The Mathematics Department has adopted the following best practices for teaching this course: offering or awarding extra-credit is forbidden, the allowance of multiple attempts at exams is forbidden, and an approved on-site proctor for online course exams is required.
A. Fundamental Concepts
1. Review of algebraic operations including rational expressions, exponents, radicals, and complex numbers
2. Review of solving equations including fractional, radical, linear, and quadratic equations
3. Review of systems of linear equations and inequalities algebraically and with a computer algebra system
or graphing utility.
B. Functions
1. Basic concepts: relation, function, domain, range
2. Characteristics: increasing, decreasing, maximum value, minimum value, odd, even, one-to-one
3. Rigid and non-rigid transformations of functions
4. Composition of functions and inverse functions
5. Graphs of polynomial and rational functions
6. Use a computer algebra system or graphing utility to graph functions and relations
C. Theory of Equations
1. Remainder and Factor theorems, synthetic division
2. Methods of finding rational zeros
3. Methods of isolating irrational zeros
4. Complex zeroes and the Fundamental Theorem of Algebra
5. Using graphing utilities to approximate roots
6. Rational functions and asymptotes
D. Analytic Geometry
1. Cartesian coordinates, distance and midpoint formulas
2. Slope and equations of lines
3. Least Squares Regression line
4. Review of the equation and graph of a circle
5. Properties and applications of the parabola using the focus
6. Properties and applications of the ellipse using focus and eccentricity
7. Properties and application of the hyperbola using focus and eccentricity
E. Exponential and Logarithmic Functions
1. Exponential functions and their graphs
2. Logarithmic functions and their graphs
3. Properties of logarithms and their application
4. Solving exponential and logarithmic equations
5. Fitting non-linear models to data
F. Sequences and Series
1. Summation notation, general term of a sequence
2. Arithmetic Sequences and Series and their applications
3. Geometric Sequences and Series and their applications
4. Proof by Mathematical Induction
5. The Binomial Theorem
G. Matrices and Determinants
1. Matrices and systems of linear equations
2. Operations with matrices
3. Inverse matrices and systems of linear equations
4. The determinant of a square matrix
5. Applications of matrices and determinants
H. Limits and their Applications
1. Limit exploration with a graphing utility
2. Limit at a point and evaluation techniques
3. Limits at infinity
4. Exploration of tangent lines to curves
I. Selected Algebraic Applications to Be Chosen From
1. Mathematics: other branches.
2. Biological Sciences: e.g., general biology, anatomy, physiology, microbiology.
3. Physical Sciences: e.g., chemistry, physics, geology, astronomy, oceanography.
4. Computer Science: e.g., computer graphics, computer animation.