## Tuesday, August 2, 2011

### Math for Grownups

Being a math guy I couldn’t resist an offer to review Math for Grownups by Laura Laing. The main focus of the book is showing how to use basic mathematics in everyday situations. It is primarily aimed at adults who are not comfortable with math.

A healthy chunk of the book deals with financial matters such as mortgage payments and debt to income ratios, but it also covers many other areas like hanging curtains, shrinking or expanding recipes in the kitchen, counting calories, and more.

On the whole, Laing does good job of explaining how to do calculations in real-world situations for people who don’t already know how. However, the book contains a disappointingly large number of errors.

One example of an error is the calculation of how much one would pay to finance a car. If the car costs \$15,000 financed at 6% for 4 years, Laing says that the total financing cost is \$15,000 x 1.06 x 1.06 x 1.06 x 1.06. This would only be true if you let the interest build without making any payments for the full 4 years.

In the section on mortgages, Canadians should be careful because we usually use semi-annual compounding rather than the monthly compounding that is common in the U.S. The discussion of when buying points on a mortgage makes sense ignores the time value of money and therefore gives incorrect results.

When leasing a car, Laing suggests that leasing may be a better option that buying for a hypothetical car buyer. I tend to disagree; leasing a car is rarely a good idea. A possible exception is when the payments can be written off on taxes.

In an extended discussion of recipe calculations, 23/12 somehow turned into 2+1/12, and then turned back into 25/12. In a discussion of credit cards, the book claims that minimum payments can be as little as “1% of the interest”. Perhaps the author meant 1% of the balance plus the interest.

The author suggests that for retirement planning, you should save \$15 or \$20 for every dollar of income you need from your savings. This corresponds to a withdrawal rate of 5% to 6.7%. This seems a little high to me, particularly for anyone who retires young.

In a section on weight loss, Laing does an excellent job of explaining how many calories are in a pound of body fat and how long it necessarily takes to lose weight. Trying to lose weight is a marathon and not a sprint.

When giving metric conversion figures, the author shows little understanding of significant figures. Apparently, one pound is 453.59 grams, and one gram is 0.002 of a pound. In a round trip calculation, you lose nearly 10% with these figures. Perhaps 454 and 0.0022 would be better.

In a discussion of gambling, the author says that “with a little strategy, you might come out on top at the craps table.” I’m not sure what the author means here, but to be clear, nothing you can do (within the rules) at a craps table will tip the odds in your favour. With the right strategy, you can minimize the odds against you so that coming out ahead over a single session isn’t too unlikely. But, over the long run, you will lose money.

When discussing odds, the book has a simple error where a \$4 bet with a 15:1 payoff is said to pay out \$75. The answer is actually \$64. The book treated the situation as a \$15 bet with a 4:1 payoff.

In the formulas at the back of the book, the surface area of a cylinder has an equals sign where there should be a plus sign. In the glossary, the example of a least common multiple says that the LCM of 3 and 6 is 12. It’s actually 6. In the definition of whole number, zero is treated as positive; it’s actually neither positive nor negative.

Despite the fact that I’ve focused heavily on the errors, this book would likely help the less mathematically inclined learn how to handle some simple numerical situations in real life. The challenge is to get these people to read a book like this.

1. I'm not so sure such a book would be helpful. Books for the novice should be error-free, or else the novice will inevitably find something that makes no sense and will conclude that they're no good at math after all.

2. @Patrick: That is definitely a risk. Perhaps a second edition will be more useful.

3. When discussing odds, the book has a simple error where a \$4 bet with a 15:1 payoff is said to pay out \$75. The answer is actually \$64.

Why is the answer \$64? I'm no gambler, but I thought the payoff referred to the total amount given to you, ie \$60 for a 15:1 payoff on a \$4 bet.

4. @Mike: By a "15:1 payoff" we mean that you get your original bet back plus 15 times your bet. So, this would be a fair bet if the odds of winning are one in 16. I've never liked this way of expressing odds and payoffs, but it is very widely used.

5. Error in your post - "you should save \$15 or \$20 for every dollar of income you need from your savings"

I'm trying to wrap my head around how to save 15-20x more than I make... sounds pretty awesome.

Craps: Her key word is "might" it appears. I could also play individual numbers at roulette and MIGHT come out ahead instead of losing 36 times. The most you can hope for in Craps is to minimize your losses, as even betting with the house has a house edge.

Regardless, these errors seem glaring and far more damaging than helpful. If you get math already, then finding an error and confirming you're right and they're wrong is fairly easy, but if you don't? Then it just becomes more frustrating for the learner, or they'll just memorize and carry those errors out in the real world.

6. @Astin: By "save" here, the author was talking about the total amount saved by the time you retire, not your yearly contribution to savings.

I should stress that I mentioned every error I found. The book contains a great many useful passages that seemed to be error-free. But I agree that errors are a problem in a book aimed at readers who lack confidence in math.