Need Suggestion regarding Programming

Hai. I am new to programming. I have some doubts in the area of Programming(Competitive Programming):

  1. What are the must learn mathematics concepts to excel in programming? I want to know the topics in mathematics that are must and common for a programmer’s life. Also some resources to learn the math related to competitive Programming.
  2. What are the best ways to improve my logical thinking skills and problem solving skills as I know that I am really weak in problem solving skills?
  3. What are the approaches for a beginner should habituate/follow so that one cannot face some problems that are general or that are being there every time in the area of programming?
  4. Is it possible to get hired by product based companies considering only the programming skills of a student who is from some private engineering college who didn’t have any references/network and without the GPA consideration?
    I want to start my career in programming but don’t know the path and where to start and how to reach my goal of getting hired by a Product-Based company like Google as a Graduate from Computer Science from South India.
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