Doing Mathematics: Convention, Subject, Calculation, Analogy 2nd edition (PDF) discusses some ways mathematical physicists and mathematicians do their work and the subject matters they uncover and fashion. The conventions they adopt, what they can prove and calculate about the physical world, the subject areas they delimit, and the analogies they
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With traditional linear algebra textbooks, the course is relatively easy for most of the students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, college students often hit a wall. Instructors seem to agree that certain concepts (such as spanning,