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/sci/ - Science & Math

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5867549 No.5867549 [Reply] [Original]

What is the difference between algebra and calculus. I want to understand =(

>> No.5867553

Calculus is like algebra but with limits.

That's the simplest way I can think of putting it.

>> No.5867562

>>5867549
Calculus is areas of curves.
Algebra can't do that shit.

>> No.5867588

>>5867549
calculus finding rate of change from a to b
and areas accumulated from point a to b

algebra finding values of unknowns

>> No.5867593

>>5867549
Depends what you mean really, the "algebra" you study in highschool is pretty elementary, and relatively similar to calculus with some new notation and a few new tricks, like integrals.
However, there are many times of algebra, some abstract, and involving fewer numbers and variables.

>> No.5867614

>>5867588
>algebra finding values of unknowns
sorta kinda not really

>> No.5867625

>>5867614
Clearly OP is referring to HS level Algebra 1 and 2. I think the definition fits it.

>> No.5867628

>>5867625
I meant overall kind of.

>> No.5867635

Calculus is the study of change.

>> No.5867636

Algebra can only be used to find average rate of change and areas of defined, finite-sided areas that are either straight-edged or perfectly circular (i.e., find the slope of y = 4x + 3, what is the area of an equiangular, equilateral pentagon of side length 4 cm?).

Calculus is a set of techniques used in conjunction with algebra that can be used to determine instantaneous rate of change, as well as areas of shapes with no well-defined sides. But that's just the thing: Calculus techniques are usually only useful on something you have a function for. You'll typically be given a function to do calculus on. Calculus isn't just some magical tool to instantly give you answers to things.

>> No.5867683

Basic arithmetic is like learning your ABCs.
Algebra is like learning to form words.
Calculus is like learning to form sentences.

>> No.5867728

>>5867683
When do we learn to form metaphorical paragraphs?

>> No.5867738

al gebra is all 'al' Ge-Bra...

and Calculus is all....

....calculating and shit....

https://www.youtube.com/watch?v=jXOgYxUf6Ts

>> No.5867975

Algebra is harder.

>> No.5867988

>>5867728

Bless you anon.

>> No.5868002 [DELETED] 

>>5867549

>> No.5868012

Calculus = ancient greek for math
Algebra = ancient persian for math

>> No.5868054

>>5867728
Upper division math

>> No.5868100

>>5867728
>When do we learn to form metaphorical paragraphs?
Category Theory

>> No.5868144

I'll answer this one from a somewhat higher-level perspective, since it's harder to see the distinction at the elementary level it's usually taught at in secondary school.

Algebra is ultimately about the study of algebraic structures — that is, sets (of numbers, functions, symmetries, rotations, permutations, vectors, whatever) with some sort of operations that obey certain axioms. These operations are usually modeled off of classical cases, e.g. fields, which are essentially number systems where addition, subtraction, multiplication, and division are possible and behave (to an extent) how they do in the rational numbers.

Analysis (the branch of mathematics that developed from calculus) is about studying limits and continuity, things that require topological (essentially, spatial) structure to formulate. In analysis, the focus is on two central objects — the real numbers and the complex numbers — which have an especially interesting interplay of both algebraic and topological structure. Integration and differentiation are key operations that arise in these contexts, and so it naturally plays the more visible role in things like physics that involve systems which dynamically, continuously change over time.

It's hard to grasp the difference without really doing some of both yourself, but algebra and analysis have a very different feel to them, and their flavors of proofs are often quite unalike.

>> No.5868152

>>5868012
Didn't Isaac Newton discover calculus?

>> No.5868156
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5868156

>>5868100
They're a special case of weakly braided n-metaphorical (ω, 1)-paragraphoids.

>> No.5868162

>>5868152
he discovered what we now call calculus, but the word is ancient greek for calculating using small stones.

>> No.5869005

>>5867549