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Bright Science is a free YouTube channel of over 1300 study videos for high schoolers (or precocious middle schoolers). Most are about five minutes (some longer, some shorter) and cover topics like chemistry, physics, calculus, geometry, biology, Algebra, trigonometry, grammar, ACT prep, and SAT prep. Futures Channel.
There are many branches of maths, including algebra, geometry, calculus and statistics. WHAT ARE YOUR PROUDEST CAREER ACHIEVEMENTS SO FAR? WHAT DOES A DAY IN THE LIFE OF A MATHEMATICIAN LOOK LIKE? Many of the classes I took didn’t end up directly contributing to my career.
But, first and foremost, the story of the Second Law is the story of a great intellectual achievement of the mid-19th century. There’s a discussion about H for systems that interact, and how there’s an equilibrium value achieved. It’s exciting now, of course, to be able to use the latest 21st-century ideas to take another step.
But what about other models of computation—like cellular automata or register machines or lambda calculus? In other words, we’re concerned more with what computational results are obtained, with what computational resources, rather than on the details of the program constructed to achieve this.
It’s not obvious that it would be feasible to find the path of the steepest descent on the “weight landscape” But calculus comes to the rescue. It turns out that the chain rule of calculus in effect lets us “unravel” the operations done by successive layers in the neural net.
For three centuries theoretical models had been based on the fairly narrow set of constructs provided by mathematical equations, and particularly calculus. And it’s one that can “mine” the specific modeling achievements of work on complexity and bring them to a broader and more foundational level.
And in what follows we’ll see the great power that arises from using this to combine the achievements and intuitions of physics and mathematics—and how this lets us think about new “general laws of mathematics”, and view the ultimate foundations of mathematics in a different light. 3 | The Metamodeling of Axiomatic Mathematics.
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