Books: Think like a MATHEMATICIAN

Picture credit to goodreads.com

I purchased this book on 31/8/2019, at MPH Bookstore, Nu Sentral, and finished reading it on 7/8/2019. It’s not it took me a year to read it but, after a year I managed to find the time to read it. The book was written by Anne Rooney. For someone who is teaching Mathematics, I found the book very practical as it helps to relate everything around us in mathematical language.

Here’s some of my take from this book:

  1. Most of the mathematics in this book falls under the heading of ‘applied mathematics’ – it’s mathematics that is being used to solve real-world problems, applied to practical solutions in the world, such as how much interest is charged on a loan, or how to measure time or a piece of string. (pg 9)
  2. The Ancient Greek philosopher and mathematician Plato proposed in the early 4th century BC that everything we experience through our senses is an imperfect copy of a theoretical idea. (pg 16)
  3. We have probably developed a base-10 number system because we have ten fingers and thumbs so that making counting in ten easy. If instead of humans, three-toed sloths had become the dominant species, perhaps they would have developed a base-6 or base-3 number system – or even base-12 if they were happy to use the toes on their hind limbs as well as those on their forelimbs. (pg 40)
  4. The division of an hour into 60 minutes and a minute into 60 seconds comes from the Babylonian number system, though the Babylonian could not measure time that accurately. (pg 61)
  5. Hign number work harder – People consider the large numbers to be more significant than smaller numbers. (pg 81)
  6. On the familiar Mercator map, Greenland looks about the size of Africa, and Antarctica looks larger than all the warmer countries put together. In fact, Greenland is about a fourteenth the size of Africa. And Russia, which looks vast using Mercator’s projection, is also smaller than Africa in reality. (pg 106)
  7. If you are just reading the results of a survey in the media, look out for the sample size and demographic to give you a rough idea of how reliable the results might be. (pg 141)
  8. A pathogen’s guide to success – Epidemic and pandemic diseases such as flu and bubonic plague are caused by pathogens – often bacteria or viruses. To cause a pandemic, a pathogen needs to; be easily transmitted between people, be transmissible before people are so ill they can’t go out and make contact with other potential victims and let people live long enough to pass it on. Ideally, a pathogen needs to know some mathematics so that it gets all right. (pg 147)
  9. Size and the speed of light – The radius of the observable universe is greater than 13.8 billion light-years, even though the universe is reckoned to be 13.8 billion years old. (pg 155)
  10. Primes had a pretty lazy time of it until the need for data encryption came along. Now we send gazillions of secure transactions and other secret data across the internet daily, primes provide the equivalent of the Securicor vans that data travels in. (pg 164)
  11. Probability is at the heart of gambling. Indeed, it was gambling that prompted the first work in probability, the mathematical face of chance, or risk. A casino owner or bookmaker has to understand probability well enough to come out ahead most of the time, otherwise, they won’t make a profit. But they have to present the odds in a way that makes a bet look attractive to people. (pg 170)
  12. Bayesian Tanks – During World War II, the Allies tried to assess the production of German tanks by carrying out Bayesian analysis on data from tanks that had been captured or destroyed. ..Comparing the results of the statistical assessment with German records (after the war) revealed that statistics was a far more reliable method of working out military capability than intelligence gathering had been. (pg 180)
  13. The animal most deadly to humans is not, as you might think, a shark, tiger, hippo or anything else large. It’s not even a dog. It’s a mosquito. (pg 183)
  14. There are two common ways of misunderstanding risk, that can be summed up in statements like these; ‘I’ve been doing this for years and it’s never gone wrong, so I’m sure it will be fine’ and ‘You’ve been lucky so far – your luck’s bound to run out’. (pg 188)
  15. Perhaps it would be fairer to say that reality does not have to mimic mathematics since the reality we know is that of continuities and if mathematics fail to model them satisfactorily, that’s mathematic’s problem, not reality’s problem.




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