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 ...
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  • 2,366
29 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 ...
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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 ...
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  • 16.3k
17 votes

Computational topology for engineers

I'm just finishing up a graduate course in computational topology which could be adapted very effectively for this purpose. We're focusing on topological data analysis and computational homology. All ...
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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 ...
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  • 1,426
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 ...
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16 votes

Walter Warwick Sawyer: How has reading his works changed your learning or teaching?

No, I was never inspired by him because I had never heard of him before you mentioned it. Note: My answer is for the original version of the question. Since then, the question has been edited so my ...
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13 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 ...
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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 ...
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11 votes

Inspirational Mathematics Books for Teenager

If you looked at those other topics, you saw the links to the books page at my blog, Math Mama Writes. There are a number of books there that would work for a teen. One of my favorites is Carry On, Mr....
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  • 17.3k
9 votes

How to react to students saying that they are allergic to applied mathematics?

Perhaps the experience of just such a student may help you? As a student, when I chose my second-year maths courses, I compared the list of topics that were in second-year courses to the topics I ...
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8 votes
Accepted

What math courses should be taught to undergrad electrical engineers: a 40 years update

In my experience teaching undergraduate engineering students, key topics include at least some calculus, linear algebra and differential equations. Exactly how much depends on the field/subfield of ...
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  • 4,318
8 votes

Computational topology for engineers

Wow, thanks for the recent shout-out. I hope this is the right place for me to add a few references that might be useful and haven't already appeared in the answers. Rob Ghrist has just written a ...
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8 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 ...
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  • 256
8 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 ...
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  • 91
8 votes
Accepted

How to come up with a Leslie matrix with convenient eigenvalues?

If I use your simplification that $f_0 = 0$, then I suggest just choosing a real eigenvalue $\lambda$ and writing out the relation for the other parameters: $$-\lambda^3+f_1s_0\lambda + f_2s_0s_1 = 0$...
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  • 7,686
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 ...
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  • 284
7 votes

New math. teaching assistant facing big problems, what to start with?

I would start with a discussion with the Engineering department about what it is they want the students to learn. Teaching different skills will need different methods, so you might as well start with ...
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  • 5,540
7 votes

Mathematics in real life

First give me an example of real life then I can tell you about the math in that activity. Now, is math central to the activity? From my perspective, it is likely. From the perspective of the person ...
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7 votes

Complex analysis (Applied versus pure)

First: there seems to be a traditional belief that "pure" math fusses over tiny uninteresting details that "applied" math takes for granted, etc. Sure, we can operate this way, and make "pure math" as ...
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  • 13.5k
7 votes

Inspirational Mathematics Books for Teenager

"(Books in German or with German translation are a plus)" and "she is particularly interested in geometry." The OP's notes suggest: Ziegler, Günter M. Do I Count?: Stories from Mathematics. CRC ...
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7 votes

Should college mathematics always be taught in such a way that real world applications are always included?

I'd like to expand a bit on The Chef's answer. Specifically, there's no need to require any kind of emphasis on "real world" applications. That is: Generally "real world" applications refers to some ...
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7 votes
Accepted

Why does a first course in linear algebra teach QR-decomposition?

I wouldn’t feel bad about leaving it out, but I think it’s a valuable conceptual example for understanding matrix algebra. Computing the QR decomposition is equivalent to applying Gram-Schmidt ...
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7 votes

Walter Warwick Sawyer: How has reading his works changed your learning or teaching?

I already loved math when I encountered his books. But yes, I was also inspired. Mathematician's Delight might be the one I put dozens of page markers in, so I could find all the great ideas again. He ...
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  • 17.3k
6 votes

Complex analysis (Applied versus pure)

This may not be a direct hit, but since you mentioned "emphasis on visualization," may I suggest you investigate Tristan Needham's Visual Complex Analysis. E.g., see this MSE answer:   &...
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5 votes

Application of Minimizing Average Cost

Cost is fairly easy to calculate, so finding the minimum average cost is also easy. Profit depends partly on revenue, which is much harder to predict. You can't know just how customers will react to ...
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  • 2,496
5 votes

Complex analysis (Applied versus pure)

Since "epsilon-delta" has been mentioned a couple of times by the question asker, I just thought I'd add my opinion that the epsilon-delta business should not be seen as a divider between pure and ...
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5 votes

New math. teaching assistant facing big problems, what to start with?

I think you need to build a support network locally. Even if it means going outside the university to a nearby university, you will need mentors, fellow TA's, administrators, and others to help you ...
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