We live in a world of numbers and mathematics, and so we need to work with numbers and some math in almost everything we do, to control our happiness and the direction of our lives. The purpose of Coming Home to Math is to make adults with little technical training more comfortable with math, in using it and enjoying it, and to allay their fears of math, enable their numerical thinking, and convince them that math is fun. In a sense, it is an adult STEM (Science, technology, engineering and mathematics) book. A range of important math concepts are presented and explained in simple terms, mostly by using arithmetic, with frequent connections to the real world of personal financial matters, health, gambling, and popular culture. See http://www.facebook.com/Coming-Home-to-Math-106010094462401/.

Coming Home to Math is geared to making the general, non-specialist, adult public more comfortable with math, though not to formally train them for new careers or to teach those first learning math. It may also be helpful to liberal arts college students who need to tackle more technical subjects. The range of topics covered may also appeal to scholars who are more math savvy, though it may not challenge them. I will post new information about it here.

Also, I am posting a series of questions and their answers that illustrate the content in the book and that are designed to further math thinking and explore new examples of math in everyday life, at

(Coming Home to Math itself is not meant to be a textbook and does not have problems.)

These will be updated periodically, sometimes with problems concerning timely topics. For example, problems addressing the ramifications of the new 2021 NBA playoff system (Ch. 15. Probability and ranking, and entering the playoffs with “play-in” games, with equal winning probabilities) and ranked choice voting (Ch. 18.  In second place after the first round but maybe winning with ranked choice voting, with all providing rankings) were recently added to the pdf. (Both are a bit more advanced than the typical problem (as given below), and both have followup problems that explore math consequences with other assumptions.) Do recent TV ads for the Apple Watch cite location coordinates with enough significant figures to make any numerical sense? (Ch. 8. Rescued by significant figures)

Also, why is it that if you count the number of the rare four-leaf clover plants in a number of similar lawns and see that the average happens to be 4, you find exactly 4 of them in only 20% of the fields? (Ch. 15.  How many “lucky” 4-leaf clovers will you find?) Moreover, what math error did Isaac Asimov make at the very beginning of his science fiction classic The Foundation? (Ch. 4. Counting on you to find out how old Hari Seldon was when he died, as noted in the science fiction classic The Foundation?) Why is extrapolating the results of studies with a very limited number of samples ridiculous and dangerous? (Ch. 16. Is this statistical sanity or insanity?) Why is it absurd to expect annual inflation rates to decrease quickly, in a few months? (Ch. 13. How fast can the annual inflation rate fall?) A spice blend of five spices lists salt and sea salt as its 4th and 5th heaviest ingredients. You are concerned about consuming too much salt. What do you really know about the blend’s salt content? (Ch. 18. Just how much salt is there?)

Some illustrative basic problems are:

Problem – Based on the Chapter 4 presentation of linking numbers and on differences (Section 4.5) – Linking differences to the Roman calendar: According to legend, The Roman calendar started with the foundation of the city or Rome by Romulus and Remus on April 21, 753 BC. If 753 BC is considered year 1, what is year is 2020 AD?

Answer: 753 + 2020 – 1 = 2772, since the year after 1 BC was 1 AD—and there was no year 0. (The calendar information is from “The Rise of Rome Great Course” Season 1, Episode 2)

Problem – Based on the Chapter 13 presentation of interest rates, including compounding – High simple and compound interest rates with loan sharks: Loan sharks charge “excessive” interest”, which is sometimes owed on a periodic basis (without paying off the principal). As used on the TV classic The Soprano’s, it can be called the “vig” and expressed as a dollar amount or in terms of points, with frequent compounding and increased amounts (and other forms of payment) if not paid on time. Some organization charge 15% biweekly for pay day loans. What is the effective annual interest rate for this, if you pay the interest only every two week or if you do not pay it back and it compounds every two weeks?

Answer: There are 26 two-week periods every year, so if you pay interest only every two weeks over a year (the vig each time), the interest rate per year is 15% × 26 = 390%. So, you are paying 3.9 × the principal—and also owe the principal. This is simple interest, but still very excessive. If you allowed not to pay it every two weeks and are instead allowed to let it compound, at the end of the year you owe in interest the principal times (1.15)²⁶ – 1, which is an annual, compounded rate of 3,686% or 36.86 × the principal, and you also have to pay the principal. [https://www.youtube.com/watch?v=DIW5wYIZtHY, https://www.investopedia.com/terms/l/loansharking.asp, https://alearningaday.blog/2014/12/03/compound-interest-and-loan-sharks-mba-learnings/amp/]

Problem – Based on the Chapter 15 presentation of Probability – Pareto principle and horse betting – Using the Pareto Principle to set horse racing betting odds: One practical way of establishing odds in a horse race adapts the Pareto Principle (Chapter 2), with 80% of the winning probability assigned to the top 20% of the horses, and 20% to the probability to the remaining 80% of the field. Let’s say there are 3 horses in this top category. If these top three were co-favorites, what would the betting odds on each of them be?

Answer: The estimated probability that any of them wins would be 80/3% = 26.67%. With 3:1 odds the probability of winning are estimated to be 1/(1 + 3) = 25%, so each would have approximately 3:1 odds. 5:2 odds would mean a 1/(1 + 2.5) = 28.6% winning probability. So, both are approximate (and sufficiently good) answers, and the real answer is in between them.  Algebra shows the exact odds are 2.75:1 (or 5.5:2 or 11:4), which is not a standard betting line.  https://www.usracing.com/news/horse-betting-101/making-fair-odds-line

Also, explore the math of:

What is the basis for basis points?

How high is a mountain?

Why don’t Roman numeral clocks use the correct Roman numerals?

Will you be selected to serve on a jury?

How do you win playing the “numbers?”

How do you bet on a horse race that is fixed so you will always win? 

Who is related to whom, and by how much?