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#### In this post, we are going in deep with the list of mathematics to be learned before going to start ahead in AI or Machine Learning

### Table of Contents

- What is the Impact of Mathematics on Machine Learning?
- What is the Approximate Distribution ratio of Topics in Mathematics
- Detailed List of Mathematical topics
- Good Sources to learn Mathematics for Machine Learning

### 1. What is the Impact of Mathematics on Machine Learning or Artificial Intelligence(AI)

Mathematics has an incredible impact on developing machine learning algorithms for real-time problem-solving. In the Machine Learning algorithm, learning insights from data is a completely numerical one. The first algorithm ( i.e., Linear regression ) to the last algorithm all are associated with Mathematics and Optimization.

Image Courtesy of Pixabay

Let us take a simple algorithm, how it is related to Mathematics ( let us take Classification algorithm for an example)

#### Classification Algorithm in Machine Learning

The classification algorithm is a supervised learning algorithm, which means dividing data into two either of two classes. It is of following types

- Yes or No
- True or False
- Positive or Negative

Image Courtesy of Wikipedia commons

#### What is the algorithm for classification

- Read the training and testing data
- Remove Null and empty values
- Apply some pre-processing algorithms like min-max scaling or normalization
- Define the threshold for this classification
- Test the algorithm against new input

#### Example Code of implementation of Classification algorithm

This code is implemented in python and by using sci-kit learn tools

Don't get bomb with code, I have just provided to know hoe exactly algorithm using mathematics to learn insights from data.

The logistic regression uses the

**sigmoid function**for classification among data points. Let me explain more in Mathematical wayImage Courtesy of Wikipedia commons

The function uses standard mathematical equations for predicting new outputs for new input data by using a sigmoid function threshold.

As we can see, the sigmoid function has the values between o to 1. If the value is predicted below 0.5, then it is treated as one class and greater 0.5 are treated as another class of classification. The working operation is a completely mathematical one.

#### 2. What is the Approximate distribution of Mathematics in Machine Learning or AI

Mathematics may impact the following parameters

- Time consumption like runtime, execution time
- Time Complexity of algorithm
- Bias and Variance trade-off
- Impact on confidence score on an algorithm

We can divide total mathematics into 4 parts. They are

#### 3. Detailed List Mathematical Topics to be learned

**Linear Algebra**

- Principle of Component Analysis
- Regression
- Matrix Operations
- Highen Vector and Highen Values
- Projects
- Vectors and Normal forms

**Probability and Statistics**

- Probability
- Random Variables
- Probability Distribution functions
- Moment Generating functions
- Bayes and Gaussian functions

**Calculus**

- Differentiation
- Integrations
- Maximum and Minimum values
- Partial derivates
- Limits and Continuity

**Optimization Algorithms**

- Linear Programming
- Stochastic and Gradient descent operations

**Others**

- Sets
- Relations
- Functions
- Activation functions

#### 4. Online Resources to learn Mathematics for Machine Learning

- Khan Academy free resources on Mathematics - https://www.khanacademy.org/math
- Harvard University YouTube series on probability - https://projects.iq.harvard.edu/stat110/youtube
- Mathematics for Machine Learning online course on Coursera- https://www.coursera.org/specializations/mathematics-machine-learning

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