85 votes

What female mathematician can I introduce to my High School students?

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 ...
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85 votes
Accepted

What's a replacement for "married couples" in combinatorics problems?

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

What's a replacement for "married couples" in combinatorics problems?

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 (...
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  • 1,143
66 votes

What's a replacement for "married couples" in combinatorics problems?

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 ...
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61 votes

What female mathematician can I introduce to my High School students?

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 ...
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50 votes

What female mathematician can I introduce to my High School students?

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 ...
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  • 601
42 votes

What female mathematician can I introduce to my High School students?

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

What female mathematician can I introduce to my High School students?

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, ...
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37 votes

What female mathematician can I introduce to my High School students?

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 ...
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  • 5,877
37 votes

What's a replacement for "married couples" in combinatorics problems?

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 ...
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  • 707
34 votes

What's a replacement for "married couples" in combinatorics problems?

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 ...
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32 votes
Accepted

How can teachers warn students about common mistakes without causing the student to make the mistake?

This is a 100% subjective opinion, but it is based on teaching in various venues for close to 20 years (although none of that teaching was pure math). Also, my college calculus courses are close to ...
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31 votes

Examples of Innumeracy

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 ...
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29 votes

What female mathematician can I introduce to my High School students?

Vi Hart, the self-termed Mathemusician. I especially enjoy her Doodling in Math Class YouTube series.
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  • 407
28 votes

What female mathematician can I introduce to my High School students?

Sonya Kovalevsky, correspondent of Weierstrass, for example.
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  • 13.5k
27 votes

What female mathematician can I introduce to my High School students?

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 (...
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26 votes

What's a replacement for "married couples" in combinatorics problems?

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 ...
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24 votes

What female mathematician can I introduce to my High School students?

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, ...
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24 votes
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An introductory example for Taylor series (12th grade)

One practical reason for choosing a Taylor Series approximation of a function over the function itself is if you are able to compute using only the four arithmetic operations. For example, if you are ...
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22 votes

What female mathematician can I introduce to my High School students?

Classically speaking, Maria Agnesi is the best classical mathematician to study. She published calculus texts that expanded and reflected upon the works of Leonhard Euler.
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  • 382
21 votes
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Simple "real world" l'Hôpital's rule problem?

Here's a possible problem: The Rayleigh–Jeans Law for black body radiation at a wavelength $\lambda$ was given by $$B_{RJ}(\lambda) = \frac{K}{\lambda^4}$$ where $K$ is a constant (depending on ...
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  • 6,350
21 votes

A Series of Unfortunate Examples!

Personally, I refer to this phenomenon as students "submarining" a broken understanding on a particular kind of problem. Example #1: Our in-house elementary algebra textbook, in its first edition, ...
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21 votes

How would you explain what a PDE is to a very educated layman with no math background?

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 ...
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  • 16.3k
21 votes
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Concrete vectors spaces without an obvious basis or many "obvious" bases?

Some physical examples from physics: Consider two spaceships that meet each other in deep space with arbitrary orientations (pitch, roll, and yaw). Even if they take the origin to be the midpoint ...
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  • 328
20 votes
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Big list of "interesting" abstract vector spaces

Here are some more examples: $C[a,b]$, the set of continuous real-valued functions on an interval $[a,b]$. This abstract vector space has some very nice properties that make it very good for a first-...
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  • 16.3k
19 votes

What female mathematician can I introduce to my High School students?

Adm. Grace Hopper earned a Ph.D. in mathematics at Yale (1934), helped program the Mark I (1944), developed the first compiler (1952) and some early computer languages, and worked on the development ...
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  • 4,579
19 votes

What are some good low-prerequisite examples for the heuristic advice "If you cannot prove it, prove something stronger."?

For a very basic example, how about proving that 59549121058965346178 can be expressed as a product of primes? It is much easier to prove the stronger result that every positive integer can be ...
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19 votes

An introductory example for Taylor series (12th grade)

An excellent introductory example would be exponential function $\exp(x) = e^x$. By definition, this is the function that is its own derivative, i.e. $\exp'(x) = \exp(x)$. That's all nice and swell ...
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18 votes
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Proof by contradiction - more than one case

(1) Here is a $3$-case proof from Larry Cusick's webpages: Theorem. There are no rational number solutions to the equation $x^3 + x + 1 = 0$. Proof. (Proof by Contradiction.) Assume to the ...
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