An introduction to the early development of mathematics (Q2793623)

This volume contains much that is misleading, inaccurate, or downright erroneous -- both historically and mathematically. The author attempts to offer a textbook that provides not necessarily mathematically-inclined students with glimpses of the mathematics of past cultures. Separate chapters discuss each of Egyptian, Chinese, Babylonian, Greek, Indian, and Islamic mathematics, and exercises are provided. However, misinformation abounds throughout; here is just a sampling:NEWLINENEWLINE(1) In the twelfth century, Bhāskara~II found that (in modern notation) \(\sqrt{a+\sqrt{b}}=\sqrt{(a+\sqrt{a^2-b})/2} + \sqrt{(a-\sqrt{a^2-b})/2} \). The book wrongly renders this as the incorrect equation \(\sqrt{a+\sqrt{b}}=\sqrt{a+\sqrt{(a^2-b)/2}} + \sqrt{a-\sqrt{(a^2-b)/2}}\). It then adds insult to injury by taking Bhāskara~II to task because when \(a=1=b\), the garbled version does not work! On the other hand, the author mistakenly claims that the erroneous equation does hold when \(a=7\) and \(b=4\).NEWLINENEWLINE(2) The book states, ``There are countless unproven conjectures about prime numbers. One is that between any number \textbf{n} and twice that number \textbf{2n} there is at least one prime.'' Of course, this is Bertrand's postulate, which was proved by Chebyshev more than 160 years ago.NEWLINENEWLINE(3) On the very next page, in discussing the proof of the infinitude of primes, the author in effect (he uses words, rather than formulas) claims falsely that \(p_1p_2\cdots p_N+1\) is prime.NEWLINENEWLINEIt should also be noted that although the book's back cover promises ``a companion website that includes additional exercises'', I was unable to find the purported exercises online.