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I hope this question relevant to this place. I am a PhD Student working in Lie algebras. I have to give a talk to Engineering student. Kindly suggests me some books or topics in Mathematics which might admire them towards Mathematics.

I want to show them Mathematics from in the perspective, different from just solving problem and want to do like some interesting historical facts, or explaining them some engineering Mathematics concept how it works and relating them to real life ......

Any idea is appreciated.

Thanks in Advance

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  • $\begingroup$ What is the background of the students? if undergrad, at what level? $\endgroup$ – felasfa Oct 10 '16 at 17:23
  • $\begingroup$ they are undergrad only, third year $\endgroup$ – GA316 Oct 10 '16 at 17:33
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    $\begingroup$ A while ago, more or less the same audience, I did a talk on pursuit curves mathworld.wolfram.com/PursuitCurve.html. I considered a simple case of 4 particles initially located at corners of a square following each other. I derived the ODE and showed the resulting curve is a logarithmic spiral. I then considered the general case of a regular polygon and ended with slightly complicated cases for non-regular polygons. $\endgroup$ – felasfa Oct 10 '16 at 18:04
  • $\begingroup$ @felasfa very nice one. thanks. any more source for the same? $\endgroup$ – GA316 Oct 10 '16 at 18:26
  • $\begingroup$ A good book is "Introduction to Nonlinear Differential and Integral Equations by Davis". Chapter 5 covers pursuit curves. You can also find a lot of resources online. I liked this resource in particular: faculty.missouri.edu/~casazzap/pdf/teach/bug.pdf. People love cool curves so most of the audience related $\endgroup$ – felasfa Oct 10 '16 at 20:17
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Providing a brief idea about the use of number theory in elementary cryptography can be quite interesting. On the other hand, applications of Boolean algebra in simplifying switching circuits can also be fruitful.

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  • $\begingroup$ both look nice. can you tell me any reference for the Boolean algebra stuff? $\endgroup$ – GA316 Oct 10 '16 at 17:50
  • $\begingroup$ Applied Abstract Algebra - R.Lidl and G.Pilz, Springer $\endgroup$ – cryptomaniac Oct 10 '16 at 17:52
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You work in Lie algebras. So the topic of Linear Transformation approached geometrically can be one good thing. All engineering students know how to manipulate matrices,calculate eigenvalues and eigenvectors or carry out Gram-Scmidt algorithm. Sometimes they do not know the geometry of orthogonality.

For example proving composition of two 3d rotations is again a 3d notation is not easy to visualize as the axis cannot be guessed. Here matrix calculation comes handy.

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