As you already know that mathematics and statistics are foundation of Artificial Intelligent algorithms and concept. Let discuss how to start with them you need for AI. Here are some of the most important mathematical concepts that you will need to know:
- Linear algebra: Linear algebra is the foundation of AI. It is used to represent data, solve equations, and perform operations on data.
- Calculus: Calculus is used to understand how AI models work. It is used to find the optimal weights for machine learning models and to understand the behavior of neural networks.
- Probability and statistics: Probability and statistics are used to understand the uncertainty in data. They are used to train machine learning models and to evaluate their performance.
- Discrete mathematics: Discrete mathematics is used to deal with problems that involve discrete objects, such as sets, graphs, and trees. It is used in AI for tasks such as natural language processing and computer vision.
In addition to these mathematical concepts, you will also need to be familiar with some of the following topics:
- Algorithms: Algorithms are the steps that a computer takes to solve a problem. You will need to be familiar with a variety of algorithms, including sorting algorithms, searching algorithms, and machine learning algorithms.
- Data structures: Data structures are the way that data is organized in a computer. You will need to be familiar with a variety of data structures, such as arrays, lists, and trees.
- Programming languages: You will need to be familiar with a programming language, such as Python, Java, or C++. This will allow you to implement the algorithms and data structures that you learn about.
Let’s start with linear algebra. Linear algebra is the study of vectors, matrices, and linear transformations. It is a fundamental mathematical tool that is used in many areas of science and engineering, including AI.
Here are some of the basic concepts of linear algebra:
- Vectors: A vector is a one-dimensional array of numbers. It can be used to represent a point in space, a direction, or a velocity.
- Matrices: A matrix is a two-dimensional array of numbers. It can be used to represent a system of equations, a transformation, or a data set.
- Linear transformations: A linear transformation is a function that takes a vector and maps it to another vector. It is a fundamental concept in linear algebra and is used in many areas of AI, such as image recognition and natural language processing.
If you are new to linear algebra, I recommend that you start with the basics. Learn about vectors, matrices, and linear transformations. Once you have a good understanding of the basics, you can start learning about more advanced topics, such as eigenvalues and eigenvectors.
There are many resources available online and in libraries that can teach you linear algebra. I recommend that you find a book or online course that is well-written and easy to understand.
Here are some resources that you may find helpful:
- Linear Algebra Done Right: This book by Gilbert Strang is a classic introduction to linear algebra. It is well-written and easy to understand.
- Linear Algebra with Applications: This book by David C. Lay is another good introduction to linear algebra. It covers a wide range of topics and includes many examples.
- Khan Academy: Khan Academy has a great set of videos on linear algebra. They are free to watch and cover a wide range of topics.
Calculus is a branch of mathematics that deals with the study of change. It is divided into two main parts: differential calculus and integral calculus.
- Differential calculus is the study of how functions change. It is used to find the slope of curves, the rate of change of functions, and the area under curves.
- Integral calculus is the study of how functions accumulate. It is used to find the volume of solids, the length of curves, and the work done by forces.
Calculus is a powerful tool that is used in many different fields, including physics, engineering, economics, and statistics. It is also used in many areas of computer science, such as machine learning and artificial intelligence.
Here are some of the basic concepts of calculus:
- Functions: A function is a relationship between two sets of numbers. It can be used to represent a real-world phenomenon, such as the relationship between the temperature and the time of day.
- Limits: A limit is the value that a function approaches as its input approaches a certain value. It is used to define the derivative and integral of a function.
- Derivatives: The derivative of a function is a measure of how the function changes as its input changes. It is used to find the slope of curves, the rate of change of functions, and the area under curves.
- Integrals: The integral of a function is a measure of how the function accumulates as its input accumulates. It is used to find the volume of solids, the length of curves, and the work done by forces.
If you are new to calculus, I recommend that you start with the basics. Learn about functions, limits, derivatives, and integrals. Once you have a good understanding of the basics, you can start learning about more advanced topics, such as differential equations and vector calculus.
There are many resources available online and in libraries that can teach you calculus. I recommend that you find a book or online course that is well-written and easy to understand.
Here are some resources that you may find helpful:
- Calculus Made Easy: This book by Silvanus Thompson is a classic introduction to calculus. It is well-written and easy to understand.
- Calculus: Early Transcendentals: This book by James Stewart is another good introduction to calculus. It covers a wide range of topics and includes many examples.
- Khan Academy: Khan Academy has a great set of videos on calculus. They are free to watch and cover a wide range of topics.
Probability and statistics are two closely related branches of mathematics that deal with the analysis of data. Probability is the study of chance, while statistics is the study of how data can be collected, analyzed, and interpreted.
Probability is used to measure the likelihood of an event occurring. For example, we can use probability to calculate the likelihood of flipping a coin and getting a head, or the likelihood of rolling a dice and getting a 6.
Statistics is used to collect, organize, and analyze data. It can be used to describe data, to make inferences about populations, and to test hypotheses. For example, we can use statistics to calculate the average height of a population, or to determine whether there is a significant difference in the average height of men and women.
Probability and statistics are used in many different fields, including science, engineering, business, and medicine. They are also used in many areas of computer science, such as machine learning and artificial intelligence.
Here are some of the basic concepts of probability and statistics:
- Random variables: A random variable is a variable whose value is determined by chance. For example, the outcome of a coin flip is a random variable.
- Probability distributions: A probability distribution is a mathematical function that describes the probability of different outcomes for a random variable. For example, the probability distribution for the outcome of a coin flip is a uniform distribution.
- Sampling: Sampling is the process of selecting a subset of data from a larger population. This is often done to make inferences about the population as a whole.
- Hypothesis testing: Hypothesis testing is a statistical method for testing whether there is a significant difference between two or more groups of data.
If you are new to probability and statistics, I recommend that you start with the basics. Learn about random variables, probability distributions, sampling, and hypothesis testing. Once you have a good understanding of the basics, you can start learning about more advanced topics, such as Bayesian statistics and machine learning.
There are many resources available online and in libraries that can teach you probability and statistics. I recommend that you find a book or online course that is well-written and easy to understand.
Here are some resources that you may find helpful:
- Probability and Statistics for Engineers and Scientists: This book by Jay L. Devore is a classic introduction to probability and statistics. It is well-written and covers a wide range of topics.
- Introduction to Probability and Statistics: This book by David Freedman is another good introduction to probability and statistics. It covers a more advanced range of topics than Devore’s book.
- Khan Academy: Khan Academy has a great set of videos on probability and statistics. They are free to watch and cover a wide range of topics.
Discrete mathematics is the study of mathematical structures that can be considered “discrete” rather than “continuous”. Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in “continuous mathematics” such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term “discrete mathematics”.
Here are some of the basic concepts of discrete mathematics:
- Sets: A set is a collection of objects that are distinct from each other. Sets can be finite or infinite.
- Relations: A relation is a way of connecting two sets. For example, the relation “greater than” connects the set of all numbers to itself.
- Functions: A function is a special type of relation that assigns exactly one output to each input. For example, the function “square” assigns the square of a number to that number.
- Logic: Logic is the study of reasoning and truth. It is used to construct proofs and to analyze arguments.
- Combinatorics: Combinatorics is the study of counting. It is used to count the number of possible arrangements of objects or the number of possible solutions to problems.
Discrete mathematics is used in many different fields, including computer science, mathematics, engineering, and economics. It is also used in many areas of artificial intelligence, such as natural language processing and machine learning.
Here are some of the applications of discrete mathematics:
- Computer science: Discrete mathematics is used in computer science to design algorithms, data structures, and programming languages.
- Mathematics: Discrete mathematics is used in mathematics to study sets, functions, logic, and combinatorics.
- Engineering: Discrete mathematics is used in engineering to design circuits, networks, and systems.
- Economics: Discrete mathematics is used in economics to study games, markets, and decision making.
- Artificial intelligence: Discrete mathematics is used in artificial intelligence to design search algorithms, knowledge representation systems, and machine learning algorithms.
If you are interested in learning more about discrete mathematics, there are many resources available online and in libraries. I recommend that you find a book or online course that is well-written and easy to understand.
Here are some resources that you may find helpful:
- Discrete Mathematics and Its Applications: This book by Kenneth H. Rosen is a classic introduction to discrete mathematics. It is well-written and covers a wide range of topics.
- Discrete Mathematics with Applications: This book by Richard Johnsonbaugh is another good introduction to discrete mathematics. It covers a more advanced range of topics than Rosen’s book.
- Khan Academy: Khan Academy has a great set of videos on discrete mathematics. They are free to watch and cover a wide range of topics.
You can find out more related articles I have already written in LinkedIn and Medium.
I am a Software Architect | AI, ML, Python, Data Science, IoT, Cloud ⌨️ 👨🏽 💻
Love to learn and share knowledge to help. Thank you.
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