Update for Math in Real Life and the Language of Mathematics

Drop-in Math Tutoring Session on Tuesday October 23 at the Prophouse Café in Vancouver (UPDATE)

NOTE: I will most likely try and set up one of these types of sessions once a month. More info once I sort out some of the logistics. Talk soon.

If you happen to be in Vancouver and need a little help with your math, may it be for school or otherwise, then please feel free to drop by the Prophouse Café on Tuesday October 23 from 6:00 to 8:00 pm. Address is 1636 Venables Ave (at Commercial) - MAP

I will try and provide help for all topics covered in high school math except for calculus (sorry, I haven’t done my review yet). Bring your notes, your books, and your questions. I’ll be in the back of the café with my thinking cap on.

The drop-in is by donation and since space is limited, if you are planning to attend, please RSVP to mathinreallife@gmail.com

The flyer below provides further information.

Hope to see you there.

Simple Unit Conversions Using Cross Multiplication: How It Works (The Language of Mathematics IV #151)

Table of Contents: The Language of Mathematics

Unit Conversion: Introduction (The Language of Mathematics IV #150)

Table of Contents: The Language of Mathematics

The Most Important Thing You Need to Know About Multiplying Fractions: Reduce It Before You Multiply It (The Language of Mathematics IV #149)

Table of Contents: The Language of Mathematics

Math in Biology: Female Reproductive Cycle: Graphing the Menstrual Cycle, a Cyclic Function (Math in Real Life)

Table of Contents: Math in Real Life

Units and Ratios: The Rosetta Stones of Mathematics (The Language of Mathematics IV #148)

Table of Contents: The Language of Mathematics

Math in Art and Design: The Art of Dirk Marwig: Creating Your Space and Setting Up a Grid (Math in Real Life)

Table of Contents: Math in Real Life

DIRK MARWIG
dirkmarwig.com

Math in Art and Design: The Art of Dirk Marwig: Introduction, Interview, Designs and Works (Math in Real Life)

Table of Contents: Math in Real Life

DIRK MARWIG
dirkmarwig.com

Personal Finance: Time Management, Using Ratios to Track Your Projects (Math in Real Life)

Table of Contents: Math in Real Life

Navigating Through this Site: Finding What You Need

Exercises and Solutions

Below you will find the exercises and solutions available for The Language of Mathematics. Over time, more will be added and those in draft form will be finalized.

Please keep in mind that like most people, I am prone to making silly mistakes, so take the answers with a grain of salt. Corrections and suggestions are always welcome.

Series I - Description, Videos.

Series II - Description, Videos.

Series IIIa - Description, Videos.

Series IIIb - Description, Videos.

Series IV (open)

Series I

Section 2: The Real Number Set

Exercises: Which number set do the following numbers belong to.

Solutions.

Section 4: Basic Operations

Exercises: Basic Operations.

Solutions to:

i) Adding,

ii) Subtracting,

iii) Multiplying,

iv) Dividing,

v) Simplifying.

Section 5: Prime Numbers

Exercises: Break down the following into their Prime factors.

Solutions.

Section 6: Fractions

Exercises:

i) Reducing Fractions,

ii) Multiplying and Dividing Fractions,

iii) Adding and Subtracting Fractions.

Solutions to:

i) Reducing Fractions,

ii) Multiplying and Dividing Fractions,

iii) Adding and Subtracting Fractions.

Section 7: Trigonometry

Exercises: Find the missing variables, and solve the following right triangles.

Solutions.

Section 8: Basic Geometry

Exercises:

i) Parallel Lines,

ii) Congruent and Similar Triangles.

Solutions to:

i) Parallel Lines,

ii) Congruent and Similar Triangles.

Section 9: Coordinate Geometry

Exercises:

i) Plotting Points and Lines,

ii) Finding Slope, Midpoint, and Distance of a Line.

Solutions to:

ia) Small Grid,

ib) Large Grid,

ic) Plotting Lines,

iia) Finding Slope and Midpoint of a Line,

iib) Finding Distance of a Line.

Section 10: Proofs

Exercises:

i) Proofs Involving Triangles,

ii) Proofs Involving a Line,

iii) Coordinate Geometry Proof.

Solutions to:

i) Proofs Involving Triangles,

ii) Proofs Involving a Line,

iii) Coordinate Geometry Proof.

Series II

Section 1: Exponents and Radicals

Exercises:

i) Adding and Subtracting,

ii) Multiplying and Dividing,

iii) Exponents to Exponents,

iv) Reducing Radicals,

v) Simplifying Radicals.

Solutions to:

i) Adding and Subtracting,

ii) Multiplying and Dividing,

iii) Exponents to Exponents,

iv) Reducing Radicals,

v) Simplifying Radicals.

Series IIIa

- No exercises available for this series at the moment.

Series IIIb

- No exercises available for this series at the moment.

Series IV

- No exercises available for this series at the moment.

About Math in Real Life

In much the same manner that the industrial revolution brought about a surge of literacy in natural languages, the advent of the Internet in combination with low-cost computing has brought about a surge in the need to be literate in the language of mathematics. Due to these advancements, math has become an integral part of our society and the need to be literate in this language a necessity.

There are, however, some major problems. Many education systems across the globe are under stress and failing. The causes are vast and varied, so we’ll refrain from discussing the details of this collapse but instead focus on possible solutions to our predicament.

It is my belief that access to a good education is a human right, an obligatory gift from one generation to the next, and as long as we have access to an open, unfiltered, and uncensored Internet, then we, as a global community, can make a difference. We can fill the gap left behind by our governments and institutions by becoming proactive educators.

For my part, I will try and show how beautiful, how powerful, how useful and how easy it is to learn the bare minimum we need to know about the language of mathematics to enhance our lives. To achieve this task I am producing instructional videos for all major topics covered in secondary school math curriculums in Canada and the United State, i.e., all major topics starting with The Real Number Set up to and including an introductory course in Calculus and one for Probability and Statistics.

Content is being presented in an online video text book format and organized into two main Tables of Contents: One geared towards teaching the rules and principles that we use in math, and the other geared towards applying this information in real life. This is the essence of this site, teaching The Language of Mathematics to those who want to use Math in Real Life.

As for how you can support this project: It takes a tremendous amount of time and energy to produce this work, so, if you enjoy this work, if you are finding the information on this site useful, and if you would like to support this project, and can afford it, then please consider making a donation.

Peace,

From the series, "Shots in the Dark" by Jonathan Dy.

Table of Contents

The following are the two main tables of contents for this site:

1. The Language of Mathematics
2. Math in Real Life

The Language of Mathematics is geared towards teaching the syntax of this language, the rules and principles that we use in math. This project began in 2007 with The Real Number Set and will conclude with an introductory series on Calculus and one for Probability and Statistics.

Math in Real Life, started in 2012, is in its infancy and will continue indefinitely. The content in this section is geared towards using The Language of Mathematics to enhance our lives.

Lessons are also accessible through the tree menu provided in the left column. Specific topics can be found through the Index (left column).

Math in Real Life: Table of Contents

By far the most common question that I have been asked over the years regarding mathematics has been, ”When am I going to use math in real life?” That is, at least, the way I choose to perceive it. Unfortunately, more often than not, this question has come my way in the form of the following absurd absolute statement, “I’m never going to use this in real life!”

This erroneous perception of math’s practical usage has been the most prevalent problem in our education system, and by addressing it, the beauty of mathematics and its relevance reveals itself. Information gets absorbed faster. The details get scrutinized and people begin to recognize the occasions for which they have, can, and are already using math in their own lives.

This is the ultimate purpose of this section, to apply what we have learned from studying The Language of Mathematics to enhance our lives.

Content for this section will be organized in the following categories:

1. Games and Gambling
2. Personal Finance
3. Food and Farming
4. Food and Fitness
5. Economics and Politics
6. Business and Investment
7. Energy and Environment
8. Art and Design
9. Film and Music (Sight and Sound)
10. Science and Technology
11. Construction and Engineering
12. Miscellaneous

I. Games and Gambling

Section 1: Shooting Dice, Playing Craps

- The Beauty of Dice, Part 1: Probability Distribution for the Sum of Two 6-sided Die

II. Personal Finance

Section 1: Time Management

- Using Ratios to Track Your Projects

III. Food and Farming

Section 1: Community Supported Agriculture, CSA

- Part 1: Introduction - Community Supported Agriculture, CSA
- Part 2: Crop and Farm Layout, plus the Greenhouse
- Part 3: Logistics of Community Supported Agriculture, Collecting Some Data - Cost and Revenue
- Part 4: The Spreadsheet, a To Do List, a Simple Calculation, Yield for Broccoli
- Part 5: The Spreadsheet, a Flowchart, The Big Picture
- Part 6: Example #1: Calculating Crop Yield
- Part 7: Example #2: Calculating Total Row-Feet of Crop Needed for Our Menu
- Part 8: An Update and Some Random Thoughts on Community Supported Agriculture, CSA
- Update from La Belle Besogne Farm for May, June, and July 2013
- Part 9: Mathematics of Farming: Update, January 2015

IV. Food and Fitness

- In the works

V. Economics and Politics

- In the works

VI. Business and Investment

- In the works

VII. Energy and Environment

- In the works

VIII. Art and Design

Section 1: The Art of Dirk Marwig

- Part 1: Introduction, Interview, Designs and Works
- Part 2: Creating Your Space and Setting Up a Grid
- Part 3: Perspective, Depth, Elements, and Ratios
- Part 4: The Golden Ratio, Rectangle, and Spiral
- Part 5: Using the Fibonacci Numbers to Create the Golden Rectangle
- Part 6: Chaos, Order, and Op Art - Five Paintings by Dirk Marwig
- Part 7: Building Three Objects: Freeform, Symmetry, Golden Rectangle
- Part 8: Building a Bucky-Ball and a Rhombicosidodecahedron with Bamboo & Zap-Straps

IX. Film and Music (Sight and Sound)

- In the works

X. Science and Technology

Biology:

-Female Reproductive Cycle: Graphing the Menstrual Cycle, a Cyclic Function

Physics:

- How Fast is a Human Punch? - Physics: Kinematics: Calculating Speed

XI. Construction and Engineering

- In the works

XII. Miscellaneous

- How to Study: Tip #2: Longer is Better - Introduction to Efficiency

Series I Description: What's Contained in this Series

The first part of this series deals with the absolute basics of mathematics: the Real Number Set; basic operations; prime numbers and their importance; and how to deal with fractions. This is where it all begins. Please be comfortable with this material before moving on.

The second part of this series deals with basic geometry and trigonometry. Topics discussed include: right triangles and trigonometric ratios; parallel lines; congruent and similar triangles; the Cartesian coordinate system; and slope, midpoint, and distance of a line. We also take a quick look at three different types of proofs related to these topics; those related to triangles, lines, and the Cartesian coordinate system. (NOTE: at some point in the future an in-depth introduction to trigonometry will be produce.)

In addition to the above, we take a rudimentary look at Zero and Infinity, and Why Two Negatives Make a Positive.

Full list and links for all the videos contained in the series are provided below and are available at: Table of Contents: The Language of Mathematics - Series I.

Exercises and Solutions are also available for this series.

See Videos Available for Download for information on the torrent for this series.

For ease of reference, included below is the Table of Contents and the expanded image of the tree menu provided in the left column of this site. Specific topics can be found through the Index (left column).

Table of Contents

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

Image of Tree Menu

From Series I Tree Menu - The Language of Mathematics

Why Two Negatives Make a Positive (The Language of Mathematics #35)

Table of Contents: The Language of Mathematics

Coordinate Geometry Proof (The Language of Mathematics #32-33)

Table of Contents: The Language of Mathematics

Coordinate Geometry Proof, Part 1 (Math #32)

Coordinate Geometry Proof, Part 2 (Math #33)

Proofs Involving a Line (The Language of Mathematics #27-29)

Table of Contents: The Language of Mathematics

Proofs Involving a Line, Part 1 (Math #27)

Proofs Involving a Line, Part 2 (Math #28)

Proofs Involving a Line, Part 3 (Math #29)

Proofs Involving Triangles (The Language of Mathematics #30)

Table of Contents: The Language of Mathematics

Introduction to Proofs (The Language of Mathematics #26)

Table of Contents: The Language of Mathematics

Distance of a Line (The Language of Mathematics #25)

Table of Contents: The Language of Mathematics

Slope and Midpoint of a Line (The Language of Mathematics #24)

Table of Contents: The Language of Mathematics

Cartesian Coordinate System, Introduction (The Language of Mathematics #23)

Table of Contents: The Language of Mathematics

Congruent and Similar Triangles (Language of Mathematics #20-21)

Table of Contents: The Language of Mathematics

Congruent and Similar Triangles, Part 1 (Math #20)

Congruent and Similar Triangles, Part 2 (Math #21)

Rules and Relationships between Angles of Parallel Lines (Language of Mathematics #31)

Table of Contents: The Language of Mathematics

Solving Right Triangles (The Language of Mathematics #18-19)

Table of Contents: The Language of Mathematics

Solving Right Triangles, Part 1 (Math #18)

Solving Right Triangles, Part 1 (Math #19)

Introduction to Right Triangles and Basic Trigonometric Ratios (Language of Mathematics #15-17)

Table of Contents: The Language of Mathematics

Right Triangles and Basic Trigonometric Ratios, Part 1 (Math #15)

Right Triangles and Basic Trigonometric Ratios, Part 2 (Math #16)

Right Triangles and Basic Trigonometric Ratios, Part 3 (Math #17)

Music by Horeja
www.youtube.com/user/horejachile
www.facebook.com/horeja
horeja.bandcamp.com

Introduction to Trigonometry and Geometry (The Language of Mathematics #14)

Table of Contents: The Language of Mathematics

Adding and Subtracting Fractions (The Language of Mathematics I #13)

Table of Contents: The Language of Mathematics

Multiplying and Dividing Fractions (The Language of Mathematics I #12)

Table of Contents: The Language of Mathematics

Reducing Fractions (The Language of Mathematics I #11)

Table of Contents: The Language of Mathematics

Finding Prime Factors (The Language of Mathematics I #10)

Table of Contents: The Language of Mathematics

Introduction to Prime Numbers (The Language of Mathematics I #9)

Table of Contents: The Language of Mathematics

Basic Operations, Dealing with Negative Numbers (The Language of Mathematics I #7)

Table of Contents: The Language of Mathematics

Basic Operations, Multiplying and Dividing (The Language of Mathematics I #8)

Table of Contents: The Language of Mathematics

Basic Operations, Adding and Subtracting (The Language of Mathematics I #6)

Table of Contents: The Language of Mathematics

Zero and Infinity, an Introduction to Limits (The Language of Mathematics I #5)

Table of Contents: The Language of Mathematics

The Real Number Set (The Language of Mathematics I #3-4)

Table of Contents: The Language of Mathematics

The Real Number Set, Part 1 (Math #3)

The Real Number Set, Part 2 (Math #4)

Music by Horeja
www.facebook.com/horeja

Introduction to Series I (The Language of Mathematics I #1)

Table of Contents: The Language of Mathematics

Series II Description: What's Contained in this Series

This series is all about exponents and radicals: how to add, subtract, multiply, and divide them; how to take a power to a power; and the process involved for simplifying radicals and large expressions.

We also take a detailed look at how exponents and radicals are related to the Real Number Set. Please note that the videos for this part of the series have overlaps. Videos #40 and #41 discuss the importance of the subsets of the Real Number Set and how they translate over to the basic operations for exponents and radicals. The information contained in these two videos is repeated in videos #42-44, with the addition of examples. If you are familiar and comfortable with the basic operations for exponents and radicals, then videos #40 and #41 should suffice. If you would like the information to be presented with examples, then it will be worth your while to view the latter set. See Video #39 for more information on how the material is being presented.

In addition to the above, five book recommendations.

Full list and links for all the videos contained in the series are provided below and are available at: Table of Contents: The Language of Mathematics - Series II.

Exercises and Solutions are also available for this series.

See Videos Available for Download for information on the torrent for this series.

For ease of reference, included below is the Table of Contents and the expanded image of the tree menu provided in the left column of this site. Specific topics can be found through the Index (left column).

Table of Contents

- 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

Image of Tree Menu

From Series II Tree Menu - The Language of Mathematics

Book Recommendations (The Language of Mathematics II #57-58)

Table of Contents: The Language of Mathematics

Book Recommendations, Part 1 (Math #57)

Book Recommendations, Part 2 (Math #58)

1. "Calculus with Analytic Geometry" by Howard Anton
2. "Gödel, Escher, Bach: An Eternal Golden Braid " by Douglas R. Hofstadter
3. "God's Equation" by Amir D. Aczel
4. "The Elegant Universe" by Brian Greene
5. "Bone" by Jeff Smith

Exponents and Radicals: Simplifying Large Expressions (The Language of Mathematics II #56)

Table of Contents: The Language of Mathematics

Exponents and Radicals: Creating a Large Problem, Parts 1 to 4 (The Language of Mathematics II #52-54)

Table of Contents: The Language of Mathematics

Creating a Large Problem, Part 1 (Math #52)

Creating a Large Problem, Part 2 (Math #53)

Creating a Large Problem, Part 3 (Math #54)

Creating a Large Problem, Part 4 (Math #55)

Simplifying Radicals, 3 Examples (The Language of Mathematics II #51)

Table of Contents: The Language of Mathematics

Adding and Subtracting Radicals, Example #1 (The Language of Mathematics II #50)

Table of Contents: The Language of Mathematics

Multiplying Radicals, Example #1 (The Language of Mathematics II #49)

Table of Contents: The Language of Mathematics

Reducing Radicals (The Language of Mathematics II #48)

Table of Contents: The Language of Mathematics

Rules for Exponents to Exponents (The Language of Mathematics II #47)

Table of Contents: The Language of Mathematics

Rules for Multiplying and Dividing Exponents and Radicals (The Language of Mathematics II #46)

Table of Contents: The Language of Mathematics

Rules for Adding and Subtracting Exponents and Radicals (The Language of Mathematics II #45)

Table of Contents: The Language of Mathematics

Exponents and Radicals: Real Number Set Introduction with Examples (The Language of Mathematics II #42-44)

Table of Contents: The Language of Mathematics

Real Number Set Introduction with Examples, Part 1 (Math #42)

Real Number Set Introduction with Examples, Part 2 (Math #43)

Real Number Set Introduction with Examples, Part 3 (Math #44)

Music by lazy Marv
soundcloud.com/lazy-marv

Exponents and Radicals: How They Relate to The Real Number Set (The Language of Mathematics II #40-41)

Table of Contents: The Language of Mathematics

Relation to The Real Number Set, Part 1 (Math #40)

Relation to The Real Number Set, Part 2 (Math #41)

Music by lazy Marv
soundcloud.com/lazy-marv

Exponents and Radicals: Introduction and Series Layout (The Language of Mathematics II #38-39)

Table of Contents: The Language of Mathematics

Introduction to Exponents and Radicals (Math #38)

Series Layout (Math #39)

Series IIIa Description: What's Contained in this Series

In this series we learn different techniques for solving equations, combine and isolate variables, talk about the equal sign, how to move around an equation, discuss the graphical meaning for solving equations, learn about restrictions, and how we would go about checking solutions.

Also included is an introduction to polynomial equations and functions, a discussion of their classifications, and factoring techniques, beginning with the Greatest Common Factor (GCF) and Simple Trinomial Factoring (Factoring techniques for polynomials is continued in Series IIIb).

In addition to the above, we also take a brief look at the difference between black holes and elementary particles.

Full list and links for all the videos contained in the series are provided below and are available at:Table of Contents: The Language of Mathematics - Series IIIa.

See Videos Available for Download for information on the torrent for this series.

For ease of reference, included below is the Table of Contents and the expanded image of the tree menu provided in the left column of this site. Specific topics can be found through the Index (left column).

Table of Contents

- 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

Image of Tree Menu

From Series IIIa Tree Menu - The Language of Mathematics

Videos Available for Download

1. Links

2. Description

3. Video Update

I. Links

Direct links to torrents on The Pirate Bay (Please note: The Pirate Bay gets taken down a lot by governments so please let me know if the links are dead and I'll fix them, thanks):

• 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

Understanding Polynomials and Defining Terms, Part 1-3: Polynomial Classifications (Language of Mathematics IIIa #89-91)

Table of Contents: The Language of Mathematics

Understanding Polynomials and Defining Terms, Part 1 (Math #89)

Understanding Polynomials and Defining Terms, Part 2 (Math #90)

Understanding Polynomials and Defining Terms, Part 3: Polynomial Classifications (Math #91)

Music by lazy Marv
soundcloud.com/lazy-marv

Simple Trinomial Factoring: Introduction and Examples: Factoring Part 4-5 (Language of Mathematics IIIa #85-86)

Table of Contents: The Language of Mathematics

Simple Trinomial Factoring Part 1: Introduction and Example (Math #85)

Simple Trinomial Factoring Part 2: Three Examples (Math #86)

Solving an Equation, Graphing the Function: Greatest Common Factor, GCF, Two Examples (Language of Mathematics IIIa #84)

Table of Contents: The Language of Mathematics

Greatest Common Factor, GCF, Introduction and Examples #1-4: Factoring P1-3 (Language of Mathematics IIIa #80-82)

Table of Contents: The Language of Mathematics

Greatest Common Factor Part 1: Introduction (Math #80)

Greatest Common Factor Part 2: Three Examples (Math #81)

Greatest Common Factor Part 3: Example #4 (Math #82)

Introduction to Quadratic Equations and Functions (The Language of Mathematics IIIa #78-79)

Table of Contents: The Language of Mathematics

Introduction to Solving Quadratic Equations, Part 1 (Math #78)

Introduction to Solving Quadratic Equations, Part 2 (Math #79)

Music by lazy Marv
soundcloud.com/lazy-marv

Finding Restrictions for Equations: No Dividing by Zero (The Language of Mathematics IIIa #87-88)

Table of Contents: The Language of Mathematics

Finding Restrictions for Equations, Part 1 (Math #87)

Finding Restrictions for Equations, Part 2 (Math #88)

How not to solve an equation: Do not eliminate solutions (The Language of Mathematics IIIa #83)

Table of Contents: The Language of Mathematics

Solving Equations: Four Examples of Simple Equations (The Language of Mathematics IIIa #77)

Table of Contents: The Language of Mathematics

Solving Equations - Examples #2 and #3: Solving Using Two Methods (The Language of Mathematics IIIa #75-76)

Table of Contents: The Language of Mathematics

Solving Equations: Example 2, Two Methods (Math #75)

Solving Equations: Example 3, Using Two Methods (Math #76)

Solving Equations and Checking Solutions: Example #1 (The Language of Mathematics IIIa #72-74)

Table of Contents: The Language of Mathematics

Solving Equations: Example #1, Part 1 of 3 (Math #72)

Solving Equations: Example #1, Part 2 of 3 (Math #73)

Solving Equations: Example #1, Part 3 of 3 (Math #74)

Music by [JERBEΔR]
soundcloud.com/jeremy-mcintyre

Solving Equations - Introduction to Examples and Methods: What are we solving for? (Language of Mathematics IIIa #70-71)

Table of Contents: The Language of Mathematics

Introduction to Examples and Methods (Language of Math #70)

What are we solving for? (Language of Math #71)

Solving Equations - Cross Multiplication (The Language of Mathematics IIIa #69)

Table of Contents: The Language of Mathematics

Solving Equations - Exponents and Radicals (The Language of Mathematics IIIa #68)

Table of Contents: The Language of Mathematics

Solving Equations - Multiplication and Division (The Language of Mathematics IIIa #67)

Table of Contents: The Language of Mathematics

Solving Equations - Addition and Subtraction (The Language of Mathematics IIIa #65)

Table of Contents: The Language of Mathematics

The Difference Between Solving an Equation and Simplifying an Expression: Entering The world of Applied Mathematics (Language of Mathematics IIIa #64)

Table of Contents: The Language of Mathematics

The Difference Between Black Holes and Elementary Particles (The Language of Mathematics IIIa #62-63)

Table of Contents: The Language of Mathematics

Black Holes and Elementary Particles: Part 1 (Math #62)

Black Holes and Elementary Particles: Part 2 (Math #63)

Music by [JERBEΔR]
soundcloud.com/jeremy-mcintyre

Robert Anton Wilson
www.rawilson.com

Summary of Series I and II, and a discussion about the Equal Sign (Language of Mathematics IIIa #61)

Table of Contents: The Language of Mathematics

Series IIIb Description: What's Contained in this Series

This series is a continuation of Series IIIa.

Series IIIa and IIIb give you the power to be able to factor and solve polynomials of any degree. Factoring techniques included in this series are: the Difference of Squares, Complex Trinomial Factoring (4-step method), Quadratic Formula including The Discriminant, and Synthetic Division.

In addition to the above, we also do an in-depth discussion of The Division Statement, Polynomial Long Division, look at the graphical meaning of factoring polynomials, use Let Statements and Substitution to factor polynomial and non-polynomial functions, and discuss The Remainder and The Factor Theorems.

Extras included in this series are a look at Why Math is Important and two tips on how to improve your study habits.

Full list and links for all the videos contained in the series are provided below and are available at: Table of Contents: The Language of Mathematics - Series IIIb.

See Videos Available for Download for information on the torrent for this series.

For ease of reference, included below is the Table of Contents and the expanded image of the tree menu provided in the left column of this site. Specific topics can be found through the Index (left column).

Table of Contents

- 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

Image of Tree Menu

From Series IIIb Tree Menu - The Language of Mathematics

How to Study: Introduction and Study Tips #1 and #2 (The Language of Mathematics IIIb #139-141)

Table of Contents: The Language of Mathematics

How to Study: Introduction (Language of Math #139)

Tip #1: Hate to Love, Why Are You Here? (Math #140)

Tip #2: Longer is Better - Introduction to Efficiency (#141)

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

Table of Contents: The Language of Mathematics

I want to address one of the most frequent questions that has come my way over the years, it being: “Why is math important?”

Upon going through countless iterations, the shortest and simplest answer that I can provide to this question, is that math is important because it is a vital step in our evolution. The creation and utilization of this language is the reason why we have been able to evolve to the state that we are in: personally, socially, and culturally.

It is widely accepted that numeracy, “the ability to reason with numbers and other mathematical concepts”, is an innate human ability - we’re hardwired for it. Thus, the development of the language of mathematics based on certain definitions and axioms, self-evident truths, may they be complete and consistent or not, was the only logical step in our evolution.

The prominent theory as to the reasons why written languages came to be is that they were developed for the purposes of accurate bookkeeping, economic necessity, and as a means for us to record important events. In essence, once we had acquired enough knowledge that could not accurately be conveyed verbally, we developed symbols, and later on structured languages, syntax, to record and pass on that information. Mathematics was not only an integral part of this, but also an end product.

As with other languages, mathematics was developed to share information and as a means for us to describe and solve real world problems. Slowly, the language matured “through the use of abstraction and logical reasoning” and in the last few hundred years has evolved to what it is today, thanks, in large part, to Franciscus Vieta and Leonhard Euler.

At present, mathematics is by far the most efficient language that we have been able to develop to seek and analyze patterns, to optimize our ability to create, and to discuss the laws governing our universe, in the process, helping us answer some of our most fundamental questions. Math is, ultimately, the most concise form of communication we have to understand who we are, where we are, and what we are capable of.

Building Gods (Rough Cut)

Without mathematics we would behave and interact with the world in a completely different manner than we do today. The creation of notations and the formalization of algebra paved the way for us to better understand and interact with the world we inhabit.

Once the syntax for this language was developed, through rigorous analysis we were able to explore the intricacies of what was being revealed. From the significance of prime numbers in our every day lives, to the discovery of the quantization of information, to the revelations that large parts of the universe are invisible to our principal senses. It is mainly due to the innovations brought about through the use of mathematics, may it be in the development of conjectures or the fabrication of instruments, that we are aware of so much, from the very large to the very small.

Marcus du Sautoy: Symmetry, reality's riddle

Math forms the fabric of our current civilization, from economics and politics to what we consume and possess. You don’t believe it? Take a look around you. Aside from the natural ecosystem, almost everything that you see has one thing in common, it was made, raised, grown, or delivered with the use of mathematics as a primary tool. The monitor or piece of paper that you are reading this on, the food you may be consuming, the pictures on your desk, the light in your room, your computer, your clothes, your shoes, your phone, your job, your home, your car and the roads you drive it on, your beverage and the cup you’re drinking it from, all of it, is because of mathematics. Without it, we would not have these luxuries, comforts, freedoms, or the prospect of equality or sustainability.

The Most IMPORTANT Video You'll Ever See (part 1 of 8)

Full Lecture

One crucial point to note, literacy in the language of mathematics was not as important in the past as it is today, or as vital as it will be for the future. Technology and the inevitabilities and necessities of life are forcing every aspect of our lives to be optimized, and the best way that we know of to achieve this task is through mathematics.

So why is math important? Because it encompasses every aspect of our lives and without it, we would not be who we are, we will not progress, and we will not realize our full potential, and thus, have no future: personally, socially, or culturally.

Related video:

Why is Math Important? Part 1: Five Reasons Why Math is Important (137)

• Reason #1: Life can be brutal. Knowing math may help you out through those moments.
• Reason #2: Math can help you be the best at what you want to be the best at.
• Reason #3: Willingly being illiterate in the most important language in the world is really stupid.
• Reason #4: Knowing math can help you be financially secure.
• Reason #5: Being intelligent, in general, makes you attractive.