Rigel Kent

Suppose we have a function \(y = f(x)\) and its value at \(x = a\), \(f(a)\) is a nice value and can be easily calculated. Apparently, a slight perturbation on \(x\) from \(x = a\) to \(x = a + \epsilon\) will be accompanied by a slight change in the value of \(y\), where \(a \gg \epsilon\). Computation of the new value of \(y\), that is, \(f(a + \epsilon)\) is one of the standard operating procedure taught in the fourth-form calculus. For instance, in 2017, the following question appeared as the second question in the second paper of the SPM additional mathematics exam. It is given that the equation of a curve is \(y = \frac{5}{x^2}\). Find the value of \(\frac{{\rm d}y}{{\rm d}x}\) when \(y = 3\). Hence estimate the value of \(\frac{5}{2.98^2}.\) The standard textbook trick uses only the first two terms in the following series: $$f(a + \epsilon) = \sum_{k=0}^\infty \frac{f^{(k)}(a) \epsilon^k}{k!}$$ that is, $$f(a + \epsilon) \approx f(a) + f'(a) \epsilon$$ a...

The SIR (susceptible/infected/removed) model in epidemiology is first considered nearly 100 years ago by two Scottish doctors, William Kermark (1898-1970) and Anderson McKendrick (1876-1943) (see W. O. Kermack and A. G. McKendrick (1927) Contribution to the mathematical theory of epidemics , Proc. Roy. Soc. Lond A 115, 700-721). In 1927, they opened their paper with the following line: One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population... When a group of infectious species, \(I\), is introduced into a community of susceptible species, \(S\) (which is not previously exposed to the RNA materials), the virus spreads from the infectious species to the susceptible species, thus diminishing the susceptible species and growing the size of the infectious species. $$I + S \longrightarrow I' + S'...

Cyril Northcote Parkinson(1909 - 1993)是馬來亞大學的第一任萊佛士歷史教授。 他是第二任萊佛士歷史教授K. G. Tregonning(1923 - 2015)的博士論文導師，而Tregonning後來是邱繼金Khoo Kay Kim(1937 - 2019)的學士論文導師。所以算起來，Parkinson是邱老師的師公。 英國人在二戰後1949年在新加坡搞了一間叫馬來亞大學的學校。當時Parkinson在利物浦大學教書，年薪400英鎊。馬來亞大學因為要招攬學術人才，所以用約1000英鎊的年薪把Parkinson從英國搬到了新加坡。1960年的1000英鎊大概是現在的120千令吉。 Parkinson原本是打算一直教到退休的，不過後來馬來亞的政治局勢迫使他在1958年辭職。他是這樣說的： . . . to teach and write history until the age of retirement . . . Fate decreed otherwise . . . for the politics of Singapore and Malaya made the post untenable. 其實馬來亞的政局可能只是一個小理由，更大的理由是因為Parkinson在1957年出版了一本叫Parkinson’s Law的暢銷書。該書在全球的大賣，是Parkinson意想不到的。大賣的必然結果是鈔票和榮譽。有了鈔票和榮譽，誰還會選擇窩在一個小島的歷史系過完餘生。 Parkinson’s Law當年是一個很轟動的理論，他在書裡面是這樣寫的： Work expands so as to fill the time available for its completion. . . Granted that work (and especially paperwork) is thus elastic in its demands on time, it is manifest that there need be little or no relationship between the work to be done and the size of the staff to wh...