Sunday, January 10, 2010

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.

Section 1: Introduction and Instructions

(1): Introduction

(2): Instructions

Section 2: The Real Number Set

(3): The Real Number Set - Part 1

(4): The Real Number Set - Part 2

(22): Instructions for Exercises - 1

Section 3: Zero and Infinity

(5): Zero and Infinity

Section 4: Basic Operations

(6): Adding and Subtracting

(8): Multiplying and Dividing

(7): Dealing with Negative Numbers

Section 5: Prime Numbers

(9): Prime Numbers

(10): Finding Prime Factors

Section 6: Fractions

(11): Reducing Fractions

(12): Multiply and Divide Fractions

(13): Adding and Subtracting Fraction

Section 7: Trigonometry

(14): Introduction to Trigonometry

(15): Right Triangles Part 1

(16): Right Triangles Part 2

(17): Right Triangles Part 3

(18): Solving Right Triangles 1

(19): Solving Right Triangles 2

Section 8: Basic Geometry

(31): Parallel Lines

(20): Congruent Similar Triangles 1

(21): Congruent Similar Triangles 2

Section 9: Coordinate Geometry

(23): Cartesian Coordinate System

(24): Slope and Midpoint of a Line

(25): Distance of a Line

Section 10: Proofs

(26): Introductions to Proofs

(30): Proofs Involving Triangles

(27): Proofs Involving a Line 1

(28): Proofs Involving a Line 2

(29): Proofs Involving a Line 3

(32): Coordinate Geometry Proof 1

(33): Coordinate Geometry Proof 2

Section 11: Why a negative and a negative makes a positive

(35): why 2 negatives make a positive

Section 12: Miscellaneous Videos

(34): Prepping for next set of videos (update 1)

(36): First Series Montage with SPM

(37): Update for Series II (update 2)

Series II

Section 1: Exponents and Radicals

(38): Exponents and Radicals (intro)

(39): Exponents and Radicals Layout

(40): Exponents and Radicals (Real 1 of 2)

(41): Exponents and Radicals (Real 2 of 2)

(42): Exponents and Radicals (1 of 3)

(43): Exponents and Radicals (2 of 3)

(44): Exponents and Radicals (3 of 3)

(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): Creating a Large Radicals Problem (Part 1 of 4)

(53): Creating a Large Radicals Problem (Part 2 of 4)

(54): Creating a Large Radicals Problem (Part 3 of 4)

(55): Creating a Large Radicals Problem (Part 4 of 4)

(56): Simplifying Large Radicals

Section 2: Book Recommendations

(57): Book Recommendations (Part 1 of 2)

(58): Book Recommendations (Part 2 of 2)

Section 3: Miscellaneous Videos II

(60): Update 3, 1 February 2009

Series IIIa

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

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

Section 2: Black Holes and Elementary Particles

(62): Black holes and elementary particles (Part 1)

(63): Black holes and elementary particles (Part 2)

Section 3: Techniques for Solving Equations

(64): The equal sign allows us to enter 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

(70): Solving Equations - Introduction to Examples and Methods

(71): Solving Equations - What are we solving for?

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

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

(74): Checking the Solution - Example 1, Part 3 of 3

(75): Solving Equations - Example 2, Two Methods

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

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

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

(87): Finding Restrictions for Equations - No Dividing by Zero (Part 1)

(88): Finding Restrictions for Equations - No Dividing by Zero (Part 2)

Section 5: Solving Quadratic Equations: Factoring Techniques

(78): Introduction to Solving Quadratic Equations (Part 1)

(79): Introduction to Solving Quadratic Equations (Part 2)

(80): Factoring: Part 1 - Greatest Common Factor (GCF)

(81): Factoring: Part 2 - Greatest Common Factor (GCF)

(82): Factoring: Part 3 - Greatest Common Factor (GCF)

(84): Solving and Graphing Equations - Greatest Common Factor (GCF)

(85): Factoring: Part 4 - Simple Trinomial Factoring

(86): Factoring: Part 5 - Three examples of Simple Trinomial Factoring

Factoring polynomials continues in Series IIIb

Section 6: Introduction to Polynomial Functions

(89): Understanding Polynomials and Defining Terms (Part 1 of 3)

(90): Understanding Polynomials and Defining Terms (Part 2 of 3)

(91): Understanding Polynomials and Defining Terms (Part 3 of 3)

Section 7: Miscellaneous

(66): Torrents now available for Series I and Series II

(92): Update October 2009

(93): Torrents are now available for Series I, II, and III

Series IIIb

Section 1: Recaps and Introductions

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

(98): Introduction to Series IIIb

(105): Why Do We Factor? Introduction to Factoring Polynomials

(122): Factoring Polynomials, a Graphical Representation

Section 2: Difference of Squares

Continues from Section 5 of Series IIIa

Lesson 1:

(99): Factoring: Part 6 - Difference of Squares (Part 1)

(100): Factoring: Part 7 - Difference of Squares (Part 2), 6 Examples

(101): Factoring: Part 8 - Difference of Squares (Part 3), Be Careful With The Following

Lesson 2:

(102): Difference of Squares: Solving Equations, a Graphical Representation (Part 1)

(103): Difference of Squares: Solving Equations, a Graphical Representation (Part 2)

(104): Difference of Squares: Solving Equations, a Graphical Representation (Part 3)

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

(106): Factoring: Part 9 - Complex Trinomials (Part 1), 4-Step Method

(107): Factoring: Part 10 - Complex Trinomials (Part 2), 4-Step Method

(108): Factoring: Part 11 - Complex Trinomials (Part 3), 4-Step Method - Ex. #2

(109): Factoring: Part 12 - Complex Trinomials (Part 4), 4-Step Method - Ex. #3

Section 4: The Quadratic Formula

(110): Factoring: Part 13 - Quadratic Formula (Part 1): Introduction

(111): Factoring: Part 14 - Quadratic Formula (Part 2): Ex. #1

(112): Factoring: Part 15 - Quadratic Formula (Part 3): Ex. #2 & #3

Section 5: The Let Statement

(113): Factoring: Part 16: Let Statement (Part 1): Substitution

(114): Factoring: Part 17: Let Statement (Part 2): Quadratic Formula

(115): Factoring: Part 18: Let Statement (Part 3): Quadratic Formula

(116): Factoring: Part 19: Let Statement (Part 4): Quadratic Formula, Checking Solutions

Section 6: Synthetic Division and The Division Statement

Lesson 1:

(117): Factoring Part 20: Synthetic Division Part 1: Introduction

(118): Factoring Part 21: Synthetic Division Part 2: Long Division, The Division Statement

(119): Factoring Part 22: Synthetic Division Part 3: The Division Statement

Lesson 2:

(120): Factoring Part 23: Synthetic Division Part 4: Polynomial Long Division (Part 1)

(121): Factoring Part 24: Synthetic Division Part 5: Polynomial Long Division (Part 2)

(123): Factoring Part 25: Synthetic Division Part 6: Polynomial Long Division (Part 3)

(124): Factoring Part 26: Synthetic Division Part 7: Polynomial Long Division (Part 4)

Lesson 3:

(125): The Division Statement, a Graphical Representation

Lesson 4:

(126): Factoring Part 27: Synthetic Division Part 8: Part 1 - When to Use It

(127): Factoring Part 28: Synthetic Division Part 9: Part 2 - Be Careful With the Following

(128): Factoring Part 29: Synthetic Division Part 10: Part 3 - A Simple Example #1

(129): Factoring Part 30: Synthetic Division Part 11: Part 4 - A Simple Example #2

Lesson 5:

(130): Factoring Part 31: Synthetic Division Part 12: Part 5 - Introduction to Factoring Large Polynomials

(131): Factoring Part 32: Synthetic Division Part 13: Part 6 - Factoring Large Polynomials, Ex1

(132): Factoring Part 33: Synthetic Division Part 14: Part 7 - Factoring Large Polynomials, 2a

(133): Factoring Part 34: Synthetic Division Part 15: Part 8 - Factoring Large Polynomials, 2b

(134): Factoring Part 35: Synthetic Division Part 16: Part 9 - Factoring Large Polynomials, 3a

(135): Factoring Part 36: Synthetic Division Part 17: Part 10 - Factoring Large Polynomials, 3b

Section 7: The Remainder Theorem and The Factor Theorem

(142): The Remainder Theorem and The Factor Theorem

Section 8: Why Math is Important

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

(138): Why is Math Important? Part 2: Because it's part of evolution, part of what makes us human

Section 9: Study Tips

Lesson 1:

(139): How to Study: Introduction

(140): How to Study: Tip #1: Why Are You Here?

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

Section 10: Miscellaneous

(93): Torrents are now available for Series I, II, and III

(94): Update January 2010: Table of Contents, torrents, and chycho

(95): Update for chycho.com and Language of Mathematics: Introducing "420math" and "Math in Real life" (Part 1)

(96): Update for chycho.com and Language of Mathematics: Introducing "420math" and "Math in Real life" (Part 2)

(136): Update for The Language of Mathematics: Series IIIb, Torrents, and Other Content)

Series IVa

Video: (144): Introduction to Series IV

Section 1: Units and Systems

(145): Units: 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

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

Video: (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

Please note, since The Pirate Bay was taken down it’s become harder to provide constant direct links to the torrents. The torrents are still available, I usually have two computer seeding them, so please look for the torrents on other file sharing sites such as KickassTorrents.

Hopefully in time we will be able to create a society where we can share content freely without government or corporate interference, until then, happy seeding.

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.