The Language of Mathematics: Table of Contents

Content on this page is geared towards teaching the syntax of the language of mathematics, the rules and principles that we use in math. See Math in Real Life for a look at how we can use this information to enhance our lives.

Series I - Description, Exercises and Solutions.

Series II - Description, Exercises and Solutions.

Series IIIa - Description

Series IIIb - Description

Series IVa - done... description coming soon

Series IVb (open)

Videos Available for Download

Series I

Formulas and definitions used in this series.
Direct link to full album. Four images total.

- Series I Description: What's Contained in this Series

Section 1: Introduction to Series I

- (1): Introduction to Series I

Section 2: The Real Number Set

- (3, 4): The Real Number Set

Section 3: Zero and Infinity

- (5): Zero and Infinity, an Introduction to Limits

Section 4: Basic Operations

- (6): Adding and Subtracting

- (8): Multiplying and Dividing

- (7): Dealing with Negative Numbers

Section 5: Prime Numbers

- (9): Introduction to Prime Numbers

- (10): Finding Prime Factors

Section 6: Fractions

- (11): Reducing Fractions

- (12): Multiplying and Dividing Fractions

- (13): Adding and Subtracting Fractions

Section 7: Trigonometry

- (14): Introduction to Trigonometry and Geometry

- (15, 16, 17): Introduction to Right Triangles and Basic Trigonometric Ratios

- (18, 19): Solving Right Triangles

Section 8: Basic Geometry

- (31): Rules and Relationships between Angles of Parallel Lines

- (20, 21): Congruent and Similar Triangles

Section 9: Coordinate Geometry

- (23): Cartesian Coordinate System, Introduction

- (24): Slope and Midpoint of a Line

- (25): Distance of a Line

Section 10: Proofs

- (26): Introduction to Proofs

- (30): Proofs Involving Triangles

- (27, 28, 29): Proofs Involving a Line

- (32, 33): Coordinate Geometry Proof

Section 11: Why a Negative and a Negative Makes a Positive

- (35): Why Two Negatives Make a Positive

Series II

- Series II Description: What's Contained in this Series

Section 1: Exponents and Radicals

- (38, 39): Introduction and Series Layout

- (40, 41): How They Relate to The Real Number Set

- (42, 43, 44): Real Number Set Introduction with Examples

- (45): Rules for Adding and Subtracting Exponents and Radicals

- (46): Rules for Multiplying and Dividing Exponents and Radicals

- (47): Rules for Exponents to Exponents

- (48): Reducing Radicals

- (49): Multiplying Radicals, Example #1

- (50): Adding and Subtracting Radicals, Example #1

- (51): Simplifying Radicals, 3 Examples

- (52, 53, 54, 55): Creating a Large Problem

- (56): Simplifying Large Expressions

Section 2: Book Recommendations

- (57, 58): Book Recommendations

Series IIIa

- Series IIIa Description: What's Contained in this Series

Section 1: Summary of Series I and II, and an Introduction to Series IIIa

- (61): Summary of Series I and II, and an Introduction to the Equal Sign

Section 2: Black Holes and Elementary Particles

- (62, 63): The Difference Between Black Holes and Elementary Particles

Section 3: Techniques for Solving Equations

- (64): The Equal Sign: The difference between solving an equation and simplifying an expression: Entering The world of Applied Mathematics

- (65): Solving Equations - Addition and Subtraction

- (67): Solving Equations - Multiplication and Division

- (68): Solving Equations - Exponents and Radicals

- (69): Solving Equations - Cross Multiplication

Section 4: Solving Equations and Checking Solutions, Examples and Methods

- (70, 71): Introduction to Examples and Methods: What are we solving for?

- (72, 73, 74): Solving Equations and Checking Solutions: Example #1

- (75, 76): Solving Equations: Examples #2 and #3: Solving Using Two Methods

- (77): Solving Equations: Four Examples of Simple Equations

- (83): How not to solve an equation: Do not eliminate solutions

- (87, 88): Finding Restrictions for Equations: No Dividing by Zero

Section 5: Solving Quadratic Equations: Factoring Techniques

- (78, 79): Introduction to Quadratic Equations and Functions

- (80, 81, 82): Greatest Common Factor, GCF, Introduction and Examples #1-4: Factoring Part #1-3

- (84): Solving an equation, Graphing the Function: Greatest Common Factor, GCF, Two Examples

- (85, 86): Simple Trinomial Factoring: Introduction and Examples: Factoring Part 4-5

*Factoring polynomials continues in Series IIIb

Section 6: Introduction to Polynomial Functions

- (89, 90, 91): Understanding Polynomials and Defining Terms, Part 1-3: Polynomial Classifications

Series IIIb

- Series IIIb Description: What's Contained in this Series

- (97): Recap of Series I, II, and IIIa

- (98): Introduction to Series IIIb

Section 1: Introduction to Factoring Polynomials

- (105): Why We Factor Polynomials

- (122): Factoring Polynomials, a Graphical Representation

Section 2: Difference of Squares

- (99, 100, 101): Difference of Squares (Part 1 to 3): Factoring Polynomials (Part 6 to 8)

- (102, 103, 104): Solving Equations, a Graphical Representation (Part 1 to 3)

Section 3: Complex Trinomials: Factoring using the 4-Step Method

- (106, 107, 108, 109): Factoring Complex Trinomials using the 4-Step Method (Part 1 to 4): Factoring Polynomials (Part 9 to 12)

Section 4: The Quadratic Formula and The Discriminant

- (110, 111, 112): The Quadratic Formula and The Discriminant (Part 1 to 3): Factoring Polynomials (Part 13 to 15)

Section 5: The Let Statement, and Substitution (with Quadratic Formula)

- (113, 114, 115, 116): The Let Statement, Substitution, and the Quadratic Formula Examples (Part 1 to 4): Factoring Polynomials (Part 16 to 19)

Section 6: Synthetic Division, Polynomial Long Division, and The Division Statement

- (117, 118, 119): Introduction to Synthetic Division, Long Division, and The Division Statement (Part 1 to 3): Factoring Polynomials (Part 20 to 22)

- (120, 121, 123, 124) Polynomial Long Division (Part 1 to 4): Factoring Polynomials (Part 23 to 26)

- (125): The Division Statement, a Graphical Representation

- (126, 127, 128, 129): Synthetic Division: Introduction With Two Simple Examples: Factoring Polynomials (Part 27 to 30)

- (130, 131): Synthetic Division: Introduction and Example for Factoring Large Polynomials: Factoring Polynomials (Part 31 to 32)

- (132, 133): Synthetic Division: Factoring Large Polynomials Example #2: Factoring Polynomials (Part 33 to 34)

- (134, 135): Synthetic Division: Factoring Large Polynomials Example #3: Factoring Polynomials (Part 35 to 36)

Section 7: The Remainder Theorem and The Factor Theorem

- (142): Introduction to The Remainder Theorem and The Factor Theorem

Section 8: Why Math is Important

- (137): Why is Math Important? Five Reasons Why Math is Important

- (138): Why is Math Important? Because the language of mathematics plays a vital role in our evolution (article and video)

Section 9: Study Tips

- (139, 140, 141): How to Study: Introduction and Study Tips #1 and #2

Series IVa

- (144): Introduction to Series IV

Section 1: Units and Systems

- (145): Introduction and Prerequisites

- (146): Systems, SI Units, and a Conversion Table for Colored Squares and Triangles

Section 2: Ratios and Fractions

- (147): Introduction to Ratios, and Their Relationship to Fractions

- (149): The Most Important Thing You Need to Know About Multiplying Fractions: Reduce It Before You Multiply It

Section 3: Units and Ratios

- (148): The Rosetta Stones of Mathematics

Section 4: Unit Conversion

- (150): Introduction

- (151): Simple Unit Conversions Using Cross Multiplication: How It Works

Series IVb

- (152): Torrent now available for Series IVa, and an Update

- (153): Recap of Series I, II, IIIa, IIIb, IVa, and a little Math in Real Life

Section 1: Infinity (My Two Infinities)

- (#154, #155, #156): Infinity, Part 1 to 3: Until the End of Time and the Universe Explodes; Limits and Asymptotes, Visualizing Infinity; Going Halfway, Travelling from A to B Forever

Section ??: Miscellaneous

- (#157): Learning Your Multiplication Table: Two Hand Tricks

- (#158): How to Break a Line into Pieces, Odd and Even, Visualizing Fractions

- (#159): How to Study: Tip #3: Find Your Happy Space

- (#160): How to Study: Tip #4: Create a Schedule, Put Together a To Do List

- (#161): How to Study: Tip #5: 20 Steps to Reading a Textbook

- (#162): How to Study: Tip #6: When Doing Algebra, Recognize the Problem, Remember the Pattern

Videos Available for Download

I. Links

Direct links to torrents on The Pirate Bay (Please note: The Pirate Bay gets taken down a lot by governments so if the links below don't work please go the "Videos Available for Download" page. It contains the most updated links):

• Series I: Videos #1 to #35 for The Language of Mathematics, produced in 2007.
• Series II: Videos #36 to #58 for The Language of Mathematics, produced in 2008.
• Series IIIa: Videos #61 to #92 for The Language of Mathematics, produced in 2009.
• Series IIIb: Videos #93 to #142 for The Language of Mathematics, produced in 2010-2011.
• Series IVa: Videos #143 to #151 for The Language of Mathematics plus some videos for Math in Real Life, produced in 2011-2013.

II. Description

At the request of my readers, in 2009 I began to provide torrents for the math videos. The torrents are available through The Pirate Bay and other file sharing networks.

Downloads are series specific and the files organized based on their video number and/or year, i.e, the order in which the videos were produced. See the table of contents for The Language of Mathematics and Math in Real Life to put things into context.

Please note that videos from Series I, II, and IIIa are tagged with chycho.com, and those for Series IIIb and Series IVa are tagged with 420math.com. Since videos have gone through an additional edit in the process of putting this site together, they may vary slightly from those in the torrents.

III. Video Update