College Algebra: Course Overview and Key Topics

Course Overview

Introduction to College Algebra

College Algebra is a foundational mathematics course that focuses on the study of functions, equations, and their applications. The course is designed to develop students' algebraic reasoning and problem-solving skills, preparing them for further study in mathematics and related fields.

• Instructor: Dr. Isaac Bancroft

• Textbook: College Algebra - University of Memphis Custom Edition

• Meeting Times: MWF 8:00 AM - 8:55 AM and MWF 9:10 AM - 10:05 AM

• Final Exam: December 5, 10:30 AM - 12:30 PM

Main Topics in College Algebra

Analysis of Functions

This topic covers the study of various types of functions, including linear, quadratic, polynomial, root, rational, and exponential functions. Students learn to analyze, graph, and interpret these functions.

• Definition: A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

• Types of Functions:

  • Linear: $f(x) = mx + b$

  • Quadratic: $f(x) = ax^2 + bx + c$

  • Polynomial: $f(x) = a_nx^n + a_{n-1}x^{n-1} + ext{...} + a_0$

  • Root: $f(x) = oot{n}{x}$

  • Rational: $f(x) = rac{p(x)}{q(x)}$

  • Exponential: $f(x) = a^x$

• Graphing: Understanding the shape and key features of function graphs, such as intercepts, asymptotes, and intervals of increase/decrease.

• Example: The graph of $f(x) = x^2$ is a parabola opening upwards.

Equations and Inequalities

Students learn to solve various types of equations and inequalities, including linear, quadratic, and systems of equations. The course also covers the theory of equations and the use of algebraic techniques to find solutions.

• Linear Equation: $ax + b = 0$

• Quadratic Equation: $ax^2 + bx + c = 0$

• Quadratic Formula: $x = rac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$

• Inequality: An expression showing the relationship between two values that are not equal, e.g., $x + 3 > 7$

• Systems of Equations: Solving for multiple variables using substitution or elimination methods.

• Example: Solve $2x + 3 = 7$; $x = 2$.

Graphical Calculations and Symbolic Notation

Graphical calculations involve plotting functions and interpreting their graphs. Symbolic notation is used to represent mathematical ideas concisely and accurately.

• Graphing Calculators: Students are required to use TI-83, TI-84, or similar calculators for computations and graphing.

• Symbolic Notation: Use of symbols such as $f(x)$, $x ightarrow ext{value}$, and interval notation.

• Example: The interval $[a, b]$ represents all real numbers $x$ such that $a \\leq x \\leq b$.

Algebraic Operations and Applications

Algebraic operations include addition, subtraction, multiplication, and division of algebraic expressions. Applications involve solving real-world problems using algebraic methods.

• Operations:

  • Addition: $(a + b) + (c + d) = (a + c) + (b + d)$

  • Multiplication: $(a + b)(c + d) = ac + ad + bc + bd$

• Applications: Word problems involving rates, mixtures, and geometric calculations.

• Example: If a car travels at 60 mph for 2 hours, the distance is $60 \\times 2 = 120$ miles.

Course Structure and Grading

The course uses a combination of lectures, group activities, quizzes, homework, and exams to assess student understanding. Grades are calculated using weighted averages of different components.

• Grading Breakdown:

  Component	Weight
  Homework	10%
  Quizzes	11%
  Attendance	10%
  Midterm Exams	60%
  Final Exam	22%

• Grade Calculation Formula: $\text{Grade} = 0.1 \\times (\text{HW AVG}) + 0.11 \\times (\text{QUIZ AVG}) + 0.6 \\times (\text{MIDTERM AVG}) + 0.22 \\times (\text{FINAL})$

• Make-up Policy: Make-up tests are allowed in advance for excused absences.

• Academic Honesty: Cheating and plagiarism are strictly prohibited.

Course Schedule Overview

The course is organized into weekly topics, covering chapters and sections from the textbook. Key dates include tests, reviews, holidays, and the final exam.

• Weeks 1-2: Introduction, Syllabus, R.1-R.4

• Weeks 3-4: Test 1, R.5-R.7, 1.1-1.2

• Weeks 5-6: Test 2, 1.3-1.6, Test 3 (Chapter 1), 2.1-2.2

• Weeks 7-8: Test 4 (Chapter 2), 2.3-3.1

• Weeks 9-10: Test 5 (Chapter 3), 3.2-3.3, Test 6 (Chapter 4), 5.1-5.2

• Weeks 11-12: Test 7 (Chapter 5), 5.3-5.6

• Week 13: Review for Final

• Week 14: Final Exam

Additional Resources and Policies

Students are encouraged to utilize tutoring centers, office hours, and online resources for additional support. Electronic devices should be used responsibly during lectures.

• Tutoring: Available in Dunn 341

• Disability Services: Accommodations available through the Office for Students with Disabilities

• Electronics Policy: Phones and laptops should not distract from learning

Summary Table: Key Course Components

Topic	Description
Functions	Linear, quadratic, polynomial, root, rational, exponential
Equations	Solving linear, quadratic, and systems of equations
Inequalities	Solving and graphing inequalities
Graphing	Graphical analysis using calculators
Applications	Word problems and real-world scenarios

Additional info: The course also emphasizes mathematical communication, symbolic notation, and the use of technology for problem-solving. Students are expected to show all work and provide exact answers unless otherwise specified.