Topics in Algebra: Course Syllabus and Study Guide

Course Overview

Topics in Algebra is a foundational course designed to prepare students for further studies in mathematics, chemistry, biology, and related fields. The course covers essential concepts in algebra and introductory pre-calculus, emphasizing both procedural fluency and conceptual understanding. Students will engage with a variety of mathematical topics, practice problem-solving skills, and apply mathematical reasoning to practical examples.

Course Structure and Resources

• Textbook: Blitzer, Algebra and Trigonometry, 7th edition, Pearson (ISBN-13: 978-1-292-44347-8)

• Online Platform: My Lab (Pearson) for e-textbook access, assignments, and study resources

• Calculator: Graphing calculator (TI 83, 84, or 89) required; calculators not permitted on the midterm

• Class Meetings: Weekly on Zoom, Sundays 12PM-2:30PM EST

Course Topics and Weekly Schedule

The following table outlines the main topics, textbook sections, and schedule for the course:

Class	Date	Textbook Sections	Topics
1	Jan. 11	P1, P2	Basic arithmetic review, order of operations, expressions and equations, exponents and scientific notation (and significant figures)
2	Jan. 18	P3, P4, P5	Radicals and rational exponents, polynomials - multiplying and factoring
3	Jan. 25	P6, 1.1, 1.2, 1.3	Rational expressions, graphing, absolute value, x and y intercepts, solving linear equations, metric conversions
4	Feb. 1	1.4, 1.5, 1.6	Introduction to complex and imaginary numbers, quadratic equations, polynomial equations, factoring
5	Feb. 8	1.7, 2.1, 2.2, 2.3, 2.4	Inequalities, functions and graphs, calculating slope of a linear function, parallel and perpendicular lines, calculating rate of change
6	Feb. 15	2.6, 2.7, 2.8	Inverse functions, important formulas, midterm review
7	Feb. 22	3.1, 3.3, 3.4	Polynomial functions, polynomial long division
8	Mar. 8	3.5, 3.6, 3.7	Rational functions, polynomial and rational inequalities
9	Mar. 15	4.1, 4.2, 4.3, 4.4, 4.5	Exponential and logarithmic functions and equations
10	Apr. 12	8.1, 8.4	Linear equations with 2 and 3 variables, nonlinear equations with 2 variables
11	Apr. 19	8.5, 8.6	Systems of inequalities, linear programming, final review
12	Apr. 26	Chapter 5	Introduction to trigonometry

Key Topics and Concepts

1. Fundamental Concepts of Algebra

• Order of Operations: The sequence in which mathematical operations are performed. The standard order is Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

• Expressions and Equations: An expression is a mathematical phrase without an equals sign; an equation sets two expressions equal to each other.

• Exponents and Scientific Notation: Exponents represent repeated multiplication. Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10.

• Significant Figures: Digits in a number that carry meaning contributing to its precision.

2. Polynomials and Factoring

• Polynomials: Algebraic expressions consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents.

• Factoring: The process of expressing a polynomial as a product of its factors.

• Radicals and Rational Exponents: Radicals involve roots (e.g., square roots), and rational exponents express roots as fractional powers.

3. Equations and Inequalities

• Linear Equations: Equations of the first degree, typically in the form $ax + b = 0$.

• Quadratic Equations: Equations of the form $ax^2 + bx + c = 0$.

• Inequalities: Mathematical statements indicating that one quantity is greater or less than another.

• Absolute Value: The distance of a number from zero on the number line, denoted $|x|$.

4. Functions and Graphs

• Function: A relation in which each input has exactly one output. Notation: $f(x)$.

• Graphing: Visual representation of functions and equations on the coordinate plane.

• Slope: The rate of change of a line, calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$.

• Parallel and Perpendicular Lines: Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals.

• Inverse Functions: Functions that "undo" each other; if $f(x)$ is a function, its inverse $f^{-1}(x)$ satisfies $f(f^{-1}(x)) = x$.

5. Polynomial and Rational Functions

• Polynomial Functions: Functions defined by polynomials, e.g., $f(x) = x^3 - 2x + 1$.

• Long Division: A method for dividing polynomials.

• Rational Functions: Functions expressed as the ratio of two polynomials.

• Polynomial and Rational Inequalities: Inequalities involving polynomial or rational expressions.

6. Exponential and Logarithmic Functions

• Exponential Functions: Functions of the form $f(x) = a \cdot b^x$.

• Logarithmic Functions: The inverse of exponential functions; $y = \log_b(x)$ means $b^y = x$.

• Properties and Equations: Includes solving equations involving exponents and logarithms.

7. Systems of Equations and Inequalities

• Linear Systems: Sets of equations with multiple variables, solved using substitution, elimination, or matrices.

• Nonlinear Systems: Systems involving at least one equation that is not linear.

• Systems of Inequalities: Multiple inequalities considered together; solutions are regions on the coordinate plane.

• Linear Programming: Optimization technique for maximizing or minimizing a linear objective function subject to constraints.

8. Introduction to Trigonometry

• Trigonometric Functions: Functions relating angles to side lengths in right triangles (sine, cosine, tangent, etc.).

• Applications: Used in geometry, physics, and engineering to model periodic phenomena.

Course Policies and Grading

• Attendance: Mandatory; excessive absences may affect course standing.

• Late Work: 2% grade reduction per day late; assignments close one week after the deadline.

• Academic Integrity: Zero tolerance for AI use and plagiarism; institutional netiquette policies enforced.

Component	Weight
Classwork (attendance, participation, in-class activities)	10%
Homework (weekly My Lab assignments)	30%
Midterm Exam	30%
Final Exam	30%

Additional Info

• Students are encouraged to use all available resources, including the e-textbook and My Lab platform, for additional practice and support.

• Midterm and final exams are proctored and cover material as indicated in the schedule.

• Students at risk of failing after the midterm will be required to seek tutoring support.