frick anyone who always recommends this god awful book as a beginner, i fell for the meme and upon the very FIRST exercise set
The first few exercises ask me to justify each step using commutativity and associative to in proving the following identities:
Ex prove. (a+b)+(c+d)=(a+d)+(b+c) using a bunch of commutative and associative laws
what the frick where do i even start isnt this equation already equal to something so whats the point ? what am i supposed to do ? frick you guys am i getting trolled
now someone better reccomend an actual good intro book not this bullshit
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>now someone better reccomend an actual good intro book not this bullshit
worry not, my friend, i know exactly what you are looking for https://people.math.harvard.edu/~lurie/papers/highertopoi.pdf
kek
but to respond to OP: of course a book like that is a meme. how could you make the mistake of trusting IQfy for a book recommendation?
now i will go against my own advice and recommend a book. if i were you (grander i have an advanced physics degree so this is a counterfactual) and i somehow never studied math but wanted to pick it up as an adult, of course i would be embarrassed and bored reading a kid’s book. but what i would honestly try to learn is Euclid’s Elements. it’s literally the book grown adults learned from when math was just getting popularized. you’d be following the steps of how men originally started doing math when it was new. and it’s a classic; tried and true for millenia
My recommendations are:
- The First Six Books of the Elements of Euclid by Oliver Byrne
- Understanding Numbers in Elementary School Mathematics by Hung-Hsi Wu
Same here, should people just starting out be proving every single axiom under the sun? The book I'm reading (a high school maths one) just had the following exercise: if [math](a;b)=(c;d)[/math] then a = c and b = d. Now, I can try to prove this in a very intuitive level, but I have no way of doing this with formalities. What's the point?
All of mathematics is a trolling contest. If your troll can be shown for what it is, you're a moron. If no one can prove you wrong, you get lulz.
So math is the perfect field for the average channer? lol
Maybe. Have you proven it?
>Now, I can try to prove this in a very intuitive level, but I have no way of doing this with formalities. What's the point?
To learn and understand what it means to prove something formally.
Read your statement again. You literally state
>There is something in real of things I'm studying that I don't understand. What's the point?
Well to learn it.
Only by learning it will you be able to judge the formal correctness of a proof that's a bit more difficult than the one from the first page of an intro to math book.
>Same here, should people just starting out be proving every single axiom under the sun?
You dont prove axioms, you assert them and see if they entail contradictions.
(a+b) + (c+d)
= a + b + c + d
= a + (b+c) + d
= a + d + (b + c)
= (a+d) + (b + c)
i dunno. just break the thing down into the basickest laws and write out as many steps as you need
Weak as frick proofs.
By the assumption that [math] + [/math] adheres both the commutative and associative laws, then we can exchange parentheses and order in which the elements are placed however we desire and therefore it follows trivially that [math] (a+b)+(c+d)=(a+d)+(b+c). [/math]
You haven't proved anything in your post, sperg.
You're a moron.
You're the moron here.
You're literally getting filtered by 2nd grade math.
Jesus christ, the absolute state of this board.
>It's true because it is.
>Can't into 2nd grade math.
Embarrassing.
I think you're missing the point of a "basic mathematics" proof for beginners.
Removing parentheses and swapping the order of variables are not difficult or advanced concepts in the slightest.
The widespread insistence normalgays have to avoid teaching more powerful tools and techniques to beginners is exactly why education is in such a sorry state.
Yes, that is what the question asks you to prove. The problem is "trivial" because it's the first fricking problem.
>It's true because of the axioms
Even if this were logically valid, you're completely missing the point of the exercise.
It's not about removing parenthesis, it's teaching the reader to applying a law to justify each step, as you would in logic, without appealing intuition like OP is.
This is something completely foreign to beginners.
>it's teaching the reader to applying a law to justify each step, as you would in logic
That shit's easy. Anybody who would need specific exercises to learn how to follow a systematic recipe is a mouthbreathing moron. Your attempts to make this exercise seem more difficult than it is for beginners are only to fuel your own ego, probably because you yourself actually did need such practice. For anyone who's not learning disabled, this exercise is just about learning the rules of the game, and better they learn the rules in both a more powerful and pedagogic manner than the stunted autism your kind preach.
Whoever called it difficult? It's routine but as evidenced by all the questions ITT and the OP itself, some beginners do in fact need to learn this.
You seem really defensive over this, like you're overcompensating.
I bet you think you're smart because you're calling a beginner problem in a high school easy, kek
>I can't read
Concession accepted
Ex prove. (a+b)+(c+d)=(a+d)+(b+c) using a bunch of commutative and associative laws
Given: (a+b)+(c+d)
Step 1: (a+b)+(d+c) By commutative property
Step 2: a+ (b+d) + c by associative property
step 3: a + (d+b) + c by commutative property
step 4: (a+d)+(b+c) by associative property
imagine getting filtered by 2nd grade math jesus christ
israelite hes new thats okay
Technically your associative steps are off. Would look more like this.
(a+b)+(c+d)
=a+(b+(c+d)) assoc a, b, (c+d)
=a+(b+(d+c)) comm c, d
=a+((d+c)+b) comm b, (d+c)
=a+(d+(c+b)) assoc d, c, b
=a+(d+(b+c)) comm c, b
=(a+d)+(b+c) assoc a, d, (b+c)
This book is for math major undergrads (or higher) who have a few weeks to kill and want to make sure they really REALLY *REALLY* fricking understand what they learned in 3rd grade. If you're doing advanced math you don't need this book and if you're not doing advanced math you don't need this book. It's a complete fricking waste of paper and I respect this otherwise great author less for having shat it out.
Everytime I see this book rec'd it's always noted that it's strictly for PURE MATH majors, yes, not engineering, physics or whatever.
Learning about the distributive, associative, and commutative properties is immensely important.
For the record the start of any math book (when you're setting up foundations) is going to be dull, but that book, if you're patient, will give you an unparalleled headstart that eliminates the need for any "intro to proofs" book all the while reviewing the basics + some things you probably don't know about like isometries.
As a pure mathemician you're supposed to be radically skeptic, to the point where you can't simply rely on intuition to tell you that b+a=a+b, if you're not aspiring to be one then just don't waste your time and instead go on khanacademy or something
I'm reading that book and enjoying it immensely. I don't care if I could be learning things faster, I'm having fun and my brain cells are getting a workout. That's good enough
Right now I'm having to figure out lots of stuff about factorials on my own though
realm of things
testd
lmao he fell for this garbage
spoiler: gelfand is a meme, too
Filtered, that's the easiest shit in the book.
(a+b)+(c+d)
(a+b)+(d+c)
a+b+d+c
a+(b+d)+c
a+(d+b)+c
a+d+b+c
(a+d)+(b+c)
>(a+b)+(c+d)=(a+d)+(b+c) using a bunch of commutative and associative laws
>what the frick where do i even start
You didn't even read to the meme part of the book and you still got filtered
Imagine being this moronic
There's no "meme part" in Lang's BM. Why are you pretending like you have read it
Gelfand is not a meme too, his "Algebra" is much easier than Basic mathematics because it was written for children. Not the same scope THOUGH.
>his "Algebra" is much easier than Basic mathematics
there are many problems in Algebra that are much harder than anything Basic Mathematics throws at you.
they're both lackluster books, anyway. Gelfand isn't even that great as a supplemental text since it pales in comparison to other small russian texts like everything in The Little Mathematics Library. As an aside, Gelfand's trigonometry text in particular is a complete travesty. It's genuinely worse than run-of-the-mill trig books, and lightyears away from Loney's trig, since the English translation butchered the exposition. Anyway, The Art of Problem Solving series shits on everything. It provides way more interesting and challenging problems than either of them, and with better pedagogy to boot.
t. did competition math back in high school and uni
I believe you that the art of problem solving is good or even better, but a single book feels like less of an investment than several ones. And are more challenging problems really better when we're talking about introductory material?
>trying to defend someone who doesn't understand commutative and associative laws and asking for easier books
eat shit homosexual this book is literally made for kids in high school, and this guy is b***hing about "difficulty" and "getting trolled".
constant shilling makes it a meme book, but that doesn't necessarily make it a bad book. the "meme" part is a feint to scare him homosexual
nta but you're delusional if you think your average high school student could go through the book.
maybe honors students that are majoring in pure math but your run of the mill student would have no chance.
For the record I went through the book from cover to cover at 9th grade or so, the content isn't very difficult obviously since it's as the book implies, basic mathematics (outside of a few pretty badly written parts like the section on isometries), but the challenge comes from the culture shock of not being able to go "that's obvious" and instead needing to logically justify each step with an axiom, theorem etc, like OP is struggling with ITT.
Proofs are very, very fatiguing and incredibly difficult to someone whose only experience would be plugging into the quadratic formula or pythagorean theorem.
No question in the book should be anything but a breeze to you or me but if you're still at the point where you should be reading the book (a beginner) then you will definitely find it challenging, maybe even overwhelmingly so, or at the very least awkward.
Any serious highschool math books that will prepare me for a stat degree in 2 years?
if you actually want a "highschool" book then literally any basic precalculus book and a calculus book
by which I mean Stewart and not Spivak or else it's not highschool
Just read spivak.
>Griffiths Quantum is recommended
All recommendations are automatically unreliable. Of course this comes as no surprise because everyone on this site is a bum...
Griffiths is a good intro quantum book, basically the standard in all ubdergrad courses in the USA. what’s your problem with it?
shitty mathlet book, the only reason to not get Shankar instead is if you know 0 lingebra
It's written for the mathematically illiterate and as such, obfuscates all the underlying beauty.
Waot, does this apply to his Electrodynamics book too? What do you guys recommend for Edynamics?
Electrodynamics is the exact reason that mathematicians don't/can't do physics, which in turn is the reason why electrodynamics textbooks are always a nightmare to get through. Probably just use Griffiths or Jackson, whichever suits you better.
Alright, thanks anon. Electrodynamics have been good so far. Almost reached Maxwell's equations.
The resources to learn maths are incredibly shit considering how fundamental it is to logic. There should be a uniform interactive learning guide that teaches you maths from the absolute basics 2 + 2 all the way to the schizo bullshit that you learn getting a maths degree all with plenty of examples and each step shown along with reasons for why you perform each step. The best you have is a crusty old book or listening to some monotone boomer in a video. How is any of this acceptable? The maths community should be ashamed of themselves
Basic Mathematics is a beautiful book, I doubt anyone seething ITT has read it.
It's the most optimal first step in developing mathematical maturity and an excellent intro to the logic that mathematicians use, you just have to be patient and more importantly humble.
If you can't handle this then it's only going to get much worse once you read more advanced books
Hello gigabrains of sci, please be gentle. I wanted to learn math so i checked out the book and i reached a problem
(a - b) + (c - d) = -(b + d) - (-a - c)
I did
(-b + a) + (c - d)
-b + (a + c) - d
-(b + d) + (a + c)
Am i supposed to just convert the additions to subtractions like this or did i do it all wrong?
-b + (a + c) - d
-(b + d) - (-a - c)
[math] + [/math] adheres to both the commutative laws and associative laws, so you can remove/replace/alter parentheses as you please, and you can change the order of variables in the expression as you please.
In an abuse of notation, [math] - [/math] is seen to be both the binary operation [math] -:(a,b)mapsto a-b [/math] but can also be seen to be the unary operation [math]-:amapsto -a [/math] taking an element to its additive inverse. The binary operation [math] - [/math] is ugly to work with since it is neither commutative nor associative, so instead, whenever you see something like [math] a-b [/math] as a binary operation, you should treat it as first the unary operation on the right-hand symbol followed by the binary operation [math] + [/math] on the two symbols, i.e. [math] a-b=a+(-b). [/math] We can do this by the properties of the additive inverse, of [math] 0, [/math] and of associativity of [math] +, [/math] as we have [math] a=a+0implies a-b=(a+0)-b=a+(0-b), [/math] and [math] b+-b=0implies-b=0-bimplies a+(0-b)=a+(-b). [/math]
Now we have a general rule for simplifying expressions involving [math] + [/math] and [math] - [/math]. First replace the binary operations [math] - [/math] with the unary operation [math] - [/math] acting on the right hand element followed by the binary operation [math] + [/math] acting on the two elements (recall [math] a-b=a+(-b) [/math]), and then rearrange as you please since + is commutative and associative.
Thank you glitchy chad, you even taught me that i can freely do anything with the parenthesis. Your post looks terrifying though and im not sure if its because my browser is blocking something or what. Im going to try to add imaginary parenthesis to all negative numbers to make it cleaner which is what i think you were trying to say
It's probably something with your browser that doesn't allow it to display tex.
The point is, yes, replace any instance where you see symbols of the form a-b with a+(-b), and then if you have expressions which only involve the binary operation of + (since our above replacement removed all instances of the binary operation -), then you can rearrange as you like - i.e. doing whatever you like with parentheses and with the order of symbols.
Just remember that terms like (-b) are there own single symbol, so something like (a+(-b))+c can be rearranged to e.g. (c+a)+(-b).
Oh i think i get why, a + (-b) is alot more flexible than a - b and leaving it without parenthesis runs into problems like a - -b which require you to put it into parenthesis anyway like a - (-b). Again, thanks alot
>(a - b) + (c - d) = -(b + d) - (-a - c)
what if :
(a + (-b)) + (c + (-d)) = a + (-b) + c + (-d)
this looks wrong but idk why
good bot