2: Introduction to Groups
One of the major topics of this course is groups . The area of mathematics that is concerned with groups is called group theory . Loosely speaking, group theory is the study of symmetry, and in my opinion is one of the most beautiful areas in all of mathematics. It arises in puzzles, visual arts, music, nature, the physical and life sciences, computer science, cryptography, and of course, throughout mathematics.
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- 2.2: Binary Operation
- Before beginning our formal study of groups, we need to have an understanding of binary operations. After learning to count as a child, you likely learned how to add, subtract, multiply, and divide with real numbers. As long as we avoid division by zero, these operations are examples of binary operations since we are combining two objects to obtain a single object.