Arithmetic versus mathematics.

I guess I was thinking more along the lines of abstract algebra and topology, where arithmetic is not as directly applicable. But yes, numerical analysis would definitely involve higher mathematics. In summary, the conversation discusses the relationship between arithmetic and mathematics, with some arguing that arithmetic is not necessarily a part of mathematics, while others believe it is essential for higher mathematics. Some also mention the importance of arithmetic in numerical analysis. The mention of Serre's "A Course in Arithmetic" is also brought up as a resource to understand the meaning of arithmetic. Overall, the conversation highlights the different perspectives on the role of arithmetic in mathematics.

Is arithmetic part of mathematics?

  • Yes! Arithmetic is needed in order to do higher maths.

    Votes: 14 87.5%

  • No! You can learn how to do algebra without any arithmetic at all.

    Votes: 2 12.5%
  • Total voters
    16
  • #1
JWHooper
IMO, I don't really think arithmetic is really mathematics. It's just pure calculations, that's all.
 
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  • #2
Some arithmetic is an essential part of Mathematics. You certainly do not need full mastery of arithmetic in order to study "elementary algebra", but you still must have basic understanding of most of arithmetic in order to effectively begin studying "elementary algebra".

Interesting: Why do some people do well with Arithmetic in grades 1 through 7, and then struggle so hard with Introductory Algebra?
 
  • #3
JWHooper said:
IMO, I don't really think arithmetic is really mathematics. It's just pure calculations, that's all.

TOTALLY WRONG... how can you build real numbers? without real numbers you cannot have an algebra well defined or at least the usual one ...


quote from a genus:

God made the integers; all else is the work of man.
Leopold Kronecker

regards
marco
 
  • #4
"Is arithmetic part of mathematics?" No, not really. I've always considered them distinct.

"Arithmetic is needed in order to do higher maths." Oh certainly, just like math is needed to do physics.

"You can learn how to do algebra without any arithmetic at all." Not really.
 
  • #5
I refer you to Serre's "A course in arithmetic" since you do not seem to understand the meaning of the word.

https://www.amazon.com/dp/0387900403/?tag=pfamazon01-20

Hardcover: 132 pages
Publisher: Springer; 1st ed. 1973. Corr. 5th printing edition (October 10, 1996)
Language: English
ISBN-10: 0387900403

Serre's A Course in Arithmetic is a concentrated, modern introduction to three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms.
 
Last edited:
  • #6
I am confused. I see two distinct and non-mutually-exclusive questions here:
1] Is arithmetic part of mathematics? (your title and your post)
2] Is arithmetic needed to do higher order math? (your poll)

Which question do you want the answer to?
 
  • #7
mathwonk said:
I refer you to Serre's "A course in arithmetic" since you do not seem to understand the meaning of the word.

Meh. That meaning of "arithmetic" was old fashioned even back when the book was published.
 
  • #8
Arithmetic is the most useful and therefore the most important part of mathematics. You don't need to be fast or good at it, but you do need it before you can do higher maths.
 
  • #9
CRGreathouse said:
"Is arithmetic part of mathematics?" No, not really. I've always considered them distinct.

"Arithmetic is needed in order to do higher maths." Oh certainly, just like math is needed to do physics.

"You can learn how to do algebra without any arithmetic at all." Not really.
Hello, CRGreathouse! This is johnny from computer science and math forum. Nice meeting you in this forum! I hope to see you around in here as well, as far as I need help on my physics homework!
 
  • #10
Numerical analysis requires arithmetic, does that count as higher mathematics? Certain aspects certainly do, IMO.
 
  • #11
Dragonfall said:
Arithmetic is the most useful and therefore the most important part of mathematics. You don't need to be fast or good at it, but you do need it before you can do higher maths.

I'd say the same about high-school algebra and physics.

Gib Z said:
Numerical analysis requires arithmetic, does that count as higher mathematics? Certain aspects certainly do, IMO.

Ah, that's a good point.
 

FAQ: Arithmetic versus mathematics.

1. What is the difference between arithmetic and mathematics?

Arithmetic is a branch of mathematics that deals with basic operations such as addition, subtraction, multiplication, and division. Mathematics, on the other hand, is a broader subject that includes not only arithmetic but also other areas such as algebra, geometry, and calculus.

2. Why is arithmetic considered a subset of mathematics?

Arithmetic is considered a subset of mathematics because it is a fundamental aspect of mathematics and serves as the foundation for more advanced mathematical concepts. In order to understand other areas of mathematics, one must have a strong understanding of arithmetic.

3. Can arithmetic be used in real-world situations?

Yes, arithmetic is used in many real-world situations such as balancing a checkbook, calculating a tip, or determining the cost of items at a store. It is also used in various fields such as engineering, science, and finance.

4. Is it necessary to learn arithmetic before moving on to other areas of mathematics?

Yes, it is necessary to learn arithmetic before moving on to other areas of mathematics. As mentioned before, arithmetic serves as the foundation for more advanced mathematical concepts. Without a solid understanding of arithmetic, it may be difficult to understand and apply other areas of mathematics.

5. Can someone be good at arithmetic but not good at mathematics?

Yes, someone can be good at arithmetic but not good at mathematics. While arithmetic is an important aspect of mathematics, it is just one part of a larger subject. One may be skilled at performing arithmetic operations, but struggle with more abstract mathematical concepts.

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