Coming Home to Math: Become Comfortable with the Numbers that Rule Your Life, by Irving P. Herman (World Scientific, 2020)
https://doi.org/10.1142/11540, ISBN: 978-981-120-984-0 (hardcover); 978-981-121-126-3 (softcover)
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.
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 am also 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 (see below). Though Coming Home to Math itself is not meant to be a textbook and does not have problems, I am posting many problems and their solutions, for those who want to review and explore more, that range from a more rudimentary to more challenging levels (below). I will also post new information, updates, and insights (below).
To learn more, link to:
Chapter questions and answers (not in the book)
New information, updates, and insights
Also see http://www.facebook.com/Coming-Home-to-Math-106010094462401/, and the Professional page on this site for a discussion of my other books (under The Three Books of Herman).
Table of Contents
Preface
Our World of Math and Numbers:
– Introduction
– We Use Numbers Here, There and Everywhere
– Numbers Are Some of My Favorite Things
The First World of Math: The Eternal Truths of Math:
– Linking Numbers: Operations on Numbers
– Words and Numbers: Being Careful
– Writing Really Big and Really Small Numbers, and Those In-between
– Touching All Bases, At Times with Logs
– Numbers Need to be Exact, But It Ain’t Necessarily So
– The Different Types of Numbers Have Not Evolved, But Our Understanding of Them Has
– Really, Really Big and Really, Really Small Numbers
– The Whole Truth of Whole Numbers
The Second World of Math: The Math of Doing:
– The Math of the Digital World: Modular Arithmetic (or Using Number Leftovers)
– The Math of What Will Be: Progressions of Growth and Decay
– Untangling The Worlds of Probability and Statistics
– The Math of What Might Be: Probability — What Are the Odds?
– The Math of What Was: Statistics — The Good, The Bad, and The Evil
– The Math of Big Data
The Third World of Math: The Math of Making Decisions and Winning:
– The Math of Optimization, Ranking, Voting, and Allocation
– The Math of Gaming
– The Math of Risk
Closing Thoughts
Chapter questions and answers (which are not in the book)
Coming Home to Math is not a textbook and does not have problems. Still, I am posting a pdf with simple to more complex problems and their solutions, for those who want to practice the presented math (at a more simple level and so to use it as a text) and those who want to explore topics in more depth and to have more of a challenge.
Most problems are easy, very straightforward and short, and are noted with an *. (When they involve the cultural use of numbers not noted in the book, you can search online about them.) Very slightly more involved questions are denoted with an **. A few problems are more involved or advanced and are noted with an ***. Problems will be updated periodically, sometimes with problems concerning timely topics.
Some timely topics are 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?
New information, updates, and insights
The math in this book will always remain current, but cultural references and such can change.
Metrics-the poverty line
- (Section 16.4.2 Metrics, page 257) As noted in the book, the official U.S. metric poverty line standard is the annual cost of the cheapest sustainable diet per person multiplied by the number of people in the household, then multiplied by three to account for other expenditures. Late in 2025, the poverty line was about $32,000 for a family with two kids; however, a new analysis recommended changing this metric in a manner that would increase the poverty line to $140,000/year. Then, this analysis was called ridiculous due its underlying concepts, details, and use of evidence. The bottom-line is: metrics are useful, but are not etched in stone. Proposed changes to them are subject to detailed scrutiny and challenges-before generally being deemed new, useful metrics. (https://www.thefp.com/p/why-do-americans-feel-poor-because, https://www.thefp.com/p/the-myth-of-the-140000-poverty-line)
Roman numerals-get them right or else
- (Chapter 9 on numbers, page 94, footnote 58) The film The Last Time I Saw Paris was made in 1954, so the copyright notice in the film should have said it was copyrighted in MCMLIV (for 1954). Instead it said MCMXLIV, which meant 1944 because of the X before the L turned the “50” in a “40.” A trivial mistake? No! MGM was supposed to be granted a 28 year copyright term for the film, and then in 1982, would be able to renew it. But MGM lost the copyright because it neglected to renew the copyright in 1972 (28 years after the stated copyright year of 1944), so the film entered the public domain then. (https://en.wikipedia.org/wiki/The_Last_Time_I_Saw_Paris)
Rounding off, and discontinuing the minting and use of pennies
- (Section 8.1.1 on rounding off, page 80) Rounding off numbers can lead to a systematic bias or skewing if not handled properly, as seen in the cited section. In 2025 it was announced that the U.S. would no longer mint pennies starting in 2026. Expecting a penny shortage, companies such as Fairway supermarket, have announced that they would not use pennies in change. Instead, they would round off receipts to the nearest 5 cents, so, for example 10.78, 10.79, 10.81, and 10.82 would each round off to 10.80, and 10.83, 10.84, 10.86, and 10.87 to 10.85. This procedure does not lead to a bias or skewing because there is equal rounding down and up for usual receipt amounts. (Show this!) (12/11/2025)
Math rules of thumb
- The 80/20 or Pareto rule is that 80% of the successes come from 20% of the causes, such as the people involved), as noted in Ch. 2, on page 12,
- The 5-Second Rule says it is safe to eat food that has been on the floor for less than 5 seconds (though this is not really the case), as noted in Section 16.4.2, on page 258.
- The Rule of Threes is a very rough guide for survival before dying. You can survive 3 min without air, 3 hours without shelter from bad weather, 3 days without water, and 3 weeks without food, as noted in Physics of the Human Body, 2nd Ed, Appendix F5, page 915:
- The 0.01% rule: Nick Maggiulli proposed that you can always make a purchase of 0.01% (or less) of your net worth without financial worry(as reported by Joe Pinsker, Wall Street Journal, Sept. 13, 2025, 9:00 ET, https://www.wsj.com/personal-finance/small-spending-money-rule-wealth-ladder-c41a96f2, On the Fence About a Spending Decision? Try the 0.01% Rule)(11/17/2025)
Hot numbers
- (Ch. 2) The numbers 6 and 7, both separately and together, have become the “in” thing for youth-used in sundry ways, for reasons that are not totally clear. [The Numbers Six and Seven Are Making Life Hell for Math Teachers: ‘Six seven’ sends teens into a frenzy that schools have been powerless to stop. ‘It’s like throwing catnip at cats.’, By Ellen Gamerman, Wall Street Journal, Oct. 13, 2025 10:00 pm ET, https://www.wsj.com/lifestyle/six-seven-meme-teens-math-teachers-42764bcb](10/16/25)
Number labels losing their meaning
- (Ch. 2, page 10) “When there were eight teams in the college football “Pac” (Pacific) conference, it was called the Pac-8. When two teams were added it became the Pac-10, and then when two more were added, the Pac-12.” This is still true, but 10 teams left and the Pac-12 now has only 2 teams, though more may join it in the future. Footnote 4 on the same page states “However, the Big-10 college football conference, which once had 10 teams, has grown to 14 teams (in football) plus affiliate members, with no corresponding change in the conference name.” The Big 10 conference now has 18 universities plus affiliates. (8/7/25)
Balloting
- (Section 18.4.2, page 298) The use of of such balloting methods has been expanding, as in the use of ranked-choice voting for an instant runoff in the NYC mayoral Democratic Party primary on June 24, 2025. (8/7/25)