Abstract Algebra Why Use It

By composition we mean the concept of two object coming together to form a new one. In algebra which is a broad division of mathematics abstract algebra occasionally called modern algebra is the study of algebraic structuresalgebraic structures include groups rings fields modules vector spaces lattices and algebrasthe term abstract algebra was coined in the early 20th century to distinguish this area of study from the other parts of algebra. Anyway abstract algebra studies more than just groups there are other mathematical objects like rings fields and vector spaces which you may or may not already be familiar with all with different properties.

Throughout the course they review things like 1 1 functions onto functions surprisingly few senior math ed majors.

Abstract algebra why use it. Favorite answer un can be rather unpredictable. Algebra is a branch of mathematics that substitutes letters for numbers and an algebraic equation represents a scale where what is done on one side of the scale is also done to the other side of the scale and the numbers act as constants. If youre lucky enough to bump into a mathematician then you might get something along the lines of. Abstract algebra is an ideal capstone course for math ed majors and for those who will go on to grad school in math.

Algebra can include real numbers complex numbers matrices vectors and many more forms of mathematic representation. Algebra is the abstract encapsulation of our intuition for composition. For instance altering the definitions of the basic arithmetic operations result in a structure known as a ring so long as the operations are consistent. First courses in abstract algebra like to use this group a lot because it is easy to give examples of abelian groups of small order that are not.

Roughly speaking abstract algebra is the study of what happens when certain properties of number systems are abstracted out. Argument in an introductory abstract algebra course is that it should be written to convince ones peers whether those peers be other students or other readers of the text. For example adding two numbers or composing real valued single variable functions. I havent studied it very much myself but hopefully this gives you a general idea.