Mathematics in real life

I am interested in examples of use of mathematics in real life situations. To be more precise, something that could be presented to undergraduate students in order to motivate them for studying maths. Is there some reference where one can find such examples?

A colleague of mine suggested me one of the following books:

• H. Parks, G. Musser, R. Borton, W. Silber, Mathematics in Life, society & the World, Prentice Hall, 1997.
• C . Miller, V. Heeren, J. Hornsby, Mathematical ideas, Addison Wesley Educational Publishers, 2001.

but I cannot find a source for it online.

Any help with either getting a source for one of the mentioned books online, or for some other references is welcome.

• These young guys! Books aren't good enough, it has to be on line. How about comap.com then? – Gerald Edgar Mar 9 '15 at 17:21
• An interesting one to introduce would be the usage of RSA and other encryption algorithms to basically secure all of their internet usage (My favorite is the ZKP). // Show them how clustering algorithms determine what is "trending" on their social media feeds. // How big data algorithms turn all their social media chatter into add revenue. – KDecker Mar 9 '15 at 18:54
• @GeraldEdgar Agreed. I'm using their "For All Practical Purposes" text this semester in a terminal math course for non-majors. Now, it won't convince any of them to switch to the math major (but that wasn't the point). However, many students have commented about how they appreciate the emphasis on real-world examples and problems. I was worried about keeping them motivated for the whole semester, but have had no problems with that, in fact! – Brendan W. Sullivan Mar 9 '15 at 21:36
• I second @brendansullivan07 and GE's recommendations to look into COMAP materials. I mentioned their text FAPP in MESE 1550 - a thread that may contain other items of interest, too. – Benjamin Dickman Mar 9 '15 at 23:05
• Mathematics is a way of understanding and interpreting the world. That's important because understanding is the key to technology, which is driving the modern world. Also, making tech makes you rich! (there, 3 sentences is enough) – bjb568 Mar 10 '15 at 3:17

First give me an example of real life then I can tell you about the math in that activity. Now, is math central to the activity? From my perspective, it is likely. From the perspective of the person you might seek to teach math, probably not.

Much of math has been black-boxed in our daily life. Cash registers are automated to the point that at least 1/4 workers cannot make change by hand (my experience). Addition of fractions and other basic arithmetic has been erased from the collective conscience thanks to misuse of calculators in early age education. We use computers, but, you most certainly do not need discrete math to use computers. This list goes on.

• We have the option to be ignorant.

The question is:

• do you want to understand the world around you?

If the answer to that is yes then finding applications of math is as simple as waking up in the morning. They're everywhere. Physics. Chemistry. Computer science. Engineering. DNA sequencing. Communications theory...

Surely being able to understand the world around you is motivation enough for an educated person, or, at least a person who seeks an education.

• Where I live, I find the majority of cashiers don't use the cash register to calculate change. They just punch the total hand you the change then close the register. There's a common trick among tradespeople here (but not taught in schools, I learned it from a friend) that instead of trying to do subtraction in your head, which is slow, ask yourself instead how much do you need to add to round it up to 10. Technically they're the same calculation but somehow the "trick" method is easier to do. – slebetman Mar 10 '15 at 0:08
• @slebetman yep, I mostly notice this problem when I give them a bit more money after initially giving some large bill. I wouldn't notice otherwise as most registers more or less automate the process. – James S. Cook Mar 10 '15 at 0:34
• In light of the mention of cashiers and COMAP, here is a COMAP lesson plan (by H. Gould) that may be of interest; in particular, see the teacher's guide at the end (by H. Pollak). – Benjamin Dickman Mar 10 '15 at 21:19

If you want to get students excited about math, why not show them some math? Talks on applications frequently send the tacit message that "you should study math because it's useful, though of course it's not really very interesting".

Students who are just getting excited about math need to be reassured that it is, in fact, possible, to make a career out of math. These "applications" talks, in my experience, send the message that "if you study math, you'll end up doing physics/economics/engineering/biology/whatever". I am sure that if I'd received that message in my formative years, it would have turned me away from math.

To send the message that math is exciting, you need to talk about math in a way that suggests that you find it exciting. If you choose to spend your hour talking about things other than math, you undercut that message.

I just ran across this book:

W.D. Wallis, Mathematics in the Real World. 2013. Birkhäuser Basel. (Springer link).

Here is a review:

“This textbook contains a treasure trove of such topics, such as sampling, cryptography, voting, and probability. While Mathematics in the Real World is intended for students with a minimal background in mathematics, the mathematics in the textbook is not dumbed down. The student will be performing calculations, using formulas, and drawing graphs. … All in all, I think Wallis has written a wonderful text. He has chosen exciting topics and explained them in a straightforward manner.”
(Kara Shane Colley, MAA Reviews, January, 2014)

Continuous compounding interest is a good example: \$1.00 at an annual rate of 100% turns into \$2.00 after one year, but compounded continuously the \$1.00 turns into$e$dollars, \$2.72:

(Image from Wikipedia article on $e$.)

• I think they're looking for a book(s) reference instead of an example. – Chris C Mar 9 '15 at 18:40

Every problem has an engineering solution. I think you're better off attacking the "what good is math" question from the opposite direction. You don't have to come up with examples of math being useful. Your message can be that having mathematics in your tool belt makes you more prepared for (almost) every problem you'll face in your whole life. I suppose you'll get some resistance if your students think math is nothing more than the memorization of arcane computation rituals… but there's another teaching opportunity there.

Have you ever thought about Realistic Mathematics Education ? That is an antique theory in Mathematics Education, which has some details how math could be applied in real life and shows some examples.

Take for example these books (online). You could read them and have some idea about Mathematics in real life.

I sometimes feel like this and have struggled to find good talks. In my opinion learning math opens your mind in all sorts of ways that can be just appreciated when you start learning.

But I like this video : https://www.youtube.com/watch?v=eD2hLhhYmbg In short, math touches all aspects of life.

• Could you incorporate why you "like" the linked video? In particular, how does it answer the question here? – Benjamin Dickman Mar 9 '15 at 23:10