My Math Forum Learning to read maths formulas

 February 5th, 2013, 07:01 AM #1 Newbie   Joined: Feb 2013 Posts: 7 Thanks: 0 Learning to read maths formulas Hi, im new in the forum, nice to meet you! I'm engineer and I want improve my mathematical reading, i.e. formula syntaxis, im very noob in this. My doubt is: having: $S= \{s_1, s_2, s_k, ... , s_n\}$ to iterate through every element of S set, its the same write: $\sum_{s_k \in S}^{}{S_k}$ that $\sum_{k=1}^{n}{S_k}$ ?Ώ Take it easy , and thanks for your time. -- Regards, r0i.
 February 5th, 2013, 07:19 AM #2 Member   Joined: Jan 2013 Posts: 93 Thanks: 0 Re: Learning to read maths formulas Yes, they are the same. In the former notation, you can drop the subscript and just write $\sum_{s\in S}s$ This is mostly used in cases where the elements are not listed nicely like $\{s_1,\ldots,s_n\}$. For example, if $S$ is the set of prime numbers less than 100, then the above is a way of expressing the sum of all primes numbers less than 100.
 February 5th, 2013, 07:27 AM #3 Newbie   Joined: Feb 2013 Posts: 7 Thanks: 0 Re: Learning to read maths formulas Hi Crimson Sunbird, thanks for your fast answer, and for the subscript tip. I understand it, in cases like you described, the abbreviation has "implicit information". Again thanks for your time. -- Regards, r0i.
 February 5th, 2013, 07:35 AM #4 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Learning to read maths formulas I don't think of that as an abbreviation. I see $\sum_{k=1}^n$ as an abbreviation for $\sum_{k\in\{1,\ldots,n\}},$ so this one works out to be $\sum_{k\in\{1,\ldots,n\}}s_k=\sum_{s\in S}s$ where the latter has the advantage of not needing an explicit numbering of the elements.
 February 5th, 2013, 07:48 AM #5 Newbie   Joined: Feb 2013 Posts: 7 Thanks: 0 Re: Learning to read maths formulas Hi CRGreathouse, in this context, n is the maximum value that can reach the subscript, i.e. indicating max. no. of elements in the set, and k is the current element, so in that case i think yes, as Crimson Sunbird said. In your last equation, I understand that you try get every element in S n times, or in python: Code: for k in range(n): for s in S: # stuff I misunderstood? Thanks for your time . -- Regards, Roi.
February 5th, 2013, 09:00 AM   #6
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Re: Learning to read maths formulas

Quote:
 Originally Posted by r0i I misunderstood?
Yes. On either side of the equation each term appears only once, not n times. (n elements total, not n^2.) So if S = {1, 2} either side gives you 1 + 2 = 3, not 1 + 1 + 2 + 2 = 6.

 February 5th, 2013, 09:08 AM #7 Newbie   Joined: Feb 2013 Posts: 7 Thanks: 0 Re: Learning to read maths formulas ok, then we cant do directly: Code: for s in S: #stuff we must iterate over the subscript, and use it as index in S: Code: for k in range(n): sk = S[k] # stuff Right?
 February 5th, 2013, 09:29 AM #8 Newbie   Joined: Feb 2013 Posts: 7 Thanks: 0 Re: Learning to read maths formulas Actually, Im reading in a paper called "A new fuzzing method using multi data samples" where a a equation in the form I posted is showed. The information given is the next: $S= \{s_1, s_2...s_k,...s_n\}$ In which: sk, kth data sample of input elements to a target software mined, S is a primitive set of the data sample. And S? is a set constituted by representative elements selected from S, and S? is the data sample combination to be used to generate test cases. [...] Tr1 and Tr2 are two different transformers form sk to sampletreek,, M is a set of mutators, The next pseudo-code is showed: Code: 1. M = {m1, , mi, , mw } 2. testsuite = {} 3. for (each sk in S?) 4. { 5. sampletreek = Tr1 (sk) 6. for (each mi in M except GAMutator) 7. { 8. MTS = ... #stuff 15. } 16. } 17. run every element in testsuite in the target software and monitor them Then the equation appears: $\sum_{s_k \in S'}^{}{\sum_{i=1}^{w}{|m_i(Tr(s_k))|}}$ With this I related the first summation with the for loop on l.3, and the boundaries of the second with the l.1 M = {m1, , mi, , mw } i, k and the for loop on l.6. In the practice it seems the same, iteratoins over arrays/lists/sets, as you can see in pseudo-code :S. Some help to clarify ?
February 5th, 2013, 11:11 AM   #9
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Re: Learning to read maths formulas

Quote:
 Originally Posted by r0i Right?
No, just the opposite: usually in post-high-school math you don't use indices, you use elements of a set.

February 5th, 2013, 11:17 AM   #10
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Re: Learning to read maths formulas

Quote:
 Originally Posted by r0i $\sum_{s_k \in S'}^{}{\sum_{i=1}^{w}{|m_i(Tr(s_k))|}}$ With this I related the first summation with the for loop on l.3, and the boundaries of the second with the l.1 M = {m1, , mi, , mw } i, k and the for loop on l.6. In the practice it seems the same, iteratoins over arrays/lists/sets, as you can see in pseudo-code :S. Some help to clarify ?
This could equally be written
$\sum_{s \in S'}^{}{\sum_{i=1}^{w}{|m_i(Tr(s))|}}$
and means the sum of the absolute value of m_i(Tr(s)) over all s in S and all i from 1 to w. There are #S * w summands in total, where #S is the number of elements in S.

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