## Math 110 - College Algebra

This is a collection of video lectures for **Math 110: College Algebra** from UMKC (University of Missouri-Kansas city). Taught by Professor Richard Delaware, this course emphasizes the concepts of college algebra,
covering a variety of topics on algebra: numbers, graphs, equations and inequalities, functions, polynomials, exponential and logarithmic functions, systems of linear equations, binomial theorem, and sequences.

More details of the videos are found:

Listing of the videos and their contents

### Unit 0 - Basics: Remembrance of Things Past

**Lecture 01 - Numbers**

Sets of Objects. Natural Numbers. Integers. Rational Numbers. Irrational Numbers. Real Numbers. The Real Line: From Numbers to Points. Real Numbers are Ordered. The Real Line: Distance Between Points. Real Numbers as Decimals

**Lecture 02 - Language of Mathematics**

Learning to Read Mathematics. Some Symbols of Algebra. Nouns, Pronouns, & The Main Verb of Algebra. Theorems, Corollaries, Lemmas, and All That

**Lecture 03 - The Powers That be: Exponents**

Integer Exponents. Operations with Integer Exponents. Square Roots: A Pair Of Equal Factors. Nth Roots & Rational Exponents. Operations with Rational Exponents

**Lecture 4a - Polynomial Expressions**

What is a Polynomial? Adding & Subtracting Polynomials. Multiplying Polynomials. A Common Error. Handy Polynomial Products. Un-Multiplying (Factoring) Polynomials. Completing A Perfect Square

**Lecture 4b - Polynomial Expressions (cont.)**

Dividing Polynomials: Rational Expressions. The Art of Simplification. Solving Some Polynomial & Rational Equations

**Lecture 05 - More Numbers and a Little Geometry**

Beyond Real Numbers: Complex Numbers. Some Area Formulas. The Pythagorean Theorem & A Visual Proof

### Unit 1 - Graphs

**Lecture 06 - Graphs**

Rectangular Coordinates: Geometry Meets Algebra. Distance Between Points. Midpoint of a Line Segment. Your Graphing Device

**Lecture 07 - Graphs (cont.)**

Graphs of Equations. Intercepts: Crossing the Axes. Symmetry of Graphs. Lines: Defining "Slope"

**Lecture 08 - Graphs (cont.)**

Lines & Their Equations. Parallel & Perpendicular Lines. Circles & Their Equations. Some Exercises Explained

### Unit 2 - Functions and Their Graphs

**Lecture 09 - Functions and Their Graphs**

Function: The Central Idea of Mathematics. The Language & Notation of Functions. More On Domains. Function Notation Practice

**Lecture 10 - Functions and Their Graphs (cont.)**

Visualizing Functions: Graphs of (x, f(x)) Pairs. Increasing & Decreasing Functions. Local Maximums & Local Minimums. Even & Odd Functions

**Lecture 11 - Functions and Their Graphs (cont.)**

A Library of Important Functions. Piecewise Defined Functions. Some Exercises Explained

**Lecture 12 - Functions and Their Graphs (cont.)**

Graphing Techniques: Vertical & Horizontal Shifts. Graphing Techniques: Compressions & Stretches. Graphing Techniques: Reflections Across the Axes. Putting It All Together: Moving The Graphs of Functions Around The Plane

**Lecture 13 - Functions and Their Graphs (cont.)**

The Algebra of Functions. A New Operation Unique To Functions: Composition

**Lecture 14 - Functions and Their Graphs (cont.)**

Mathematical Models of Real World Problems: Constructing Functions

### Unit 3 - Equations and Inequalities

**Lecture 15 - Equations in One Variable**

Solving Equations (Approximately) with a Graphing Device & The Intermediate Value Theorem. Solving Linear Equations: The "Linear Formula" or, Graphing. Solving Non-Linear Equations That Lead To Linear Equations

**Lecture 16 - Equations in One Variable (cont.)**

Solving Quadratic Equations: Factoring, or, Graphing. A Complex Reminder & The Principal Square Root of a Negative Number. Solving Quadratic Equations: The "Quadratic Formula" & The Discriminant or, Graphing

**Lecture 17 - Equations in One Variable (cont.)**

Some Linear & Quadratic Equation Exercises Explained

**Lecture 18 - Equations in One Variable (cont.)**

Setting Up Equations: More Mathematical Models

**Lecture 19 - Equations in One Variable (cont.)**

Solving "Radical" Equations. Solving Equations "Quadratic in Form". Solving Factorable Equations

**Lecture 20 - Inequalities in One Variable**

Properties of Inequalities. Solving Inequalities In General. Solving Linear Inequalities

**Lecture 21 - Inequalities in One Variable (cont.)**

Solving Quadratic Inequalities. Solving Higher-Degree Polynomial Inequalities. Solving Rational Inequalities

**Lecture 22 - Inequalities in One Variable (cont.)**

When Absolute Value Appears: Equations. When Absolute Value Appears: Inequalities. More Exercises Explained

### Unit 4 - Polynomial and Rational Functions

**Lecture 23 - Polynomial and Rational Functions**

Degree 2: Quadratic Functions. Graphing Quadratic Functions. Quadratic Functions As Mathematical Models

**Lecture 24 - Polynomial and Rational Functions (cont.)**

Degree "n": General Polynomial Functions. Special Case: Power Functions & Their Graphs. Graphing General Polynomial Functions: Zeros, Multiplicity, Turning Points & End Behavior

**Lecture 25 - Locating the Zeros of a Polynomial Function**

How Many Zeros Are There? How Many Zeros Are Real? How Many Real Zeros Are Positive? Negative? Where (On What Interval) Are All Real Zeros? How Can You Guess The Location of Real Zeros? How Can You Reduce The Number of Real Zeros?

**Lecture 26 - Locating the Zeros of a Polynomial Function (cont.)**

Strategy & Tools: A Practical Checklist. Some Polynomial Exercises Explained

**Lecture 27 - Rational Functions**

General Rational Functions. What Is An Asymptote? Finding Asymptotes of Rational Functions. Graphing Rational Functions

### Unit 5 - Exponential and Logarithmic Functions

**Lecture 28 - Exponential Functions**

One-To-One Functions. Exponential Functions & Their Graphs. The Natural Exponential Function

**Lecture 29 - Logarithmic Functions**

Inverse Functions. Logarithmic Functions & Their Graphs. The Natural Logarithmic Function

**Lecture 30 - Logarithmic Functions (cont.)**

Properties of Logarithms. All Logarithms are Natural (or Common)! Solving Logarithmic Equations. Logarithmic Models: Sound (Loudness) & Fury (Earthquakes)

**Lecture 31 - Exponential Functions (cont.)**

Solving Exponential Equations. Exponential Models: Compounded Interest, and Growth & Decay

### Unit 6 - Systems of Equations

**Lecture 32 - Systems of Linear Equations**

Systems of Linear Equations in General. Solving A System of 2 (or 3) Linear Equations in 2 (or 3) Variables: Substitution. Solving A System of 2 (or 3) Linear Equations in 2 (or 3) Variables: Elimination

**Lecture 33 - Systems of Linear Equations (cont.)**

Some Exercises Explained. An Application: Writing Proper Rational Functions As Sums of Simpler Proper Rational Functions (Partial Fractions)

**Lecture 34 - Systems of Non-Linear Equations**

Solving (Mostly Graphically) a System of 2 Non-Linear Equations in 2 Variables

### Unit 7 - Some Discrete Topics

**Lecture 35 - Sequences**

Infinite Sequences: Functions With Domain N. The Factorial Symbol: !. Adding The First n Terms of a Sequence: nth Partial Sums & Summation Notation

**Lecture 36 - Sequences (cont.)**

Arithmetic Sequences: Adding Your Way to Infinity. Geometric Sequences: Multiplying Your Way to Infinity

**Lecture 37 - Series & Induction**

Geometric Series & Their (Infinite) Sums. The Principle of Mathematical Induction

**Lecture 38 - Binomial Theorem**

The "Binomial Coefficient" Symbol. Pascal's Triangle. The Binomial Theorem: How to Expand (x+a)^n

### The X-Y Files: The Proof is in Here

**Lecture 39 - The X-Y Files**

A Proof That There Are The Same Number of Rational Numbers as Natural Numbers! A Proof That There Are More Real Numbers Than Natural Numbers! Algebra For Science: Variation. How Can You Find Rational Zeros (if any) of a Polynomial Function?