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The Role of Mathematics in Education: What Professions You Can Get in the Future Have you ever found yourself pondering the real-world applications of those algebraic formulas or geometric theorems you spent hours trying to decipher in school? But what makes mathematics the lingua franca of computerscience?
However, one thing that’s often overlooked is computerscience education, an incredibly essential subject and skill in today’s digital era. While the science aspect (chemistry, biology, and physics) and mathematics (calculus and algebra) is a breeze to figure out, the engineering and technology aspects are less straightforward.
But the computer let me discover just by systematic enumeration the 2-state, 3-color machine that in 2007 was proved universal (and, yes, it’s the simplest possible universal Turing machine). In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be. Let’s look at a very simple case.
Mathematics is normally done at the level of “specific mathematical concepts” (like, say, algebraic equations or hyperbolic geometry)—that are effectively the “populated places” (or “populated reference frames”) of metamathematical space. Imagine for example that one has a neural net with a certain architecture.
Mathematics is normally done at the level of “specific mathematical concepts” (like, say, algebraic equations or hyperbolic geometry)—that are effectively the “populated places” (or “populated reference frames”) of metamathematical space. Imagine for example that one has a neural net with a certain architecture.
. “Lick” Licklider —who persuaded Ed to join BBN to “teach them about computers”. It didn’t really come to light until he was at BBN, but while at Lincoln Lab Ed had made what would eventually become his first lasting contribution to computerscience. Then McCarthy started to explain ways a computer could do algebra.
For example, we know (as I discovered in 2000) that (( b · c ) · a ) · ( b · (( b · a ) · b )) = a is the minimal axiom system for Boolean algebra , because FindEquationalProof finds a path that proves it. Some correspond to theoretical computerscience.
Algebra , which incorporates unknown variables into arithmetic equations. Those who are interested in a career in Cryptography should consider a bachelor’s degree in computerscience, computer engineering, mathematics or similar, as well as a master’s degree in a complementary field. Explore the STEAM Series.
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