Abstract ideas are concepts that need to be visualized, as they cannot be illustrated through concrete (real) examples. In a simple way, explaining the progression of logic in a (computer) program will be possible only if the reader can correctly visualize (imagine) it in his mind.

Although the terms cement and concrete often are used interchangeably, cement is actually an ingredient of concrete. Concrete is a mixture of aggregates and paste. The aggregates are sand and gravel or crushed stone; the paste is water and portland cement.

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In most Christian traditions, God is the Holy Trinity—made up of the Father, the Son (Jesus), and the Holy Spirit. In the case of God, the idea is that we form the abstract concept by building up from the concept of “person”—with its associated physical, biological, and psychological intuitions.

Happiness is defined by Google as “the state of being happy”. It’s really interesting; no one can adequately define what it is, everybody experiences it in diverse ways, each his own experience, but the general consensus is that you feel good — ecstatic even. The feeling is abstract, yet real.

They want to know the exact steps and often have little patience with changing plans or new ideas. They don’t like it when they have to try to read between the lines, or when instructions are ambiguous. Abstract thinkers can’t help but think about how everything relates to the bigger picture.

Algebra usually begins in the imagination with variables and formulas (the abstract); Geometry begins with what we can see and touch (the concrete).

Some of the mathematical subjects taught at university level – Calculus, Real Analysis, Linear Algebra, Topology, Category Theory, Functional Analysis and Set Theory among them – are very advanced examples of abstraction. This is because of the way mathematics was taught at high school.

Math is abstract because numbers are not real entities. They are purely imaginary concepts. We cannot experience numbers. We can make up stories about them, such as “1+1=2”, but we can never experience such an operation since there is no such thing as ONE of anything in our experience.

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. Linear algebra, elementary number theory, and discrete mathematics are sometimes considered branches of abstract algebra.

Reasons why abstract algebra can be a hard class An introductory class in abstract algebra tends to focus on things such as groups, rings and fields. These tend to be reasonably abstract concepts and it can be hard to see their usefulness like you can in a class such as calculus or linear algebra.