#book-recommendations

1 messages · Page 46 of 1

analog lava
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but thanks for the recommendation king , its a standard book obv :king

small cobalt
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Can anyone tell me the differences between the various probability books written by at least one of Grimmett or Stirzaker. For instance there is Probability and Random Processes by the pair of them, Probability an Introduction by Grimmett and Welsh, and Elementary Probability by Stirzaker.

orchid mortar
small cobalt
orchid mortar
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Perhaps Grimmett Welsh should be compared to Ross' First Course as well

small cobalt
sand crescent
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Just read varadhan

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(That was a joke)

orchid mortar
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Grimmett and Stirzaker is both a textbook and reference. It's just really good

wheat trout
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IMO, if you want study more about differential functions (e.g. you really like differential geometry or functions), Tu's book is a good way to learn about AT. Hatcher's book stresses more about geometric intuitions. If you like more about topology (e.g. low dimensional topology, knots and such), you should choose Hatcher.

small cobalt
analog lava
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i dont like anything

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i just want the thing most grad schools expect

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like the most core thing

sand crescent
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Read Fourier stuff with me

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Oh nvm then

wheat trout
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Moreover, I recall tu's book includes spectral sequence while Hatcher has a seperate book for that.

analog lava
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i only stopped at like

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radon-nikodym

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and basic functional analysis like the uniform principle or somthing

wheat trout
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Then I guess Hatcher. Because only anecdotally, but I hear more people use Hatcher.

sand crescent
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uniform boundedness 😻

analog lava
wheat trout
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Though a lot of people dont like Hatcher but indeed a lot of people do use Hatcher

analog lava
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in diff geo someone recommended Tu's textbook and i relaly liked it

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i managed to make progress in it ( it was easy )

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so i know where to learn diff geo atleast

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but idk any AT

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also i like a more diff thm proof style

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hatcher is like a novel mfao

sand crescent
analog lava
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i just finished my algebra exam

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yesterday

sand crescent
analog lava
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🏺

wheat trout
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I am not in the US so I have no idea what core means here. For me it is more relevant what subject you want to research on.

analog lava
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well ig both wont hurt lmfao

wheat trout
#

My friends working on knots like Hatcher's book

analog lava
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so ig bredon it is

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lmfaao

wheat trout
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The problem about AT is it is a very big subject and recent years it undergoes some modern renovation.

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It is very hard to learn everything. You have to make a choice somehow.

analog lava
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yea im just like hovering over the basic stuff

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i still dk what i like about math so i just want to learn the ground stuff in everything first

wheat trout
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I mean some people are still arguing what is really basic about AT. Weeks ago someone tries to convince me that, since category theory is more accepted nowadays, it is more clear to starts with simplicial sets, then homotopy theory, under the assumption people can learn AT before differential geometry.

analog lava
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for me homotopy theory seems advacned ig

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i would guess like u would go fundamental groups --> covering spaces and maybe like homology but idk

orchid mortar
small cobalt
wheat trout
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Maybe talk to some of your professors?

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They are much more experienced than me. In their research, what do they use and what kind of AT do they think a student should learn

orchid mortar
# small cobalt thank you <:thumbsupyeah:837339888781099058>

Just a note, if you're starting out and don't get Chapter 1 (specifically, sigma algebras and probability space formalism), maybe don't sweat too much about it. First courses hardly concern themselves with formalisation with probability. You do want to get used to random variables and random variable algebra

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The book itself notes as well: you should gather intuition first
(image is immediately after defining random variable)

image.png
analog lava
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on what textbook they use

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for their courses

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i agree with all of what ur saying

small cobalt
orchid mortar
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There is that

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But also, formalism really helps in seeing things sometimes

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Because all we have in math is formalism monkey

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So I like the fact that it's presented, rather than hidden as many courses would choose

sleek hawk
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Depending on what you are aiming for there's lots of good knot specific references

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Burde & Zieschang's Knots is good

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Very comprehensive

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Lickorish's An Introduction To Knot Theory is also nice

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Most of these will assume a background in algebraic topology & abstract algebra

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I don't believe any of them cover finite type invariants either

wheat trout
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I know very little about knots. When I ask about AT reference years ago, a friend recommends hatcher's AT. He is a PhD student working on knots at that time. For him, I think hatcher's AT is kind of more geometric compared to May's AT.

sleek hawk
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Haha

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May's Concise is a VERY different kind of textbook

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It is not recommended for a first approach

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More geometric is really an understatement

finite gale
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hatcher is very geometric

wheat trout
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People normally take a course in differential geometry or topology before AT. I doubt if otherwise someone who knows not much geometry but have a solid background in algebra, he will like more about May's book.

sleek hawk
finite gale
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the only course prereq hatcher has is like some point-set

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i think

sleek hawk
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abstract algebra...

finite gale
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oh right

gray gazelle
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lemme see what book we used in A.Alg

finite gale
#

but the actual prereq is geometric intuition to understand whatever hatcher is thinking when he dumps a half-page wall of text on you

gray gazelle
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🙇‍♂️

sand crescent
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not clicking on that

gray gazelle
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Abstract Algebra: Theory and Applications, Thomas W. Judson, Full Text, 2022 edition

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Me when I click on a edu link and get my entire network DDOS'd

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Hi guys
Can someone recommend me book for coordinate geometry that gives me idea to approach problems

ionic marten
misty wyvern
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y'all see this?

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A guy called Jet writing about jets

hollow peak
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Instant click

jaunty quail
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My life was easier a couple of days ago. I lost access to my university library because I am alumni account. Is this sad or what?

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No more high quality pdfs ):

magic moth
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theres a really good website

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that might help u

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not telling u though

jaunty quail
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The pdfs on that website aren't high quality

magic moth
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i wonder if were talking about the same website

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now that u mention it

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since im getting researcher freebies from my uni

vital iris
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what real analysis texts talk about total variation and absolute continuity (for real functions, not the general definition for measures)

magic moth
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i should get springer

jaunty quail
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yes

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Can you really trust every mirror?

magic moth
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does this look lowq to u?

vital iris
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hmm does it talk about the things I mentioned in later chapters?

magic moth
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also it offers supplemental readings

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which help on going beyond

vital iris
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Bro are u just advertising this book 😭

magic moth
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ur the one who asked for it

vital iris
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I’m asking for a book that has specifically this stuff (at least)

narrow relic
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(note: absolute continuity is mentioned in the context of measures but it's a definition for real functions)

vital iris
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Thanks

narrow relic
rigid sierra
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Give me a good book recommendation for undergraduate college algebra.

heady ember
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Probably good to specify whether you mean hs algebra or abstract algebra

turbid fox
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anyone know what prereqs to stein and shakarchi vol 3 and vol 4 are?

tawny copper
heady ember
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Or is college a synonym for highschool in the us or something

tawny copper
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they said undergraduate college algebra, ie, university level algebra, not high school related. As far as I understand

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so no clarification needed

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I think

heady ember
tawny copper
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well they said undergraduate too

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mmh well can that mean high school too? lol

heady ember
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hm ok yeah I get what you mean

remote sparrow
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false

tawny copper
gray gazelle
quiet rose
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hello this might be a bit of a different request but i'm currently looking for books on the history of calculus (pretty sure thats the topics name in english, the one with integrals an derivitives) are there any good books or articles out there? i tried to find some but my english is not my first language so it's hard to find the right search words

gray gazelle
#

can anyone give me a roamap to study maths from algebra1

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nd the concepts involved
dm me

dusk wind
gray gazelle
#

Anyone have reading recommendations for spirals? I'm looking to learn about hyperbolic spirals, but also an overview of the types of spiral that comes up frequently in mathematics.

gray gazelle
#

What’s a fun math book you read? Any level

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Pleasures of probability is a nice one

primal spear
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linear algebra book that focuses more on proofs and less on repetitive computation?

primal spear
novel obsidian
remote sparrow
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there are also proof-based first courses

mossy flume
restive lake
rare jetty
magic moth
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is this a good book to get into logic for a pregrad math major course?

lavish void
#

anyone recommond websites/books for calculus 1 problems w solutions

remote sparrow
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immediately above is calc 3 but it's a natural continuation

lavish void
#

do you have stuff for practice midterm

narrow relic
remote sparrow
# magic moth is this a good book to get into logic for a pregrad math major course?

from the preface:

Unlike most books and textbooks on logic, this one purports to teach logic not so much as a subject to study, but rather as a tool to master and use for performing and structuring correct reasoning. It introduces classical logic rather informally, with very few theorems and proofs (which are mainly located in the supplementary sections). Nevertheless, the exposition is systematic and precise, without compromising on the essential technical and conceptual issues and subtle points inherent in logic.

magic moth
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i droped out of math so long ago

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idk if thats a good thing

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or a bad thing

remote sparrow
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so it's not a book for studying logic as a subject in its own right, such as mendelson, enderton, leary and kristiansen, etc.

magic moth
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ill take that as a no

narrow relic
magic moth
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yeah

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so i would start from chapter 4 in that one

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it seems to do the job

analog lava
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pro tip:

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learn math from problem books

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that have solutions for every problem

gray gazelle
narrow relic
# magic moth so i would start from chapter 4 in that one

Cool, I hope you enjoy it. I had already learned a lot of that material elsewhere from a few disparate sources but I read several chapters of that book somewhat recently because I wanted a source that presented this stuff in a more unified way than I'd learned it in the past.

crude sage
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Does anyone have a reference where I can learn how to parse a sentence like "The second derivative is to be regarded as a bilinear map from $\mathbb{R}^n\times\mathbb{R}^n\to\mathbb{R}^m$, namely $$(v_1,v_2)\mapsto\left(\sum_{j,k=1}^n\frac{\partial^2 f_1}{\partial x_j\partial x_k}(v_{1,j}v_{2,k}),\dotsc,\sum_{k,j=1}^n\frac{\partial ^2 f_m}{\partial x_j\partial x_k}(v_{1,j}v_{2,k})\right)$$"?

#

I've taken first-year univariate calculus and intro proof-based linear algebra. I'm taking vector calculus, but it does not go near anything like this

hasty eagleBOT
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person2709505

823037739749867560.png
gray gazelle
#

any book recommendations regarding mental math?

magic moth
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everything u need at this point

dusk wind
#

lets keep buying overpriced outdated tomes instead

limpid rose
#

Hey does anyone have a recommendation for a recreational math book? Something with riddles that'll keep me entertained on long commutes

sage python
#

Maybe try "Combinatorial Problems and Exercises" by Laszlo Lovasz?

limpid rose
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Looks just like what I'm looking for but damn American books are really expensive.

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I don't mind spending money on a good book but I've seen books for over 500$ even for a hardcover that's a lot.

remote sparrow
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a couple messages down i suggested smullyan as well for recreational puzzles in logic

limpid rose
gray jungle
limpid rose
remote sparrow
#

here's some example puzzles

limpid rose
#

Looks amazing.

limpid rose
tawny copper
tawny copper
sage python
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I have not but my prof recommended it

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And it seemed a bit like the kinds of stuff you could just toss around in your head

tulip blade
limpid rose
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Something's onNumber theory would also be nice

tawny copper
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Oh I see

tawny copper
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volume 2 is nt, volume 4 is combinatorics, I like them

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they are all probably really good, level is intermediate Id say, and usually start from first principles.

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Also these books are very small and light

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well not all those books are the same level probably

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because some are essentially about China mathematical olympiad, which is harder than the IMO. But for example volume 4 is not intended to go that far (stated in the preface)

limpid rose
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That looks just like what I was looking for.

I think I'm going to buy the ebook. I am going to need it I am currently on a night train to Austria and I won't be home until 11:00AM

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I like Olympiad problems they are perfect for passing time

tawny copper
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I agree 🙂

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even if you don't solve them

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still fun

limpid rose
#

Are you from Spain by any chance?

tawny copper
#

yeah

livid lichen
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Any book recommendations for algebra 1?

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Also any book recommendations for geometry

narrow relic
dusk wind
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are there any good pre calculus worksheets etc

rare estuary
#

Any book recommendations for statistical mechanics/thermo with a math focus?

cold elbow
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any books for precalc?

remote sparrow
#

as someone who speaks vietnamese natively and is trying to study how to read and write vietnamese, i'd like to recommend the following books:
https://www.tuttlepublishing.com/vietnam/elementary-vietnamese-9780804855150
https://www.tuttlepublishing.com/vietnam/continuing-vietnamese-9780804857628
it should be noted that the book teaches the hanoi dialect, which is in the northern part of vietnam. my family and i speak a southern dialect. if you are american, this is probably the most common dialect you will encounter. however, southerners generally understand the hanoi dialect just fine.

downloadable content for those books can be found here:
https://tuttlepublishing.com/downloadable-content

the downloadable content includes audio for you to listen to.

remote sparrow
cold elbow
west gorge
cold elbow
west gorge
#

lol

cold elbow
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and yes i asked for precalc

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that is totally precalc

west gorge
#

yup

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check math sorcerer's channel, there are a lot of recommendations for precalc

rare jetty
cold elbow
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havent seen alot of math sorcerer

west gorge
cold elbow
restive hawk
#

What is a good book for people starting mathematical proof?

west gorge
restive hawk
#

I heard of that

novel obsidian
#

I would suggest aluffis notes: An introduction to advanced mathematics, and also I would suggest using what yoy learn in a course like 18.06 on mit ocw

narrow relic
ebon frigate
#

I need a book recommendation for studying partial differential equations

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I have read L.C Evans

compact lark
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Could i have course or book recommendations for learning about fourier series and the fft algorithm?
And what kind of background knowledge do i need? Multi variable calculus, partial differential equations, etc?

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Struggling to fill in the gaps from my own high school maths curriculum

final swallow
final swallow
mortal yoke
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is there some suggestions about pure exercise books of elementary number theory and linear algebra?

cold elbow
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i really like his voice

narrow relic
cold elbow
#

he has vids about working out

narrow relic
# cold elbow i guess

Yeah seems like a really nice and cool dude, he made a good video about Bartle and Sherbert's Analysis book that I liked

keen orbit
#

what book offers calc 2 and multivariable calc in a more abstract and rigorous way than stewart's calc

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and what does it require as prerequisites

narrow relic
sage python
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Second half of a single variable calculus class

narrow relic
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(sorry maybe that is a waste of time to ask you to answer that)

sage python
#

So I wanted to make sure my school wasn't unique in this regard so I found a few places online

narrow relic
sage python
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Basically, you do some integration topics (substitution if you didn't already get to it, parts, partial fraction decomposition, trigonometric integrals, and improper integrals), differential equations, sequences and series, and power/Taylor series

narrow relic
narrow relic
sage python
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Yeah it's not super common to have something that does both single variable and multivariable calculus in one go, and in particular just the second half of the single variable stuff

inner token
#

Does anyone have anything to say about either of these books? I'm thinking about studying the one on the left to get some more background for my intuition before diving into the one on the right. or just doing the one on the right and skipping the one on the left

20231001_141151.jpg
keen orbit
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i have already read all of stewart

sage python
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So in that case I'd recommend you a book on analysis

keen orbit
#

i am reading linear alg by greub rn

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isnt it better to study LA before real analysis ?

sage python
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Really it's better to study it before calc 3. Single variable analysis doesn't rest on linear algebra, multivariable does

keen orbit
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you mean bc of determinants and so on

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right?

sage python
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Much more than that

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The fact that you take a matrix of partial derivatives is a linear algebra fact, that the derivative is a linear approximation

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Many ideas in calc 3 boil down to this fact

keen orbit
#

which matrix of partial derivatives are you talking about

sage python
#

Jacobian matrix

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The fact that you take a matrix of partial derivatives, the chain rule, you'll soon learn the inverse/implicit function theorems, etc

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All of that as thinking of derivative as linear approximation

keen orbit
#

yea ive learnt all of these

sage python
#

I think it's a hard mistake that so many departments do calc 3 first, at least from a conceptual angle (I think they prob do it since some other majors are trying to rush you getting there)

keen orbit
#

actually at first i started with LA by axler after i was done from series which is end of calc 2

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then tried friedberg

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but i didnt dive alot

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i barely studied some stuff about vector spaces

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but didnt like these 2 books

sage python
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FIS is basically the standard nowadays. Axler has a stupid dogma surrounding determinants

keen orbit
#

so i stopped and jumped to calc 3

sage python
#

Greub is higher powered than both

keen orbit
#

after calc 3 i started searching for LA book

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i asked about some books here you gave me some recommendations

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i chose shilov's but i didnt like the starting with dets

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so went to greub now

sage python
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Are you liking it?

keen orbit
#

greub is more fun

gray jungle
#

H&K >>

keen orbit
#

the fact that it talks about vector spaces as groups and so on

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it is showing interactions between LA and abstract algebra

sage python
#

Yeah Greub is basically the ultimate reference on linear algebra as far as can tell

jaunty quail
#

thats a big claim

keen orbit
#

it is harder than FIS and axler's but it is more abstract and fun

sage python
#

Maybe along with Roman or smth. I've seen a description once which said yeah one day you may need to know 10 ways to decompose a matrix. Your options are Greub and Bourbaki, go with Greub

jaunty quail
#

10 ways?

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i only know 4 and can only perform 1 from memory

keen orbit
#

i am finding some problems with proofs bc i am basically considered new to proofs but i will get into that with time

jaunty quail
#

or 5 i guess

sage python
#

See why Greub is the ultimate? 😛

keen orbit
#

i mean LA itself is considered intro to proof no ?

sage python
#

Nah but jokes aside a few are situational

sage python
jaunty quail
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the most ive used were for a computing class

sage python
#

Discrete math and linear algebra are probably easier than calculus in that regard since you don't have nested quantifiers

jaunty quail
#

i think analysis is probably a rougher intro to proofs

keen orbit
#

but doesnt analysis need LA

sage python
#

I mean idk many either. LU factorization is basically Gaussian elimination. QR factorization is Gram-Schmidt orthogonalization matrixified

jaunty quail
#

yea sometimes

sage python
#

Polar/singular value decomposition is extremely important

jaunty quail
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yeah i know lu qr svd polar cholesky

sage python
#

Eg low rank approximation to matrices

jaunty quail
#

i think its called youngs theorem or something

sage python
#

Some decompositions from Lie theory which tbh might be variants of the ones you mention. Cartan, Bruhat, Iwasawa decomposition

jaunty quail
#

eckart-young

sage python
keen orbit
#

where are algebras introduced usually ?

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abstract algebra ?

jaunty quail
#

the first time I saw the definition of an algebra was in a grad algebra class

sage python
#

So in calculus you'll learn the idea of limits. But then what exactly is the definition of a limit? What's the sup property of R? How do we prove all those facts and rules that we use in calculus?

jaunty quail
#

but then second time was in diff top

keen orbit
sage python
#

If you're working in one variable you don't need linear algebra, but once you do multiple variables and you're giving the theory needed in calc 3, then yeah you're referencing linear algebra a lot more

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As for where you learn what an algebra is, on paper you can do a bit even in linear algebra

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If anything you'd mostly care about polynomial and matrix algebras

keen orbit
#

wdym by on paper

sage python
#

Meaning not all LA books will use that terminology

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Really an algebra is basically just a vector space that's also a ring

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So for instance, if V is a vector space, the linear maps V->V form a vector space, right?

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I can add them and I can scale them

keen orbit
#

i was asking bc i saw this in LA by greub eventhough rings,ideals and related stuff are introduced in ring theory prob?

jaunty quail
#

yea for sure

sage python
#

The full force treatment of those topics would be in an algebra class. But you do have to play with polynomials, in fact polynomials in matrices/linear maps, already in linear algebra

jaunty quail
sage python
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So some books just decide to introduce it right away and use it

keen orbit
#

for me i didnt even see sequences and series in class bc i am still high school XD

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i am last year high school finally

keen orbit
sage python
#

I mean Axler kinda does the algebra in a dodgy way

keen orbit
#

greub is the best

#

but i was asking for a more rigorous/abstract book than stewart calc to check what it covers and the level it covers

sage python
keen orbit
#

ik but is there a calc book like that

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or the most level of rigor of calc is level of stewart

rare estuary
#

Spivak

keen orbit
#

isnt spivak analysis

rare estuary
#

It's called "Calculus"

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So I guess ask him

sage python
#

I mean calculus is part of analysis

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It's just that usually if a class is called calculus they're taking a non-rigorous angle on certain topics in analysis

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Exceptions include stuff like Spivak and Apostol

rare estuary
#

I have taken calc 1-3, etc, in my engineering undergrad, and I am finding Spivak to be way more rigorous but not hopelessly abstract

jaunty quail
keen orbit
#

are there many editions of these books just like stewarts

jaunty quail
#

I dont think you will find hopelessly abstract math until later on

rare estuary
#

I did maybe 4 epsilon delta proofs in my calc. 1. class, but it wasn't the focus

sage python
#

Stewart I think is uniquely edition-inflated

jaunty quail
#

But since you are engineering you don't need a rigorous understanding of too much

keen orbit
sage python
#

Yup, the formal definition of the limit is delta-epsilon

keen orbit
rare estuary
#

Tbh, I don't entirely buy that explanation... Most of the computations you do in calc. 1 through 3 are not things you do often in the average engineering career

jaunty quail
#

If you want to broaden your horizon with what you can do with math you don't necessarily need rigor. There is a certain point where there will be some tricks that you won't fully understand though

sage python
#

Usual calc 1-3 classes are trying to simultaneously appeal to many different types of people

rare estuary
#

It's stuff that you have to understand, and depending on where you end up, sure you might need to do an integral

sage python
#

Some people in the audience are math students. Some are physics students. Some are chem. Some are engineering. Some are compsci. Some are econ. etc etc

remote sparrow
sage python
#

So if you say oh we don't need to teach engineers this topic since they won't actually use it

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Well... maybe the economists or the theoretical physicists will need it

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And now your class is deficient for them so they open their own in house "Math for econ/physics" class and you lose funding

jaunty quail
#

Does this actually happen?

#

I know it does for linear algebra classes

sage python
#

It can happen yeah

rare estuary
#

That's fair, but by that logic, you should cover everything that anyone taking the class will need

sage python
#

My undergrad had "Math for Physical Sciences"

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Which was chemistry

jaunty quail
#

ive seen it happen with statistics too

sage python
#

Since physics needed different stuff

oak inlet
#

I'm an early adopter

sage python
#

And opened their own in house math for physics classes

sage python
rare estuary
#

I took a "statistics for chemical engineers" and my stat courses for my minor

oak inlet
#

I have an IT and a CS background but CS was taught horribly back in mid 2010s

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esp AP CS

rare estuary
#

They wouldn't let me substitute, and the engineering class was taught by someone who could use stat, but really shouldn't have been teaching it

oak inlet
#

things have gotten better

sage python
#

Math department can (and often will) just make the math majors sit through a calculus class devoid of conceptual content and then later make you do it properly in analysis

oak inlet
#

I also did AutoCAD and Autodesk Inventor when I was given a lenovo school laptop

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But Dell laptops are much better

remote sparrow
oak inlet
#

its either that or i have a scholarship that enables me to live in dorms

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on a uni

crimson leaf
inner token
#

@remote sparrow go ahead these are library copies

magic moth
remote sparrow
#

it's marketed as an undergraduate textbook, but it covers some graduate topics.

#

i heard this is good too

inner token
#

Thanks!

remote sparrow
#

this is a good reference too

#

it's missing some topics in the standard graduate curriculum though

sage python
# magic moth they dont do that where I come from though

It's less common outside the United States. Students often have to make up their minds sooner about their degree (perhaps they even apply directly to it), funding works differently, and in general the US has a very hand holding style when it comes to certain things in education that isn't as prevalent everywhere else

old elk
gentle arrow
remote sparrow
magic moth
#

is this baby rudin?

forest iron
#

I have blue one same with that book

loud cradle
#

that brown/orange cover is an abomination

#

baby rudin should always be blue

forest iron
#

oh

#

yep

gray gazelle
#

Orange is the new black.

forest iron
#

I am still had it in my room

loud cradle
#

adult rudin should always be green (although it's allowable if it came with a blue dust jacket like mine did)

forest iron
#

oh yeah

#

but the blue book was have a lot of pages pages of math inside

ionic marten
gray gazelle
#

Is there a really good book to learn calculus for beginners

gentle arrow
#

big rudi

#

n

gentle arrow
#

edition doesnt matter

#

if you are feeling spicy try spivak

loud cradle
#

feel spicy

#

spivak is the best calculus book

gray gazelle
gentle arrow
#

and it's pretty good

#

its like a 6/10 for math majors and like 8-9/10 for literally everyone else

gray gazelle
gentle arrow
gray gazelle
#

ah okay

inner token
gray gazelle
#

Just received my salary

gray gazelle
#

It has to be a simple one

gentle arrow
gray gazelle
#

It doesn’t?

#

Can you link me one then

#

So I can buy

vagrant sedge
#

Hi. Just for curiosity... what is an interesting book talking about themes of undergraduate or masters level algebra applied to analysis, or numerical analysis or pdes (any of those)?

#

Except for the more usual linear algebra stuff.

livid lichen
#

also does anyone have book recommendations for geometry

olive bloom
#

Any good books for real analysis?

compact lark
#

Any course or book recommendations for learning about fourier series and the fft algorithm?
And what kind of background knowledge do i need? Multi variable calculus, partial differential equations, etc?

#

I’m struggling to fill in my gaps from my own high school curriculum

narrow relic
livid lichen
#

Ohh thanksill do that

narrow relic
livid lichen
#

should I do this

#

also is this good

#

i thought it would be good to have atleast one real life textbook so idk if that is good

narrow relic
olive bloom
storm fossil
#

Any good companion material for Spivak's Calculus? I've been working through it and having a great time. He doesn't explicitly write everything down which I've found to be very helpful since it forces me to connect the dots.

But occasionally I get stuck and it would be nice to have a secondary resources to go alongside it. I've seen some lecture notes online, but they're very set theory heavy and I'm not familiar with it.

I'd like to have another proofs-based Calc1/Cal2 book to go along side it.

Preferably one that doesn't use set theory (like Spivak).

vagrant sedge
magic moth
#

introduction to real analysis?

#

@vagrant sedge

hollow shore
narrow relic
heady ember
jaunty quail
#

Not exactly a book recommendation, any tips at reducing eye-strain if you want to keep reading on laptop?

#

Besides closing your eyes because you can't read with eyes closed

magic moth
#

thats actually a good question

jaunty quail
#

No it might be stupid

magic moth
#

i mean by that point i print the damn pdf

jaunty quail
#

high chance its stupid

magic moth
#

no copyright here

final swallow
#

i mainly watch him for his book reviews

magic moth
#

math sorcerer is based

#

ngl

old elk
#

real analysis Elon lages Lima :3

grand thistle
old elk
#

Rudin, it's quite complex, start with measurement, if you don't know measurement you don't know Rudin, moreover, it will be difficult to learn.

sage python
#

It's a bit ambiguous in this setting whether Baby Rudin or Big Rudin is being talked about here

#

Though I'd more likely guess Baby Rudin

magic moth
#

@sage python i suggest checking chill

dire torrent
#

Any Indian here who has got a copy of Abstract Algebra by Dummit and Foote? If so, how..?

white jasper
#

nope

vagrant sedge
inner niche
#

They are very helpful 🙂

fierce hedge
dire torrent
fierce hedge
#

I got it from Amazon

dire torrent
dire torrent
fierce hedge
#

I think like 650-700

dire torrent
#

wait where..how!!?

#

is it no longer available?

fierce hedge
#

That was 6 years ago lol

dire torrent
#

dang it

fierce hedge
#

Your best bet is to get it printed

dire torrent
#

as in, how?

fierce hedge
#

Get the pdf from a certain website and send it to Printster to print it

#

Probably cut the book into two parts to get two volumes

dire torrent
#

can you pay for the pdf like an ebook insomeway?

fierce hedge
#

The certain website part is illegal and the printing part also probably NervousSweat

#

You'll be fine as long as it stays in India

dire torrent
#

well..ok then.

#

Thanks for the info

heady ember
rare jetty
heady ember
kindred crest
fierce hedge
#

@remote sparrow do you think this book binding is fine?

IMG20231002202714.jpg
remote sparrow
#

this is a paperback?

fierce hedge
remote sparrow
fierce hedge
#

alr

dusk wind
delicate valley
#

Hi, I need some advice on math. I want to restart my math journey. My first year of college I was put into calculus 1 and struggled badly. I am currently at a community college. I was wondering if I should take college algebra to help me get started?

narrow relic
narrow relic
delicate valley
narrow relic
sick kelp
#

hello

rustic grove
#

Anyone happen to know any books on green's functions that can be dipped in and out of (i.e. I don't need to read it cover to cover to pick some things up). I also am going to be focusing on using them for ode's for now, so please no pde books...

fair pawn
#

hi is there any good book to understand elementary probability

#

conditional probability, partition theorem that kinda stuff

remote sparrow
fair pawn
undone finch
#

Does anyone know of good sources for getting into Quarternion analysis?
( a.k.a. "Quarternionic Analysis" )
( It exists https://en.wikipedia.org/wiki/Quaternionic_analysis )
( I've seen some books developing the algebra with Quarternions and Octonions, but I'm specifically looking for Quarternion analysis in this case please )

gray gazelle
#

is basic mathematics by serge lang a good book for high school algebra

finite gale
#

Yes

undone finch
#

Another question, does anyone know of any good books or articles that are like "Counterexamples in Measure Theory" or something like that?

finite gale
remote sparrow
#

this is a companion volume to schilling's measure theory book

undone finch
livid lichen
#

Any book reccomendations for geometry?

#

I'm new to geometry btw I just finished an algebra 1 textbook

#

I'm 13 btw so I can't really get anything over the price of like 60

finite gale
#

khan academy is free

pseudo salmon
#

yeah I use Khan Academy all the time

pseudo salmon
small cobalt
#

AoPS stuff if you are interested in competitions

#

Kiselev is good too actually, but idk how well it matches the USA curriculum

pseudo salmon
#

ok

remote sparrow
#

what are some references for order theory and lattice theory?

zinc lantern
finite gale
#

depends on what aops stuff, but in general yes

vivid fern
small cobalt
flat jackal
#

any good books for number theory?

#

I’m looking for books that have very precise and clear explanations with worked examples

#

and then a few practice problems in there too would be nice

finite gale
#

what kind of number theory are you looking for

flat jackal
#

like divisibility tests, modular arithmetic, maybe multiplying large numbers very fast if that’s even a thing?

#

i guess just proof based number theory

#

proving all the results

zinc lantern
ocean spindle
#

GH Hardy?

sage python
#

"Number Theory for Beginners" by Weil

tall carbon
#

though it's obviously aimed towards analysis in the latter chapters

finite gale
#

I don't think an analytic nt book rec is suitable (for now)

tall carbon
#

ehhhh I guess. the first few chapters cover the basics pretty well

#

though with multiplying large numbers they are probably wanting something more computational?

finite gale
#

Honestly i don't think I've seen a text explicitly cover multiplying large numbers

pseudo salmon
#

nice

flat jackal
#

because the calculator does it so work

#

so surely it just use a method from there

livid lichen
#

Is the mcgrawhill algebra 1 book good?

#

I saw It at my school

lusty ermine
#

hi guys

#

what book do I need to solve this?

#

"Represent the polynomial ( f(x) = 3x^5 + x^4 + 15x^3 + 12x + 4 ) as the product of its linear factors."

honest cave
#

Someone has leithold calculus in spanish?

magic moth
#

no i have spivak in spanish @honest cave

tardy oasis
#

Good book from what (little) I've read in it so far tho

honest cave
tardy oasis
#

And yeah the other text is a pretty decent one from what I've seen so far, but is an intro text afaik, so if you're looking for something advanced maybe look elsewhere

magic moth
#

depending on your objectives

#

i might not recommend it though

covert bane
#

does anyone have some reference texts for introductory topos theory in the context of logic (so not grothendieck topoi)

#

I've worked through a bit of goldblatt's Topoi, but not finding it super helpful

#

I've heard mac lane and moerdijk's Sheaves in Geometry and Logic is good

#

but any additional resources would be appreciated

proud shuttle
#

i want to learn calculus from scratch. can anyone recommend some good books?

finite gale
#

Stewart

proud shuttle
finite gale
#

Spivak then

#

Stewart is computational

magic moth
#

isnt spivak analysis?

#

i was about to suggest apostol

finite gale
#

Spivak is calculus but can be treated as intro analysis

magic moth
#

same for apóstol?

finite gale
#

I do not know that one

vivid fern
#

Page 5 also has a nice list of other resources for this subject, including those standard ones that you mentioned above as well

#

Since the semester started i hadn't gotten the chance to really read this subject so I'd appreciate it if you could let me know later on what you found good/helpful after you have tried it yourself 👍 🙏

vagrant blade
#

currently studying for the SHSAT, any study material / website reccomendations?

narrow relic
modern silo
#

Hi!
I was planning to make a general combinatorics book guide for my acquaintances. Can I get some aid from here? Thanks!

#

Note: There's no level of familiarity I can assume at the moment, so feel free to cover any difficulty range of books, as long as you think they're approachable by an undergrad.

narrow relic
#

I don't know. You can make an account on the Internet Archive and borrow the book hour-by-hour and check out the contents

small cobalt
modern silo
#

ah
haven't heard of the latter, will check out, thanks!

#

what do you think of the books, by the way?

#

in terms of 'niceness' in your own metric, technical requirements and coverage

small cobalt
#

KokoroThink in terms of "niceness" I'd rate them very highly, I thought they were engagingly written (I find this rare in maths book) with good problem sets. I've seen other books where I think the problems tend to skew almost entirely too easy or entirely too hard. I don't remember them having any requirements that go beyond highschool maths (I'm UK based for context) and the coverage contained everything I think you would see in a first course and more (I can provide links if you want to see more detailed breakdowns). If you've done combinatorics for Olympiads in highschool I might recommend looking somewhere else unless you want some review, likewise I'd probably use different books to prep for competitions even though these would give you all the tools you need.

gray gazelle
#

Miachel Sullivan's algebra and trigonometry or james stewart, lothar redlin and saleem Watson's precalculus mathematics for calculus?

Also I need a good geometry book which covers from basic to advanced or atleast first year college.

modern silo
spiral patio
#

Does edition matter for textbooks?

remote sparrow
#

sometimes

spiral patio
#

Cuz the older editions are usually cheap

remote sparrow
#

yes

spiral patio
#

But have less content or problems

#

The newer editions have way more problems and more content usually

#

But are more expensive

remote sparrow
#

depends on what the subject matter is

spiral patio
#

Like for example: linear algebra

#

Say i want to buy Howard Anton's book. He has the old editions like 4th

#

And the newer editions like the 11th editions

#

Usually 4x the price

remote sparrow
#

the marginal benefit of getting the latest edition of a book like, say, lay's Linear Algebra and Its Applications compared to getting a previous edition is not worth it

spiral patio
#

Ah i see

#

Same thing for calculus?

remote sparrow
#

yes

spiral patio
#

So like for older subjects

#

With not much progressions in the past years

#

Like calculus has been calculus for a long time now haha

#

So for subjects that are already developed fully then its not worth it

#

An older edition will suffice

remote sparrow
spiral patio
#

Well thanks very much. I am taking a class and they telling me to buy a linear book that costs 160$ cad and i dont want. Im gonna get the 4th edition which is like 10$ haha

spiral patio
#

So like buying a calculus book made in 1980s is obsolete

#

So maybe for the calculus book, its better to buy like a more recent like maybe in year 2010

magic moth
gray gazelle
spiral patio
#

I heard its very challenging

magic moth
#

if ur doing an engineering degree

spiral patio
#

Maybe when i take cal 3

magic moth
#

and require computations

#

i dont recommend it

#

tbh

spiral patio
#

Ah ok i am gonna do engineering haha

remote sparrow
spiral patio
remote sparrow
spiral patio
#

Ah ok

remote sparrow
#

Understanding Analysis by abbott is accessible

magic moth
remote sparrow
spiral patio
remote sparrow
#

this electrical engineer used abbott

small cobalt
magic moth
#

yeah zach is great

remote sparrow
#

if not content-wise, then at least with respect to how well-made the book is

spiral patio
small cobalt
#

it varies from book to book, older editions of books like Stewart's Calculus tend to be better, but the 2nd edition of Artin's Algebra is superior to the first

magic moth
#

the thing is @remote sparrow electrical engineers tend to need the math and they dont realise it until their doing 4th year stuff or grad level research

#

its quite common actually

spiral patio
magic moth
#

electronic engineer phd who works with me always tells me "ill deal with the bureacracy of publishing u just learn math"

spiral patio
#

I wanna do electrical engineer

remote sparrow
#

i'm not an electrical engineering student

magic moth
#

there is a electrical engineering discord

#

its quite good

spiral patio
#

Ah well ill probably join it when i do my 1st semester in that

#

Rn il finishing up college

small cobalt
#

I think Apostol is a good choice for someone who isn't so set on pure maths (it's perfectly fine for those too however) fwiw

spiral patio
#

For me the most important thing in textbook are the problems they give

#

The theory is secondary

#

Cuz in a test ur tested on problems that u have to solve

small cobalt
#

Apostol has a good mix of involved computational problems and theoretical ones

#

it's better balanced than Spivak from that point of view imo

magic moth
#

true

#

spivak is analysis

small cobalt
#

yeah Spivak is closer to straight up analysis than Apostol

magic moth
#

wasnt apostol an engineer too?

small cobalt
#

in fact Spivak matches quite well with 1st year Analysis courses in the UK imo, since we don't tend to introduce topological notions then

small cobalt
spiral patio
#

Some textbooks have like 60 😂

#

My cal textbook has like 60 problems

remote sparrow
#

spivak feels slightly awkward since he completely omits any topology in favor of epsilons and deltas

magic moth
#

u see sometimes its not about the number of problems

#

its how hard they are

spiral patio
#

Ye true

#

In a 60 problem per chapter textbook most of them are too easy

#

I never did more than like 12

#

Cuz it was way too easy

small cobalt
#

the amount varies throughout apostol, and they follow ends of sections rather than being at the end of every chapter

spiral patio
#

Yea. The linear book im getting has 12 per section. Lots of proofs very little computation

small cobalt
#

Zorich is an even better fit than Spivak though because of the ordering of material

small cobalt
remote sparrow
#

or a course webpage

small cobalt
#

nothing public I'm afraid

remote sparrow
#

one that tells which problems from the book should be done is especially appreciated

small cobalt
#

courses in the UK don't tend to set problems from the book either (even if some are sometimes lifted)

#

everything I had was assigned as a problem sheet without references, book were just suggested as supplemental

rustic grove
small cobalt
rustic grove
#

That's a good uni... U first or second year?

small cobalt
arctic dew
#

Can anyone recommend a book which is about the mathematical background of models in machine learning? Or a book that is about going thru the process of building out a model and describe its mathematical background?

rustic grove
#

Not bad, last year!

small cobalt
maiden halo
arctic dew
#

These are really good as well

small cobalt
#

measure theory, galois theory, manifolds, functional analysis I, galois theory, geometry of curves and surfaces, algebraic topology, advanced real analysis, functional analysis II I think KokoroThink

#

still can change some

rustic grove
#

what would advanced real analysis cover?

arctic dew
finite gale
#

Why would you need that for programming

small cobalt
# rustic grove what would advanced real analysis cover?

here's the syllabus:

Aims:
Setting up a rigorous calculus of rough objects, such as distributions.
Studying the boundedness of singular integrals and their applications.
Understanding the scaling properties of inequalities.
Defining Sobolev spaces using the Fourier Transform and the connections between the decay of the Fourier Transform and the regularity of functions.

Outline:

Distributions on Euclidean space.
Tempered distributions and Fourier transforms.
Singular integral operators and Calderon-Zygmund theory.
Theory of Fourier multipliers.
Littlewood-Paley theory.

small cobalt
#

I haven't enjoyed the programming I've done much

rustic grove
arctic dew
arctic dew
small cobalt
rustic grove
#

Idk why they make it compulsory

arctic dew
small cobalt
small cobalt
rustic grove
#

My feelings also

gray gazelle
#

Which is better;

  1. T. Y. Lam: A first course in noncommutative rings, Springer, 1991.

  2. T. Y. Lam: Lectures on modules and rings, Springer, 1999.

arctic dew
remote sparrow
#

i'm interested in working with proof assistants like lean, but yeah i didn't enjoy my programming classes

small cobalt
#

basic programming skills are usually better developed through self tuition imo, at least compared to the way programming modules are taught by maths departments in particular

#

I'm curious if it's taught better within CS departments, but the best CS students I personally know did also have extensive experience programming prior to uni CirnoShrug

finite gale
#

Well there's more to cs than just programming

small cobalt
finite gale
#

Programming itself doesn't seem very fun or interesting, but some of the theoretical cs classes seem more fun

rustic grove
small cobalt
magic moth
#

ehh

#

lets just call those guys programmers

remote sparrow
finite gale
#

If you're going to college to learn how to code, you are actually just wasting money for no reason

remote sparrow
#

mfw the cs theory classes are gated behind the programming ones

magic moth
#

best case scenario u go there so that HR says this guy has a degree

#

let him go to the technical interview

remote sparrow
#

could just get a coding certificate at one of those coding bootcamps instead

magic moth
#

true

#

but if u actually want to get into the fun stuff it opens doors

#

like doing a master at math

#

provided u study the necessary requirements by urself

halcyon trail
#

Hello guys,

I'm studying Further Pure 1 at Further Maths A Level does anyone have any reccomendations on books that will support me in deepening my knowledge other than the textbook of course

small cobalt
halcyon trail
small cobalt
#

Hmm for topics like these I would probably consult the linear algebra section of a vector calculus book - maybe something like chapter 1 of Hubbard/Hubbard's Vector Calculus, Linear Algebra and Differential Forms or chapter 1 of Colley's Vector Calculus

small cobalt
halcyon trail
#

okie dokie

heady ember
#

Khan academy probably has some resources on vectors

small cobalt
#

khan academy would be another good resource but I doubt it would go deeper than the textbook

#

it's hard to think of resources that will go particularly deep on those topics without introducing a lot of surplus material though chima_shrug

halcyon trail
#

Oh dam :(

storm fossil
#

Trying to make this question coherent:

Is there a good resource that explains a tensor from a maths perspective? Online, I keep finding physics representations and arrows, etc. Those are useful, but I'm wanting to understand the maths perspective.

I haven't taken linear algebra yet, so it might be impossible without that background.

I'm not looking for a total treatment of tensors, just a chapter or less that describes the basics. A video is also fine if it's mathematical.

sturdy shore
#

should probably learn linear algebra first

storm fossil
#

Do you think the basics of a tensor would be unapproachable without it? Pretty much just want the definition/explanation of the simplest tensor (3d) in a form that I can understand.

#

If not, then I'll just grab a linear algebra textbook

sturdy shore
#

I mean, tensors in the mathematical sense are just multilinear maps, I don't see how that makes sense to anyone that doesn't know linear algebra

storm fossil
#

Alright, thanks 🙂

sturdy shore
#

you'll need to know linalg for pretty much everything anyway

remote sparrow
#

this is mileti's course webpage for measure theory. however, i didn't post this because of his measure theory notes (although i found a new reference for measure theory to investigate), but because i found some high quality notes on single-variable real analysis which follows abbott to an extent.

charred estuary
#

looking for a multivariable calc book to supplement my school workload - it's junior year HS so id rather not have something TOO rigorous

#

having trouble deciding bewteen multivariable calculus by larson, calc of several variables by edwards, and calc on manifolds by spivak

#

i cant tell if spivak is rigorous or not

#

ive heard his name a lot before tho

narrow relic
charred estuary
narrow relic
charred estuary
narrow relic
#

I have a recommendation for you

charred estuary
#

sure

#

price isn't an issue btw and i can always find pdfs online

narrow relic
charred estuary
#

HOLY SHIT THANKS MAN

narrow relic
# charred estuary HOLY SHIT THANKS MAN

You're welcome, but I think you need to have the notes from the previous quarter too, since it says "We have already seen what it means for a function Rn → Rm to be continuous, by taking any of the versions of continuity we had for functions between metric spaces last quarter and specializing them to the Euclidean metric."

charred estuary
#

alr thats fine

narrow relic
#

"Math 320-3" is the one I showed you above

#

So you can refer to "Math 320-2" and "Math 320-1" as you need

charred estuary
#

northwestern -> cmu? how does that work

narrow relic
charred estuary
#

ohh in 4th quarter

#

okie

narrow relic
#

At the time, he didn't have 320-1 nor 320-2 up, I wish I'd had these back when I was reading 320-3

small cobalt
#

based on what you said, definitely don't bother with spivak's calculus on manifolds

dapper root
#

More peach

small cobalt
small cobalt
remote sparrow
#

what are some good resources to learn programming on my own? i took a couple of programming classes in college through the cs department but i didn't enjoy any of them.

magic moth
#

depends on your objectived

#

objectives*

#

i suggest using Microsoft documentation for c# and going from there

sage python
#

"but i didn't enjoy any of them"

Can be a mood sometimes

small cobalt
#

I think the most important thing is to find anything that motivates you to do a lot of it and often

#

maybe check out project euler

#

I'm not massively fond of any intros to programming I've seen and it sounds like your courses would put you beyond those anyway?

remote sparrow
#

course desc:

Object oriented programming and design for large scale software. Class design, interfaces, inheritance, and polymorphism. Robust programming with exceptions, streams, iterators, and testing.

#

here's an older course desc:

Disciplined methods of design, coding and testing using the Java programming language. Topics include the structure and semantics of Java classes, data abstraction, encapsulation, cohesion, coupling, information hiding, object-oriented design, inheritance, interfaces, composition, delegation, polymorphism and design patterns.

remote sparrow
#

it's a functional programming language so reading sicp might be helpful?

magic moth
#

mm

#

they also work on a c compiler thats memory safe

#

u might find that interesting

small cobalt
winged matrix
#

Does anyone have any good resources and lectures for matrix multiplication and linear estimation

hollow shore
#

I am looking for a good competition math problem book which starts easy then slowly get harder.

gray gazelle
#

I have finished pre algebra and algebra 1, can you guys recommend me algebra 2 books that are easy to understand.

stone sage
gray gazelle
cold elbow
pine vapor
#

good book?

tribal eagle
#

Can someone pls tell me what I'm learning in this course??
In Dutch (translated) it's called "Logic for computer science"

#

We have some predicates, functions
Transitive, equivalence relations...

#

Idk exactly, our professor ain't the best ngl

rare jetty
tribal eagle
#

I'm looking for Books in whatever this topic is.. ain't that semi-relevant?

#

😅😅

pine vapor
#

good book?

tribal eagle
pine vapor
#

just give me a good book

#

like

tribal eagle
#

Crime and Punishment by Dostoevsky

rare jetty
#

you can find a newer one tho

tribal eagle
#

What's the topic I'm learning called, if you know..?

tribal eagle
rare jetty
tribal eagle
#

Discrete math huh.. kk tnx

tawny copper
storm fossil
#

Is there a reason Serge Lang's Basic Mathematics is pretty much only sold new or maybe like 5% off for used copies? I swear it's an older book.

#

Usually older books you can find them for 50-60 percent off

#

used at least

gray gazelle
#

Best ways you can learn algebra-pre-calculus online

storm fossil
#

I just like the book/style.

maiden halo
storm fossil
maiden halo
#

I don't know. I got it 50% when Springer had a sale awhile back. you can try bookfinder.com to see if you can find it cheaper

storm fossil
#

Thanks 🙂

small cobalt
# hollow shore I am looking for a good competition math problem book which starts easy then slo...

Ukmt topic books ("Intro to...") do this and start at a lower level than Problem Solving Tactics imo. Problem Solving Tactics is good if you have at least a bit of competiton experience and at that point is probably the best general book. Possibly you could check out PST first and if it seems hard have a look at some UKMT stuff. You can also look at the handouts by Everaise which are close in spirit to the AoPS volume I and II books, targetting amc and aime level stuff

remote sparrow
hearty steppe
#

There are some parts of tolstov’s fourier series I don’t quite like in terms of exposition. It does feel a bit weird at times. I am going to consider another book I haven’t looked at in my collection before i decide jumping into Folland’s Fourier analysis.

Seems like Tolstov has some pretty weird notation and there are parts where some important rigor gets skipped over and some points feel confusing and misleading

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I’ve managed to come across these texts so maybe I’ll trial by fire working through them to see which one feels like a good fit… not sure anyone has heard of these

https://books.google.com/books?id=0ZWsoaeSgnQC&newbks=1&newbks_redir=0&printsec=frontcover&hl=en&source=gb_mobile_entity#v=onepage&q&f=false

https://books.google.com/books?id=W4v1Rn7UA5IC&newbks=1&newbks_redir=0&printsec=frontcover&hl=en&source=gb_mobile_entity#v=onepage&q&f=false

https://www.amazon.com/dp/0471292885

https://books.google.com/books/about/Fourier_Analysis.html?id=OcZ5iKsGrmoC&printsec=frontcover&source=kp_read_button&hl=en&newbks=1&newbks_redir=0&gboemv=1#v=onepage&q&f=false

https://books.google.com/books/about/A_First_Course_in_Wavelets_with_Fourier.html?id=gwV1uykfzWYC&printsec=frontcover&source=kp_read_button&hl=en&newbks=1&newbks_redir=0&gboemv=1#v=onepage&q&f=false

https://books.google.com/books?id=irnkBwAAQBAJ&newbks=1&newbks_redir=0&printsec=frontcover&hl=en&source=gb_mobile_entity#v=onepage&q&f=false

https://www.amazon.com/Fourier-Boundary-Value-Problems-Churchill/dp/007803597X

Linear Systems, Fourier Transforms, and Optics

A complete and balanced account of communication theory, providing an understanding of both Fourier analysis (and the concepts associated with linear systems) and the characterization of such systems by mathematical operators. Presents applications of the theories to the diffraction of optical wa...

Google Books
A First Course in Wavelets with Fourier Analysis
Google Books
Fourier Analysis
Google Books
A First Course in Fourier Analysis
Google Books
A New Twist to Fourier Transforms
hearty steppe
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And I liked the first 4 chapters of his functional analysis book but once it got to the spectral theory chapters, it got too heavy for me with the rigor

remote nova
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Looking for books like "Primes of the form x^2+ny^2" for algebraic NT (could be CFT, Iwasawa theory, etc.) that very cohesively develop material to solve a problem

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but not looking for books that teach all the basic of ANT.. so no Neukrich or anything like that

mellow wren
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It requires a lot of alg NT knowledge

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Tho

finite gale
mellow wren
finite gale
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I see

mellow wren
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it'll randomly just throw out like
Let H/K be the maximal unramified abelian extension of K and it's well known that Gal(H/K) is isomorphic to the ideal class group of K

gray gazelle
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Can you guys recommend me a math book I have completed algebra 1 I need to study algebra 2, my final goal is to learn calculus for physics so that I can get started with physics

copper axle
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Hi! I’m a first year physics student trying to understand statistics and probability, along with its applications. Is this a good book? Thx

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Or any other recommendations would also be helpful XD

gray gazelle
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Can I dm you

copper axle
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Of course

remote sparrow
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probably the best probability resource for understanding probability

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less sure about statistics

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i used wackerly, mendenhall, and scheaffer

copper axle
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OK thx!

rare estuary
tawny copper
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Does someone know about Stephen Willard's book "General topology"? How does it compare to other standard books like Munkres?

hearty steppe
hearty steppe
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But at this point it seems like multiple people have suggested to work through his engineering math book and I’m just going to take that suggestion to heart at this point instead of randomly selecting another text before I work through folland and see if it works out for me, only to be disappointed again with too little or too much rigor

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Tolstov started out promising but very quickly toward the end of the first chapter seemed to fall off a cliff and the exposition got very awkward

maiden halo
# copper axle https://link.springer.com/book/10.1007/1-84628-168-7

This book might be a bit tough for a very first look. For probability you can check out Blitzstein & Hwang. For (mathematical) statistics, there's Hogg-McKean-Craig, or Wackerly-Mendenhall-Schaefer (I think are the authors), or Larsen & Marx. The latter is a bit more "applied"

rare estuary
hearty steppe
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So I should jump right to the Fourier stuff or just go through the review of what he covers?

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I would prefer to go into a Fourier series focused book I have an idea of a text that I peaked at that seems interesting but I would rather go through folland first but I feel like I may need a pretext to prepare for folland

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It’s weird cuz I’ve went through Folland’s measure theory heavy focused analysis book which I managed to work through with limitations but I enjoyed going through it

rare estuary
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There's Fourier stuff in AEM. I can't comment on it due to general ignorance of Fourier analysis

hearty steppe
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I guess Fourier series is just a whole beast of complexity and maybe there is stuff I did not cover well to prepare going through a Fourier series text cuz I already struggled too much to work through two books so far… Stein shackarki and Tolstov so maybe I’m missing fundamentals or something

rare estuary
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AEM has one chapter on it. About 40 pgs

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So it's probably introductory

hearty steppe
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But Tolstov just seemed like it lacked thoroughness althogether. Idk why people would recommend that book. Extremely awkward notation and weird exposition

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Well I liked the Fourier transformation chapter in Folland’s real analysis but I feel like it lacked more broken down exposition

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Like I feel like there were so many missing pieces even though it was well worded

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Like definitely was not enough to grasp the depth of Fourier series

rare estuary
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Looking through the old edition I have, I would describe the treatment as abbreviated in AEM, so not some with a lot exposition

hearty steppe
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I think maybe it’s worth trying to work through Folland’s Fourier analysis text if I enjoyed his real analysis text. I don’t know. Maybe I just am limited in really grasping the depth of Fourier series past transformations and I may have to accept that

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And it seems a lot of people really struggle with it and it’s not just me

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Like it’s just really wild and my brain breaks over it

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Or maybe I should just go the Ergodic theory route of dynamical systems since that’s the area of math that seems to make sense to me and it might come together that way

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Different strokes for different folks sort of thing

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Cuz Ergodic theory comes back to understanding patterns again and possible paths

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Maybe it’s just more fundamental than Fourier series

rare estuary
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Hopefully someone has advice. I don't have any good resources on Harmonic Analysis

hearty steppe
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Yea that shit is so fucking complicated to understand I feel like maybe I should just keep pursuing the dynamical systems/complex systems route. There are some more fundamental representation theory books that I haven’t worked through yet that maybe I should also work through that are not too rigor heavy. I’m considering giving them a chance as well but maybe the problem with Fourier series is the perspective of it that does not align with my reasoning

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And it seems Ergodic theory does seem more fundamental to understanding symmetry and symmetry breaking and that’s more purely focused on dynamical systems than Fourier series

hearty steppe
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There are certain areas of math that don’t seem to play nice with me usually in terms of material I’ve found. Representation theory/spectral theory being another problem area for me. But there are about a dozen more books I haven’t tried yet so I’m not giving up on that.

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But I think I’m going to take a break from trying to grasp Fourier series more directly and go back to studying dynamical/complex systems more directly for sure. However before I do that, I’m going to go through some of those representation theory books or perspective focused books that I haven’t given a chance yet

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After all… a couple of models for my work is focused on being able to more properly put together spectral graphs so… I should spend a little more time in the territory of representations

gray gazelle
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What's the book with the most clear explanations that you have read, trying not to pick the one you're most proud of reading?

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(math books)

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For me it's WWSawyer books

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Almost no one knows him here though, may be better known in other less technical areas

orchid mortar
remote nova
patent trail
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Hi, around summer i asked for differential geometry resources here for a first course here. Last tuesday my differential geometry professor recommended these books:

``Elementary Differential Geometry by Andrew Pressley, 2nd Edition Springer (2012)

Differential Geometry of curves and surfaces by manfedo P. Do Carmo (1976)

Elementary Differential Geometry, Barret O' Neill Academic Press INC. (1966)``

First lecture was based around definition of Affine Spaces and properties of an affine space.

based on the given recommendations here and the recommendations my professor gave, which one is best to complete first before starting to others? (i've been trying to look for affine spaces on the given books but couldnt find it)

hollow peak
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Honestly, I would say reading do carmo's curves and surfaces book is completely useless

hollow peak
gray jungle
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Pressleys book is lovely

storm fossil
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Can anyone recommend a good fiction maths book? I'm thinking something like Flatland. I've seen a couple of romance books, but not really interested in that genre. It doesn't literally have to be like flatland (fourth walling, people are literally shapes, etc.).

remote sparrow
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don't know if it's "good" since i've never read it

storm fossil
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I'll take a look at it, thanks

small cobalt
storm fossil
heady ember
magic moth
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he has some novels

dusk wind
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any good documentaries/books on the history of math? (nothing too controversial)

hollow shore
remote sparrow
gray gazelle
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Recommendations for basic geometry book?

small cobalt
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although I am told the third edition of Jacob's geometry is worse than the earlier ones (I am familiar with the 1st)

gray gazelle
small cobalt
gray gazelle
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Oh

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Ok thanks, I will try to find it.

small cobalt
eternal stag
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Any bk recommand for basic algebra

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I need to ensure all my basics are there

fierce hedge
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basic Algebra as in college algebra or abstract algebra?

cobalt arch
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Although he is advanced now that I look at it so maybe it is the latter

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Inconclusive

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Anyway I stand by my first message, if it were abstract algebra he would specify it since he knows that algebra by itself is an ambiguous term and if he wasn't aware of other algebras he would not have specified it, as he did, because he wasn't aware. Lastly, he said basic algebra which could only mean elementary. In all cases the conclusion is elementary algebra and not abstract algebra by pure reasoning alone.

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Although phenomena may be deceptive so who knows, I might be completely wrong still

gray jungle
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over analyzing wont help just wait for the answer

civic python
subtle mango
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look here

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(“free textbooks online” is not pirating, they literally write their own textbooks and publish them for free)