Questions about the field scientific computing I have heard about the field of Applied and Computational Mathematics, Scientific Computing and want to get some information. Is this a combination of computer science and mathematics? What subjects are related with this field? 
 A: It seems that most of what you want to know about lies within the domain of computational mathematics.  
Indeed, there is an intersection between computational mathematics and computer science; certainly in the context of computer algorithms.  
An essential aspect of computational mathematics is the study of numerical methods which includes (but is not limited to) optimization, linear programming, numerical quadrature, and interpolation, to name a few of the areas a course on the topic of computational mathematics might cover.
I think that should be enough information to give you a general idea of the scope of the field.  You may get a more useful answer if you explained why exactly you're asking this question in the first place.
A: Scientific computing deals with solving mathematical/scientific problems using computers. 
Typically, those problems have large scale, so solving them without computers is impractical, so computational mathematics deals with the challenges arise when using computers. The algorithm should be practical. Here are examples for typical challenges:
1) Efficiency - the algorithm should run in a reasonable time.
2) Computer memory limitation. How to fit a large scale problem into the memory?
3) Utilizing computer architecture - Parallel, etc.
4) Accuracy/Numerical stability - Does our solution is accurate and numerically stable? Both from "pure" mathematical perspective and by computer considerations (floating point precision, etc.)
Though the field may sound a little bit "too practical", there are often proofs for bounding condition numbers, error, convergence rate, etc. So it is strictly mathematical.
As more concrete examples for research in mathematics: numerical linear algebra, optimization, Lp minimization and sparse representations.
In engineering: computer vision, Big data, recommendation systems, bioinformatics.
Hope it helps.
