does "mathematical concepts" mean the same as "mathematical terms or theorem"?

Discussion in 'English Only' started by roniy, Sep 5, 2006.

  1. roniy Senior Member

    Brooklyn NY
    ISRAEL: Fluent Hebrew ( Speak Russian, Learning English)
    does "mathematical concepts" mean the same as mathematical terms or theorem"?

    I know that "mathematical theorem" can be used like "pythagoras theorem".

    And mathematical terms are used like with the term "acute angle".

    But when is "mathematical concepts" used ? and can you add an example with your response, please ?

  2. Jamnica New Member

    US English
    In my opinion, "mathematical concepts" can include in its definition "mathematical theorems" and "mathematical terms," and even include "mathematical methods" (such as: algebraic method, hypothesis testing in statistics, or proofs) because a "concept" is the same as "idea" relating to mathematics, in this sense.

    I hope that helps!
  3. SPQR Senior Member

    American English
    The words "theorem" and "terms" at least partially subtend (pun intended :)) the overarching concept of "concepts".

    For the purposes of this discussion I would use "theorum" formally, as you have, such as the Pythagorean Theorem, Bayes Theorem (more statistics than pure math), the Last Theorem of Fermat, etc. It is a specific statement that clearly demonstrates one outcome based on a series of first premises (a proven theorem) or posits an outcome based on possibilities (Fermat's Theorem, until recently).

    In mathematics "term" is extremely broad. "Term" is part of an equation X + Y / Q = Z - Each of the X,Y,Q and Z's is a "term" in the sense it is a known or unknown variable in part of an equation. But "term" can also be used to describe any mathematical word. "Angle", "hypotenuse", "manifold", "torus", "prior odds", and thousands more are mathematical "terms" in terms of "words".

    The most debatable part of this discussion would be the word "concepts". It is likely the most "colloquial" in the sense that it might rarely be used in academic writing. Addition, subtraction, integration, differential equations, trigonometry, maps, plane and surface geometry, and thousands of others can be considered "concepts".

    So I shall walk out on a thin limb and be bold. I shall present three targets, and allow others to shoot at them.
    Individual electrons don't hurt when they hit you!

    Theorem - a formal, accepted, specific mathematical statement that combines a series of facts and leads to a conclusion. May be proven or unproven.

    Term - any element of a mathematical equation, or any word that is generally attributable to the field of mathematics (not exclusively)

    Concept - Any rational "idea" having to do with mathematics.

    Fire away!
  4. modus.irrealis Senior Member

    English, Canada
    I agree with Jamnica. "Mathematical concept" is a broader category than the other two. In my experience, "mathematical term" refers specifically to something that has a precise definition (although "term" can also mean a part of an equation or formula), and "theorem" is a statement that has been proven.

    I used Google, but a nice example of a "mathematical concept" would be "symmetry" which has different definitions depending on the context and is more of an organizing principle for doing math, and also e.g. lets you carry approaches from one area of mathematics to another.
  5. papillon Senior Member

    Barcelona, Spain
    Russian (Ukraine)
    I think the definitionof concept is broader than just a theorem or a term, it's more a way to think about something. For example, in physics, people can say things like "the concept of Big Bang is gaining a widespread acceptance among general public". In this case, Big Bang is not a theorem (although there ARE theorems related to that), but a way to think about the past and future of the Universe.

    Similarly, with mathematical concepts you can talk about the concept of prime numbers, or the concept of differencial equation.
    Do you understand the concept of matrices?
    where matrix is just a mathematical way to arrange numbers or values in a nice little table...

    EDIT: OK, I think I am a little late with my response...

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