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https://github.com/dacili/math-for-ai
https://github.com/dacili/math-for-ai
Last synced: 7 days ago
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- Host: GitHub
- URL: https://github.com/dacili/math-for-ai
- Owner: Dacili
- Created: 2024-10-18T12:39:51.000Z (27 days ago)
- Default Branch: master
- Last Pushed: 2024-11-07T11:32:46.000Z (7 days ago)
- Last Synced: 2024-11-07T12:29:48.292Z (7 days ago)
- Size: 15.6 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
# Math for AI
https://www.freecodecamp.org/news/all-the-math-you-need-in-artificial-intelligence/
> In order to be a good with AI, you gotta be good with some specific branches of math.
> Repetitio est mater studiorum (lat.) Repetition is the mother of all learning.
## Concepts of mathematics:
### 1. Algebra
### 2. Linear Algebra
### 3. Calculus
### 4. Statistics & Probability
### 5. Information Theory
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## 1. Algebra
- **Exponents** - An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (2^3) means: 2 x 2 x 2 = 8.
- **Radicals** - The √ symbol that is used to denote square root or nth roots.
**Radicand** - A number or expression inside the radical symbol
Laws (rules) of radicals:
- **Factorials** - operation of multiplying any natural number with all the natural numbers that are smaller than it. Factorial is used for questions that ask you to find how many ways you can arrange or order a set number of things.
- **Summations** - summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.
- 
Rules:
**Closed form** - an expression or equation is in closed form if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations (+, −, ×, /, and integer powers) and function composition. Commonly, the allowed functions are nth root, exponential function, logarithm, and trigonometric functions.
- **Scientific notations** - The base should be always 10.
Other things to remind yourself:
- **logarithms**
- **trigonometric functions**
trigonometric table:
trigonometric graphs:
- formulas for square, ...
- quadratic equation
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### 2. Linear Algebra
- **Matrix operations** -
- **Vector spaces** -
- **Linear transformation** -
cool course:
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/
**Scalars** — a single number (can be real or natural).
**Vectors** — a list of numbers, arranged in order. Consider them as points in space with each element representing the coordinate along an axis.
**Matrices** — a 2-D array of numbers where each number is identified by 2 indices.
**Tensors** — an N-D array (N>2) of numbers, arranged on a regular grid with N-axes. Important in Machine Learning, Deep Learning and Computer Vision.
**Eigenvectors & Eigenvalues** — special vectors and their corresponding scalar quantity. Understand the significance and how to find them.
**Singular Value Decomposition** — factorization of a matrix into 3 matrices. Understand the properties and applications.
**Principal Component Analysis (PCA)** — understand the significance, properties, and applications.
Properties such as the **Dot product**, **Vector product** and the **Hadamard product** are useful to know as well.
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### 3. Calculus
- **Derivatives** -
- **Integrals** -
- **Fundamental theorems** -
https://www.khanacademy.org/math/calculus-1/cs1-limits-and-continuity
**Derivatives** — rules (addition, product, chain rule, and so on), hyperbolic derivatives (tanh, cosh, and so on) and partial derivatives.
**Vector/Matrix Calculus** — different derivative operators (Gradient, Jacobian, Hessian and Laplacian)
**Gradient Algorithms** — local/global maxima and minima, saddle points, convex functions, batches and mini-batches, stochastic gradient descent, and performance comparison.
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### 4. Statistics & Probability
- **Counting** -
- **Random variables** -
- **Distributions** -
- **Limit theorem** -
- **Linear regression** -
- **Classification** -
- **Tree-based methods** -
**Basic Statistics** — Mean, median, mode, variance, covariance, and so on.
**Basic rules in probability** — events (dependent and independent), sample spaces, conditional probability.
**Random variables** — continuous and discrete, expectation, variance, distributions (joint and conditional).
**Bayes’ Theorem** — calculates validity of beliefs. Bayesian software helps machines recognize patterns and make decisions.
**Maximum Likelihood Estimation (MLE)** — parameter estimation. Requires knowledge of fundamental probability concepts (joint probability and independence of events).
**Common Distributions** — binomial, poisson, bernoulli, gaussian, exponential.
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### 5. Information Theory
**Entropy** — also called Shannon Entropy. Used to measure the uncertainty in an experiment.
**Cross-Entropy** — compares two probability distributions and tells us how similar they are.
**Kullback Leibler Divergence** — another measure of how similar two probability distributions are.
**Viterbi Algorithm** — widely used in Natural Language Processing (NLP) and Speech.
**Encoder-Decoder** — used in Machine Translation RNNs and other models.
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