Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract.

At upper-division level, the majority of mathematics is presented in an abstract way. This course will train you in understanding and creating abstract mathematics, and it is our hope that you will develop an …

If you’re lucky enough to bump into a mathematician then you might get something along the lines of: “Algebra is the abstract encapsulation of our intuition for composition”.

Oct 21, 2022 · Abstract math, a subgroup of mathematics, encompasses the constructions of math problems, formats, and equations to further deepen math concepts for practical use in real-world …

Abstract math is mathematics for its own sake. In doing abstract math, you state theorems and prove them mostly in the context of mathematical ideas rather than applications or ideas from other fields.

Jun 27, 2025 · This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields.

This textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces …

Mathematical propositions are often of the form “If P, then Q”. Such a statement is called an implication. “P” is called the hypothesis and “Q” is called the conclusion. For example, “If x and y are odd …

Dec 22, 2025 · Group theory is the mathematical study of abstract groups, namely sets of elements and a binary operation that together satisfy the four fundamental properties of closure, associativity, the …

The term abstract algebra was coined in the early 20th century to distinguish it from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in …