Algebra is the mathematics of the "equals" sign, of identity, and of the "main term"; analysis is the mathematics of the "less than" sign, of magnitude, and of the "error term".
Algebra prizes structure, symmetry, and exact formulae; analysis prizes smoothness, stability, and estimates.
It is because of these complementary foci that either subfield of mathematics looks strange when viewed through the lens of the other.
No comments:
Post a Comment