Mathematics for Computer Science - Study Roadmap (Khan Academy)

This roadmap lists essential math topics for programming, algorithms, data science, AI, and more. Khan Academy links are included for each topic.

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1. Basic / Fundamental Math

Goal: Fluency in algebra and basic logic.

• Arithmetic
  Operations with integers, decimals, fractions, and percentages.
  Khan Academy: Arithmetic

• Pre-Algebra
  Basic algebra: equations, inequalities, properties of operations.
  Khan Academy: Pre-Algebra

• Algebra 1
  Linear and quadratic functions, systems of equations.
  Khan Academy: Algebra 1

• Algebra 2 (optional, recommended)
  Advanced factorization, polynomials, exponential and logarithmic functions.
  Khan Academy: Algebra 2

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2. Discrete Mathematics

Goal: Foundation for algorithms, data structures, and logic.

• Precalculus → Combinatorics
  Permutations, combinations, and counting.
  Khan Academy: Probability and combinatorics

• Probability & Statistics → Probability
  Combinatorial probability concepts.
  Khan Academy: Probability

• Logic (Computer Science)
  Logical connectives, truth tables, Boolean algebra.
  Khan Academy: Logic gates

• Computer Science → Algorithms
  Basic notions of graphs and data structures.
  Khan Academy: Algorithms

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3. Linear Algebra

• Linear Algebra
  Vectors, vector operations, matrices, matrix multiplication, determinants, linear systems.
  Khan Academy: Linear Algebra

• Applications
  Linear transformations and coordinates.
  Khan Academy: Linear transformations

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4. Calculus

• Differential Calculus
  Limits, derivatives, and applications (rate of change).
  Khan Academy: Differential Calculus

• Integral Calculus
  Indefinite and definite integrals.
  Khan Academy: Integral Calculus

• Multivariable Calculus (optional)
  Useful for computational physics and 3D graphics.
  Khan Academy: Multivariable Calculus

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5. Probability and Statistics

• Probability & Statistics
  Basic probability, combinatorics, random variables, distributions, mean, variance, and basic inferential statistics.
  Khan Academy: Probability and Statistics

• Data Analysis
  Graphs, regression, and data visualization.
  Khan Academy: Data Analysis

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Study Tips

1. Reinforce basics first: Arithmetic → Pre-Algebra → Algebra 1 → Algebra 2.
2. Parallel practice: Probability & Logic while studying Linear Algebra.
3. Calculus later: After a strong algebra foundation, useful for ML or graphics.

This roadmap prepares you for programming, algorithms, data science, AI, and other computer science fields.