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17 votes

How can I build a protractor without a protractor?

As Will Orrick says in the comments under user20315's answer, it is possible, with straightedge and compass, to construct a regular 120-gon, and therefore it is possible to mark off every 3 degrees on ...
mweiss's user avatar
  • 17.4k
13 votes

How can I build a protractor without a protractor?

Step 1: Find a machinable material that is reasonably incompressible. Step 2. Find a string material that is reasonably non-stretchy. Step 3: Make a cylinder out of the machinable material (perhaps ...
Jasper's user avatar
  • 3,178
9 votes

How to incorporate optional higher level mathematical content in an Engineering Maths course?

In our department, large introductory math courses, such as calculus, linear algebra, and discrete mathematics, come together with little satellite courses called "advanced investigations in *", where ...
Fedor Duzhin'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
  • 14.7k
7 votes

What do I study in calculus beyond the minimum required for undergraduate engineering?

There is a big old textbook Advanced Engineering Mathematics by Kreyszig. Maybe looking at its table of contents HERE will show you what mathematics he thought was useful for engineering students. (...
Gerald Edgar's user avatar
  • 7,607
7 votes

Introducing derivative concept and definition

It occurs to me that maybe you can approach this from the viewpoint of approximations. Briefly, I’m thinking of the kinds of approximations they likely use in practice, and which are often given in an ...
Dave L Renfro'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
6 votes

Teaching Mathematics to a Machine Learning Class

This may help, the labs and associated materials for a course CSC 294: Computational Machine Learning: github link. See course-materials/Labs/, Jupyter Notebooks: ...
Joseph O'Rourke's user avatar
6 votes

How can I build a protractor without a protractor?

In mweiss' method, the outer angles ∠AOC and ∠DOB are shy of 1° by slightly more than 0.0001°, and the inner angle ∠COD exceeds 1° by slightly more than 0.0002°. On a (huge!) one meter diameter ...
Jasper's user avatar
  • 3,178
6 votes

What to do with "wild goose chase" or "quantum leap"-types of incorrect solutions when you ask students to prove/show something?

It's quite likely to be a consequence of the belief that they have to answer the question. When they can't work it out, when they've gone around in circles and got lost, but still they have to give an ...
Nullius in Verba's user avatar
6 votes

Math tools for restructured lectures

If you're looking into Python, SageMath (https://www.sagemath.org/) is free and gathers together a bunch of open source mathematics libraries in Python to produce something comparable to Mathematica.
TomKern's user avatar
  • 4,425
5 votes

What do I study in calculus beyond the minimum required for undergraduate engineering?

Are you an undergrad majoring in aerospace engineering, or are you interested prerequisites from graduate programs in aerospace engineering? In either case, the following syllabus may help you ...
amWhy's user avatar
  • 2,095
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

Polar form before Cartesian form when introducing complex numbers

Let me suggest the following story: if we consider $z = x+iy$ as a point in the complex plane then we have $z = (x,y)$ in the usual Cartesian coordinate notation. Since $$ z=x+iy = x(1)+y(i) = x(1,0)+...
James S. Cook's user avatar
5 votes

English book for math for (electrical) engineering similar to German "Higher Mathematics"

(edited) I have used Kreyszig, Advanced Engineering Mathematics, fifth edition, as an undergrad, a practicing engineer, and in grad school. I love it. (1) It is in English, composed in English, ...
guest's user avatar
  • 1,828
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

What is the best way to introduce Laplace transforms on an Engineering Mathematics course?

In a classical control theory course, Laplace transforms are used to calculate transfer functions. As suggested by @Isaiah, see what your colleagues are doing. Skipping material can be risky when ...
J W's user avatar
  • 4,733
4 votes

Reference requests: Is there a text that is even more advanced than books on "advanced engineering mathematics"

Let's take Kreyszig as the reference case, since I'm familiar with it. In terms of next harder books, I would say: Arfken and Weber: unfortunately I HATE this book as do many physicists. (It's ...
guest's user avatar
  • 1,828
4 votes

Is it necessary to teach the definition of a limit for engineering majors?

Well it doesn't really feel right to get degrees in engineering and gain years of engineering experience without even knowing what a limit actually is. And even though many engineers will do just fine ...
numdar335's user avatar
4 votes

Is it necessary to teach the definition of a limit for engineering majors?

It is probably not the place of mathematics educators to decide what mathematics courses engineering majors should take. But a good reference point is ABET accreditation. Over 600 universities in the ...
user52817's user avatar
  • 11k
4 votes

What do I study in calculus beyond the minimum required for undergraduate engineering?

You do not mention differential equations, but this is a very useful topic in engineering, aerospace included, and the list of topics/courses you have studied mean that you would be well prepared for ...
J W's user avatar
  • 4,733
4 votes
Accepted

How can I visualize differential equations and Integration in real life?

You have asked two very different questions. I'll leave the differential equations for someone else. There is one particular application of integration which is my favorite last problem to do in Calc ...
Sue VanHattum's user avatar
  • 20.8k
4 votes

How and what to teach on a second year Engineering Mathematics?

I'm unaware of a major reform in engine math. If you look at the major selling textbooks, for instance, they remain pretty traditional. The most popular, Kreyszig, is one that I had in the mid-80s (...
guest's user avatar
  • 41
3 votes

What do I study in calculus beyond the minimum required for undergraduate engineering?

Here is the stereotypical undergraduate engineering math curriculum in the US. Of course every person/school is different, but this is a useful reference point for initial awareness. (The last ...
guest's user avatar
  • 31
3 votes

Teaching Mathematics to a Machine Learning Class

Dustin Mixon at The Ohio State University has written rigorous notes on the Mathematics of Data Science that cover both "fundamentals" (matrix analysis, convex optimization, probability) and ...
Hans Parshall's user avatar
3 votes

Need to learn recurrence relation discrete mathematics

I liked this Discrete Mathematics: An Open Introduction, by Oscar Levin, for generating functions, so I'm guessing it will be good for recurrence relations.
Sue VanHattum's user avatar
  • 20.8k
3 votes

Applied ODEs for Numerical Methods

I would consider to add two items to the list, both from a systems slant: Predator prey relations. The behavior can be graphically investigated, but the actual solution function is not analytically ...
guest's user avatar
  • 31
3 votes

Introducing derivative concept and definition

A good approach for engineers might be to connect the "slope of a graph" to sensitivity: the factor by which a small change in input gets multiplied to produce a change in the output. You ...
TomKern's user avatar
  • 4,425
3 votes

Introducing derivative concept and definition

I think you should take whatever motivation you are most excited to show them based on (a) their interests and background (b) your passion and go that way. Everyone will have a different answer to ...
cheyne's user avatar
  • 280
3 votes

Teaching science and engineering students the field of inverse problems

You should start by figuring out what you want students to understand and be able to do with the material that you will teach them. This includes issues of course content but you should also consider ...
Brian Borchers's user avatar

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