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Jun
8
answered To prove : Perfect square
May
9
revised Where does binary arithmetic/manipulation enter the mathematics/engineering curriculum?
extra question
May
9
asked Where does binary arithmetic/manipulation enter the mathematics/engineering curriculum?
Apr
25
comment History of dot product and cosine
The dot product as an explicit algebraic operation is not so necessary to the 'dischord of appearances', it is the $a d + b e + c f$ a decidedly open calculation in comparison to the obscurantist length of a vector and angle formula (requiring much more machinery). Any idea if this (what Hamilton knew) was popular before Gibbs?
Apr
10
comment How do you explain the concept of logarithm to a five year old?
@DanNeely: Yes, you're right. There are many contexts where an explanation could work/be meaningful and useful to a 5 yar old (JohnS keeps coming up with good ones). I think I was caught up in the symbol manipulation. But I still think the simple 'number of digits' concept, which would totally work for older kids (8-10 yoa) would be obscurantist to even a curious 5 year old.
Apr
8
comment How do you explain the concept of logarithm to a five year old?
To a -5- year old? Aren't you stretching the limits of relevance? Most (even bright) kids are only about to 'get' negative numbers (which is arguably a much prior concept (inverse of addition) that is much more accessible. If this is just for fun (for a child that can 'get' things), then @JohnS's example looks to be aan excellent idea with lo-tech/lo-conceptual overhead.
Mar
29
comment Bounding ${n \choose k}$
${n \choose k}$ increases up to $k = \lfloor n/2 \rfloor$, then goes down. So you only really need to worry about the left side up to the max.
Mar
25
comment Pseudo Proofs that are intuitively reasonable
Isn't everything rigorous until you throw some doubt on it (which further elucidation (notational conventions, development of concepts) makes more rigorous)?
Feb
28
revised Connecting finite automata and regular languages in teaching/applications
added links
Feb
28
comment How to pronounce $\setminus$
But is that the way you in practice pronounce it?
Feb
28
comment “Binomial theorem”-like identities
@anon: falling factorials are counting (iteratively) selection without replacement (and rising factorials do the same starting from the top).
Feb
25
asked Connecting finite automata and regular languages in teaching/applications
Feb
13
comment Category of Trees as sub-category of Category of Graphs
@DamianSobota: you could make that a full answer rather than a comment.
Dec
4
comment A list of all algebras?
Here's a WP list of algebras.
Oct
31
comment New to probability - Is this true?
20-sided die (and also 12-sided die) are notoriously non-random. Because the angles at the vertices and edges are so obtuse, even without deliberate modification, they are very easy to wear to the point where some sides are favored rather than others. A better physical device to get 1 through 12 would be to roll a 6-sided side and flip a coin: add 6 for tails and 0 for heads. But of course theoretically, leaving out 13 through 20 works just fine.
Oct
22
answered If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$?
Oct
17
comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
@Mariano: Re: not counting NNx or C(x)(tautology) - you might be able to syntactically ignore the latter (if you enumerate a system that includes enumerating tautologies, but eliminating double negation seems hard (just intractable to create the system of equations). Anyway, might as well include those because those are viable tautologies.
Oct
17
revised How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
brief extra explanation
Oct
17
comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
@Mariano: sorry, it was typed on an iPhone..somehow hard to think in a really tiny screen! I'll try to embellish my answer to help explain.
Oct
17
comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
@Mariano: oh duh... but easy to miss.