 # College Algebra

We have a series of free College Algebra Video Lessons from UMKC - The University of Missouri-Kansas City.

The topics are Algebra Review, Graphs, Functions and their Graphs, Equations and Inequalities, Polynomial and Rational Functions, Exponential and Logarithmic Functions, Systems of Equations, Sequence, Series and Binomial Theorem.

### UNIT 0 - BASICS: Remembrance of Things Past

Sets of Objects [4 min.]
Natural Numbers [7 min.]
Integers [5 min.]
Rational Numbers [13 min.]
Irrational Numbers [2 min.]
Real Numbers [1 min.]
The Real Line: From Numbers to Points [4 min.]
Real Numbers are Ordered [19 min,]
The Real Line: Distance Between Points [8 min.]
Real Numbers as Decimals [11 min.]

Learning to Read Mathematics [7 min.]
Some Symbols of Algebra [9 min.]
Nouns, Pronouns, & The Main Verb of Algebra [4 min.]
Theorems, Corollaries, Lemmas, and All That [7 min.]

Integer Exponents [12 min.]
Operations with Integer Exponents [31 min.]
Square Roots: A Pair Of Equal Factors [13 min.]
Nth Roots & Rational Exponents [12 min.]
Operations with Rational Exponents [21 min.]

What is a Polynomial? [18 min.]
Adding & Subtracting Polynomials [3 min.]
Multiplying Polynomials [19 min.]
A Common Error [5 min.]
Handy Polynomial Products [15 min.]
Un-Multiplying (Factoring) Polynomials [28 min.]
Completing A Perfect Square [10 min.]

Dividing Polynomials: Rational Expressions [24 min.]
The Art of Simplification [14 min.]
Solving Some Polynomial & Rational Equations [46 min.]

Beyond Real Numbers: Complex Numbers [19 min.]
Some Area Formulas [8 min.]
The Pythagorean Theorem & A Visual Proof [12 min.]

### UNIT 1 - GRAPHS

Rectangular Coordinates: Geometry Meets Algebra [11 min.]
Distance Between Points [18 min.]
Midpoint of a Line Segment [7 min.]

Graphs of Equations [25 min.]
Intercepts: Crossing the Axes [12 min.]
Symmetry of Graphs [14 min.]
Lines: Defining "Slope" [34 min.]

Lines & Their Equations [24 min.]
Parallel & Perpendicular Lines [26 min.]
Circles & Their Equations [28 min.]
Some Exercises Explained [16 min.]

### UNIT 2 - FUNCTIONS AND THEIR GRAPHS

Function: The Central Idea of Mathematics [26 min.]
The Language & Notation of Functions [20 min.]
More On Domains [19 min.]
Function Notation Practice [16 min.]

Visualizing Functions: Graphs of (x, f(x)) Pairs [26 min.]
Increasing & Decreasing Functions [23 min.]
Local Maximums & Local Minimums [18 min.]
Even & Odd Functions [20 min.]

A Library of Important Functions [20 min.]
Piecewise Defined Functions [19 min.]
Some Exercises Explained [11 min.]

Graphing Techniques: Vertical & Horizontal Shifts [28 min.]
Graphing Techniques: Compressions & Stretches [27 min.]
Graphing Techniques: Reflections Across the Axes [17 min.]
Putting It All Together: Moving The Graphs of Functions Around The Plane [36 min.]

The Algebra of Functions [16 min.]
A New Operation Unique To Functions: Composition [24 min.]

Mathematical Models of Real World Problems: Constructing Functions [55 min.]

### UNIT 3 - EQUATIONS & INEQUALITIES

Solving Equations (Approximately) with a Graphing Device & The Intermediate Value Theorem [44 min.]
Solving Linear Equations: The "Linear Formula" or, Graphing [23 min.]
Solving Non-Linear Equations That Lead To Linear Equations [13 min.]

Solving Quadratic Equations: Factoring, or, Graphing [11 min.]
A Complex Reminder & The Principal Square Root of a Negative Number [12 min.]
Solving Quadratic Equations: The "Quadratic Formula" & The Discriminant or, Graphing [50 min.]

Some Linear & Quadratic Equation Exercises Explained [24 min.]

Setting Up Equations: More Mathematical Models [65 min.]

Solving Equations "Quadratic in Form" [15 min.]
Solving Factorable Equations [7 min.]

Properties of Inequalities [20 min.]
Solving Inequalities In General [17 min.]
Solving Linear Inequalities [19 min.]

Solving Higher-Degree Polynomial Inequalities [14 min.]
Solving Rational Inequalities [27 min.]

When Absolute Value Appears: Equations [12 min.]
When Absolute Value Appears: Inequalities [17 min.]
More Exercises Explained [15 min.]

### UNIT 4 - POLYNOMIAL & RATIONAL FUNCTIONS

Degree 2: Quadratic Functions [19 min.]
Quadratic Functions As Mathematical Models [25 min.]

Degree "n": General Polynomial Functions [8 min.]
Special Case: Power Functions & Their Graphs [18 min.]
Graphing General Polynomial Functions: Zeros, Multiplicity, Turning Points & End Behavior [40 min.]

How Many Zeros Are There? [12 min.]
How Many Zeros Are Real? [13 min.]
How Many Real Zeros Are Positive Negative? [16 min.]
Where (On What Interval) Are All Real Zeros? [22 min.]
How Can You Guess The Location of Real Zeros? [4 min.]
How Can You Reduce The Number of Real Zeros? [21 min.]

Strategy & Tools: A Practical Checklist [14 min.]
Some Polynomial Exercises Explained [22 min.]

General Rational Functions [14 min.]
What Is An Asymptote? [17 min.]
Finding Asymptotes of Rational Functions [35 min.]
Graphing Rational Functions [19 min.]

### UNIT 5 - EXPONENTIAL & LOGARITHMIC FUNCTIONS

One-To-One Functions [14 min.]
Exponential Functions & Their Graphs [26 min.]
The Natural Exponential Function [15 min.]

Inverse Functions [23 min.]
Logarithmic Functions & Their Graphs [24 min.]
The Natural Logarithmic Function [4 min.]

Properties of Logarithms [17 min.]
All Logarithms are Natural (or Common)! [15 min.]
Solving Logarithmic Equations [20 min.]
Logarithmic Models: Sound (Loudness) & Fury (Earthquakes) [16 min.]

Solving Exponential Equations [15 min.]
Exponential Models: Compounded Interest, and Growth & Decay [32 min.]

### UNIT 6 - SYSTEMS OF EQUATIONS

Systems of Linear Equations in General [19 min.]
Solving A System of 2 (or 3) Linear Equations in 2 (or 3) Variables: Substitution [20 min.]
Solving A System of 2 (or 3) Linear Equations in 2 (or 3) Variables: Elimination [36 min.]

Some Exercises Explained [31 min.]
An Application: Writing Proper Rational Functions As Sums of Simpler Proper Rational Functions (Partial Fractions) [43 min.]

Solving (Mostly Graphically) a System of 2 Non-Linear Equations in 2 Variables [14 min.]

### UNIT 7 - SOME DISCRETE TOPICS

Infinite Sequences: Functions With Domain N [28 min.]
The Factorial Symbol: ! [8 min.]
Adding The First n Terms of a Sequence: nth Partial Sums & Summation Notation [17 min.]

Geometric Sequences: Multiplying Your Way to Infinity [30 min.]

Geometric Series & Their (Infinite) Sums [26 min.]
The Principle of Mathematical Induction [30 min.]

The "Binomial Coefficient" Symbol [11 min.]
Pascal's Triangle [19 min.]
The Binomial Theorem: How to Expand (x+a)n [32 min.]

### THE X-Y FILES: The Proof is in Here

[29 min.]
• A Proof That Squareoot 2 Is Irrational [6 min.]
• A Proof That There Are The Same Number of Rational Numbers as Natural Numbers! [9 min.]
• A Proof That There Are More Real Numbers Than Natural Numbers! [14 min.]

FOR UNIT 2 [17 min.]

• Algebra For Science: Variation [17 min.]

FOR UNIT 4 [21 min.]

• How Can You Find Rational Zeros (if any) of a Polynomial Function? [21 min.]

FOR UNIT 7 [19 min.]

• A Proof That "e" Is Irrational [19 min.]

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