In order to succeed in applied mathematics, it is necessary to be a good mathematician and to know well the area to which the mathematics is being applied. Mathematicians build models that describe observed phenomena, but the models are never completely correct and knowing when to trust and when not to trust the output of such models requires a good understanding of both the mathematics and the phenomenon being studied. This is the reason the BSCF degree includes both mathematical sciences and finance.
However, there is more to quantitative finance than one can learn in classes. In his autobiography My Life as a Quant, Emanual Derman, the physicist who became a partner at Goldman Sachs, writes, "I'm still embarrassed to admit to myself that [during my undergraduate years] I almost never studied anything I wasn't officially taught." Computational finance attracts highly motivated people who do study things they are not officially taught, and Derman's example notwithstanding, doing so can confer a competitive edge. A good place to begin is Derman's book, Chapters 9 to 15, which describe his years at Goldman Sachs.
A more dramatic account of computational finance in action is When Genius Failed by Roger Lowenstein. This is the story of the hedge fund Long-Term Capital Management, in which both Robert Merton and Myron Scholes were partners. This fund began in 1994 and over the next five years managed to use quantitative finance methods and market savvy to make $4 billion. In the next 18 months, they lost everything and in the process threatened the stability of the U.S. financial system.
A classic book, which is more about the stock market and the trade-off between risk and return is A Random Walk Down Wall Street by Burton Malkiel. This is an excellent book for anyone who plans to ever invest money in the stock market. That includes anyone who has some control over how his or her retirement plan is managed.
Finally, people who are successful in computational finance pay attention to current events in the field. In the busy life of a student, it is not possible to read the Wall Street Journal every day, but it is possible to check it a few times each week in order to find one good story about finance and read it carefully. It is better to read a few things in detail than to try to skim many things and thereby acquire only a shallow understanding. When firms interview for internships and full-time jobs, they tend to first figure out what a student should know or claims to know, and then ask a series of questions, each one probing more deeply than the previous. A student who claims to know something should be prepared for questioning about it.