Foundational subjects of science and engineering

For people interested in science, technology, engineering, and mathematics (STEM) who wish to gain a deeper understanding of STEM, there is no substitute for truly learning the foundational science and mathematics. There is only so much one can learn from pop-science books. In this article I propose a list of foundational subjects that are important in many fields of science and engineering. With the knowledge of these subjects, one will gain the ability to branch out and go deeper into specific fields. This is an attempt at making a basic list of scientific knowledge required for a well-rounded introductory STEM education. All the topics are supposed to be at the introductory undergraduate level.

It goes without saying that mathematics is essential in all fields of engineering. The most widely applicable mathematics subjects are:

• Single variable calculus
• Multi-variable calculus
• Linear algebra
• Ordinary differential equations

Then come the sciences. Special attention is paid to physics, which is split into two topics: classical mechanics and electromagnetism. If you have special interest in chemistry or biology, feel free to split them into more detailed subjects. For example, you may want to focus on organic and inorganic chemistry separately.

• Classical mechanics
• Electromagnetism

• General chemistry

• General biology

With the knowledge here, one will have a solid foundation for learning mechanical, electrical, civil, aeronautical engineering, and other related subjects. Each listed subject corresponds to a one semester course at the introductory undergraduate level, so one could use introductory university textbooks to acquire knowledge in the listed subjects. One may also want to learn computer programming in addition to the subjects listed above.

This is the list that I use myself. I regard this list as the minimum amount of science and mathematics that a serious STEM enthusiast should aim to understand.