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Author Topic: Light reading - Math Jargon  (Read 443 times)  Share 

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RuiAce

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Light reading - Math Jargon
« on: November 08, 2017, 11:48:07 pm »
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Some of my replies to math questions on various threads involve big or intimidating/confronting words that people would be frightened by. In this post, I elaborate on some math jargon I happen to use in some questions. (If you're really interested, there's actually a whole Wikipedia page on this; I'm just taking some that I use on the forums.)

Writing up a proof
The reader - Whoever the target audience is
Clearly - I attempt to use this word only when the computations are actually that, clear and obvious. But "clearly" usually just means that a reader is expected to be able to do it eventually and without giving deep thought. It says nothing at all about how tedious the computations might actually be though.
Trivially - If I use this word, I mean the same thing as above but this time the computations should actually be near minimal. (But in general, it's used when something is certainly true. Could be as a consequence of being a definition in the world of math.)
In general - Something that should pretty much address all possible variations. A generalisation could be providing a formula where you don't know what \( x \) is and need to assume it's arbitrary, or it's just lazy induction (like what 2U students do in financial maths) or something else.
Brute force - Some very very tedious computation. Generally, avoiding anything that's clever.
By inspection - I try to stray away from this phrase because it tends to be unhelpful, but if it's possible to just "look" at your working out and figure out the answer from there, that's what I mean
"It can be shown..." - Jumping straight to a result without proof. I tend to do this for stuff like 3U projectiles - the equation of the time of flight etc. which are quite standard to the subject

Assumptions, statements and methods a proof
W.L.O.G. - Without loss of generality; related to 'in general' in that by proving something for one particular case we've actually catered for ALL possible cases.
Q.E.D. - Quod Erat Demonstrandum; essentially 'as required' in Latin, but generally viewed as old nowadays. (More accurately: as was to be demonstrated)
T.F.A.E. - The following are equivalent; used to list a whole bunch of propositions (i.e. statements) that are related, in that if one of them is true then so are all of them.
Exhaustion - Taking care of all cases, but actually doing it case by case.
Induction - (Actually a part of 3U) Relying on the truth of a base case to prove the truth of a whole sequence of cases
Contradiction - Assuming the opposite of what you're trying to prove, but then disqualifying it because you break math in the process of doing so
Implies - A statement's truth gives rise to another statement's truth. (Usually associated with 'therefore', but has the symbol \(\implies\))
Equivalence - As above, but going the other way as well (i.e. they both imply each other; essentially the key ingredient of T.F.A.E.)

Some informal notation
LHS - Left hand side of an equation
RHS - Right hand side of an equation
"MHS" - Sometimes, when an equation/inequality involves three sides to it, I call this the "middle hand side" (i.e. the centred expression)
"Nice" - Used for a whole bunch of things. Generally just means that something does what you expect it to
Vanish - In math, vanish basically means it goes to 0.
"Smooth" - Usually don't need this, but as far as the HSC goes 'smooth' just means it has a derivative there
Arbitrary - Essentially the same as "unknown". e.g. \( x \) is an arbitrary variable, until you do something like say "let \( x = 2\)"
Eventually - Something that happens but only after some condition involving a really large number is involved. Common when dealing with stuff like limits to infinity

And also some extra stuff
Note - Reminds the reader of something usually previously stated, or known (e.g. formula)
Remark - Either reminds the reader of something presently unknown, and/or provides information on alternative approaches
Standard - Fairly common method that you're expected to know and reproduce off-by-heart
« Last Edit: November 10, 2017, 10:07:47 am by RuiAce »