81

I've been using "pets" and "owners" (as in: possible pet-shelter adoptees) in recent years.


79

Emmy Noether comes first to mind, as one of the most influential mathematicians in abstract algebra, specifically in the development of Noetherian rings (along with many properties of ideals). One aspect of her work that high school students might like is from another area, analysis. Noether's theorem says that every symmetry of the laws of nature (or the ...


74

In the stable marriage problem, you can introduce the problem as it is. But then you ask your students how things change if you assume there are not only heterosexual but also gay and lesbian people (assuming that a heterosexual person will never marry a person of the same gender, and a gay or lesbian person will never marry a person of the opposite gender). ...


62

A few possibilities off the top of my head: Students and chairs. How many ways are there for $n$ students to sit in $k$ chairs. The game of musical chairs might be fun to play around with. One can also consider natural restrictions, such as myopic students who need to sit near the front. Replace "men" and "women" with faculty from different departments. ...


51

Julia Robinson! I recommend her for a high school audience for a few reasons: Mathematical reasons: She is best known for her work towards the solution of Hilbert's 10th Problem, regarding an algorithm for solving Diophantine Equations. High school students can absolutely recognize and solve particular Diophantine Equations. Furthermore, and more relevant ...


49

Here's the example I had which inspired me to post the question in the first place: The game League of Legends was the most-played PC game, in number of hours played, in North America and Europe in 2012. There is a good chance that League of Legends is a part of many of your students' daily life, especially if you are teaching engineering calculus. It doesn'...


48

Perhaps not strictly a mathematician in the traditional sense, but I think Ada Lovelace might be a great woman to start with in today's digital world. She even has an important programming language named after her: Ada. Augusta Ada King, Countess of Lovelace (10 December 1815 – 27 November 1852), born Augusta Ada Byron and now commonly known as Ada ...


39

Sophie Germain and her work on Fermat's Last Theorem.


34

The issue is not making problems about heterosexual married couples. The issues are: Implicitly making the assumption that all married couples are heterosexual. Making problems about heterosexual marriages but not about other kinds of couples. Both points are unengaging for people following other types of marriage, but they can easily be solved while ...


32

Try objects that often occur in pairs but are distinct from each other: forks and spoons (or forks and knives), left and right shoes, salt and pepper shakers, and so on (where each fork has an obvious partner spoon, perhaps sharing the same color or design, and so on).


31

Bad Optimization Problems I thought that Jack M made an interesting comment about this question: There aren't any. There may be situations where it's possible to apply optimization to solve a problem you've encountered, but in none of these cases is it honestly worth the effort of solving the problem analytically. I optimize path lengths every day when I ...


31

Maryam Mirzakhani, who just won the Fields Medal, and also was the first Iranian student to win a gold medal in the IMO in 1995 with a perfect score. My colleague Mohammad Javaheri was on Iran's IMO team with her in 1995. He told us the other day that after Maryam won the gold, when the rest of the team went up to congratulate her she said "next, the Fields ...


30

This one can be presented to students at any level, really, although the way to explain "repeat to infinity" will certainly change for your audience. It can be used to teach them that weird things happen with limits and we can't just pass things through to the other side. It's also a good way to jumpstart a discussion of definitions: what's a proper way to ...


29

Any Living One who is friendly enough to come talk with them. Seriously, learning about "people in books" can sometimes be inspiring. But actual live role models are best. Write a local college, university, or business to find a woman who self-identifies as a mathematician. Invite her to your school to spend some time with your students. You want a real ...


27

What is striking about the Lebesgue integral is how relatively nicely limits play together with this integral, things like the Dominated convergenece theorem are great. I think one can appreciate this result (especially when contrasted with the more clumsy Riemann Integral analogues) right away. One could mention this right at the start, before everything ...


26

Edit (Jan 2018) I recommend checking Annie Perkins' page: The Mathematicians Project: Mathematicians Are Not Just White Dudes If you scroll down, then you will find a section entitled Women (alphabetical by last name). There are some great sources/names there, and - as a bonus - the project keeps evolving! $$ $$ $$ $$ $$ $$ Edit: Marjorie Rice has ...


25

A recent Times article titled Americans Are Bad at Math, but It’s Not Too Late to Fix offered an example - A&W's "Third Pounder hamburger failed to catch on because During focus groups, the company discovered that customers believed they were getting less meat. Because the “3” in ⅓ was smaller than “4” in ¼, “customers believed they were being ...


25

Sonya Kovalevsky, correspondent of Weierstrass, for example.


25

Vi Hart, the self-termed Mathemusician. I especially enjoy her Doodling in Math Class YouTube series.


24

The problem with induction proofs is that too often the problem is given by "Prove that..." After a few examples and explanations of induction, if the students know elementary calculus, the following sequence might prove interesting: Find the first ten derivatives of $x\cdot e^x$. What seems to be the formula for the $n$th derivative of $x\cdot e^x$?...


23

Two more examples. Proving that a $2^n \times 2^n$ chessboard with a single square missing can be covered using L-shaped (made out of three squares) pieces. Proving that a convex $n$-gon can be divided into $n-2$ triangles.


23

There's the Verizon "0.002 cents versus 0.002 dollars" mishap, wherein an unhappy customer calls to complain that he was billed 0.002 $/kB after being told the rate is 0.002 cents/kB. The confusion is perhaps deeper than expected.


22

The Curry Paradox is a classic. This animation resolves it:


22

Re-Re-Edit (May 2019): Found in a selection of tweets here but pasted as images to preserve. Credit for the first one goes to @lizardbill and to the rest to @GeneticJen: Re-Edit (Jan 2016): Perhaps this does not quite qualify, but I was rather surprised to spot the following question (#6 in the image below) in a recent airplane Mensa quiz: (Side-note: #2 ...


21

If your main interest is to provide a role model that students can identify with, you might want to look at Danica McKellar. According to her Wikipedia entry: McKellar studied mathematics at UCLA, graduating summa cum laude in 1998. As an undergraduate, she coauthored a scientific paper with Professor Lincoln Chayes and fellow student Brandy Winn ...


20

$\mathbb Z_n$ since it is very easy to compute in and you have one of order $n$ for every $n\ge 1$. $S_3$, since it's the smallest non-abelian group. $S_4$, since $S_3$ is sometimes too small. $A_4$, Since it is the smallest group that does not contain a subgroup of every possible order dividing its order. $\mathbb Z_2 \times \mathbb Z_2$ since it's ...


20

I would say something like this: "Often in complicated systems one needs to study multiple quantities, each of which varies at rates that depend on the other quantities and on how fast they are varying. For example the rate at which a drug metabolizes may depend not only on how much of the drug is in the body but also on how much blood sugar is in the body,...


20

When I taught a class about the stable marriage problem last week, I replaced "men" and "women" with "medical students" and "hospitals": the classical instance in which the Gale-Shapley algorithm is used in real life. In addition to the gender issues already mentioned, this has the benefits that: We avoid envisioning a dystopian future where everyone's ...


19

Isolines and isosurfaces Isolines and isosurfaces (i.e., lines and areas of equal whatever) correspond to the graphs of implicit functions and are relevant in many sciences, e.g., isopotentials (physics), isobars and isotherms (metereology). Probably the best-known example of this kind are topographical contour lines (lines of equal altitude, see image ...


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