One thing I've noticed is that programming today involves working with strings and manipulation of strings.

Math [in school] seems mostly to deal with numbers.

One difference between programming and math might be that programming works with strings a lot, whereas math not.

Concatenating strings, replacing substrings in a string, parsing strings.

We don't learn this in math. Do we? does math have anything to do with strings? 

''There is a branch of mathematics that deals with strings. Pretty much, if it has abstract structure, there's a branch of mathematics that deals with it. [Yes, if by "in school" you mean primary education. In college I did a great deal of math that had little to do with numbers (as well as a great deal that did). Doesn't change the fact that there is a branch of mathematics that deals with strings.]''

Which branch? Any information on it online? Does it deal with substrings and parsing?

See http://en.wikipedia.org/wiki/Formal_language for the theoretical part
See http://en.wikipedia.org/wiki/String_(computer_science) for strings in particular
See http://en.wikipedia.org/wiki/Regular_language for the popular area of RegularExpression''''''s

''Formal languages, which in turn is part of mathematical logic. Yes it deals with substrings and parsing, although it's probably presented in a way you aren't used to.''
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Maybe the "math of lists" can be partly adopted for this use.

''What are you talking about?''

Strings are often modeled or viewed as lists of characters.

And Characters can be modeled or viewed as lists of bits.

{''Arrays more so than lists, unless you're speaking with a lisp in your voice. Which begs the next question: what branch of math deals with characters, or arrays of characters? ''}

Algebra
* a = 65
* a = 00100001

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String theory in physics attempts to study strings, but it's not very clear or obvious in string theory what concatenation means.  Concatenation is something programmers take for granted, and string theory hasn't really a clue about it (or doesn't explain it clearly and simply).  Maybe it's something string theory is missing: a description of how concatenation of information works in the universe.  Possibly programming and physics and math are not separate - they are three of similar studies that could be unified more than they are now. Why doesn't string theory in physics also study strings in programs, if the universe is a quantum program. I get the impression that physics is a gobblydegook of its own, and programming is a gobblydegook of its own, even though both physics and programming have "strings" if we are to take string theory semi seriously.

''Universe string A + Universe string B = BSOD''
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See also: StringTheory, IsProgrammingMath
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CategoryDataStructure