This article list out some of the foundational mathematics courses freely available on YouTube.

A strong foundation flags off a voyage to knowledge and success. Anyone wish to have a great problem solving skill in science, technology or engineering will have to aquire the fundamental nuggets of mathematical ideas. This is because almost any problem can be broken down into those fundamental concepts. Having a solid and deep understanding of such concepts helps one to understand and solve problems quickly.

Foundational mathematics courses are important for career success in a variety of ways.

Here are some reasons why:

- Problem-solving skills: Mathematics courses teach critical thinking, analytical reasoning, and problem-solving skills. These skills are highly valued in the workplace and are essential for success in many fields.
- Quantitative analysis: Many professions require individuals to analyze data, make decisions based on numerical information, and work with mathematical models. Foundational mathematics courses provide the necessary skills to perform these tasks with ease.
- Computer programming: Computer programming requires a solid foundation in mathematics, especially in the areas of logic and algorithms. Understanding mathematical concepts can help individuals write efficient and effective computer programs.
- Communication skills: The ability to communicate complex mathematical ideas in a clear and concise manner is essential in many professions, such as teaching, research, and consulting.
- Career advancement: Having a strong foundation in mathematics can open up opportunities for career advancement. It can make individuals more competitive in the job market and can lead to higher-paying jobs.

## Importance of Visualization

Visualization is a powerful tool for understanding mathematical concepts because it can help individuals develop a more intuitive understanding of abstract concepts.

Visualizing mathematical concepts can help individuals see connections between different ideas that might not be immediately apparent. This can help them develop a more comprehensive understanding of the subject matter.

Visualization can provide a concrete representation of abstract concepts, making them easier to understand and remember. For example, visualizing a function as a graph can help individuals see how changes in the input affect the output.

Visualization can also be used to create analogies that make complex ideas more relatable. Analogies can help individuals see how mathematical concepts relate to real-world situations and can help them remember the concepts more effectively.

Visualization can be used as a tool for exploration, allowing individuals to experiment with different values and see how they affect the outcome. This can help individuals develop a more intuitive understanding of the concept and can make it easier to remember and apply in different situations.

Visualization can also be used as a tool for communication, allowing individuals to convey complex ideas in a simple and intuitive way. This can be particularly important when teaching or presenting mathematical concepts to others.

Foundational mathematics courses provide individuals with essential skills that are highly valued in many professions. These skills can help individuals succeed in their careers and achieve their professional goals.

I am curating a list of free undergraduate courses. All of them are freely available on YouTube.

This list particularly focuses on math-oriented courses. The reason for that is because most of the underlying concepts in various fields can be explained using mathematical principles. The motivation behind this blog itself is to create a resource of such concepts which are explained using a layman’s language.

Once we have enough fundamental building blocks, we can creatively combine them to create or understand advanced concepts. Two scenarios are possible in this regard. One is the process of breaking down a complex idea into its fundamental components and the other is to create advanced concepts.

If you observe enough you can see that scientific research is often done in three ways. One is physical experiments, empirical research, and theoretical research. Theoretical research has become the defacto standard because of its fundamental nature. The rules of nature are written in the language of mathematics and to understand that it is essential to learn the alphabets which construct it.

Undergraduate materials don’t assume much of prerequisites. Such resources are ideal for someone persistent and patient enough to follow and upskill themselves.

## List of foundational math courses

- Map Videos – Domain of Science
- Abstract Algebra 1
- A full course in econometrics
- Financial Management
- Boundary Value Problems and Partial Differential Equations
- Undergrad Complexity Theory
- Differential and Integral Calculus 1
- ME-130 Thermodynamics-I
- Undergraduate Control Systems
- Undergraduate Topology
- A first course in Linear Algebra
- Undergraduate abstract algebra
- Undergraduate Machine Learning
- Applied Statistics Course
- Linear Algebra
- Mathematical Analysis

All of the above foundational math courses provides insights into mathematical concepts and often explain the intuition behind those concepts.

Understanding the intuition behind a mathematical concept is important because it can help individuals develop a deeper and more intuitive understanding of the concept, which can make it easier to remember and apply in different contexts. Here are some specific reasons why understanding the intuition behind a mathematical concept is helpful:

- Flexibility: When individuals understand the intuition behind a mathematical concept, they are better equipped to apply the concept in different situations and to solve problems that may be slightly different from the ones they have encountered before.
- Creativity: Understanding the intuition behind a mathematical concept can inspire creativity and lead to new insights and ideas. This can be particularly important in research or when solving complex problems that require innovative solutions.
- Efficiency: When individuals understand the intuition behind a mathematical concept, they can often arrive at solutions more quickly and efficiently. This can be especially important in time-sensitive situations or when working on large-scale projects.
- Retention: Understanding the intuition behind a mathematical concept can help individuals remember it more effectively. Rather than simply memorizing formulas or procedures, individuals who understand the intuition behind a concept can often reconstruct it from memory and apply it in new situations.

The philosophy of this blog itself is to explain concepts in enough details using visualizations, intuition and code. Many articles attempt to break down concepts into its fundamental mathematical concepts. This approach is top down. But for someone starting out (e.g. an undergraduate), it is required for them to go through the bottom up approach also so that later it will be easy for them to learn any concept using the top down way.

The above list is not a complete list of free foundational math courses, but contains a few interesting courses that help you build strong foundational concepts. If you are looking for more granular level ideas which is often the foundations to these courses, please see here.