"In mathematics, you don't understand things; you just get used to them." — John von Neumann
Algebra Curriculum Outline
Introduction to Algebra
- Introduction to variables and constants
- Simplifying algebraic expressions
- Evaluating expressions
Real example of a function rendered with LaTeX: $f(x) = x^2$, with the quadratic formula $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
Mathematics LibreTexts
Solving Linear Equations
- Solving one-step equations
- Solving multi-step equations
- Equations with variables on both sides
- Word problems involving linear equations
Graphing Linear Equations
- Understanding the coordinate plane
- Graphing linear equations
- Finding the slope of a line
- Writing equations of lines
Systems of Equations
- Solving systems of linear equations graphically
- Solving systems of linear equations algebraically (substitution and elimination)
- Applications of systems of equations
Exponents and Exponential Functions
- Understanding exponents and their properties
- Evaluating exponential expressions
- Graphing exponential functions
- Applications of exponential growth and decay
Polynomials
- Classifying polynomials by degree and number of terms
- Adding and subtracting polynomials
- Multiplying polynomials
- Factoring polynomials
- Dividing polynomials
- Roots and zeros of polynomials
Rational Expressions
- Understanding rational expressions
- Graphing rational functions
- Solving rational equations
- Applications of rational expressions
Radical Expressions
- Understanding radicals and their properties
- Simplifying radical expressions
- Adding, subtracting, and multiplying radicals
- Dividing radicals
- Radical equations
- Applications involving radicals
Quadratic Equations
- Finding roots of quadratic equations
- Factoring quadratic equations
- Completing the square
- Using the quadratic formula
- Graphing quadratic functions
- Applications of quadratic equations
Inequalities
- Solving and graphing linear inequalities
- Solving and graphing compound inequalities
- Absolute value equations and inequalities
- Quadratic inequalities
- Systems of inequalities
- Applications of inequalities
Sequences and Series
- Arithmetic sequences and series
- Geometric sequences and series
- Recursive sequences
- Summation notation
- Infinite geometric series
- Applications involving sequences and series
Logarithmic Functions
- Understanding logarithms and exponents
- Properties of logarithms
- Common logarithms and natural logarithms
- Solving exponential equations using logarithms
- Graphing logarithmic functions
- Applications of logarithms
Conic Sections
- Classifying conic sections (parabolas, circles, ellipses, and hyperbolas)
- Graphing conic sections
- Conic sections in polar coordinates
- Applications involving conic sections
Introduction to Matrices
- Understanding matrices and their components
- Matrix operations (addition, subtraction, scalar multiplication)
- Multiplication of matrices
- Identity and inverse matrices
- Applications of matrices