45
votes
Response to Students Who Say "This Is Not Important"
"Lately, my students keep telling me why what we are learning is not important. They ask me when will we use this in the real world?"
There's a quick reply to this that I think people won't ...
- 459
40
votes
Should college mathematics always be taught in such a way that real world applications are always included?
I have worked with a lot of students coming out of courses such as yours who:
passed the course by blindly memorising proofs, theorems, and algorithms;
learnt nothing (lasting) except solving some ...
- 2,538
40
votes
Do I really need to cover solids of revolution in my Calculus I class?
An operation is born when we recognize the regularity in repeated reasoning.
Take multiplication for example. If we are living lives which involve even a modest amount of arithmetic thinking, we will ...
- 23.2k
38
votes
Response to Students Who Say "This Is Not Important"
Math is just as useless as almost any other subject
As a math tutor, I've thought about this a lot over the last 15 years or so. Aside from tutoring, I don't use my math education in "the real ...
- 576
30
votes
Why do we teach complex numbers?
We owe students a presentation of the Fundamental Theorem of Algebra -- that every nonconstant polynomial has a root; or, equivalently, the marvelous fact that every polynomial of nth degree has ...
- 22.8k
21
votes
Should college mathematics always be taught in such a way that real world applications are always included?
At my University, there are four different first-semester Linear Algebra courses taken by Undergraduates:
Math 214, Applied Linear Algebra, is "an introduction to matrices and linear algebra... The ...
- 17.1k
19
votes
Do I really need to cover solids of revolution in my Calculus I class?
A point to consider that has not been emphasized much in other answers so far: removing a topic from a syllabus in a service course should not be done before getting input from instructors of other ...
- 3,008
18
votes
Response to Students Who Say "This Is Not Important"
I've never had success with giving a list of applications to such students - because, realistically, we don't use most of the math we teach. For example, I teach early equations in one of my classes, ...
- 1,954
16
votes
Why do we teach complex numbers?
I am surprised that nobody has mentioned differential equations. If you know about complex numbers and Euler's formula then there is a beautiful unified theory of linear differential equations with ...
- 1,486
16
votes
Should college mathematics always be taught in such a way that real world applications are always included?
I believe you need to listen beyond what your student is saying. Your student is not saying "I want to do some applications in class." What your student is really saying is "I'm bored and lost and ...
- 161
15
votes
Response to Students Who Say "This Is Not Important"
The American Mathematical Society provides posters promoting awareness of mathematics, its beauty, and applications. Here's a quote from the AMS Posters website:
"Students frequently ask when ...
- 10.7k
14
votes
Why do we teach complex numbers?
I think the fundamental tenet of this question is simply false. Here are some of the many encounters that undergraduate college students have in my classes:
In Calculus II, as an application of power ...
- 360
14
votes
Do I really need to cover solids of revolution in my Calculus I class?
Pardon me ignoring your Calculus question,
but there is some beautiful mathematics here, e.g.,
Cavalieri’s principle. So there is an opportunity to connect
the calculus to these "fascinating ...
- 28.9k
13
votes
Should I teach Laplace Transforms? How much?
Consider something besides an "all or nothing" approach.
Here's what I did a couple of times when the topic was optional and I didn't have much time, but I still wanted to give students an ...
- 5,672
13
votes
Accepted
Application of perpendicular lines
There's a reason why you can't find a good non-geometric example: when the dimensions of the axes on a graph are distinct, perpendicularity is units-dependent. There is thus no natural aspect ratio ...
- 246
12
votes
Should college mathematics always be taught in such a way that real world applications are always included?
I challenge the assertion that students need to see applications in everything.
When I first started teaching I labored under the delusion that I should explain connections to physics whenever I ...
- 10.4k
12
votes
Do I really need to cover solids of revolution in my Calculus I class?
At my institution, we teach out of Thomas' Calculus (not the early transcendentals version, thank goodness). Volumes and surfaces of revolution show up in a chapter titled "Applications of ...
- 7,137
11
votes
Greatest common divisor applications
Another classic is the following:
A rectangular floor measures $300 \text{ cm} \times 195 \text{ cm}$. What is the largest square tiles that can be used to cover the floor exactly?
- 2,520
11
votes
Response to Students Who Say "This Is Not Important"
Trigger warning: math enthusiasts do not like this answer.
They ask me when will we use this in the real world?
When students ask when they will use something in "real life", they are ...
- 1,213
11
votes
Applications for logarithms in a business math course
I feel compelled to provide your "of course" answer of exponential growth/decay. This answer is hopefully appropriate for lower-level business courses such as high-school level.
Here's a ...
- 241
10
votes
Why do we teach complex numbers?
Most people are not going to use most of what they use in high school. High school (in the US, at least) is about building a broad foundation for students to be able to jump into any specialization ...
- 276
9
votes
Greatest common divisor applications
Going back to Euclid, I have found questions such as `Given a large supply of rods of length $15$ and $21$, what lengths can be measured?' can appeal to students. This also motivates the result $\gcd(...
- 859
8
votes
Should I teach Laplace Transforms? How much?
Also having a short period of time to introduce my DE students to Laplace Transforms I began with two 'Axioms':
(1) $\mathcal{L}\{c_1y_1(t)+c_2y_2(t)\}=c_1Y_1(s)+c_2Y_2(s)$
(2) $\mathcal{L}\{y^\...
8
votes
Greatest common divisor applications
Some nice geometrical applications arise in the analysis of periodical curves such as Roulettes (Spirograph curves), Star Polygons, etc. Concrete experience with implementations in toys like ...
- 1,029
8
votes
Application of perpendicular lines
Given a set of sites determine which points are closer one of the sites than any of the others? If closer is measured by Euclidean distance then given the distinct points A and B the points ...
- 1,862
8
votes
Examples of real-life vector fields for vector calculus
Air speed/direction on a weather map) is a very intuitive one. There's also other fluid velocity (and flux) vector fields in various chemE, mechE, and nukeE applications.
I personally think the air ...
- 284
8
votes
Do I really need to cover solids of revolution in my Calculus I class?
It is usually covered in Calculus II, I believe. I do a little of it at the end of Calculus I, because it is so beautiful, and it feels like a perfect closing to the show.
Useful? What in Calculus I ...
- 19.2k
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