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Mathematics vs computer science





Mathematics originates from a Greek word máthēma, which means “knowledge, study, learning" is the study of such topics such as quantity, structure space and change It has no generally accepted definition. Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written record exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
When we talk about computer science computer science is the study of the theory, experimentation and engineering that form the basis for the design and use of computers. Computer science offers you the best of both worlds. You get to study math because without math there would be no computer science. Computer science is just mathematics making an immediate impact on society. The best strategy is: major in math, but also learn a lot CS stuff and programming by yourself.
While when we say about the relation b/w two computer science is currently one of the most advanced and most widely-used branch of math. More and more advances of science, technology and business are directly linked to breakthroughs of computer science. Where computer science is today is where calculus and differential equations was 50-100 years ago in terms of their innovative power.
As computers started out as powerful assistants for "traditional" math, you'd likely encounter most interesting "traditional" math problems when learning CS. The converse is much less true. When we talk about the math it is the base of computer science without that we can’t think anything. We use it in many ways like programming, flowcharts, algorithms etc and it gives the shape to the computer world.
Topics which you should know:-
1. Set Theory (falls under Abstract Alg.) 
2. Probability 
3. Graph Theory 
4. Abstract Algebra [Ring, fields, Sets]
5. Number Theory  
6. Convex Optimizations [Important from Research Prospective]
7. Statistics [Important from Research Prospective]
8. Propositional Logic and Proofs.
9. Counting or Permutations and Combination
10. Linear Algebra and Some trigonometry [Required for Computer Graphics or GameDev]
11. Computational Geometry [Important from Research Prospective].


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