Many educators say that strong algebra skills are part of the key to success in calculus. In addition to reviewing the trigonometric functions, precalculus courses cover commonly used algebraic functions such as quadratic, exponential, polynomial and logarithmic. The graphing of functions is an importa...
business problems. Also, a Data Analyst must know how to use tables, charts, graphs, and more. It is essential to be comfortable with college-level algebra, thereby making the visualization of data more appealing. Knowing linear algebra and multivariate calculus is very helpful for Data Analysts...
of functions defined on elements of the ultrafliter. For instance, if is the natural numbers, then itself is an order of infinity, as is , , , , and so forth. But we exclude ; it will be important for us that the order of infinity is strictly positive for all sufficiently large . ...
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The entire game is now to use Shannon entropy inequalities and “entropic Ruzsa calculus” to deduce a contradiction from (1) for small enough. This we will do below the fold, but before doing so, let us first make some adjustments to (1) that will make it more useful for our purposes...
Combinators, there's a technical definition for it, but it's mostly used as a function that will take one or more functions and transform them into a new function. There is a technical term in lambda calculus, a technical usage for it, but in practice, in the industry, that's what ...
Walter Pitts and Warren S McCulloch, two mathematicians, published ‘A Logical Calculus of the Ideas Immanent in Nervous Activity’ in the Journal of Mathematical Biophysics. They described the behavior of human neurons with the help of simple logical functions that inspired an English mathematician ...
The field of “BERTology” aims to locate linguistic representations in large language models (LLMs). These have commonly been interpreted as rep
Yes, we could do the analog of generating pictures like the ones above, separately for each of the weights. But it turns out that a standard result from calculus gives us a vastly more efficient procedure that in effect “maximally reuses” parts of the computation that h...
The one chapter which uses heavier mathematics extensively is Chapter 2, which requires a little multivariable calculus and linear algebra. If those aren't familiar, I begin Chapter 2 with a discussion of how to navigate the mathematics. If you're finding it really heavy going, you can simply...