| ( red = incorrect --> blue = correct ) |
| Errors to be correctedd |
| Errors that have been corrected |
| Notes |
| Note 1 : It is worth adding the following item to the bibliography: Geroch, Robert, Mathematical Physics, The University of Chicago Press, 1985. It is an excellent graduate-level text that shows the utility of category theory in physics. |
Note 2: Page 22: Formula (1.7), 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 (1.7) 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 (1.7) is therefore not well-defined without a further specification. For example, in formula (1.8), which has three real roots, if one takes the so-called "principal" cube root of 2+11i, namely 2+i, formula (1.10) gives x = (2+i) + (2−i) = 4; the other two roots of (1.8), −2−√3 and −2+√3, are obtained using the other determinations of the cube root. For further details, see a textbook on complex numbers. |