College Algebra


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




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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

Lecture 1: NUMBERS
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.]

Lecture 2: THE LANGUAGE OF MATHEMATICS
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.]

Lecture 3: THE POWERS THAT BE: EXPONENTS
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.]

Lecture 4 Part 1: POLYNOMIAL EXPRESSIONS
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.]

Lecture 4 Part 2: POLYNOMIAL EXPRESSION
Dividing Polynomials: Rational Expressions [24 min.]
The Art of Simplification [14 min.]
Solving Some Polynomial & Rational Equations [46 min.]

Lecture 5: MORE NUMBERS and GEOMETRY
Beyond Real Numbers: Complex Numbers [19 min.]
Some Area Formulas [8 min.]
The Pythagorean Theorem & A Visual Proof [12 min.]




UNIT 1 - GRAPHS

Lecture 6: GRAPHS
Rectangular Coordinates: Geometry Meets Algebra [11 min.]
Distance Between Points [18 min.]
Midpoint of a Line Segment [7 min.]
Your Graphing Device [17 min.]

Lecture 7: GRAPHS
Graphs of Equations [25 min.]
Intercepts: Crossing the Axes [12 min.]
Symmetry of Graphs [14 min.]
Lines: Defining “Slope” [34 min.]

Lecture 8: GRAPHS
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

Lecture 9: 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.]

Lecture 10: FUNCTIONS AND THEIR GRAPHS
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.]

Lecture 11: FUNCTIONS AND THEIR GRAPHS
A Library of Important Functions [20 min.]
Piecewise Defined Functions [19 min.]
Some Exercises Explained [11 min.]

Lecture 12: FUNCTIONS AND THEIR GRAPHS
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.]

Lecture 13: FUNCTIONS AND THEIR GRAPHS
The Algebra of Functions [16 min.]
A New Operation Unique To Functions: Composition [24 min.]

Lecture 14: FUNCTIONS AND THEIR GRAPHS
Mathematical Models of Real World Problems: Constructing Functions [55 min.]



UNIT 3 - EQUATIONS & INEQUALITIES

Lecture 15: EQUATIONS IN 1 VARIABLE
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.]

Lecture 16: EQUATIONS IN 1 VARIABLE
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.]

Lecture 17: EQUATIONS IN 1 VARIABLE]
Some Linear & Quadratic Equation Exercises Explained [24 min.]

Lecture 18: EQUATIONS IN 1 VARIABLE
Setting Up Equations: More Mathematical Models [65 min.]

Lecture 19: EQUATIONS IN 1 VARIABLE]
Solving “Radical” Equations [14 min.]
Solving Equations “Quadratic in Form” [15 min.]
Solving Factorable Equations [7 min.]

Lecture 20: INEQUALITIES IN 1 VARIABLE
Properties of Inequalities [20 min.]
Solving Inequalities In General [17 min.]
Solving Linear Inequalities [19 min.]

Lecture 21: INEQUALITIES IN 1 VARIABLE
Solving Quadratic Inequalities [17 min.]
Solving Higher-Degree Polynomial Inequalities [14 min.]
Solving Rational Inequalities [27 min.]

Lecture 22: EQUATIONS & INEQUALITIES IN 1 VARIABLE
When Absolute Value Appears: Equations [12 min.]
When Absolute Value Appears: Inequalities [17 min.]
More Exercises Explained [15 min.]



UNIT 4 - POLYNOMIAL & RATIONAL FUNCTIONS

Lecture 23: POLYNOMIAL FUNCTIONS
Degree 2: Quadratic Functions [19 min.]
Graphing Quadratic Functions [39 min.]
Quadratic Functions As Mathematical Models [25 min.]

Lecture 24: POLYNOMIAL FUNCTIONS
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.]

Lecture 25: LOCATING THE ZEROS OF A POLYNOMIAL FUNCTION
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.]

Lecture 26: LOCATING THE ZEROS OF A POLYNOMIAL FUNCTION
Strategy & Tools: A Practical Checklist [14 min.]
Some Polynomial Exercises Explained [22 min.]

Lecture 27: RATIONAL FUNCTIONS
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

Lecture 28: EXPONENTIAL FUNCTIONS
One-To-One Functions [14 min.]
Exponential Functions & Their Graphs [26 min.]
The Natural Exponential Function [15 min.]

Lecture 29: LOGARITHMIC FUNCTIONS
Inverse Functions [23 min.]
Logarithmic Functions & Their Graphs [24 min.]
The Natural Logarithmic Function [4 min.]

Lecture 30: LOGARITHMIC FUNCTIONS
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.]

Lecture 31: EXPONENTIAL FUNCTIONS (con.)
Solving Exponential Equations [15 min.]
Exponential Models: Compounded Interest, and Growth & Decay [32 min.]

UNIT 6 - SYSTEMS OF EQUATIONS

Lecture 32: SYSTEMS OF LINEAR 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.]

Lecture 33: SYSTEMS OF LINEAR EQUATIONS
Some Exercises Explained [31 min.]
An Application: Writing Proper Rational Functions As Sums of Simpler Proper Rational Functions (Partial Fractions) [43 min.]

Lecture 34: SYSTEMS OF NON-LINEAR EQUATIONS
Solving (Mostly Graphically) a System of 2 Non-Linear Equations in 2 Variables [14 min.]

UNIT 7 - SOME DISCRETE TOPICS

Lecture 35: SEQUENCES
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.]

Lecture 36: SEQUENCES
Arithmetic Sequences: Adding Your Way to Infinity [18 min.]
Geometric Sequences: Multiplying Your Way to Infinity [30 min.]

Lecture 37: SERIES & INDUCTION
Geometric Series & Their (Infinite) Sums [26 min.]
The Principle of Mathematical Induction [30 min.]

Lecture 38: THE BINOMIAL THEOREM
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

Lecture 39 FOR UNIT 0 [29 min.]

  • A Proof That Squareroot 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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