Q:

Requirements for a masters degree in pure mathematics

I am in the second year of a Bachelors of Science program in business administration and economics.  My program is in English and I am studying in Sweden.  I attended elementary school in Romania and high school, with major in economics and business administration, in Germany.  In high school I selected computer science as a subject, which was optional, because I was interested in the world of computer science and its mysteries, especially that of programming.  The programming language taught in the course, in high school, was visual basic.  Currently I know C++, HTML, CSS and PHP, and some JQuery.  I have been programming for about four years now.  The book I used was C++ Primer by Stanley B. Lippman for most of my C++ knowledge and internet resources, and for the web development, HTML, CSS, and PHP, I mainly used w3schools.com and other internet resources, and of course practice. 
The mathematics at high school included some linear algebra and calculus, both differentiation and integration, but at a computational level.  After high school I was unsure which academic path I should follow, which led to a one year break between high school and university.  During this year I attended as a guest, lectures in computer science and mathematics (mainly propositional logic, set theory and proofs) in Germany.  Then I decided to follow a business administration and economics path as my Bachelor of Science and go back to pure mathematics in my Masters program.  In my free time I work through mathematical books.  I worked through Precalculus by Jeff Zeager and Carl Stitz, How to prove it: A structured approach by Daniel J. Velleman, Book of proof by Richard Hammack and I am currently going through Calculus by Michael Spivak, where I recently finished the Differentiation part of the book.  And as from my experience so far, Spivak's book will stay with me for some more months to come before I finish it. 
I will graduate with a Bachelor of Science degree in business administration and economics and after that I want to pursue a Masters degree in pure mathematics with major in computer science and physics, preferably.  The only course which is of mathematical nature in my program, is "Business Statistics", which essentially is a course in statistics, but with business applications and exercises.  
Long story short:
What are the requirements for a Masters program in pure mathematics, with preferable computer science and physics majors?  Is it realistic to be accepted in a Masters program with a Bachelor of Science in economics and business administration?  I already have knowledge from mathematics courses, which Bachelor of Science students in mathematics take, but I do not have proof for this knowledge, in form of a degree or courses passed.  Will I have to somehow prove this knowledge when applying for a masters program?  If yes, how?  I want to avoid after the degree in business administration and economics to enroll into a Bachelor of Science in mathematics, because that would be redundant for me, if I already have the knowledge but it is not recognized, because it is not in form of a formal document. 
PS:
I will graduate in 2018.  My goals are to finish Calculus by Michael Spivak, start and finish Calculus Volume 2 by Tom Apostol, Principles of Mathematical Analysis by Walter Rudin and a book in linear algebra. 

A:

I would propose that while carrying on your studies for Bachelors of Science program in business administration and economics you keep studying math courses with a focus and orientation towards a high score in the GRE subject test in Mathematics.  That might provide a good argument -for postgraduate applications-  against the lack of a formal degree in maths or a math related science.  But again, you have to contact postgraduate departments of interest to you and directly ask their opinion, on whether a high score in GRE subject test in Mathematics will be enough and what more they might ask from you. 