> Pure mathematics departments for at least the past maybe 80 years often look down on numerical analysis, statistics, engineering, and natural science, and adopt a position that education of students should be optimized in the direction of helping them prove the maximally general results using the most abstract and technical machinery, with an unfortunate emphasis on symbol twiddling vs. examining concrete examples.
I had this view when I took linear algebra as an undergraduate, but I have gradually changed on the subject over time. I took a standard "linear algebra for scientists and engineers" course but I found it too abstract at the time. The instructor rarely concentrated on examples and applications despite the more applied focus in the course title. Later I came to appreciate the abstraction, since it helped me understand more advanced mathematical topics unrelated to the "number-crunching" I originally associated the topic with. I now think the instructor had a more "unified" approach, but I didn't realize it at the time.
I had this view when I took linear algebra as an undergraduate, but I have gradually changed on the subject over time. I took a standard "linear algebra for scientists and engineers" course but I found it too abstract at the time. The instructor rarely concentrated on examples and applications despite the more applied focus in the course title. Later I came to appreciate the abstraction, since it helped me understand more advanced mathematical topics unrelated to the "number-crunching" I originally associated the topic with. I now think the instructor had a more "unified" approach, but I didn't realize it at the time.