Study Guides

Mathematics:

I personally consider mathematics to be extremely important. It trains the brain to think mathematically, both in specific terms and abstract terms. Since mathematics are basically applied in every other STEM subject, a thorough grasp of concepts is very important to improve mathematical maturity. Moreover, I believe that although those concepts won’t be of much use in non-mathematics-related occupations, the way of thought we learned from mathematics can accompany us for a lifetime – to think logically, analytically, and obviously, mathematically.

Multivariable Calculus

Multivariable calculus, a subject built on single-variable calculus, features a return of our familiar concepts: limits, derivatives, and integrals. However, as we add in more variables, each familiar concept will expand itself to cover the “trouble” new variables bring with them: derivatives will expand into partial derivatives and directional derivatives while integrals will expand into double and triple integrals. As a finale, vectors will play an important part in this subject, bringing forth the concept of vector calculus.

Linear Algebra

Linear algebra can be found in a lot of STEM applications such as electrical engineering. However, as complicated as it may sound, it can be interpreted geometrically and intuitively. The interpretations stemming from complicated concepts can be rather beautiful sometimes, especially if we can graph them, animate them, and play with them.

Introduction to Differential Equations

Differentiating functions are considered relatively easy when compared to solving differential equations. Fourier series, the Heat equation, RC circuits, and many more depend on differential equations to be fully comprehended and studied. Therefore, let’s start with the simple second-order, linear, homogeneous ODE and work our way to the Fourier Series just to have a taste of what differential equations can become.

Discrete Mathematics

As the name suggests, concepts discussed here will be rather discrete. We will jump from one field of mathematics to another (e.g. from counting to graph theory). Most big ideas presented here will very well be fields of mathematics themselves. The subject is more of a gallery display of what mathematics can reach and its potential rather than a further discussion of certain topics.

Chemistry:

General Chemistry

The building blocks of Chemistry. We will talk about the periodic table, thermodynamics, kinetics, acid and base, and many more.

Organic Chemistry

The building blocks of life.

Physics:

Basic Physics

The laws of the universe

Basic Physics with Calculus

The laws of the universe, but harder

Western European Music Theory can be roughly concluded as a trip up the overtone series. We start from the basic root, third, and fifths, and make our way to the sevenths, and then the ninths, and eventually augmented triads.