Archive for February, 2013

The Swingin’ Spring

Oscillations surround us, pervading the universe from the vibrations of subatomic particles to fluctuations at galactic scales. Our hearts beat rhythmically and we are sensitive to the oscillations of light and sound. We are vibrating systems.

An exhibition called Oscillator is running at the Trinity College Science Gallery and this week’s “That’s Maths” column ( TM015 ) gives a taste of what can be seen there.

Fascinating Dynamics
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Singularly Valuable SVD

In many fields of mathematics there is a result of central importance, called the “Fundamental Theorem” of that field. Thus, the fundamental theorem of arithmetic is the unique prime factorization theorem, stating that any integer greater than 1 is either prime itself or is the product of prime numbers, unique apart from their order.

The fundamental theorem of algebra states that every non-constant polynomial has at least one (complex) root. And the fundamental theorem of calculus shows that integration and differentiation are inverse operations, uniting differential and integral calculus.

The Fundamental Theorem of Linear Algebra
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Computer Maths

Will computers ever be able to do mathematical research? Automatic computers have amazing power to analyze huge data bases and carry out extensive searches far beyond human capabilities. They can assist mathematicians in checking cases and evaluating functions at lightning speed, and they have been essential in producing proofs that depend on exhaustive searches. 

The That’s Maths column in this week’s Irish Times ( TM014 ) is about the use of computers for proving mathematical theorems, and also for simulating physical systems. Continue reading ‘Computer Maths’

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