8

This might go over differently at a liberal arts school, but we've had some success inviting students to an optional, uncredited program where they work in groups on fun problems from various topics in math (ideally associated with upper level courses, so we can say, "and if you liked this, you should take..."), supervised by two older undergrads. (There ...


7

For both options below, first and foremost the Math Department should be institutionally Friendly In my book this means letting students try to do what they want. Err on the side of bending policy to help students with unusual paths. Don't make students retake things they've already taken if at all possible. But, do give warnings if your institution has ...


7

There are a lot of resources for problem solving online. One place to look is MIT's OpenCourseware; see their Problem Solving Seminar: Course Description This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are ...


6

I wrote to a professor of mathematics at a liberal arts college that has, in recent years, found great success in attracting more math majors. Here are lightly edited excerpts from the two emails I received in response: Initial email: Excellent teaching, welcoming classrooms, caring attitudes, support in and out of the classroom, etc. Don't make it a tough-...


5

My first idea would be to aim to include applications at different levels (ones they might be able to calculate, ones they can get maths software to do, high-level maths research) and also across different subjects. Some ideas: relationship between area/volume/perimeter/surface-area of circles and spheres, maybe cones some fluid dynamics, maybe in relation ...


5

Here is one very easy thing that has gotten good results at the University of Michigan: Every term , a few weeks before the end of the term, our director of undergraduate studies sends an e-mail to the math faculty saying roughly "if you are teaching a class with a lot of undergraduate non-math majors, please choose 1-3 students in it who you think would do ...


4

There is quite a bit of literature under the banner "humanizing mathematics" (or cognate phrases). I am just beginning to read this literature, so I can do no more than point to a few references. This seems a slightly different emphasis than your first bullet on "a culture of diversity." Luis A. Leyva. "Toward humanizing undergraduate mathematics ...


4

This is a fairly minor issue, but probably worth a mention. At a technical university there was (and probably still is) a question about how to attract more female students. One aspect was the diversity in promotional material. The outcome was that male students reacted equally well to diverse promotional material than to material with mostly white male ...


4

My advice is to emphasize the "get a job" aspect. The university is filled with the dreamy beauty of knowledge stuff. (And that's fine. But you need to distinguish yourself and provide additional info that kids might not have.) Do you even know what percent of graduating kids go into what fields? How easy/hard it is to get jobs (like some sort of ...


4

Key points for goal #1: Professor Krugman's intuitive summary of how a derivative is the limit of a sequence of differentials. Start with the graph of a function you want to differentiate. Find the slope over a modest delta X. Repeat for the next delta X. Optionally repeat again. The shape of the derivative should now be obvious, but also obviously has ...


3

Have you checked out the Discovering the Art of Mathematics project? Their 11 books, one of which is Calculus, are free for educational use, and they provide lots of supportive community. If we taught a liberal arts calculus course, this is what I'd want to use, I think. I see that your question was about topics, not textbooks. They have lots of experience ...


3

For a look at the intellectual development of calculus (not a textbook nor a skeleton for a course, but something to peek at for the instructor), I'd recommend Dunham's "The Calculus Gallery" (2005). His books on the history of mathematics are outstanding expositions, accessible with a high-school background (and interest enough to work through the material)....


3

One really long answer to your question that I am fond of is the book Calculus in Context. Selected topics from the first four chapters might make for a nice one-semester course, though perhaps it has too much of an emphasis on technique for what you have in mind. But I like the explanation of why calculus is relevant and why successive approximation is ...


3

This will also say little in comparison to the breadth of your question. I would include some of the history of how the notion of limit of a function, $\lim_{x \to a} f(x)$, emerged over time. I was surprised to learn this concept was not present (or at least not clear) in the work of either Newton or Liebnitz. It took another hundred$+$ years for this to ...


2

One very brief answer is to have multiple entry points to the major, or even just to taking more courses. That is to say, at many colleges the typical Calc I-II-III entry sequence may not be attended by a very large number of students who would love to take more math. So have clear options for them. To elaborate into something not so brief, consider a ...


1

Kinematics is easiest conceptual example of derivative and something everyone has visceral physical experience with (acceleration, speed, position). Optimization (particularly business or manufacturing type problems) is something everyone can understand as a practical use of calculus. And is a KEY concept, use of calculus. Something I learned about ...


1

Do hand-waving-in-the-air lectures building up to the calculus of variations. Then get them to build two slopes - one with a straight path and one with a cycloid path that they can actually roll two balls down side-by-side to see the fastest one for real.


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