for the sake of precision it should be pointed out that learning about mathematics by reading alone is not the logical compliment of learning about mathematics

for the sake of precision it should be pointed out that learning about mathematics by reading alone is not the logical compliment of learning about mathematics through reading and book exercises. the term "exercise" by its nature implies something that is "practice". one may, however, simply learn by doing (rather than "exercising"). for a programmer, there is a clear distinction. this might not be the case for a mathematician.