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 ...
Wrzlprmft's user avatar
  • 2,538
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 ...
Daniel R. Collins's user avatar
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 ...
mweiss's user avatar
  • 17.3k
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 ...
John Coleman's user avatar
  • 1,506
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 ...
Greg Blumberg's user avatar
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 ...
JRN's user avatar
  • 10.8k
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
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
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....
Sue VanHattum's user avatar
  • 20.1k
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 ...
PGnome's user avatar
  • 276
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
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$...
Nick C's user avatar
  • 9,184
7 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
  • 89
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 ...
Joseph O'Rourke's user avatar
7 votes

Modeling vs. Application vs. Context

What is Mathematical Modeling? You might think this to be a simple, straightforward answer, but unfortunately we have no such luck. The definition of mathematical modeling varies depending on the ...
Andrew Sanfratello's user avatar
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 ...
paul garrett's user avatar
  • 14.2k
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 ...
AmagicalFishy's user avatar
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 ...
Henry Cohn's user avatar
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 ...
Sue VanHattum's user avatar
  • 20.1k
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 ...
user6894's user avatar
5 votes

Why do we teach complex numbers?

There are many subjects in High School that are taught which some will never use. Accounting, Drama, Band, Woodshop etc. These are entire subjects that students learn and most will never use. Does ...
Gene's user avatar
  • 51
5 votes
Accepted

Inspirational Mathematics Books for Teenager

For your particular case, I highly recommend "The Joy of X" by Dr. Steven Strogatz. And although you didn't request it, for higher level students and adults I also recommend "Mathematics for Non-...
Axiomaric's user avatar
  • 106
5 votes

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

Solving least squares problems by QR factorization is much more numerically stable than solving them by Cholesky factorization of the normal equations. This can easily be demonstrated on an ill-...
Brian Borchers's user avatar
5 votes

If one wants to conduct a 1/2 day workshop in Mathematics for 12-16 year old students - how one should go about preparing the workshop

Glad you are seeking peer support for this. Leaders' connections to good math friends make their mathematics events shine! Some suggestions, based on my experiences organizing math events: Know your ...
Maria Droujkova's user avatar
5 votes

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

Yes, I remember vividly my chance encounter at the library with that book of his! Yes, it had a big impact on me. The idea that mathematics was a real thing in its own right, like music, and not just ...
paul garrett's user avatar
  • 14.2k
4 votes

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

Should they be taught without any applications? (Note the lack of the over-limiting adjective "real world".) I would say no; at the very least, applications give us the answer to the question "Why ...
Adam's user avatar
  • 5,182
4 votes

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

I understand why you think a "pure" mathematics course should avoid "applications". But applications don't have to be in the "applied mathematics" sense of the term; they ...
J.G.'s user avatar
  • 521

Only top scored, non community-wiki answers of a minimum length are eligible