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I am a computer science graduate and slacked my way through high school and college and don't have a solid understanding of the basic concepts in mathematics I also don't have the mathematical way of thinking. I am trying to build a product which requires understanding loads of theory, on the subject at hand. But whenever mathematics comes into the picture it goes above and over my head. This question will hopefully be useful to people like me in similar situations. I am willing to invest years to learn the basics right.

From the top of my head, i can think of the following areas that i have no familiarity

  • Harmonic Numbers
  • Infinite series
  • Probability
  • Combinatorics,permutation and combination
  • Set theory
  • Discrete mathematics
  • Trigonometry
  • Calculus
  • Logarithms
  • Matrices and determinants
  • Vectors

If you know of any more fundamental areas that i missed out please do add it along with reference books for the same.

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Probability - Introduction to Probability Theory William Feller

Linear Algebra - Gilbert Strang

Calculus - Apostol Calculus Vol 1 and 2

Number theory - Hardy and Wright Theory of numbers

These books will give you a basic idea of these topics. These are comparitively easy to understand even for a high school student with a strong mathematical foundation. All the areas you have mentioned are included in these books.

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Concrete Mathematics: A Foundation for Computer Science would be my suggestion for a book to consider in covering the basics of most of the areas you mention at least in terms of getting an understanding of the Abstract Algebra along with Calculus, Analysis and other areas of Mathematics.

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