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# Formulas, Algorithms and Number Tracking

Joseph A. Gallian has been tracking often-used numbers for decades.

**UMD’s Joseph A. Gallian on Credit Cards and the New FBI Number Scheme**

**CREDIT CARDS**

Joseph A. Gallian has been tracking often-used numbers for decades. He’s tracked, cracked algorithms, and explained the intricacies of numbers — lots of numbers, such as bank account, passport, driver’s license, airline ticket and even library card numbers.

These days, he gets lots of questions about credit card numbers and his answers are surprising.

Here’s a question. When you order something online and type in your credit card number, how do they know, in a millisecond, if you typed it wrong? A vendor can’t check your typing against every credit card number on the planet. So, how do they know so fast?

“With a check sum formula,” is Gallian’s answer.

“Usually a formula creates the last digit,” says Gallian. “A simple calculation uses an algorithm involving the digits preceding the final credit card digit.” It’s called the ‘check digit.’ For instance, the first four digits of the bank account number 87151 together with the ‘weights’ 7, 3, 9, 7 yields the check sum: 8 x 7 + 7 x 3 + 1 x 9 + 5 x 7 = 121. Because the last digit of 121 matches the last digit of 87151 the account number is a valid possibility. If those two final digits do not match, the account number cannot be valid.

Maybe you didn't follow all of Gallian's math, but all you have to know is *when the formula behind the numbers is applied, errors are detected instantly. *The error could be because of a typo, a transmission glitch, or even a thief trying to fake a valid number. Credit cards use a more complicated check sum algorithm.

A check sum formula is standard practice in more than credit cards. UMD identification cards have a number with a check digit. In fact, every card with a magnetic strip or chip uses a check digit. The availability of inexpensive, fast, reliable scanning devices and computers has moved check sums into bar codes, mail tracking, and hundreds of other areas of modern life.

*It’s hard to stump Gallian.* Give him numbers from the same source and he can often determine the algorithm that arrives at the check sum.

**THE FBI**

Recently, a reporter from the *Wall Street Journal* called on Gallian to help explain the FBI tracking numbers adopted in 2015. The FBI tracks more than criminals, it does background checks on government employees, police, military, teachers, coaches, pilots, caregivers and other licensed professionals. That’s a lot of numbers in one data base.

The FBI predicted it would run out of numbers in the old numbering system in about 10 years so they had to make a change. They added letters to previous the nine-digit system. That made billions of numbers available, instead of the millions they had before.

The FBI also needs to know immediately if a number in question is correct and so we are back to Gallian’s algorithms. “Letters are converted to numbers, and each of the first eight digits of the ID is multiplied by a weight number assigned to its position,” Gallian said. *Multiply, add, divide, and Bingo, the FBI agent’s computer knows the nine-digit number is valid if the last number is correct.*

Numbers, numbers, numbers. Gallian can mesmerize his students and he has put UMD on the map with his algorithms and his other amazing mathematical solutions for the everyday (and exotic) math world.

**ABOUT JOSEPH A. GALLIAN**

Gallian is a professor in the Department of Mathematics and Statistics at the University of Minnesota Duluth. He has received many awards and honors including the Morse Alumni Distinguished University Professor and the Carnegie Foundation for the Advancement of Teaching Minnesota Professor of the Year Award. He is the author or editor of five books and more than 100 articles

http://www.d.umn.edu/~jgallian/vita.html

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