Can I skip numerical analysis altogether and jump to other courses

Question

So the situation is I have completed Single and multivariate calculus, linear algebra, differential equations and and Real analysis. Now I'm thinking about skipping numerical analysis as it's of no use to my area of study which particularly programming and coding. My prof. told me that you should skip numerical analysis and jump to probability, statistics and discrete mathematics courses. Now I want to know that is it mandatory to learn numerical analysis in order to do well in probability statistics, discrete mathematics, linear programming and mathematical modelling. I mean is numerical analysis a prequisite to learn other courses well. Also throw some light on how important it is for a coder to learn numerical analysis.

Answer 1

I think you should strongly consider doing what your adviser recommends. Presumably he/she knows something about you and about the contents and quality of the numerical analysis course in your department.

Having said that, I agree with the Comments of @PeterDiehr and @BigbearZaa that numerical analysis is crucial background to many kinds of programming. I hope circumstances will arise later in which you take a numerical analysis course.

Here are some questions that should be easy for you to understand as related to your question. Answers are among topics considered in most numerical analysis courses. (These topics from my last month doing statistical computations.)

1) Digital computers do not deal with the real numbers, but instead with a carefully-chosen subset of the rationals that is very large, but finite. Usually, the computations on that subset of the rationals are satisfactory. But there are occasional rude surprises when they are not satisfactory. Do you know what sort of surprises to guard against?

2) There are good reasons why many computer packages define $0^0 = 1$ instead of 'undefined'. For example, in R the expression 0^0 returns 1. Why is that?

3) If $M$ is a $10 \times 10$ invertible matrix, under what circumstances can you trust the computed inverse to be correct?

4) You are evaluating whether a particular commercial software package gives sufficiently accurate results for the current work of your group. What benchmark tests should you use in your evaluation?