’s very cool

[covert ore]

Anyone know Physics For Dummies from Steven Holzner?

I'm looking for a physics book to read for fun

or to expand my knowledge

I'm a beginner in this field. Any books reccommendations?

Please let me know. Thanks 🙏

[idle brook]

https://m.media-amazon.com/images/I/71vCoXAxhjL._SY466_.jpg

just read it
u wont regret it

[timber mesa]

might be best to read one of the standard textbooks, personally I liked Serway and Sears-Zemansky for intro university physics

skimming the "for Dummies" book though I get the impression that it's a good overview of the very basics

not a bad investment if you can get it and want to read for fun

[marsh ingot]

Some one who had purchased from AMS bookstore, how can I track my order?

[trail hemlock]

https://github.com/psibi/how-to-prove

[nocturne marsh]

do u guys know any olympiad-level calculus workbooks ?

[timber mesa]

closest thing I can think of is Putnam and Beyond

which is just a book about solving competitive maths exercises that use calculus among other things

[quiet forge]

My online notes.

[woeful ravine]

Do you have a link? I would love to see them

[quiet forge]

Certainly!

https://siegelmaxwellc.wordpress.com/mathematics/math-notes/

[woeful ravine]

Thank you

[quiet forge]

You’re welcome.

[heady ember]

See the pinned messages for some reviews by dami

[trail hemlock]

ch1 and 2 seem to be in markdown, so just thug it out until chapter 3

then u can use pdflatex

[normal crystal]

there's an instructor's solutions manual drifting in the aether

[trail hemlock]

oh? sorry i didnt realize

[normal crystal]

disappointed your own name origin🤡

[trail hemlock]

this has all the solns as it seems

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

[trail hemlock]

well i found it, i just cant post it here

[normal crystal]

that's why I was obtuse, as well

[trail hemlock]

obtuse?

[normal crystal]

the solutions for the Solow book are on archive.org though

[normal crystal]

why I didn't specify how to find it

[trail hemlock]

i dont think so

there is a pdf floating around somewhere, u can just try to find it

[hushed hound]

can i get some book recommendations on how to get good at mathematics

[willow merlin]

hardest engineering linear algebra book?

is there a spivak for algebra?

[pine tundra]

<@&268886789983436800>

[astral river]

I think it is important to enjoy it, to get good at it. Beyond that, there are certain good books for each topics, and good learning approaches. If you can find a mentor of some kind, do so, and they will hopefully prompt you to think about it

A good position is when you have a teacher (or book) that prompts you to do your own research, and figure out the answers to things on your own, since practice is very important in maths

maths is very much a problem-solving science, and it is more about figuring out ways to look at/interpret things, than it is about learning processes

[heady ember]

Yeah

[safe wharf]

im gonna fcuk up i cant understand this

[remote vortex]

Extremely this

[heady ember]

Credit to James for sharing it the other day.

[signal mountain]

whats it from ?

[heady ember]

Halmos

[signal mountain]

vector spaces or i want to be a mathematician

or smth else

[gray jungle]

a hilbert space problem book

[signal mountain]

ahh ok thanks !

[wet sentinel]

which book is better baby rudin or analysis by browder

[jagged axle]

good books for tetrahedrons?

[molten gulch]

What context are you working with tetrahedrons in? Crystal Structure Modelling? Group Theory? Euclidean Geometry?

[jagged axle]

Euclidean Geometry

specifically for computational simulations between tetrahedrons

[vital bane]

I saw "Among" and was scared for a second

[wet sentinel]

are there solutions to the exercises somewhere

[halcyon parcel]

Y'all should try the Schaum's outline series

For any mathematics branch

Whether it be college algebra, intermediate algebra, geometry, anything

Even calculus or anything

[normal sandal]

bit of a general question, but what prereqs would I need to start learning complex geometry (was thinking to just pick up huybrechts)?

[mellow wren]

I think to get the most out of it you should be familiar with some diff geo and algebraic geometry
He sort of builds the elements of algebraic geometry needed but it's a much easier read if you're already familiar with sheaves and stuff

[burnt sorrel]

I mean the appendix of Huybrechts about sheaves is very minimalist lol. I think knowing about sheaves is definitely a prereq

[hollow depot]

book recs pls

[rose talon]

for?

[hollow depot]

physics or math

but not super crazy insane people

i need some basic things

but i also don’t want a children’s book

[rose talon]

anything specific you want to learn?

i have degrees in both so I can probably point you in a (potentially helpful) direction

[rose talon]

also how basic?

[hollow depot]

uhh

i can understand english and i know how math works

[hollow depot]

something regarding space

[rose talon]

do you know calculus?

[hollow depot]

astrophisics

orbits

astrophysics**

[hollow depot]

meh i could figure it out maybe

i would prefer something i could read that explains it

[rose talon]

so you definitely absolutely need to learn calculus first

gimme a sec to think of the best calc books

probably spivak or stewart

you can't really do any physics without calculus so thats just a thing you need to have down first

it has been a long time since i read stewart, but i remember it being a straightforward intro to calculus

spivak is definitely harder and you probably won't be ready for it, but it is an option if you want something with a bit more depth and mathematical maturitiy

lmk if you have any questions

[rose talon]

also once you know multi var. calc the go to book is Modern Astrophysics by Caroll

[hollow depot]

I like to say i’m good with conceptual things

so that isn’t really an issue

[rose talon]

i mean you can check out any flavor of pop-sci book if you want

and those can definitely be interesting

but if you want to actually understand orbits and stars and cosmic radiation that usually means sitting down and solving PDE's

i understand though that that might not be super helpful as learning calculus is a lot of work

[hollow depot]

i’ll be there next year

[rose talon]

then i would suggest finding a solid intro to physics text to follow along with your calc course. until then i don't think you would be ready to study proper astrophysics

haliday and resnick is a great intro to physics

[hollow depot]

alr tyy

[rose talon]

no problem. once you get the hang of calc and get through halliday and resnick then you have a lot more avaiable to you (Caroll for astrophysics, Schroeder for thermal, marion for classical, Griffiths for enm). This is of course quite a lot of stuff, its like half a bachelors worth. Good luck!

[rose hazel]

Anyone book recommendations for lambda calculus and type theory?

[remote sparrow]

#book-recommendations message

https://www.amazon.com/Lambda-Calculus-Syntax-Semantics-Studies/dp/184890066X

[rose hazel]

thanks

[willow merlin]

which book explains how to extend a basis

[pine tundra]

Any linear algebra book, I guess?

[thin swan]

Dont read book, watch film

[gray gazelle]

[green wolf]

Is FB fine to supplement with a vector calculus based complex variables class? Taking real analysis and some “complex variables” class this term and want to read real complex analysis. I can fairly easily read ahlfors but FB looks better

[glad elm]

Am I stupid for actually tapping the pause button?

😭

[gray gazelle]

if you are referring to my bio, then yes 😭

[glad elm]

😭

[gray gazelle]

Hi all, I'm looking for a book that can help me answer mathematical questions with a kind of decision tree. For example: "how would you model high-level outcomes for workforce training programs" would be answered nicely with a multilevel regression model, but I don't simply want to memorize that, I want to have a systematic approach to deciding which models to use and combine together in certain ways. A heuristic. There's a book called "Chance in Biology" that gives something like this for specific modeling problems in biology, but I want something more general and that can be used as a practical handbook

[rugged lance]

Next Semester i will hear my introduction to Abstract Algebra(Startimg Next month) does smbdy have a book rec?

[remote sparrow]

#book-recommendations message

[molten gulch]

Artin's algebra
Gallian's algebra
Pinter's algebra

[rugged lance]

Is the artin one like one of the standard/popular ones?

[sage python]

I think so, yeah

[pliant wadi]

Yep

[signal zenith]

I don’t think you’re gonna have much luck here cause this sounds more like business mumbo jumbo than math to me

Like what is a “high level outcome” for a workforce training program

Best bet would probably be some sort of book on mathematical modeling

But I don’t actually know much abt that

[gray gazelle]

So here's an example from chatGPT, where GPT kind of gives an overly complex strategy. Again, I don't necessarily need to focus on a specific domain, I just want to be able to be comfortable with mathematical structures enough to have an intuition about when to use a certain kind (e.g. a certain kind of graph, a hidden markov model, a matrix, etc.). I'd mostly be interested in applications in health or government policy

To improve the efficiency of a customer support process, the following models can be used:

Process Mapping and BPMN: Create detailed diagrams of the current workflow to identify bottlenecks and inefficiencies, such as delays in ticket assignment or frequent escalations.
Discrete Event Simulation (DES): Model the support process to test scenarios like increasing the number of agents or adjusting ticket prioritization. Simulate these changes to assess their impact on resolution times and productivity.
Hidden Markov Models (HMMs): Analyze historical data to predict ticket state transitions and identify patterns leading to delays or escalations.
Dynamic Bayesian Networks (DBNs): Model how factors like workload and resource availability interact over time, affecting ticket resolution and customer satisfaction.
Process Mining: Extract insights from actual event logs to detect deviations from the intended process and pinpoint inefficiencies.
Value Stream Mapping: Visualize and eliminate non-value-added activities in the process to streamline workflows.
Implementing these models leads to informed changes such as increasing staffing, improving ticket triage, and streamlining processes, resulting in reduced resolution times and enhanced customer satisfaction.

[glad rampart]

!nogpt

[hybrid sparrow]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[gray gazelle]

So yeah, don't necessarily need to use generator tools to come up with an example here. The Schelling model, for example, is a famous social science model which you can look up which is an ABM. I want to know if there is a book which will let me quickly know when and what types of models to use in a certain subproblem to an interview question or another kind of setting.

[signal zenith]

I think your best bet is to find a book on mathematical modeling for health or government policy (there are probably specific books for each). I doubt you will get many responses here bc not many people here are interested in modeling. Also it kinda seems to me like you’re looking for a panacea - there will be no one book which you can use as a heuristic for every problem that’s slightly mathematical…

[gray gazelle]

Got it, thanks for answering!

[signal zenith]

Np

[marble moat]

Hello folks, any recommendations on analytic geometry books? (Undergrad level)

[buoyant halo]

When you guys read textbooks, do you try understand each and every single little detail in the porga

Or did you sometimes jump right to the results

[tribal crow]

I usually make an effort to understand all the examples and theorems, yes

maybe every little detail is too much though

the more important part of a book is usually the exercises

that's usually where most of the learning happens

[molten gulch]

yep, every little thing

else we don't go to the next page

[rain hound]

Depends how well I need to know the topic. If I need to know it cold then yeah I try to understand everything.

Most stuff though, understanding well enough to parse the results is usually good enough working knowledge

sometimes it’ll be somewhere in between and you adjust accordingly

[buoyant halo]

most reasonable answer imo lol

if I try to understand every detail rn reading Rudin's for my RA class, I am going to get super behind

esp since we're not following a textbook

[tribal crow]

oh for a class, I would not try to understand every last detail of a book

I thought we were talking about self-study

my mistake

[buoyant halo]

Are you doing a PhD?

[tribal crow]

I am nowhere near a PhD at this moment

[buoyant halo]

Getting to self-studying from books with no class in a PhD sounds super fun

[buoyant halo]

Masters?

[tribal crow]

no haha

[buoyant halo]

aren't you graduate?

oh wait nvm

honourable

[tribal crow]

what makes you think that

I'm a rising 2nd year UG student

[buoyant halo]

ohhh same as me

[tribal crow]

I'll start my 2nd year in a week

[buoyant halo]

nvm

im halfway thru

American?

[tribal crow]

I've never read Rudin, but I've mostly heard that it likes to leave out lots of details for the reader to fill in

so I imagine it's not the easiest read

[tribal crow]

Canadian

[buoyant halo]

all da same to me 🥰

[signal zenith]

depends what you're reading it for

general textbooks definitely

but the closer you get to modern research the less true this needs to be

[marble solar]

It's very good for a book in a class, it's not well suited for self-study

[tribal crow]

that sounds about right

[signal zenith]

In particular, for papers (which are of course not textbooks) you do almost the opposite - skim the results and look for proofs only later if you need to use ther esults

[marble solar]

If you're going for self-study Apostles Mathematical Analysis book is probably the best

It's just Rudin w/ exposition

[signal zenith]

I've heard anecdotally some PhD students and professors tell me that when doing more advanced books which serve as background/references for research it is also often good to just skim

and look for results

[marble solar]

Once you're at a base line level of mastery, this is very accurate

It's that you're at the point where you can fill in the details if you have the time

[rain hound]

It is possible but you need to read the book at least once (at the parsing level) before the class

then you gotta practice in the class in a particular way to learn the topic cold

like doing all your homeworks as if they were exams with zero references

[tribal crow]

mhm, but this is generally unfeasible for most students

I certainly couldn't read all of Munkres before taking a point set course

[rain hound]

Oh I couldn’t cuz Munkres was too dry and boring

[tribal crow]

I wouldn't expect most students to be able to either

[rain hound]

Croom I could do just fine

[tribal crow]

luckily for me, I'm not reading Munkres

but I still probably couldn't finish a general topology text before a class

and if I did, that class would almost seem like a waste of time

[rain hound]

yeah that’s part of why I didn’t take many math classes

Just the bare minimum to get the degree

[tribal crow]

fair

[rain hound]

it’s more fun to self study anyway imo

[tribal crow]

I'm with you there

[rain hound]

your university doesn’t have a cat theory course? no problem!

well they do, but that’s not the point

[tribal crow]

self-study is so much better for me than a classroom

but I have to do what I have to do for the program

[heady ember]

That doesn't matter when you already prove everything yourself

[trail hemlock]

wait what i thought u were a hs student

mann

[tribal crow]

??

I've told you many times what I am before

[trail hemlock]

yes

u said and i quote "18 soon to be 19"

[tribal crow]

sure, that leaves the possibility of UG well within reach, no?

I think I've also told you outright before too

but I digress, this isn't a conversation we should have in book reccs

[trail hemlock]

ok

[celest estuary]

Do someone has recommendation of real Analysis books ( baby Rudin) which has same style as Rudin ( using metric space approach) ? Which can be relatively easier to follow that Rudin

[toxic willow]

#book-recommendations message

[willow merlin]

Which book explain recurrent sequences and sequences
that follow recurrence
relations

[tired glen]

can anyone give me a breif overview and concepts and content of " concept of physics" by H.C. Verma

[karmic tangle]

Hello, I've read that some knowledge of topology would be helpful in reading through Steve Awodey's "Category Theory"

Does anyone here know how much that "some" is?

[vocal egret]

any diff between How To Prove It 3rd edition vs 2nd edition?

idk which to buy rn, both seems highly regarded

[stray veldt]

if you can get a look at the intro of the 3rd edition, it will probably mention the changes from 2nd edition

[rain hound]

Tao Analysis II uses metric spaces for as long as it can get away with.

[vocal egret]

imma check a page of it rn, thx

[turbid mural]

recommendations for algebraic number theory?

[stray veldt]

Neukirch is very good

[turbid mural]

thanks

[vocal egret]

is Basic Topology text a good introduction after "How To Prove It" and "Linear Algebra by Strang" good?

[stray veldt]

hm?

[vocal egret]

I plan to learn Calc II and Calc III alongside proof for easier understanding rn

[stray veldt]

i wouldnt read a book on topology before learning real analysis

you should familiarize yourself with metric space topology first

i.e. topology of R^n

[vocal egret]

alr then, thx. imma try finding books about this after Linear Algebra

[stray veldt]

maybe its in your calculus book(s)

[vocal egret]

just checked, and it turns out Apostol or Strang have. I checked Spivak but he only covers single variable calculus. Gonna try out George's calculis book rn, it seems neat

James Stewart text have long bum texts tho, kinda sad

[karmic tangle]

some introductory topology books start with metric spaces first from what I've seen

[wide dock]

Any guides for ioqm

[wide anvil]

what books would I need to be ready for Stein's Fourier Analysis

[astral river]

Not really. It is pretty approachable

Of course, it helps to have some basic mathematical maturity, and know basic calculus and whatnot

[wide anvil]

do I need to know about lebesgue measure?

[astral river]

You should

But I would say the prerequisite knowledge is very fundamental

[wide anvil]

I j completed undergrad real analysis

how do I proceed from there?

[astral river]

In general, or in learning fourier analysis?

[wide anvil]

fourier analysis

[astral river]

For fourier analysis, I think stein is a pretty good book tbh, and it's pretty approachable. In general, I'd say it's worth learning some basic measure theory if you don't already know it, and get some exposure to functional analysis, even if you don't plan to specialise in it

[astral river]

You should presumably be ready to read stein, but you should understand what lebesgue measure is, what a norm is, and what L^p norms are

Stein has other books that teach all that and more, but you don't need a full course on it to understand fourier analysis

[wide anvil]

is undergrad real analysis a very foundational course that opens doors to wider fields for study in higher levels, where people usually specialize, so it would probably be very unlikely and impractical to master everything?

[astral river]

Pretty much. As a mathematician, you generally need analysis skills, but there are eventually somewhat disjoint areas of mathematics. Whilst it's good to have a fundamental knowledge of each, it's a very big task to become an expert in any of them, let alone all of them

[wide anvil]

btw, I have this book that I picked up from local library which was p cheap - "fourier Series" by tolstov. will it help me?

[astral river]

For instance, people who specialise in functional analysis aren't necessarily great at differential geometry, even though some areas of study exist at their intersection. I know a handful of professors who specialise in either one or the other, but can't say a lot about studies that combine them at a high level

[astral river]

I'm not very familiar with that book. I just searched it on google, and it looks good, but I can't really comment

Whichever book helps you understand it best is ideal. It's worth referring to other books sometimes for different perspectives and whatnot, so even if it doesn't become your go-to book, it can still be helpful as a companion text

[wide anvil]

thanks a lot, Neckmaster

[astral river]

No worries

[wide anvil]

oh, I forgot a question. does research in pde require a lot of prereqs and generally off limits to undergrads?

[astral river]

It's not off-limits to undergrads by any means. That said, research in PDEs has a lot of different approaches, some of which are more advanced than others

I am currently working on weakly solving PDEs, exploring rigidity, and studying various results in sobolev spaces (I'm still somewhat new to it, tbf)

But the sobolev spaces are slightly more advanced (well, there is more prerequisite knowledge) than solving PDEs traditionally

[wide anvil]

ok, so to be clear, I don't need all of grad real analysis or even things like lebesgue differentiation, right? jus understanding what lebesgue measure is, l_p spaces etc..

[astral river]

Either way, I would suggest Partial Differential Equations by Evans. It's one of the main books used, and for good reason. It explains things very well, without sacrificing rigour, and I'd say it's one of the best math books around

[wide anvil]

but doesn't that have fa as prereq?

[astral river]

I would say you don't strictly need to have taken a functional analysis course for most chapters of Evans, but it really helps

[astral river]

That is my opinion, yes. Most good books on topics are reasonably self-contained, and learning background is more for the context and mathematical maturity than strict prerequisite knowledge

It REALLY helps to know some measure theory and functional analysis, but you don't strictly require it to solve PDEs or do fourier analysis

But if you don't have a good understanding of what the L^p spaces are, fourier analysis might be hard to understand

And dominated convergence theorem form measure theory is used in a lot of fourier proofs

Anyway, I've gotta go. Feel free to message me if you have more questions

[wide anvil]

ofc, ty

[formal parcel]

anyone know a good geometry book for college students to prepare for certain problems that might rise up in calculus and other places

[wide anvil]

trust, not much geometry will appear in calc. The only things I can think of are: you should know how to calculate the area of a rectangle, trapezoid (for reimann sums, trapezoid rule), formula for area of a triangle, volume of a cone, cylinder, (to calculate rates of change problems that might appear in differentiation chapters) and also basic trigonometry (you should know what sine, cosine is to understand how polar coordinates work). That's pretty much all you need to know.

oh, you will also need to know how to caclulate the area of a circle

[gray gazelle]

what is a good book for multivariable calculus (with lots of standard test exercises)

i was looking at the stewart one but im not sure if it is good

[cursive orbit]

that's the standard one, so in some sense that will get you closest to "standard exercises"

[celest estuary]

I think I would ask here again
.
Recommendation for calculus of variation for student (me) that has background of measure theory, some functional analysis, Fourier analysis

[molten gulch]

Stewart and thomas are the standard textbooks used in most US institutions for that course

[thin swan]

Dark Brilliance

[toxic tendon]

whats the difference between the 2nd and 5th edition of Discrete Mathematics with Applications second by sussanna epp

i tried to find edition 2 online but could only find 5

[normal crystal]

why do you want the 2nd, seems like the onus is on you

[wide anvil]

Why not? What's wrong with previous editions?

[toxic tendon]

i seen it recommended online

i just want to know if there is really any difference between any of the editions

[wide anvil]

Some courses explicitly require a certain edition which may not necessarily be the latest. Also, some books are revised in the later editions to the extent that the content is dumbed down.

[toxic tendon]

im just doing some self learning

would you recommend i just stick to the 5th edition

[wide anvil]

NGL, I'm taking discrete math this semester

If it's for self learning, in most cases ig, use whatever you can get

But if you're trying to self learn to take a higher level course later on, only then it'll matter.

[wide anvil]

Yeah. Don't worry too much about the edition

[toxic tendon]

alright thanks

I appreciate it :)

[gray gazelle]

like the ones they will ask in tests?

[gray gazelle]

are they good books tho?

[wide anvil]

Wdym 'good'? They are among the most widely used college courses for multivariable courses.

Is that good enough?

[molten gulch]

I mean, they're average, most calculus textbooks are average

[gray gazelle]

yes but will the exercises prepare me for exams

because i remember i had a stewart textbook and the exercises didnt prepare me at all.

[wide anvil]

Bruh, what have you learnt so far?

[molten gulch]

Depends on your professor

[gray gazelle]

ye my professor was crazy hahaha

[molten gulch]

If your professor wants to be annoying, they'll come up with painful exams

the book doesn't correlate to exams

[gray gazelle]

i did cal 1 and 2

now im doing cal 3

[wide anvil]

Are those AP calc?

[gray gazelle]

idk i guess they are

differential and integral calc

[molten gulch]

Calc 1 and 2 is differential and integral calculus at the university level

[gray gazelle]

now i move on to multivariable calculus which i assume is calc 3

[molten gulch]

yes that's calc 3

[wide anvil]

Did you take them with honors?

Calc 1&2?

[gray gazelle]

yes i was in an advanced class

the "recommended" textbook (stewart) was so bad it did not help at all

wasted all my money

it was single variable calculus early transcedentals i think

[wide anvil]

Well you might want to try either Marsden & Tromba's Vector Calculus or Hubbard & Hubbard's book

[gray gazelle]

ok i will take a look at them

[wide anvil]

You can also try Shrifin's multi variable calc

One of those three

[gray gazelle]

ok

[molten gulch]

The issue here I believe is that your professor was giving exams that the problems wouldn't prepare you for, this is not an issue with the problems in and of themselves, but rather the issue of the professor scaling the exam difficulty far higher than the homework he was having you complete

[wide anvil]

Do you have a couple of sample questions which you find hard that you can post it here?

[gray gazelle]

well, i took these classes like a year ago hahaha

now i havent started cal 3 yet

im starting tomorrow

now the problems that i found difficult last year are very easy

because i know how to do them

[wide anvil]

Maybe try to give an example of some questions. I can look at them and see whether the books I've recommended are at your level

[gray gazelle]

but, when i was learning the material, these problems were not in the textbook. I needed to do my own research

ok

let me go find a question

ill give a limit question

$\lim_{x\to1} \dfrac{x^5-5x+4}{(x-1)^2}$

[hasty eagle]

Derivative

[gray gazelle]

this is easy for me now because i know how to factor the top (manipulate the top and turn it into x^5 -1 -5x + 5)

but, in the stewart textbook this type of problem is not there at all

for differential calculus of course

[normal crystal]

I wasn't saying there's anything wrong with it, but he was particularly looking for a 3 editions old textbook, so it seemed the onus was in him for why
no we know, no real reason, just what he happened to see recommended

[wide anvil]

Bruh, thought you were gonna give something crazy. This is very basic, probably week 1 or 2 content for calc 1. NGL, you might want to stick to Stewart's as the others are honors level books. Let me take a look at the book about these types of questions and I'll answer in a bit about whether you should stick to Stewart or not.

[gray gazelle]

idk maybe its in the bigger stewart i have the smaller one

i have the "baby" stewart

[wide anvil]

The books I've recommended most likely doesn't even have limit types of questions. They are much harder on average

[gray gazelle]

ah ok

[wide anvil]

In page 83 of Stewart, I found the method is basically implied

[gray gazelle]

which stewart one

[wide anvil]

Which one do you use btw?

Like do you have edition number? Is it early transcendental?

[gray gazelle]

yes

single variable essential calculus early transcedental second edition

its small

[wide anvil]

Second edition ☠️☠️☠️

That must be kinda old but then again, I don't think Stewart changes much between editions.

[gray gazelle]

its the newest one of the essential calculus series

Essential calculus is condensed

which one were you referring to for page 83?

[wide anvil]

Ohh it's 'essential' calculus. Mb

Didn't see that

[signal zenith]

As someone who has recently taught a calc 1 equivalent I would say that this is conceptually easy but practically hard

The vast majority of students wouldn’t know to do the manipulation

[rose talon]

If you are finding a lack of problems then the condensed essential calculus will probably not be the best book

[signal zenith]

They would know they need to do a manipulation but not how

[gray gazelle]

yes i need the biggest one

[rose talon]

Stewart's "calculus" book is solid

[gray gazelle]

i wasted money on that book

[rose talon]

I learned calculus from his 8th edition I think and found it very solid

[gray gazelle]

ah i see

[wide anvil]

Lmao yes. And here I am, suggesting ppl proof based calc 3 when they can't do this. I'm a bad person to come for advice because I'm basically setting them up for failure.

By giving them hard books

[gray gazelle]

hard books arent bad

[rose talon]

The only other calc book I can think of is spivak but if you are struggling with the limit type stuff spivak is prob too hard

[gray gazelle]

im doing an engineering degree tho, not math

[wide anvil]

Yeah.

[gray gazelle]

if i was doing math degree then i would probably learn proof stuff more rigourously

but my math is for engineering essentially

not sure if that changes anything

[wide anvil]

Nah ur good

Lemme check the book

@rose talon btw what are u studying?

[rose talon]

mathematical physics and algebraic topology

[wide anvil]

What is ur intended specialization in ur postgraduate program?

I see

[rose talon]

idk about any good vector calc books

I took a class w tromba and he didn't even use his book lol so idk

[gray gazelle]

ive wasted so much money on books

[wide anvil]

Damn. Wait ur from Caltech?

[gray gazelle]

literal fortunes

ye i should do that

i just dont like the online stuff

i like physical copy

[molten gulch]

don't discus piracy on this server

[rose talon]

nah i went to ucsc for undergrad anmd he teaches there

[molten gulch]

it's not allowed

[rose talon]

apologies

[gray gazelle]

so i try to get them used or second hand

[wide anvil]

Oh I thought tromba was from Caltech lmao

@gray gazelle I'll get back to you soon

[gray gazelle]

ok no problem

[wide anvil]

I'll need a study partner for PDE's 🥺🥺

I'm fine with the computational part. NGL those are the easiest parts of higher math but I'm taking proof based PDE's. Those are hard ones

@gray gazelle what grade are you?

Are you incoming freshman?

[wide anvil]

In general it isn't, but my advice is bad because it gives you something which are kinda challenging to the extent that you might be unmotivated to continue to study. So my advice was bad

@gray gazelle it's in page 26

Of ur book

@gray gazelle did you take calc in college? Or in HS?

[rose talon]

I would just recommend Stewart’s main books for both single and multi variable calculus

I found them to be very solid and taught all the required computational stuff