When Johann Bernoulli published his lectures on integrals in 1742, integral calculus had become very advanced since the time of their composition in 1692. Nevertheless, these lectures are of excellent clarity and simplicity even when the book deals with major problems of Mathematical Physics. Just to pique some interest, we offer a commented…

Most any students can explain the meaning of "a[superscript b]", for "a" [element-of] [set of real numbers] and for "b" [element-of] [set of integers]. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" [element-of] [set of real numbers] and for…

Real numbers are often a missing link in mathematical education. The standard working assumption in calculus courses is that there exists a system of "numbers", extending the rational number system, adequate for measuring continuous quantities. Moreover, that such "numbers" are in one-to-one correspondence with points on a "number line". But…

The paper details a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers…

The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…

Several methods of teaching college-level mathematics sequences are examined for their advantages, disadvantages, and costs. Materials considered include textbooks, film sequences, videotaped lectures, and individualized teaching machines. (SD)