| ( red = incorrect --> blue = correct ) |
| Errors to be corrected |
| page 63: Eugen Wigner should be written Eugene Wigner. Further down the page, the word unknown is cut after the k, it should be cut after the first n. |
| page 82: We discuss the discriminant, and we mistakenly write that it is the square root of b² - 4ac. It is, of course, b² - 4ac itself. And depending on whether it is positive or negative, it does or does not have a square root. |
| page 91: This function is called the vector product, or cross product, or outer product. --> This function is called the vector product, or cross product. (the outer product is something else) |
| page 130, third paragraph: it gave raise to --> it gave rise to |
| page 163, formula (10.3): matrix M should be matrix I |
| page 230: coninuous -> continuous |
| page 320: we write that the Z3 computer built by Konrad Zuse in 1941 was an entirely electronic machine; this is not correct: it still incorporated electromechanical devices. The first entirely electronic machine is the ENIAC. |
| Errors that have been corrected |
| Notes |
|
Pages 83, 84, 85: Formula (5.13), known as "Cardano's formula," is not as simple as it appears. When q2/4 + p3/27 is positive, it is straightforward, since the two numbers under the cube roots are real and each has a unique real cube root. But when q2/4 + p3/27 is negative, formula (5.13) is ambiguous. The square root of q2/4 + p3/27 is then a non-real complex number, and so are the two numbers under the cube roots, which are moreover conjugates of one another. Now, a nonzero complex number has three distinct cube roots, not just one: formula (5.13) is therefore not well-defined without a further specification. For example, in formula (5.15), which has three real roots, if one takes the so-called "principal" cube root of 2+11i, namely 2+i, formula (5.16) gives x = (2+i) + (2−i) = 4; the other two roots of (5.15), −2−√3 and −2+√3, are obtained using the other determinations of the cube root. For further details, see a textbook on complex numbers. |