book-recommendations

[flint forge]

(not just adv calc)

[viral falcon]

@robust palm okay is there anything else you recommend?

[robust palm]

it depends on what you're looking for

what's your goal for learning calculus

[hearty steppe]

I think it is just understanding formality to better gauge intuition honestly but of course it is much easier to learn through visualization/demonstration at times too which is the benefit of taking a course if your professor doesn't suck.

[viral falcon]

I like physics I might go into aero/theoretical study. But there's 4 years for that. So I'm learning calc rn in freshman by myself. My course requires till CII and touches surface of C3 @robust palm

[robust palm]

in that case, I think it would be worthwhile to go over stewart's calculus

that's the book we used when I took calc 1+2 in high school, and after taking analysis I still think that book provided me with valuable intuition

it aims to provide intuition, albeit at the expense of formal proofs, but I usually prefer an informal convincing argument over a formal proof that doesn't tell me "why" something is true, so that doesn't really matter to me

to an extent

[smoky surge]

@robust palm question for you would you recommend stewart for someone who just wants a refresher on calc? Going to be taking a machine learning course and think a bit of a intuitive overview would be nice

[robust palm]

eh it couldn't hurt. I'm not sure what you need to do machine learning, but I imagine reading the sections where they introduce the derivative and the ones where they show how to solve some types of optimization problems will be helpful

chances are you'll need multivariable calculus, but I'm not sure how stewart's multivariable is

[smoky surge]

yea i took calc 1 -2 in college and went over mv around a year and half ago on my own

and want a bit of a refersher tbh

[sterile pelican]

Maybe Lang's Short Calculus might help? Though it would be better to buy a Schaum's outline and do a lot of the exercises

[robust palm]

schaum's outlines are underrated

I went through their topology book, surprisingly good

[sterile pelican]

Oh as a first exposure or a supplement?

I have not read topology at all, I bought Willard's book and awaiting its arrival

[robust palm]

It was my first exposure, but I think if I looked at it two years from now (assuming I don't see any math until then) I would have a good idea of what I know now

in a first exposure it probably works best as a supplement to a more standard book like munkres

munkres has great proofs and he gives a great deal of motivation, but there's no getting around that it's a tough subject

schaum's topology is great because it has so many worked solutions to problems

[gray gazelle]

nah just read that categorical approach book

inb4 max comes in and says "but actually"

[flint forge]

but actually

its the best point set book

i stand by this take

[sterile pelican]

we talking munkres or willard?

[dapper root]

the categorical one

is what Max is saying

[sterile pelican]

(out of curiosity is it munk-rees or mun-kres?)

[flint forge]

it teaches two useful things

instead of .5 useful things

making it the best book

[robust palm]

what book is this referring to?

[flint forge]

Topology and Category Theory

its what aluffi tried to be

cant wait for Linear Algebra and Category Theory

[sterile pelican]

is category theory some spice you add on other math concepts?

:^)

[flint forge]

yes

[sterile pelican]

category theory and number theory?

[gray gazelle]

category theory and differential geometry....

ah yes

natural transformations...

~~covariant and contravariant tensors ~~

[robust palm]

what's the author

[flint forge]

dont remember

Topology: A Categorical Approach

thats the real name

[robust palm]

I just found it, thank you!

[dapper root]

REEEEEEEE

[flint forge]

i really think they are using graduate-level generously here

[robust palm]

what should I know before diving into it

[flint forge]

uh

honestly not a ton

basic set stuff

maybe some familiarity w metric spaces

[dapper root]

You should know that Max is a goober for dissing Aluffi

that's the only prereq

[flint forge]

literally everyone agrees with me

[dapper root]

no

^

[flint forge]

disliking aluffi is my one popular take

[dapper root]

not that guy

[flint forge]

anyway all i really meant by it that time

was in the vein of 'introducing category theory as a useful language for introducing another subject'

this book does it better

(and, i think, topology is better suited)

[dapper root]

Aluffi doesn't lean into it as hard

Until the end

[flint forge]

one of the many flaws

in that book

[dapper root]

Pffft

at least it does it

[flint forge]

?

[dapper root]

introduce it at all

[flint forge]

i can't say i think doing something half heartedly is much better than not doing it

just read riehl and DF

[dapper root]

Hurb

[flint forge]

at that point

[valid moth]

@true veldt thoughts on aluffi?

[true veldt]

cant say I have a solid opinion on most books

[hasty turret]

Technically,Df does do some category theory (via exercises)

[flint forge]

nah

[true veldt]

not many thoughts on aluffi

[flint forge]

dont do category theory from DF

if you wanna learn category theory

Riehl is just too good

jhu please let me work w her shes an icon

[sterile pelican]

hungerford? I recall seeing a section on his grad text

(I am currently only going through herstein's topics of algebra so no category theory for me yet)

though after herstein what would you recommend as a first exposure to analysis?

or somewhere along the lines of learning differential geometry

[gray gazelle]

differential geometry.....

do carmo

[sterile pelican]

prerequisites for do carmo?

[gray gazelle]

which do carmo book

[sterile pelican]

the one you stated for differential geometry

[gray gazelle]

curves and surfaces?

[sterile pelican]

unless there are more than 1 of them like Spivak's legacy

Yeah Differential Geometry of Curves and Surfaces

[gray gazelle]

for curves and surfaces i would say you only need some basic differential MVC as well as linear algebra. some familiarity with ODEs would be nice but not too much is needed for the classical DG material, i'd think

a lot of things in DG are described by differential equations so it helps to be a bit familiar with them

idk specifically what do carmo's curves and surfaces book needs outside of mvc and la

[sterile pelican]

hmm should I learn Spivak's manifolds first or apostol's calc vol 2?

[gray gazelle]

i don't know much about apostol's book but i think spivak has everything you'd need for DG

spivak CoM is basically an intro to DG

(i am biased towards it, it's one of my favorite books)

[sterile pelican]

I like it too

but given I only have herstein atm I should learn some of it soon

Spivak is relentlessly clear so I guess that is the best place to start

for linear algebra I guess H&K or Axler will do

[gray gazelle]

spivak's CoM reviews basic LA stuff in the beginning

[sterile pelican]

Oh really?

[gray gazelle]

yup

not in much depth but it's something

[sterile pelican]

but is that enough for the entire book?

it's like 1 chapter

upon reading it it does seem to cover all the essentials

here I thought I need Spivak's Calculus and some LA, now I realise I just need the first one

[gray gazelle]

any amount of linear algebra helps immensely

especially for the later chapters

maybe the first chapter isn't entirely sufficient

chapter 4 goes into multilinear algebra and chapter 5 does stuff on manifolds, both of which require a lot of LA

[sterile pelican]

oh then H&K it is

[gray gazelle]

those are part of mvc in my mind

[hollow jetty]

Do Do Carmo and Spivak CoM cover the same material?

[karmic thorn]

du-du-Carmo

[gray gazelle]

nah lol

that's spivak

[hollow jetty]

looks like vector calc + differential forms.

Spivak has a five volume beast as well, yeah?

[gray gazelle]

yup

[sterile pelican]

with some interesting covers

[wooden sparrow]

Spivak has 5 books?

[gray gazelle]

he has a 5 volume differential geometry series

[heavy garden]

Isnt vectors mostly physics?

THANKS FOR ANSWER

[stray veldt]

[valid moth]

@heavy garden

[heavy garden]

You make me sad

I know its math but don't you use them for physics like measure speed and acceleration

WTF

Stop

[stray veldt]

you use vectors in physics, yes

vector spaces appear everywhere, so

[wise vine]

Chapter 1 of Artin's algebra is so dull kek. The rest is really fun to read and has a lot of good problems. But I still feel that I lack some LA background.

[obsidian valley]

Isn't chapter 1 of every book dull

[gray gazelle]

Can I study analysis by terry tao, if I am hood with Calc?

Studied Calc from Thomas calculus

[stray veldt]

hood?

[obsidian valley]

good

[static crest]

I found the organization of Artin to be weirdchamp

idk, maybe it works

but I didn't like it

[wise vine]

Perhaps. But the presentation about the matrices bored me to death lmao.

[obsidian valley]

I thought the general advice was to skip Ch1 most of the time

slash skim

[static crest]

matrices -> surface level group definitions -> vector spaces -> linear operators -> symmetries -> return to group theory? -> other stuff -> group theory again

artin's flow really was interesting

[karmic thorn]

Yes.

[fossil island]

Thoughts on Conceptual Mathematics: An introduction to categories by Lawvere and Schanuel? Using it for exactly what the title says. https://s3.amazonaws.com/arena-attachments/325201/2ff932bf546d8985eb613fccf02b69c7.pdf

[sudden kindle]

I picked it up

But never really read it

It seems like a good book for a cpurse

[drifting elm]

looking for a first book on the subject, Stephen Abbott Understanding Analysis better than Walter Rudin The Principles of Mathematical Analysis?

[static crest]

first book? ya prob

[karmic thorn]

Abbott is better than Rudin for intro, I guess.

[static crest]

rudin is pretty difficult

if you think you can manage the difficulty level though, rudin is better

[drifting elm]

I want super easy mode

fluffed up with examples

[static crest]

terrence tao analysis is also good in that case

[karmic thorn]

Although Amann-Escher is definitely worth checking out.

[static crest]

you don't even need much knowledge of proofs

for tao

[karmic thorn]

Or Tao. Or Pugh.

[static crest]

lol isn't pugh hard

[drifting elm]

I'm not sure I want to get distracted with proof writing right now. just need to understand analysis so I can read it.

[karmic thorn]

I've heard it's great for intro. Didn't go into much depth but it looked promising from the little bit I covered.

[drifting elm]

I will do proofs with logic books anyway

[static crest]

I haven't looked at pugh, so idk

tao is just a good intro analysis book

[karmic thorn]

Then Abbott should be fine. Tao takes time on building number systems, although you can skip that bit and you'll be fine.

[drifting elm]

I am not doing this for school just for my own study

abbot does that also

so they must be equivalent

[karmic thorn]

I'm using Tao for studying analysis on my own as well. It's a friendly read for self-learners.

Amann-Escher is largely self-contained as well.

[drifting elm]

ok thanks everyone for the suggestions

[karmic thorn]

Any suggestions for expository articles on combinatorics, group theory or analysis(all three geared towards fresh undergrads, if possible)?

[gray gazelle]

expository articles
you might find something here https://kconrad.math.uconn.edu/blurbs/

[flint forge]

wdym

by expository articles?

[velvet briar]

We can recommend many pdf books haha

[flint forge]

expository articles turn into textbooks once theres enough exposition, i feel

so for older (lower UG classes) subjects, textbooks are probably what you want?

[karmic thorn]

Uhh I actually feel a bit overwhelmed dealing with textbooks by the evening, but can still use that time to explore stuff I learn from books maybe in more depth, or from different perspectives.

Kinda looking for them so I can kill time but productively.

[static crest]

just print a section of a textbook

[flint forge]

ah

maybe like

Terry Tao's blog?

[static crest]

and pretend it's a single article

[flint forge]

John Baez has a decent blog

[polar tulip]

@karmic thorn it's ok to just give your brain a break too, no need to make every second productive

[karmic thorn]

Oh, okay. Will take a look. Also, thanks @gray gazelle !

[polar tulip]

you'll work better that way anyway

terry tao does have some accessible posts on his blog occasionally

most wouldn't be tho

[gray gazelle]

occasionally

evan chen has a decent blog

if walrus says evan chen i'm gonna fucking scream

god damnit

[polar tulip]

very occasionally lol

[gray gazelle]

it is actually good though

[static crest]

whomst is evan chen

[hasty turret]

Is there anything wrong with evan chen?

[static crest]

why is he so popular

[karmic thorn]

I just feel I'm not moving fast enough through the books. :3 The least I could do is to reinforce what I learn from the books in greater detail.

[hasty turret]

He wrote a book on olympiad geometry

[gray gazelle]

napkin author

https://usamo.wordpress.com/

[polar tulip]

@karmic thorn like this tao article and a lot of the stuff linked in it is probably of interest to you https://terrytao.wordpress.com/career-advice/work-hard/

[karmic thorn]

I guess I might have read this before, I do admire Terry's blog haha.

[polar tulip]

basically the "career advice" stuff has lots of meta advice about doing math

[karmic thorn]

I see.

[polar tulip]

in this article that last paragraph is super important imo

[karmic thorn]

I'll revisit this article.

[polar tulip]

i didn't understand that for way too longer personally

[karmic thorn]

Thanks, will take a look. 😄

[karmic thorn]

Aah, the last para resonated with my HS burnout experience.

Hmmm, I should probably not push myself. I just feel compelled to keep doing math because what lies ahead intrigues me, and I want to get there quick.

[polar tulip]

extremely understandable

but you have to live with the fact that it's gonna take some time, and you really can't rush it

[karmic thorn]

True. As a self-learner atm I often feel I'm not moving too slowly. Learning feels tough, I'm stuck on some problems for hours(sometimes days).

I wonder how things will change at uni.

[lusty jacinth]

Isn’t uni mostly studying outside of the class

[marble solar]

It is, but if you do 10 problems a week for 10 or 16 weeks for 3 to 4 classes a term

Let's say it's 10 week course, 10 problems a week, 3 courses a term that's 300 problems per quarter

so about 900 a quarter just in homework

900 a year*

That's like near impossible to do on your own

[karmic thorn]

When you say 10 problems a week per subject for 3-4 different subjects, what sort of problems are you talking about @marble solar ? The ones which can be solved based on what I've learnt, or trying to figure out proofs of more important theorems(which I find generally tougher)?

[marble solar]

It's usually a mix of both

standard routine computations + complicated proofs

Examples, counter examples, easy ones that just develop comfortability with notation/sets/theorems

Depending on the level of the class

[karmic thorn]

I see. 10 problems a week for each subject doesn't sound bad, but for 3-4 subjects it could be overwhelming eventually.

[marble solar]

Welcome to upper division/graduate school

how may I help you

[hearty steppe]

Depends on the level of the problems

[karmic thorn]

I just hope I get a hang of things. I would not want uni to be HS 2.0

[marble solar]

It's definitely not, there's little to no busy work once you hit upper division

[karmic thorn]

I see.

[fossil island]

I know this is more of a math discord, but it seems like many people have done algorithms. So, thoughts on Introduction to Algorithms by Cormen, et al for a first course in algorithms and what about its mathematical rigor? (https://edutechlearners.com/download/Introduction_to_algorithms-3rd Edition.pdf)

[static crest]

yes

CLRS is one of the best

for intro to algos

I'm actually reading it right now lol

you don't require much mathematical basis

but it's very thorough

in proving the theorems and algorithms it does

it's about as complete an intro algos tb can be

(it's also extremely long, so do beware, to do all of it, will take multiple semesters worth of effort)

[hearty steppe]

Yea that’s a good book and you don’t need much math rigor to get thru it

[ripe granite]

does anyone have an opinion on modern classical homotopy theory by Jeffrey Strom?

yes, it does have a weird name

[gray gazelle]

Hello, is anyone familiar with Mathematical Analysis I by Zorich? I am looking for a first analysis book

[static crest]

not familiar with that

but tao is good

for a first analysis tb

[gray gazelle]

Tao looks good, I was looking to get ahead for my course in spring though. I was not sure if Tao would be of much help, since I heard it is a bit unorthodox

[fossil island]

yeah when i told my professor that Tao introduces cauchy sequences before regular sequences he was confused

[cobalt arch]

Is jech a good intro book to axiomatic set theory? Is the book self-contained?

[sterile pelican]

you talking about Jech's Introduction to Set Theory or his Set Theory book?

[cobalt arch]

The latter

Anyone?

[sterile pelican]

The latter is a graduate level text so it would be better to read Jech's Introduction to Set Theory first

[cobalt arch]

What are the prerequisites for the graduate text?

[sterile pelican]

read Jech's Introduction to Set Theory

[cobalt arch]

Okay

Are the prerequisites, for the latter book, covered in the former one?

[sterile pelican]

It is best to read that first

[gray gazelle]

😯 thumb reveal?

that blue-yellow mix

[sage python]

tfw doxxed

[velvet briar]

Finally, the thumb tracking software I've been developing for years can meet it's full potential!

[heavy garden]

Its swedish flag!

[static crest]

I'm using my wall tracking software instead

I'll have your location in no time

[sudden kindle]

People use figure prints to track people

So why not thumbs

[blissful pike]

Can anyone recommend a rigrous proof based Probability Book

[sage python]

The standard seems to be Durrett

https://services.math.duke.edu/~rtd/PTE/PTE5_011119.pdf

[marble solar]

Just read stein and shakarchi volume 4 chapter 5

[sage python]

Jesus christ lol

[marble solar]

I mean if you want a rigorous introduction ; )

[past yew]

Hey

Moonbears, how do I formalize the notion of a strand in terms of a curve

[marble solar]

uh I'm in trouble now

[dapper root]

use a different channel

pls

[marble solar]

It has to be in relation to the diagram

[past yew]

Sure, sorry

[blissful pike]

@sage python any other good books

[sage python]

Uh I've heard of one which might be easier lemme find it

[marble solar]

Probability for dummies

[sterile pelican]

How about Feller's Introduction to Probability Theory & Its Applications?

[sterile pelican]

What are the prerequisites for Tao's Analysis? I understand from the #books-old section that Calculus is not strictly needed, my assumption is hs Calculus not Spivak or Apostol, but is hs maths and proofs sufficient to try out the text?

[fast portal]

I mean

Tao's Analysis starts from 0

Literally

introduces peano axioms

gives you proof writting

and proceeds as expected

It feels like it has no prequiste

[sterile pelican]

then it goes all the way to multivariable in volume 2?

That is quite the feat

[sterile pelican]

Wow this is really accessible

[marble solar]

@fast portal that's not true, he starts with a justification for analysis

Going over examples and counter examples of when you can swap limits

[fast portal]

I feel like that is needlessly pedantry

[sterile pelican]

Hmm

This might be a good book to have

[marble solar]

Hrm? Starting there?

IDK it seems he outlines the pre-req is calculus

[sterile pelican]

I mean just in general I just read the pdf

[marble solar]

It's good, but Terry's writing is a little dry

[fast portal]

Like yes that is true but it says right here he started from natural numbers

[marble solar]

Seems like it starts at the introduction

:/

[fast portal]

Hence why I said that is true but that isn't where you start rigorously learning mathematics

And that is the beginning that really counts imo

[marble solar]

I tend to disagree, he gives a motivation for why one should do rigorous mathematics

before doing it

To that end, Spivak actually begins there and is overall a better book

I think Terry spends too much time building all of this up

[molten wave]

if you're new to it it might be a good thing

[sterile pelican]

That is true but even he explicitly stated from the book but it may be a good first exposure

[molten wave]

any intro to proof looks ridiculous from the perspective of knowing mathematics

how can you have an entire book of problems about induction

[sterile pelican]

especially for self studies as one does not have the benefit of a professor at all times

[quick hornet]

how can you have an entire book of problems about induction
all of elementary number theory is just applications of the division algorithm, which is induction

so

:^)

[this statement isnt even really false TBH]

[marble solar]

Ok, so in my experience this approach by Terry would be good if Spivak's Calculus didn't exist

But it does exist

[quick hornet]

[there are very few sophisticated statements in ENT which dont rely on the division algorithm at some point]

[marble solar]

So :?

[quick hornet]

[perhaps zeta function stuff being the main exception? if that even counts as ENT]

[maybe quadratic reciprocity?]

[marble solar]

There's just no point in doing all that much in a first course of analysis

[quick hornet]

moonbears take:

[marble solar]

I think the point is to get to differentiation, integration, fourier, and PDEs

[quick hornet]

cover it all and only test on the easiest 80%

that way, in learning more than necessary

[marble solar]

huh?

[quick hornet]

students get really good at the basics

trust me this totally makes sense

absolutely no problems whatsoever

[marble solar]

What?

My point on the 50 minute analysis exams I had was I shouldn't walk in and see 3 or 4 problems with new material defined on the problem

[quick hornet]

¯_(ツ)_/¯

[marble solar]

That uses a technique + something I have to invent to work on

[quick hornet]

is that really what you were given?

[marble solar]

Yes

[quick hornet]

i dont think thats a problem of tao in any case

[marble solar]

The averages were in the 20s

out of 100

[quick hornet]

yikes

[marble solar]

The first half of my take home complex analysis exam was giving a topologically correct proof of Riemann's Open Mapping Theorem

Which was based on the professors colleague published paper

The second half was intro to theta function over lattices?

I just really don't see the point in building up from the naturals in an upper division analysis course

Freshman honors/sophomore honors calculus?

Sure

[quick hornet]

wait maybe im confused

tao's target audience, at least the first dozen or so chapters

[marble solar]

Junior year analysis at UCLA

Math 131AH/BH

[quick hornet]

really?

[marble solar]

Yes

[quick hornet]

thats junior yeaer

??

huh

[marble solar]

Yes, that's how they teach 131AH/BH

[quick hornet]

and yet they give you wild ass exams

thats

bizarre

[marble solar]

Yes.

[quick hornet]

i thought tao was intended for like

freshmen maybe sophomores

[marble solar]

No, it's for juniors

[quick hornet]

maybe the number 131 misled me

but still

im surprised

[marble solar]

Yeah 100 = upper division

He based his notes on the honors version of undergrad analysis at UCLA

Now whenever they teach 131AH they start out with N and the induction

You spend a week or two just doing that

And then you get hit by topology in 2 days

[quick hornet]

yeah that seems really weird for a junior level course

[marble solar]

Now you understand my take on this text?

I prefer Pugh or even Rudin to this, although Tao's book is a good supplement

Since there is insight in there

[sage python]

Igor Kriz smh

[marble solar]

I'm not a huge fan Dami

Maybe if I actually TA'd a course with it my opinion would change

[sage python]

Not fond of ]a,b[ for (a,b)?

😛

[marble solar]

But namington, I don't have bad opinions on these things. I have pretty good reasons

je detest France, ils sont bete

[sage python]

But yeah idk the writing or problems I'm mostly drawn to it for topic selection lol

I was like yeah man imagine if there was Rudin but actually treated Lebesgue integration and differential forms well

And whoa okay there is, and also it does extra stuff

:0

But yeah it's possible that the writing/problems aren't as good for sure

[sterile pelican]

I mean for self-study like me it would be good to go a bit slowly, albeit with more narrative, I am not sure what was the book originally for but as someone who self studies it might be a good book in conjunction to books like Spivak and all.

[marble solar]

Yeah, I think it pairs well with Spivak in particular or Pugh

[sterile pelican]

I am not exactly looking for something like Rudin, though it is the gold standard and I aim to read it, but it is more a sequel rather than a replacement of the such. Surprisingly I did not expect the book to be meant on the same level as Rudin and all.

[marble solar]

Rudin is antiquated

[lusty jacinth]

https://www.youtube.com/watch?v=pTnEG_WGd2Q

thought this was worth sharing here

¯_(ツ)_/¯

[karmic thorn]

Huh, Terry's text is probably one of the most engaging ones I've ever read.

[marble solar]

Yeah, his stories or intro is great

but when he does the math part its where he loses me

maybe I'm too smol brain for him

[karmic thorn]

His Analysis text is probably the best first book a math undergrad should pick up right after HS.

[marble solar]

It was like that when I was in his lectures too

i.e. I didn't get the point and got lost in his detail

[karmic thorn]

Hmmm, I really haven't gotten to the 'real' math in his Analysis text yet, but he does leave a lot to exercises haha.

[hasty turret]

Maybe,You just didn't get time to get used to the material,during the lectures

[marble solar]

Quite possible, also I hate quarters

[static crest]

Ah this is cursed

[gray gazelle]

I’m trying to buy Lev Beklemishev’s mathematical logic book “Provability, Computability, and Reflection”, but every site that claims to sell it is really selling a completely different book, it seems to be some kind of glitch involving its ISBN number or something. Can someone help me find the book?

And no two sites that claim to sell it are selling the same book as each other. Each site is selling an independently randomly chosen logic book while claiming to sell the book I want. It’s a really weird glitch.

[hasty turret]

Just libgen

Ok,libgen doesn't have that book

[wooden sparrow]

Zlib?

[prisma snow]

Amazon says it has one copy left. How do you know its a different book?

https://www.amazon.com/Provability-Computability-Reflection-Foundations-Mathematics/dp/0444854029

[gray gazelle]

Here is the thing: that’s not an actual book cover, that’s a mock-up cover that Amazon creates when it doesn’t have a picture of the book cover. And the thing is, every site/listing which claims to have the book and shows an actual cover actually shows a cover of a completely different book. So I’m distrustful of listings that don’t even show an actual cover.

[prisma snow]

I trust Amazon not to give you a completely wrong book. And you can get a refund if it's really wrong.

[gray gazelle]

@prisma snow Well, Amazon is also selling the same book in other listings with wrong covers and the wrong book when you click search inside. So clearly there’s something not to trust.

[karmic thorn]

Have you checked the reviews?

Ah, no reviews on Amazon.

[prisma snow]

If you can't find it anywhere else, it's worth a shot

[static crest]

Amazon has sent me wrong things (just yesterday actually)

[gray gazelle]

Why does amazon always have 1 left in stock

[cobalt arch]

Is there a complete solutions manual for spivak's calculus, fourth edition?

[prisma snow]

Yes, in your brain

You just need to put it on paper

[cobalt arch]

Project my 3d brain onto a plane you mean? That is hard work:).

[gray gazelle]

it's simple linear algebra

[cobalt arch]

[prisma snow]

Yes, it is hard work. But sadly the inverse is useless. Mapping from the solutions to your brain, I mean.

[subtle torrent]

do someone uses python ?

[prisma snow]

I have used python but I have forgotten all the syntax, and there are definitely other people who have. So what's your question?

And if it's not related to books, ask it elsewhere

[gray gazelle]

there is

[cobalt arch]

My man

[gray gazelle]

but I would recommend that you don't use it

[cobalt arch]

:(

[prisma snow]

Alex is trolling you. They also mean the one in your brain.

[gray gazelle]

I'm reading spivak rn and I absolutely hate it when I can't stop myself from peeking the solution

[prisma snow]

Indeed, but there's nothing wrong with peeking in your brain for the solution

[cobalt arch]

That is if you have a brain

[prisma snow]

If you have no brain, just give up

[cobalt arch]

I don't have one

[prisma snow]

Then I am impressed by your imitation of someone with a brain

Brava

[karmic thorn]

The point here is to struggle through Spivak, for that will actually help you learn. Having a solution manual at bay will make you lazy and tempted to peek at solutions, harming the process of learning.

The better thing is to ask for hints whenever you're stuck.

[gray gazelle]

I deleted my solution manual because of exactly this reason

[prisma snow]

^ which is why you're lucky, there is no solution manual except for the one in your brain

[cobalt arch]

Luna I know you are being sarcastic:)

[gray gazelle]

ignore him

[prisma snow]

Rude :(

[cobalt arch]

Apparently I didn't know the gravitas of this word. My apologies Lunasong.

[prisma snow]

Lol, I was saying Alexander is rude, not you

[hollow current]

hi luna

[prisma snow]

Hi

[hollow current]

wotsup

[prisma snow]

It's sad your username doesn't render as latex

[static crest]

@hollow current

[hasty eagle]

PorosInMyAshe

[static crest]

does when you @ them

(sry for ping)

[prisma snow]

Cool

[hollow current]

[static crest]

you're not a mod stay bad

😎

[hollow current]

but i am commander vimes

and you are arrested in the name of law!

[static crest]

[rocky owl]

Looking to solve a set of coupled ODEs with the finite difference difference method

my boundary values are on y, and i'm aiming to extract theta(0)
anyone know some good resources to get started on this?
keywords are nonlinear coupled ODEs, finite difference

[static crest]

#❓how-to-get-help

man just read the damned channel lmfao

[gray gazelle]

[pine igloo]

🤔

[rocky owl]

good lord the help channel says "The help channels are solely for help with math" right at the top

this isn't maths

this is a request for a good book on numerical methods

[gray gazelle]

poros see question, poros go #❓how-to-get-help

[static crest]

it's true

my brain is a finite state machine:
state 1 -> see question -> post #❓how-to-get-help -> go to state 1

[hollow current]

@static crest
?

[static crest]

#❓how-to-get-help

[hollow current]

?

[static crest]

#❓how-to-get-help

[hollow current]

help me do hw pls!

[gray gazelle]

@static crest @hollow current both of you read the fucking #❓how-to-get-help

[hollow current]

@gray gazelle no u read the fucking #❓how-to-get-help

[gray gazelle]

ok ty

[hollow current]

i do read #❓how-to-get-help every second

[gray gazelle]

i posted in questions alpha

[oak rivet]

From

#❓how-to-get-help

Rule 3

Stick to one channel and don't post the same question in multiple channels. Please don't ask for help in other channels if no one is responding in the one you have posted your question in.

[calm crane]

idk much but ik jacksons electrodynamics had quite good numerical resources in the references of the first 2 chapters, idk if it is the usual books those you prob should ping phys server

[cobalt arch]

Anyone here that has read both of jech's texts on set theory?

[calm crane]

isnt the naive set theory or smt a subset of the set theory🤔

[cobalt arch]

What does smt stand for?

[calm crane]

somethihng

[cobalt arch]

I thought so

Yeah it is

I would like to know if there is any overlap between the two texts and if so where it begins.

[calm crane]

iirc the overlap was that the easier book covers like 30%ish of part 1?

[cobalt arch]

I think it covers some ground that the graduate text doesn't even gloss over. I believe that around 2/3 of the easier book has overlap with the harder one.

[spice sparrow]

any book suggestion, good book on multilinear algebra ?

[drifting elm]

taken from a syllabus I found online, Linear Algebra for Calculus james stewart

[spice sparrow]

not great, can't even find it online, and by its name, it seems to be a first course

yeah it is a basic book

[hasty turret]

You might get something out of hofman kunze

He has a chapter on tensors

[spice sparrow]

yeah, but that is quite limited

i have seen introductory books, axler, hoffman, friedberg/insel/spence , strang (useless)

[hasty turret]

Try a big algebra book,ig

https://math.stackexchange.com/questions/266848/any-suggestions-for-abstract-algebra-multilinear-algebra-books

[karmic thorn]

Do the three volumes of Amann-Escher contain all of analysis that courses at the undergrad level would cover?

[thick thicket]

for an average undergrad curriculum? those books cover more than that

[drifting elm]

from amann-escher's first book "The axiomatic foundations of
logic and set theory are beyond the scope of this book"

I have a book on axiomatic set theory already

but it does not cover godel at all

https://www.amazon.com/Axiomatic-Theory-Dover-Books-Mathematics/dp/0486616304

do I need anything else?

I have this https://www.amazon.com/first-course-abstract-algebra/dp/0201168472

[daring reef]

has anyone looked through this by any chance? https://web.evanchen.cc/napkin.html

as someone who's just getting into upper-div university math, it looks pretty cool

[calm crane]

yes

it is garbage

i dont rlly like it lol

looked at it once heh

try like

proper intro books

honestly i find se intro to xxx books ans quite good usually

then just download like 5 of them and see what you like

[sterile pelican]

what is your goal and what level are you at?

[daring reef]

idk what my goal is

as for level im about to finish a proof-based linear algebra class and have basic familarity with real analysis

damn i was kinda excited

[calm crane]

should just touch random areas of math and get even more lost at what your interest are like me

[daring reef]

oof

im not even a math major so am also going through an identity crisis

[calm crane]

oh ooft

if want recommendations can check out like point set topology and some abstract algebra

[ripe granite]

algebra helps with that, guaranteed identity element

[calm crane]

heh

[daring reef]

lol

[calm crane]

just skim nlab

[daring reef]

ah that makes sense

formally study something as in just chug my way through a textbook on it?

[calm crane]

like jus read first few sections/chapters of a textbook

course seem like too much dedication to me

my interest swings every month so if i take a course on func anal then next month decides im not interested im screwed

[daring reef]

when do you feel like you know enough about something to say "this is what im interested in"

[calm crane]

hopefully inb4 i become a doctor

i know im lying

[daring reef]

doctor

imagine being useful to society

ok

i was going to take analysis next quarter but all the classes are full ;–;

[warped cedar]

[daring reef]

dimensional analysis

[warped cedar]

[calm crane]

dimensional analysis is the true imposter

[daring reef]

i remember learning it thinking it was gonna be cool but nope tis just canceling out units

thats what im banking on

people usually do but idk if remote classes might have lower drop rates or something

[static crest]

but dimensional analysis has real theorems too

buckingham pi theorem

[drifting elm]

I tried to google m^-1 but got nothing

then I figured out out. the unit was in the denominator

[daring reef]

doesnt anything have theorems

[drifting elm]

this is how they write it on one line

[sterile pelican]

business analysis is fake analysis 🌝

[drifting elm]

my chem teacher never told us

we could do all our dimensional analysis problems without fractions this way. what a wonderful way.

back on topic though. I never realized before how good this book was till I got better at number theory https://www.amazon.com/Topics-Number-Theory-Volumes-Mathematics/dp/0486425398/

the book is so fast you need to work it all out slowly

like I could spend a day on 6 pages of this book just playing with proofs

[warped cedar]

do you guys have any good websites that sell used books

i know where to find the pdfs

but i dont want pdfs

[timber mesa]

search on bookfinder.com, it'll show you the cheapest providers and you can find very good deals on used books

I've bought quite a few, with cheap intl. shipping even

[warped cedar]

awesome

ty

[gray gazelle]

I use abebooks and ebay

[pure shuttle]

vialibre @gray gazelle is also good for unearthing old texts

[sterile pelican]

I found a lot of treasures from bookfinder like Bellman's Inequality and Coexter's Geometry revisited

[civic python]

I was thinking of heading into linear algebra, i have been reading axler langleys "linear algebra done right". I have no background in reading or writing proofs nor linear algebra, should i try to find another book on the subject? I try to do the excersizes(proof based), but i really can't tell whether or not i have correctly solved the excersizes.

[sage python]

I don't like Axler because he teaches you to think about a lot of things the wrong way

People seem to like Linear Algebra Done Wrong

Which I think is designed to be introductory too

[hasty turret]

Any good answers to this?

[marble solar]

Schaum's outline to Linear + Schaum's outline to tensor calculus @spice sparrow

[spice sparrow]

Thanks Drunken Drake. Thanks MoonBears-C- , I wiil look over it.

What I found out, after searching on internet, some books covering the topic in great detail which others told me about are, I am putting it here, in case anyone needs: 1. Advanced Linear Algebra - Steven Roman (seems to have a good discussion on tensor products) , 2) Multilinear Algebra - Greub, one of my seniors recommended it , 3) Linear Algebra Via Exterior Products -Sergei Winitzki ( a lot of people are saying this is a good book) - as its name, it covers linear algebra in different way than traditional, etc.

[sterile pelican]

I wanted to recommned Hoffman & Kunze but one would need a background on proofs. One that I hear a lot is Strang's Linear Algebra book, or the one from Anton.

[spice sparrow]

I will look over Hoffman's determinants chapter again as well since so many people are recommending it, although it seemed a bit elementary to me on first reading

[sterile pelican]

I mean it is before Roman, I would like to read Roman at some point in time

[cobalt arch]

An introductory book on logic that is rigorous?

Something akin to enderton's logic but more rigorous

[spice sparrow]

@cobalt arch I have heard of Mathematical Logic, - H.-D. Ebbinghaus ..... is good

mathematical logic - Stephen Cole Kleene,

[cobalt arch]

Which one is better?

[spice sparrow]

well how about seeing both of them, I haven't read either, so I can't say

[cobalt arch]

I see thank you

I have found a guide to logic for those interested I will post it here.

https://www.logicmatters.net/wp-content/uploads/2020/07/TeachYourselfLogic2020.5.pdf

A very thorough guide

[obsidian valley]

What rigour was lacking in Enderton?

it's shallow on some concepts maybe

[fossil island]

Thoughts on Numerical Mathematics and Computing by Cheney and Kincaid? (http://134.208.26.59/NM/電子書/BOOK6.pdf)

Also, thoughts on A First Course in the Numerical Analysis of Differential Equations by Iserles ? (http://read.pudn.com/downloads679/ebook/2742932/A.first.course.in.the.numerical.analysis.of.differential.equations,.Iserles,.2ed,.CUP,.2009.pdf)

[silk quartz]

You'll likely get more informed reviews on the Physics server.

[fossil island]

Thanks

[plucky rose]

looking for a book that explains conic sections in a level similar to the math discussed here http://www.andreasaristidou.com/publications/papers/FABRIK.pdf

[drifting elm]

any calc 3 book

@plucky rose

[gray gazelle]

Advanced number theory books recommendation ?

in particular it should have topics other than what was already in hardy's intro to nt

[marble solar]

Tao's notes, Ergodic theory book, intro to probabilistic number theory

[gray gazelle]

tao's notes?

[marble solar]

Ya

254A?

Analytic prime number theory

[valid moth]

@gray gazelle what does hardy cover

[gray gazelle]

@valid moth

alot

[gray gazelle]

wdym

[marble solar]

Ya analytic prime number theory tao

254a

[gray gazelle]

guess I'll study some more algebra before ergodic theory

or any other nt book

[valid moth]

im not sure how much algebra they know right now

[gray gazelle]

my analysis ass knows only little algebra

[marble solar]

Algebra is ass

[gray gazelle]

as they say, shouldn't an adult know to eat their vegetables

[marble solar]

Well, y'know algebra sux

[gray gazelle]

Moonbears u a grad student?

[marble solar]

yA

Well in a morally grey area. I basically have my Masters degree in Math

I'm applying out for PhDs now

I know it doesn't seem like it cuz I'm mostly a math potato

[hasty turret]

Wdym morally gray?

[ripe granite]

moonbears will your phd be shorter as you already have a masters or the usual length

[marble solar]

It's hard to say. It all depends on where I get in and who wants to work with me

I can pass most doctoral quals with a summer of studying

[grave egret]

Any good books on topology? I'm just starting with topology.

[marble solar]

Munkre

[grave egret]

What are the pre-reqs?

[marble solar]

If I get into Davis, SB, Or Irvine I think I can finish I'm a little over 3 years of i bust my ass

[hasty turret]

Would study of continuous functions be topology or analysis?

[marble solar]

It could be Algebra

Rings of continuous functions

[hasty turret]

What does topology deal with?(As in main objects of study)

[marble solar]

Continuous functions on sets

[warped cedar]

continuity except its in space

[grave egret]

I mean it was in rudins real analysis book under the topology chapter sooooo...

[gray gazelle]

Arrows from spaces to spaces

[plucky rose]

@drifting elm can you recommend one?

[drifting elm]

now that I started reading the paper you posted, I want to change my answer

this paper is %90 inverse kinematics

you would want a book on robotics and inverse kinematics

but the paper also has statistics, graph theory, algorithms, operations on a jacobian matrix

[cobalt arch]

Is the book on proofs by chartrand, polimeni and zhang good?

[drifting elm]

so this would be in linear algebra text book

@plucky rose

[cobalt arch]

Anyone that has read it?

[spice sparrow]

@hasty turret study of continuous functions, depends where are you doing it. You can study continuity of functions on R^2 , you can study continuous functions on topological spaces, manifolds etc. There is no end.

now saying that studying continuous functions is just analysis or topology, depends what and where you are actually doing it

there is a chapter in baby rudin on basic topology, I think it gives a nice preliminary introduction to the subject. But I am not sure if it is the best

[radiant pier]

Is there a book you guys recommend on learning calculus? Something that goes in-depth on the topic

[gray gazelle]

something that goes in depth on the topic
spivak

[radiant pier]

Thank you

[gray gazelle]

before someone else jumps in and says "you should have comfortability with computational calculus before doing spivak" ill say it's not needed but helps plenty

[radiant pier]

I had a realization that I now have to teach myself since I can't learn from professors

[radiant pier]

What's your review of the book?

Also would you suggest Apostol?

[fossil island]

there is something nice about seeing formulas that you sort of took for granted in computational calculus and then see how they all beautifully fit together

[radiant pier]

What's computational calculus?

[quick hornet]

calculus focused on, well, computing things

taking limits/derivatives/integrals

maybe some areas, volumes

solving kinematics problems or related rates problems or what-have-you

[radiant pier]

Ah, got it

[quick hornet]

this is usually as opposed to "proof-based calculus"

which focuses on, as you may guess, proving things

rigorous definitions of the limit, reasoning from definitions and theorems, proving propositions

there does tend to be a bit of overlap

"proof-based calculus" courses will still cover how to actually do calculus, naturally

though they'll spend less time on it

and "computational" courses might still touch on stuff like epsilon-delta proofs, or give a proof sketch of the big results like MVT or FTC

but there's a clear philosophic difference

[gray gazelle]

How is "proof-based calculus" different from analysis?

[quick hornet]

well "analysis" is an entire field of mathematics

but im assuming you mean like

intro analysis

if so, that kinda depends who you ask lmao

some people would consider them synonymous

those people would be likely to call Spivak an "analysis" text

others would consider intro analysis to be "deeper"

and spend little-to-no time on computations of any sort

whereas proofsy calc would still cover computations

the exact point where "the line is drawn" will vary from person to person

but it honestly doesnt matter too much

[wooden sparrow]

Bruh wait

@karmic thorn

[wooden sparrow]

I can learn calculus from intro to analysis right?

[mossy flume]

I'd imagine it'd be alot alot harder to learn analysis without knowing calc

[wooden sparrow]

Double dual said you can learn calc from analysis

[fossil island]

i mean it in the same sense as TTransport, just like calculus 1, 2

[karmic thorn]

@wooden sparrow

[wooden sparrow]

Bruh everytime it gets me anxious

Thanks

[karmic thorn]

Lol don't be so worried about things before starting, even if you were to study in a totally linear way, you'd still have to overcome several difficulties in understanding.

[wooden sparrow]

Okayy... It's just the fear of prereqs that gets me everytime

[karmic thorn]

Dw, it isn't like you're jumping to algebraic geometry or something lmao.

[mossy flume]

I think like having the computational and intuitive background might be helpful with analysis

But not nessessary persay

[karmic thorn]

I think learning the two in conjunction is possible.

[gray gazelle]

i should probably change back to terra

[mossy flume]

True

You can learn both at the same time

[calm crane]

i suggest if you're interested but uncertain just go ahead, you'll know if you are missing prereq and you will also know what prereq you need

[wooden sparrow]

Thanks Ari

[cobalt arch]

Is apostol's one-variable calculus less demanding than spivak?

[karmic thorn]

Definitely.

[cobalt arch]

Do they cover the same ground?

[karmic thorn]

Spivak is more challenging on the problems front, but I guess the contents covered are more or less the same.

[gray gazelle]

spivak's problems

[plucky rose]

i want a book specifcially for the conic sections part of the paper

i dare say i'm ok with the other parts

[cobalt arch]

I need some help with deciding what books to study from for three of my classes, below is the curriculum for each one of them:

Analytic Geometry:
Matrices. Matrix operations and their basic properties. Row-echelon form of matrix. Rank of a matrix. Transpose and inverse of a square matrix. Elementary matrices and elementary row operations. Equivalent matrices. Calculation of the inverse matrix by reduction to reduced row-echelon form.
Determinant of square matrix. Properties of determinants. Minors and cofactors. Finding the inverse matrix using determinants.
Methods of solving systems of linear equations. (Gauss method and Cramer method). Study of systems of linear equations. Homogeneous systems of linear equations.
Vector space. Vector operations. Linearly dependent and linearly independent vectors. Orientation of plane and space. Coordinate systems in the plane and in space (general, orthonormal and polar). Transformations of coordinate systems. Vector Algebra (dot products, cross products and mixed products and their applications in calculating areas and volumes).
Lines and planes in space (parametric equations, vector equations, equations of straight line as the intersection of two planes, Cartesian equation of a plane). Bundle of parallel levels. Bundle of planes intersecting at a line. Distance of a point from a line and a plane. Distance between lines. Orthogonal projections.
Surfaces of second degree.

Introduction to Algebra and Set Theory:
Introduction to Set Theory. Sets, naïve definition, description, subsets, power set. Algebra of sets. Infinite unions and intersections, examples (examples of subsets of the real line). Cartesian product. Binary relations, functions, composition of functions, one-to-one functions, reversible functions, line and inverse image of subset, lines and inverse images of unions and intersections. Equivalence relations, Equivalence classes, set-quotient, partitions, order relations. Countability, countability of NxN, uncountability of real numbers, algebraic and transcendent numbers.
Introduction to Number Theory.The set of natural numbers. Standard and strong induction, well-ordering principle. The Euclidean division, the greatest common divisor, the least common multiple, prime numbers, the fundamental theorem of arithmetic, equivalence relation mod n, equivalence classes and their algebra.
Introduction to the field of Complex Numbers. Complex plane, algebra and modulus of complex numbers, polar form and roots of unity.
Polynomials: Division, factorization, roots of polynomials

Calculus I:
Positive integers, induction, real numbers, operations, ordering, the concepts of supremum and infimum. Axiom of completeness, n-th root function. Sequences, increasing and bounded sequences, sequences that converge to their supremum. Algebra of limits. Series of numbers, geometric series, absolute convergence, ratio test and n-th root test. Definition of e, exponential and logarithmic function. Limit of a function, continuity of a function, algebra of limits and continuity of functions. Intermediate value theorem, derivatives, algebra of derivatives, geometric interpretation, differential, Rolle’s theorem, mean value theorem, monotonicity, extrema, convexity and graph of a function.

I am sorry for the long messages

Anyone that can help me out, it would be greatly appreciated.

[obsidian valley]

Analytic geometry just use Axler linear algebra probably

Calculus 1 idk use Apostol or something

Idk about the second one it's pretty broad

[cobalt arch]

Yeah it has number theory, polynomials, set theory and complex numbers

does axler cover all of these?

[obsidian valley]

Axler is fine for the first course

[cobalt arch]

Like second degree surfaces?

[obsidian valley]

The second one idk just use a discrete math textbook or something

[cobalt arch]

hm

[obsidian valley]

Most of those are basic facts/definitions about sets

[cobalt arch]

Yeah

[obsidian valley]

So ch0/ch1 of most textbooks will cover

Like most of that is stuff you pick up in other math courses

if that makes sense

[cobalt arch]

I don't know about axler since it is more so la than analytic geometry.

or vector algebra for that case

[obsidian valley]

No

If the class is taught according to that description

it's literally an Axler class

lol

[cobalt arch]

oh lol

[obsidian valley]

even avoids determinant

[cobalt arch]

so it does cover second degree surfaces?

or parametric equations?

[obsidian valley]

peq are usually covered in like a calculus course or something idk

You won't be able to find a textbook that's specifically tailored to your course unless the course is based off a textbook

Just reference different stuff

[cobalt arch]

Yeah I guess

thank you jesse

[weary nymph]

I'm looking for a book that compiles a huge amount of [preferably solved] integrals. Can anyone recommend me a good book on the matter?

[obsidian valley]

Any computational calculus book

[weary nymph]

My knowledge is that of a twelfth grader studying late calc 1

[obsidian valley]

Are you doing AP calc or something

or do you just enjoy doing integrals

[weary nymph]

I don't know what AP calculus is about

But prolly yea

Both

I'm into calculating indefinite integrals atm

[obsidian valley]

Oh well if it was for AP calc I was gonna say just do practice exams but idk just go find any calculus book on libgen and go to the integration chapter

And then just use wolfram or differentiate to check your answer

[weary nymph]

Alright

Was hoping for one that goes exclusively into solving thousands of integrals

I've used one for trig identity demonstrations not too long ago. Trig or Treat it's title was. Very good book. Hundreds of proven identities.

[obsidian valley]

I will not judge how you choose to spend your time

[craggy glade]

for a beginner who wants to learn more about logic and model theory, where is the place to start?

[obsidian valley]

Enderton or Ebbinghaus

[sudden kindle]

https://www.springer.com/gp/book/9781493912773

[weary nymph]

" Stupendously Clever, Awesomely Wicked, and Devilishly Seductive Maneuvers for Computing Nearly 200 Perplexing Definite Integrals "

Looking good

Thank you amin

[sudden kindle]

np

i just googled book of integrals

[timber mesa]

it's a good book tho

[sudden kindle]

yep my friend recc'd it too

[lusty jacinth]

This is more directed to people who have taken actuarial exam P but is A First Course in Probability (Ninth Edition), 2012, by Ross rly enough for the actuarial exam? The SOA has it listed as a recommended text (https://www.soa.org/globalassets/assets/files/edu/2020/fall/syllabi/edu-10-exam-p-syllabus.pdf) but I’m just surprised by this as my AP stats course covers a decent amount of the material in that textbook.

[valid moth]

@fickle pond

you can account on steak to answer this question

[spice sparrow]

@sudden kindle there is a book , Problem in Calculus in one variable - IA Maron, it has some good problems

[fickle pond]

@valid moth acktually, I haven't taken that exam, I'm probably skipping it

[valid moth]

actuary?

[lusty jacinth]

Oh ok

[lusty jacinth]

Yes

[hearty steppe]

Don’t you have to at least take 5 exams

To have all the certs you need to be well paid actuary

[valid moth]

@lusty jacinth that was directed at steak

[hearty steppe]

Actuaries are just quants that usually get paid more if they have all the important certs

Hot take*

[drifting elm]

math scorcerer on youtube was recommending this for learning proof writing https://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0201710900

now I understand why people were in here asking about it.

5 stars on amazon

[hearty steppe]

There’s another one he suggested as well

[lusty jacinth]

I rly like Math Sorcerer

[hearty steppe]

Yea he’s really down to earth

[broken meadow]

i like that book

pretty chill with the writing

lowkey prefer it over hammack

i still haven’t looked at velleman but eh

at this stage i might as well move on

[sterile pelican]

Agreed, Chartrand goes over the proofs again on the review chapters and its proof analysis is something I would wish to see in Hammack (I did not read all of Hammack but yeah), another one I am looking at is Bloch's Proofs & Fundamentals a newer book on these transition books math books

[broken meadow]

mmm i see

[grave egret]

All books start with set theory I hate that so much. I feel guilty skipping it.

[hearty steppe]

Velleman is good but mostly set theory

[sterile pelican]

set theory is essential

but if one is very familiar they could skip it

[flint forge]

Almost no books start w set theory

Only like intro to proofs books afaik?

Or, obviously, set theory books

[fast portal]

Munkers starts with set theory

[drifting elm]

what is this ism?

[fast portal]

Probably the one written by Lee

[drifting elm]

introduction to smooth manifolds?

[fast portal]

yea

[sterile pelican]

baby Rudin has set theory :^)

herstein has set theory

[summer moth]

So I'm looking for a refresher on Algebra II so I can go into Calc. Are there any books or resources that do that?

[drifting elm]

https://spot.pcc.edu/math/orcca/ed2/html/orcca.html

start at the begging then skip everything you know

@summer moth

[summer moth]

Thanks! Funny that it's PCC as it's like 2 hours away. Lol

[drifting elm]

ORCCA provides the materials to many schools

this one has the best online interface for ORCCA that I have seen

[summer moth]

Oh nice! Well thanks a lot. :) I will make myself busy. XD

[drifting elm]

@summer moth before you enter calc 1 you will need to be %100 on trigonometry. I paid for this for two months it was $10 total no subscription. it has practice mode and solver mode. it is the fastest way to review. https://www.symbolab.com/

[undone ermine]

Do you guys have a reco for Discrete Math books that are roughly beginner friendly?

[hasty turret]

Have you tried kenneth rosen's book?

[undone ermine]

not yet

i will check it out now

[drifting elm]

https://www.amazon.com/Schaums-Outline-Discrete-Mathematics-Revised-ebook/dp/B009SVX6NK

https://www.amazon.com/Problem-Solving-Reasoning-Discrete-Mathematics/dp/0974772488/

the second link here is more for proofs the first link is more for boolean algebra

[summer moth]

I would totally do that, but currently have no money. I'm mainly just trying to get ready for college next year.

[drifting elm]

then do this for free https://www.mathsisfun.com/algebra/trigonometry.html

[undone ermine]

seems very promising

thanks!

[drifting elm]

https://www.mathsisfun.com/algebra/trigonometry-index.html

[summer moth]

Thanks! Also just curious, I know a bunch of people learned trig in alg 2, but my school did it in geometry. Is that weird?

[drifting elm]

my HS did algebra 1 then geometry 1 then trigonometry 1

[mossy flume]

I did intro to trig in geometry

And then trig hit hard in Alg 2 + Trig and also in Precalc

[drifting elm]

but in college algebra II is something completely different than high school algebra II

[mossy flume]

Algebra 2 + Trig at my HS went from the end of geometry all the way through conics

Which was alot of material >_>

[drifting elm]

conics in HS I feel bad for you

[mossy flume]

Very fast class, precalc was more chill afterwards

Conics aren't bad

[drifting elm]

that should be at the end of calc 1 or the start of calc II

[mossy flume]

Learning conics fast is bad

Nah it was fine honestly just some if the word problems were wack

[summer moth]

Ahh. Okay. I only did a bit of conics in the very end of geom.

[mossy flume]

Or like finding equations of comics given a very very minimal amount of info

[drifting elm]

getting into related rates and eliptic curves if you do it right

that is all advanced

[mossy flume]

Oh we didn't touch that

It was just working with circles, ellipses, parabolas, and hyperbolas

[karmic thorn]

Equations of comics must be fun.

[drifting elm]

the elipses goes right into eliptic curves

[mossy flume]

Oop equations of conics

Never looked at elliptic curves

They're cool tho

I think I read about them in the context of cryptography

[drifting elm]

for reference https://mathworld.wolfram.com/Ellipse.html
https://mathworld.wolfram.com/EllipticCurve.html

[summer moth]

Oooh. Honestly I'm excited to start learning more math. I just have so much more stuff to get through till I get the more fun stuff like discrete mathematics. Since I'm assuming calc III is a pre-requesite.

[mossy flume]

At my college you can do intro to proofs concurrently with calc 3

[drifting elm]

be careful with getting sidetracked into discrete mathematics

[mossy flume]

Intro to proofs doesn't need calc knowledge until maybe the very end but even then not really

[drifting elm]

it covers a lot of sub topics

[mossy flume]

And it differs from college to college

[drifting elm]

if you do study discrete math think about why you want to do that and what you hope to learn exactly

[mossy flume]

Like in mine I'm doing intro to abstract algebra and also construction of number systems

But that's not common afaik

Some courses do other topics

[undone ermine]

did u guys have to learn the eccentricity, focus and directrix for conics?

[mossy flume]

Yea

[drifting elm]

that is number theory or analysis depending on what you are constructing

[mossy flume]

I don't remember them now but I remember learning them

[drifting elm]

abstract algebra is group theory

[mossy flume]

I mean we did stuff with like "prove this forms a (group monoid ring field)" and "prove this is a homomorphism/isomorphism"

[undone ermine]

the one where parabola (e=1), ellipse (0<e<1), hyperbola (e>1)

[mossy flume]

Then we did shit with well defined functions

[drifting elm]

all group theory exactly

which is also abstract algebra

[mossy flume]

Showing well defined operations in terms of rings and shit

relations and equivalence classes

But this is all in my intro to proofs class

[drifting elm]

yeah that is abstract algebra because group theory doesn't teach proofs

[summer moth]

Ooh. Okie. Good to know. And yeah, I want to go into more pure mathematics and proofs/logic type stuff. Unless there is a better branch of science than discrete mathematics for that?

[mossy flume]

After a healthy amount of set theory >_>

[drifting elm]

@summer moth that is the right branch but discrete math is so big it fans out to many things

proofs can also be considered meta mathematics or category theory

so it can balloon out to some huge stack of books very quickly

you have to put a limit on what you want for now

[summer moth]

Ahh. Okay. I'll keep that in mind. XD

[drifting elm]

if you want to get good at proofs you can read books on proofs that have mathematical proof writing in the title

[mossy flume]

I'm excited to take a course in abstract algebra but I have to take two sections of analysis first 😭

[drifting elm]

but if you read some abstract algebra books it may already have that in there

[summer moth]

Also "Meta mathematics" honestly sounds amazing.

And cool! I already read one from my library last year and it was a huge help. But I am planning on getting some more.

[drifting elm]

https://www.amazon.com/First-Course-Abstract-Algebra/dp/0201104059/

I got this when I was starting out

I didn't understand most of it

[calm crane]

what is your bacckground in math

[drifting elm]

then later I went back and it was too easy so both times it was not useful

[mossy flume]

I've never self studied a book but I plan on learning linear algebra at a computational and intuitive level before I get to my abstract lin Alg class next semester

[calm crane]

oh lmao

[mossy flume]

Abstract algebra is very cool from the little of it I've done

[drifting elm]

socratica videos on youtube have all the group theory

too bad she is just reading off a teleprompter

[mossy flume]

Is group theory just the study of just groups and presumably monoids?

[drifting elm]

she is a daytime tv actress from brazil

[mossy flume]

So no rings and fields and stuff?

If so that seems narrow

[drifting elm]

groups rings fields

[hasty turret]

I don't think you care about monoids in group theory

[mossy flume]

Oh ok

[drifting elm]

monoids maybe

more an abstract algebra thing

[mossy flume]

Well a ring is a group + monoid

[drifting elm]

you don't need monoids to do group theory

[mossy flume]

😎😎

[hasty turret]

I think finite group theory is more about group actions

[mossy flume]

Hm I see, makes sense

[drifting elm]

groups rings fields

[mossy flume]

Like homomorphisms and isomorphisms??

[drifting elm]

abelian and non-abelian groups

[mossy flume]

idk

Ye

[drifting elm]

yes homomorphism and isomorphisms

[hasty turret]

Also,Quotient groups

[mossy flume]

Oh fun ☠️

I've been struggling with those

Tho I'm kinda starting to get them?

Like with well defined functions and stuff

It's hard for me to see those questions and find even what the end goal is

[drifting elm]

thats when I close the book and get a new book to supplement

[mossy flume]

Like on my HW we had to prove the full construction of the rationals from the integers and that's a whole lot of well defined function stuff

That was painful but I understand it better now

[drifting elm]

that is in a book

not very hard to write it down for your teacher

[mossy flume]

I don't have a textbook for this course

Just the notes he gives

[drifting elm]

lame

[mossy flume]

Also where's the fun in copying down proofs until you get unbearably stuck