Mathematics.md

📘 Mathematics Roadmap

Mathematics is divided into three focused parts, depending on application area:

• Mathematics 1 – General Programming
• Mathematics 2 – Machine Learning
• Mathematics 3 – Graphics & Geometry

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📐 Mathematics 1 – General Programming

Reference: http://ncert.nic.in/textbook/textbook.htm?kemh1=ps-16

☐ Algebra

• Permutations and Combinations
• Binomial Series
• Sequences and Series
  • Infinite Series
  • Binomial Theorem (any index)
  • Exponential Series
  • Logarithmic Series

☐ Statistics (Basics)

• Mean
• Median
• Mode

☐ Sets and Logic

• Sets and Relations
• Functions
• Reasoning and Logic
• Knowledge Representation

☐ Discrete Mathematics

Reference: http://home.iitk.ac.in/~arlal/book/mth202.pdf

☐ Matrices

• Matrix and Types of Matrices
• Matrix Operations
• Transpose of a Matrix
• Symmetric and Skew-Symmetric Matrices
• Elementary Row/Column Operations
• Invertible Matrices

☐ Determinants

• Determinant and Properties
• Minors and Cofactors
• Adjoint and Inverse of a Matrix
• Area of a Triangle
• Applications of Determinants and Matrices

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📊 Mathematics 2 – Machine Learning

☐ Probability

• Random Experiments and Events
• Conditional Probability
• Multiplication Theorem
• Bayes’ Theorem
• Bernoulli Trials
• Binomial Distribution
• Poisson Distribution

☐ Statistics

• Mean, Median, Mode
• Range and Dispersion
• Deviation
• Variance and Standard Deviation
• Hypothesis Testing
  • Z-Test
  • T-Test
  • F-Test
  • Chi-Square Test

☐ Calculus

Limits & Continuity

• Limits
• Continuity

Differentiation

• Differentiability
• Exponential and Logarithmic Functions
• Logarithmic Differentiation
• Parametric Differentiation
• Second Order Derivatives
• Mean Value Theorem
• Rate of Change
• Increasing & Decreasing Functions
• Tangents and Normals
• Approximations
• Maxima and Minima

Integration

• Integration as Inverse of Differentiation
• Methods of Integration
• Standard Integrals
• Partial Fractions
• Integration by Parts
• Definite Integrals
• Fundamental Theorem of Calculus
• Substitution Method
• Area Under Curves
• Area Between Two Curves

Differential Equations

• Basic Concepts
• General and Particular Solutions
• Formation of Differential Equations
• First Order, First Degree Equations

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🎮 Mathematics 3 – Graphics & Geometry

☐ Functions and Equations

• Quadratic Equations
• Cubic Equations
• Complex Numbers
• Trigonometry
• Inverse Trigonometric Functions

☐ Coordinate Geometry

Lines

• General Equation of a Line
• Slope of a Line
• Distance of a Point from a Line

Conic Sections

• Cone and Its Sections
• Parabola
• Ellipse

Vector Algebra

• Types of Vectors
• Vector Addition
• Scalar Multiplication
• Dot Product
• Cross Product

Three-Dimensional Geometry

• Coordinate Axes and Planes
• Section Formula
• Direction Cosines and Ratios
• Equation of a Line in Space
• Angle Between Two Lines
• Shortest Distance Between Two Lines
• Planes and Co-Planarity
• Angle Between Two Planes
• Distance of a Point from a Plane
• Angle Between a Line and a Plane

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📄 License

Mozilla Public License