The Best Mathematical Path (first Draft by David I Nyirenda)

I believe that students need to understand concepts, rather than mimic steps,
to be successful in a mathematics course. This is especially true in most
introductory courses. One of my main goals in writing this text was to help
students understand mathematics, to understand the “why” as well as the
“how.” Toward this end, the many examples of motivating scenarios to be a
successful mathematics pursuer in this text are supplemented by clear
explanations. Whenever possible, I have tried to show how the so-called
mathematical challenges can be met and dealt with. 

I try to foreshadow
material that will show up in later at various levels of doing mathematics,
while referring back to material you need at an earlier stage. In general, I try
to bring about the motivation and energy one needs to pursue mathematics
and the significance of doing it. While ‘mathematics’ is an underlying term
here, this text is meant for all individuals who pursue mathematics as a career
or who intend to use mathematics.