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When studying linear algebra in mathematics (I mean, for the people studying mathematics) there are many ways of approaching it, depending of your needs, however supposedly every mathematician should have about the same basic concepts, which I think I have.

I've been asked to help this kid, who's studying engineering, and is having a lot of trouble with linear algebra, nonetheless I'm a little nervous because I don't know how to help him well. Some friends tell me that is practically the same as pure mathematics except without proofs and that is just doing excercices. But what does that mean? Getting really good with Gram–Schmidt without understanding where it came from? Do they study dual spaces? What is the best way to help without making a mess in his mind?

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    $\begingroup$ I recommend looking at the web page for the course, or if there is no web page, try to find what textbook is being used. Also, faculty who have previously taught the course might have old homework assignemnts, tests, handouts, etc. for the course still on their faculty web pages. Sometimes these are not visible from the faculty member's web page, but you can (sometimes) still find them by googling things like the professor's name along with "linear algebra" and the course number. $\endgroup$ – Dave L Renfro May 28 '14 at 18:59
  • $\begingroup$ @DaveLRenfro: You could post your comment as an answer. $\endgroup$ – J W May 29 '14 at 4:37
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    $\begingroup$ matheducators.stackexchange.com/questions/899/… may also be of interest. $\endgroup$ – J W May 29 '14 at 7:50
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    $\begingroup$ dual space is unlikely. $\endgroup$ – James S. Cook May 29 '14 at 17:40
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    $\begingroup$ @J W: I've been away a couple of days, so I'll just include my comment into your answer. $\endgroup$ – Dave L Renfro Jun 2 '14 at 14:11
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Dave Renfro's advice [below] in his comment to your question is eminently sensible. Familiarize yourself with this particular course and what is expected of the student so you can help him/her best.

I would also add that many engineering mathematics courses, but certainly not all, have less emphasis on proofs than courses on the same topic intended for mathematics majors. Correspondingly, there may be more emphasis on applications to/in engineering. However, to be sure, it would be wise to check.

Renfro -- I recommend looking at the web page for the course, or if there is no web page, try to find what textbook is being used. Also, faculty who have previously taught the course might have old homework assignments, tests, handouts, etc. for the course still on their faculty web pages. Sometimes these are not visible from the faculty member's web page, but you can (sometimes) still find them by googling things like the professor's name along with "linear algebra" and the course number.

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I learned linear algebra (decades ago) as an "adjunct" to "engineering mathematics."

The focus of most engineering students is "systems of equations." As long as you remember that, you're fine. So engineers are most focused on those parts of linear algebra that provide solutions to systems of equations, including lower echelon row reduction and eigenvalue problems.

Just avoid the more abstract issues, such as "kernels" of spaces, where they'll get lost.

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    $\begingroup$ I used to teach a university linear algebra course, and got sent many sample textbooks by publishers. The engineering books took linear algebra to mean "matrix techniques", where the mathematics ones took it to mean "vector spaces and linear maps", so this agrees very much with your answer. $\endgroup$ – AndrewC Jun 5 '14 at 23:07

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