By Gregory P. Bullock Ph.D.

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Complexity classifications of Boolean constraint satisfaction problems

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Lectures on Lie Algebras

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Additional info for Algebra in Words: A Guide of Hints, Strategies and Simple Explanations

Example text

In the meantime, I hope this book helps you realize that these concepts are closely connected and not just separate entities. Below are simple examples of an expression and an equation. Notice the small details which set them apart. An expression: 3x2 + x - 10 An equation: 3x2 + x – 10 = 0, or Also an equation: y = 3x2 + x - 10 LINEAR EQUATIONS A linear equation is an equation of the first degree; it produces a straight line. Lines are generally known to have: a slope (m), one y-intercept (b), one x-intercept (there is no symbol, but the x-intercept is x when y = 0), and the (slope-intercept) form: y = mx + b.

This is a frequently made mistake. Also, when distributing an exponent, do not forget to apply that power to the coefficient if there is one. This is another common mistake, often forgotten by students. This may be because students look for the conspicuous exponents written with the obvious variables, but when coefficients don’t have exponents associated with them, they are just shown with an inconspicuous unwritten power of 1. SOLVING SIMPLE ALGEBRAIC EQUATIONS Solving a Simple Algebraic Equation with One Variable (First Degree) The goal is to completely isolate the variable and to have it equal a number, which is the answer.

If anything, consider PEMDAS a loose reminder of the complete Order of Operations, although if it were up to me, PEMDAS be thrown away completely and replaced with GEMA: Groups (simplify, inner to outer) Exponents or roots Multiplication or division Addition or subtraction Actually, since: Roots are technically a form of exponents, when converted to rational exponents*; Division is technically multiplication of a fraction; and Subtraction is technically addition of negative numbers, it could even be condensed to just: Groups, Exponents, Multiplication, Addition *Note: Roots are converted to “rational exponents” when the radical sign is removed and the root-number is moved to the denominator of the exponent.