Understanding Algebra: Operations, Patterns, and More

Explore the fundamental concepts of algebra through sets, operations, patterns, axioms, identities, examples, inverses, groups, modular arithmetic, and matrices. Delve into the world of square matrices and gain insights into various algebraic structures.

• Algebra
• Operations
• Patterns
• Axioms
• Identities
• Groups

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1. MATH 308 Algebra Chapter 1 Class Notes For August 29, 2022 Prof. David Singer

2. Operations Algebra is about sets with operations. An operation takes elements of a set and produces a new element. Example: Addition + takes two numbers a and b and gives a new number a+b

3. Patterns 3x2=6 4x6=24 2x3=6 6x4=24

4. Pattern Becomes Axiom

5. Identity

6. Some Examples

7. Some Examples

8. A Different Example

9. A Different Example

10. Inverses

11. Another Example

12. Groups

13. Groups

14. Modular Arithmetic

15. Modular Arithmetic

16. Modular Arithmetic

17. Matrices

18. Square Matrices

19. Square Matrices

20. Square Matrices