Explain Algebra to me like I'm retarded; that is, everything

>>9070145
no

1+1=2
I leave the rest as an exercise to the reader.

>>9070145
>Read
All the Math You'll Ever Need: A Self-Teaching Guide by Slavin
Elements of Algebra by Leonhard Euler
Precalculus with Unit Circle Trigonometry by Cohen
Calculus: An Intuitive and Physical Approach by Kline
Book of Proof by Hammack
Linear Algebra by Jim Hefferon
Calculus of Several Variables by Lang
Ordinary Differential Equations by Tenenbaum & Pollard
Partial Differential Equations for Scientists and Engineers by Farlow

>>9070212
Thanks, anon. I'll check all of that out.

Algebra is using letters instead of numbers when you count.

What is linear algebra?

>>9070394
the study of vector spaces

>>9070414
I get that I guess, but I never understod how it relates to algebra. I dont see the connection.

>>9070425
It's because you can perform algebras on the vector spaces. It's the algebra of lines (vectors).

>>9070425
It's just algebra that uses vectors instead of scalars.

>>9070145
Algebra is the study of operations. If you have any set of objects, and a way to combine two objects into another object (for example, the combination of 1 with 1 is 2, with addition) then you have algebra.

Depending on the type of objects and the properties the operation has we group different algebra system under the name of algebraic structures. And while some algebraic structures like vector spaces and groups are famous (because they appear everywhere) technically anything can be a structure. For example, a group operation is associative but not necessarily commutative, but there are operations that are commutative but not associative so you could instead study those operations.

Algebra is interesting because after you leave the abstractions, algebra is the rules for symbol manipulation. With algebra you prove how you can manipulate symbols in different systems. For example, many theorems in arithmetic can be proven just by algebraic manipulation. For example: Prove that a non-zero difference of squares is composite.

This is a theorem about prime numbers, but it is provable just by applying algebra.