The Mathematics of Everyday Life

Explore the marvel Albert Einstein called “the eighth wonder of the world”—compound interest, which is the strategy of reinvesting interest rather than paying it out. Simple calculations show that a retirement nest egg of $1 million or more is within reach for those who start investing early. Learn why the average rate of return can be misleading. Also get tips for building a college fund.

Go house hunting, analyzing your payments at different mortgage interest rates and terms (15-year versus 30-year). Learn the formulas behind online mortgage calculators to get deeper insight into the snowballing effect of interest expenses across time. Also consider whether it makes more sense to rent than to buy, weighing the hidden costs of home ownership over the benefits.

The miracle of compound interest that enriches savers can make paupers of those with credit card debt. Learn why this form of borrowing is so risky and potentially ruinous. Explore strategies for paying off credit card debt and consider whether it makes sense to keep credit cards for perks. Then look into college loans, weighing costs versus benefits, and also examining alternatives to loans.

Over our working lives, many of us spend a total of a year or more driving to and from the office. Is it worth it? Professor Omar uses simple calculations to assess the true costs of commuting, taking into consideration the relative price of real estate in the city and suburbs, the expense of cars and upkeep, and not least the psychological toll of sitting in a traffic jam day after day.

Investigate numbers you are likely to encounter in the doctor’s office. What do body mass index (BMI) and blood pressure signify? Both correlate measured values with possible health issues. But as you learn, correlation does not imply causation. Also consider questions to ask when faced with statistics for different medical treatments, bearing in mind a phenomenon called Simpson’s paradox.

Apply math to the crisis of global warming. First, define carbon footprint. Then test your instincts about the relative impact of recycling, electricity consumption, automobile use, and commercial air travel. Discover that simple measures like carpooling are among the most effective steps you can take to reduce your carbon emissions.

One of the best uses of math in everyday life is gauging how much insurance you need, especially in the confusing realms of life and health coverage. First, analyze two types of life insurance and the advantages and drawbacks of each. Then dive into health insurance, comparing a generic Health Maintenance Organization (HMO) with a generic Preferred Provider Organization (PPO).

Professor Omar tells how his harried life in graduate school led to an unwelcome weight gain. Determined to lose 50 pounds, he used mathematics to come up with a reasonable dieting plan. Learn how to estimate basal metabolic rate and caloric intake, develop an exercise regime, and choose among carbohydrates, proteins and fats.

Get the “feel” for the right answer to seemingly intractable problems by using the approach of theoretical physicist Enrico Fermi: break the problem into easy steps and come up with an order-of-magnitude estimate. Next, learn a statistical approach to problems that obey a normal distribution, using bell curves to get a surprising amount of information from relatively little data.

Discover how mathematics can solve crimes. First, study logarithms, which are the exponents used when numbers are written as a power of 10. Employ this concept to understand Benford’s law, which governs the frequency distribution of digits in common sets of numerical data. See how this hard-to-fake property helps prove financial fraud and also expose cheating in elections.

See how two mathematical tools reveal when gerrymandering is very likely occurring. The Polsby-Popper score shows how close a given district is to the optimum compact shape—a circle. The efficiency gap measures the impact of “packing” and “cracking” in different districts, which has an outsize effect on party success.

Finish the course by learning how to divide goods fairly among different numbers of people. Find that cutting a cake into mutually acceptable pieces is a problem that generalizes to many situations in life. Then tackle another approach to apportioning assets (or liabilities) that uses a geometric technique.