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Artificial Intelligence

AI Mathematics

The main branches of mathematics involved in AI are:

  • Calculus
  • Probability
  • Statistics
  • Linear Algebra

AI is Mathematics

The purpose of AI is to create models for human understanding or thinking.

Behind every AI success there is mathematics.

All AI models are constructed using solutions and ideas from math.

If you want an AI career:

  • Data Scientist
  • Machine Learning Engineer
  • Robot Scientist
  • Data Analyst
  • Natural Language Expert
You should focus on the mathematic concepts described below.


Calculus

The main calculus concepts used in AI are:

  • Differential Calculus
  • Multivariate Calculus
  • Integral Calculus
  • Error Minimization
  • Logistic regressions

Statistics

Statistics is about how to collect, analyze, interpret, and present data.

Inferential statistics are methods for quantifying properties of a domain (a population) from a small set of data called a Sample.

Descriptive Statistics are methods for summarizing observations into information that we can understand.

Statistics works with questions like:

  • What is the most Common?
  • What is the most Expected?
  • What is Normal?

The Mean is the mean value of all observations.

Variation is the average of the squared differences from the mean value.

Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the Greek letter sigma), and the formula is the square root of the Variance.

Standard Normal Distribution

For the Normal Distribution Curve (Bell Curve), values less than one Standard Deviation away from the Mean account for 68.27% of the set, two standard deviations away account for 95.45%, and three standard deviations away account for 99.73%.


Linear Algebra

An AI expert cannot live without linear algebra:

  • Linear algebra is a branch of mathematics
  • Linear algebra plays an important role inn statistics
  • Linear algebra represents the math of data

Linear algebra uses Vectors and Matrices (Arrays) and with AI (especially Machine Learning) everything is done with data in vectors and matrices.

Linear means straight. A linear graph is a strait line.

In general, a linear graph displays function values:

Graph