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Maths › 00. General Mathematics ›

05.2 Algebraic Abstraction

5.2 Algebraic Abstraction Algebraic abstraction replaces specific values with symbols and replaces repeated calculations with general rules. It keeps operations explicit, but removes dependence on particular instances. A concrete computation shows: $$ (2 + 3)^2 = 25. $$ An algebraic statement expresses the same pattern in general form: $$ (a+b)^2 = a^2 + 2ab + b^2. $$ The second statement applies to all admissible values of $a$ and $b$. A...

Maths › 00. General Mathematics ›

03.1 Symbols and Notation

3.1 Symbols and Notation Design Mathematical notation is a compressed interface for ideas. It allows long statements to be written in small space, but compression has a cost. A symbol is useful only when its meaning is clear from context. A symbol has no independent mathematical meaning until it is assigned one. The letter x may denote a number, a vector, a function, a point, a variable in a polynomial...