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Phase 1: Core Mathematical Foundations

1. Arithmetic & Number Theory

What to Learn?

• Basic Operations: Addition, Subtraction, Multiplication, Division (with shortcuts)

• Divisibility Rules: Rules for 2, 3, 4, 5, 6, 9, 10, 11, etc.

• Factors & Multiples: Prime factorization, Greatest Common Divisor (GCD), Least Common Multiple (LCM)

• Modular Arithmetic: Modulo operations, Modular Inverses, Chinese Remainder Theorem

• Prime Numbers: Sieve of Eratosthenes, Prime Testing, Primality Proofs

• Number Bases: Binary, Octal, Hexadecimal conversions (important for CS)

Why Important?

• Used in Cryptography, Competitive Programming

• Helps in Efficient Algorithms & Modular Exponentiation

Practice:

• Solve problems from Project Euler, Codeforces

• Master mental calculations (Vedic Math techniques)

2. Algebra

What to Learn?

• Basic Algebraic Operations: Polynomials, Rational Expressions

• Equations: Linear, Quadratic, Higher Order

• Functions & Graphs: Transformations, Inverses

• Logarithms & Exponents: Properties, Exponential Growth/Decay

• Sequences & Series: Arithmetic, Geometric, Harmonic Progressions

Why Important?

• Used in Algorithms (Logarithmic Complexity, Sorting, Searching)

• Helps in Data Structures (Hashing, Trees, Heaps)

Practice:

• Solve equations manually (without a calculator)

• Work on pattern recognition techniques

3. Geometry & Trigonometry

What to Learn?

• Basic Shapes & Properties: Triangles, Circles, Quadrilaterals

• Coordinate Geometry: Line Equations, Midpoint, Distance, Area

• Trigonometric Identities: Sine, Cosine, Tangent, Cotangent, Secant, Cosecant

• Applications: Sine/Cosine Laws, Polar Coordinates

Why Important?

• Used in Graphics Programming, Game Development, Computer Vision

• Essential for Physics Simulations, Robotics, AI

Practice:

• Solve real-world geometric problems

• Apply trigonometry in Game Development (3D Transformations, Camera Rotations)

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Phase 2: Advanced Math (For CS, AI, and Data Science)

4. Discrete Mathematics

What to Learn?

• Propositional & Predicate Logic: Boolean Algebra, Logical Operators

• Set Theory & Relations: Unions, Intersections, Venn Diagrams

• Combinatorics: Permutations, Combinations, Binomial Theorem

• Graph Theory: BFS, DFS, Euler Paths, Hamiltonian Cycles

Why Important?

• Used in Data Structures, Algorithms, AI, Cryptography

• Basis for Theoretical CS, Automata Theory, Complexity Theory

Practice:

• Solve Graph Theory & Combinatorial Problems

• Implement Graph Algorithms in C, Java, Python

5. Probability & Statistics

What to Learn?

• Probability Theorems: Bayes' Theorem, Conditional Probability

• Distributions: Normal, Binomial, Poisson

• Statistical Inference: Mean, Median, Mode, Variance, Standard Deviation

• Hypothesis Testing & Regression Analysis

Why Important?

• Used in Machine Learning, AI, Data Science, A/B Testing

• Helps in Decision-Making, Financial Predictions

Practice:

• Solve real-world probability problems

• Apply statistics in Python (NumPy, Pandas, Matplotlib)

6. Linear Algebra

What to Learn?

• Matrix Operations: Addition, Multiplication, Determinants, Inverses

• Eigenvalues & Eigenvectors: Characteristic Equation, Applications

• Vector Spaces & Transformations: Basis, Rank, Linear Dependence

Why Important?

• Used in AI, Deep Learning (Neural Networks, Principal Component Analysis)

• Crucial in Graphics, Computer Vision, Robotics

Practice:

• Implement Matrix Operations in Python

• Solve Eigenvector Problems

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Phase 3: Expert-Level Math (For Research, AI, and Quantum Computing)

7. Calculus

What to Learn?

• Differentiation & Integration: Basic Rules, Chain Rule, Applications

• Partial Derivatives & Multivariable Calculus

• Gradient Descent & Optimization Techniques

Why Important?

• Used in AI, Physics Simulations, Robotics, Game Engines

• Optimization techniques for Machine Learning & Neural Networks

Practice:

• Solve Real-World Optimization Problems

• Implement Gradient Descent for ML Models

8. Advanced Topics

What to Learn?

• Abstract Algebra: Group Theory, Rings, Fields (Used in Cryptography)

• Fourier Analysis: Fourier Series, Fourier Transforms (Used in Image Processing, Sound Engineering)

• Topology & Differential Equations: Used in Robotics, Physics Simulations

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Conclusion

• You already studied these topics in school & college. Now, it's time to recover, retain, and apply them practically.

• Focus on understanding the logic behind each concept, not just memorization.

• The more you use math, the more it becomes second nature.

• This roadmap covers everything needed to become a Math Professional and CS expert. Start small, be consistent, and apply your knowledge! ✨