Whoever thinks **algebra** is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that **algebra** and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.

Through **algebra** you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of invention so greatly exercised and refined in this analysis.

Von Neumann languages do not have useful properties for reasoning about programs. Axiomatic and denotational semantics are precise tools for describing and understanding conventional programs, but they only talk about them and cannot alter their ungainly properties. Unlike von Neumann languages, the language of ordinary **algebra** is suitable both for stating its laws and for transforming an equation into its solution, all within the "language."

I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix **algebra** used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen’s, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell’s equations.

My **algebra** was relatively poor. I found it very difficult to use equations that substituted numbers — to which I had a synesthetic and emotional response — for letters, to which I had none. It was because of this that I decided not to continue math at Advanced level, but chose to study history, French and German instead.

Addition and multiplication In our study of oscillating systems we shall have occasion to use one of the most remarkable, almost astounding, formulas in all of mathematics. From the physicist's point of view we could bring forth this formula in two minutes or so, and be done with it. But science is as much for intellectual enjoyment as for practical utility, so instead of just spending a few minutes, we shall surround the jewel by its proper setting in the grand design of that branch of mathematics called elementary **algebra**.

The truth is that Mozart , Pascal , Boolean **algebra**, Shakespeare , parliamentary government, baroque churches, Newton , the emancipation of women, Kant , Marx , and Balanchine ballets don't redeem what this particular civilization has wrought upon the world. The white race is the cancer of human history.

Linear Programming is a generalization of Linear **algebra**. It is capable of handling a variety of problems, ranging from ?nding schedules for airlines or movies in a theater to distributing oil from re?neries to markets. The reason for this great versatility is the ease at which constraints can be incorporated into the model.

The absolute scholar is in fact a rather uncanny being. He is instinct with Nietzsche's finding that to be interested in something, to be totally interested in it, is a libidinal thrust more powerful than love or hatred, more tenacious than faith or friendship — not infrequently, indeed, more compelling than personal life itself. Archimedes does not flee from his killers, he does not even turn his head to acknowledge their rush into his garden when he is immersed in the **algebra** of conic sections.

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