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46 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 ...
Nullius in Verba's user avatar
43 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 ...
Todd Wilcox's user avatar
41 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 ...
Wrzlprmft's user avatar
  • 2,548
41 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 ...
Steven Gubkin's user avatar
32 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 ...
Daniel R. Collins's user avatar
31 votes

Applications of High School Geometry

Every time I'm doing carpentry/DIY remodeling on my house, I use so much high school geometry that it makes me chuckle. I've had instances where I need to cut angles to make pieces parallel and used ...
Aeryk's user avatar
  • 8,021
22 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 ...
mweiss's user avatar
  • 17.4k
20 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 ...
KCd's user avatar
  • 3,516
18 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 ...
John Coleman's user avatar
  • 1,536
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, ...
Reese Johnston's user avatar
16 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 ...
JRN's user avatar
  • 10.8k
15 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 ...
Greg Blumberg's user avatar
15 votes

Applications of High School Geometry

Here's my rant that I gave to my students: You are learning this right now because some of you will need this later in life. You may need this information for your daily job. You may need this ...
abestrange's user avatar
14 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 ...
Dave L Renfro's user avatar
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 ...
Mark McClure's user avatar
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 ...
Joseph O'Rourke's user avatar
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 ...
Davis Herring's user avatar
12 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 ...
PGnome's user avatar
  • 296
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 ...
James S. Cook's user avatar
12 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 ...
BKE's user avatar
  • 1,282
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 ...
Xander Henderson's user avatar
  • 8,225
12 votes

Earliest real-world uses of Calculus and Linear Algebra

I want to find what the earliest real-world applications of Calculus were. By real-world application, I mean a device, instrument or technology which made lives better. Let's assume that: Earliest = ...
Pedro's user avatar
  • 1,800
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?
Dag Oskar Madsen's user avatar
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 ...
Wyck's user avatar
  • 241
9 votes

Why do we teach complex numbers?

Just another question from a math guy showing his ignorance of math as a service course. 2nd order diffyQ with constant coeffiecients (most important diffyQ for applications) has complex roots in the ...
guest's user avatar
  • 109
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(...
Mark Wildon's user avatar
9 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 ...
guest's user avatar
  • 304

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