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
Wednesday, February 29, 2012
Solving Equations and Checking Solutions: Example #1 (The Language of Mathematics IIIa #72-74)
Table of Contents: The Language of Mathematics
Music by [JERBEΔR]
soundcloud.com/jeremy-mcintyre
Tuesday, February 28, 2012
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)
Monday, February 27, 2012
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
Thursday, February 23, 2012
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
- Section 1: Introduction to Factoring Polynomials
- Section 2: Difference of Squares
- Section 3: Complex Trinomials: Factoring using the 4-Step Method
- Section 4: The Quadratic Formula and The Discriminant
- Section 5: The Let Statement, and Substitution (with Quadratic Formula)
- Section 6: Synthetic Division, Polynomial Long Division, and The Division Statement
- Section 7: The Remainder Theorem and The Factor Theorem
- Section 8: Why Math is Important
- Section 9: Study Tips
Image of Tree Menu
 |
| From Series IIIb Tree Menu - The Language of Mathematics |
Wednesday, February 22, 2012
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)
Tuesday, February 21, 2012
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.
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.
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.
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:
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)
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.
Why is Math Important? Five Reasons Why Math is Important (Language of Mathematics IIIb #137)
Table of Contents: The Language of Mathematics
- 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.
Monday, February 20, 2012
Introduction to The Remainder Theorem and The Factor Theorem (Language of Mathematics IIIb #142)
Table of Contents: The Language of Mathematics
Video by Elia Regazzi
eligiozy.posterous.com/
www.flickr.com/photos/eligiozy
Music by Grapes "I dunno"
ccmixter.org/people/grapes
www.facebook.com/510triphop
www.youtube.com/user/smokegrapes
Synthetic Division: Factoring Large Polynomials Example #3: Factoring P35-36 (Language of Mathematics IIIb #134-135)
Table of Contents: The Language of Mathematics
Factoring Large Polynomials Example #3a (Math 134)
Factoring Large Polynomials Example #3b (Math 135)
Synthetic Division: Factoring Large Polynomials Example #2: Factoring P33-34 (Language of Mathematics IIIb #132-133)
Table of Contents: The Language of Mathematics
Factoring Large Polynomials Example #2a (Math 132)
Factoring Large Polynomials Example #2b (Math 133)
Bill Hicks
www.billhicks.com
Sunday, February 19, 2012
Synthetic Division: Introduction and Example for Factoring Large Polynomials: Factoring P31-32 (Language of Mathematics IIIb #130-131)
Table of Contents: The Language of Mathematics
Introduction to Factoring Large Polynomials (Math 130)
Factoring Large Polynomials Example #1 (Math 131)
Bill Hicks
www.billhicks.com
Synthetic Division: Introduction With Two Simple Examples: Factoring Polynomials Part 27-30 (Language of Mathematics IIIb #126-129)
Table of Contents: The Language of Mathematics
Synthetic Division Part 1: When to Use It (Math #126)
Synthetic Division Part 2: Be Careful With the Following (Math #127)
Synthetic Division Part 3: A Simple Example #1 (Math #128)
Synthetic Division Part 4: A Simple Example #2 (Math #129)
Music by Horeja
www.facebook.com/horeja
Saturday, February 18, 2012
Polynomial Long Division Part 1-4: Synthetic Division Part 4-7: Factoring Polynomials Part 23-26 (Language of Mathematics IIIb #120-124)
Table of Contents: The Language of Mathematics
Polynomial Long Division Part 1 (Language of Math #120)
Polynomial Long Division Part 2 (Language of Math #121)
Polynomial Long Division Part 3 (Language of Math #123)
Polynomial Long Division Part 4 (Language of Math #124)
Music by lazy Marv
soundcloud.com/lazy-marv
Friday, February 17, 2012
Synthetic Division: Introduction, Long Division, and The Division Statement Part 1-3: Factoring Polynomials Part 20-22 (Language of Mathematics IIIb #117-119)
Table of Contents: The Language of Mathematics
Synthetic Division Part 1: Introduction (Language of Math #117)
Synthetic Division Part 2: Long Division and The Division Statement (Language of Math #118)
Synthetic Division Part 3: The Division Statement (Language of Math #119)
Music by Jol-sone
www.youtube.com/user/TheJolsonetube
The Let Statement, Substitution, and the Quadratic Formula, Part 1 to 4: Factoring Polynomials, Part 16 to 19 (Language of Mathematics IIIb #113-116)
Table of Contents: The Language of Mathematics
The Let Statement Part 1: Substitution (Language of Math #113)
The Let Statement Part 2: Quadratic Formula, Ex. #1 (Language of Math #114)
The Let Statement Part 3: Quadratic Formula, Ex. #2 (Language of Math #115)
The Let Statement Part 4: Quadratic Formula, Ex. #3 (Language of Math #116)
Thursday, February 16, 2012
The Quadratic Formula and The Discriminant, Part 1 to 3 : Factoring Polynomials, Part 13 to 15 (The Language of Mathematics IIIb #110-112)
Table of Contents: The Language of Mathematics
Quadratic Formula Part 1: Introduction (Language of Math #110)
Quadratic Formula Part 2: Example #1 (Language of Math #111)
Quadratic Formula Part 3: Example #2 and #3 (Language of Math #112)
Factoring Complex Trinomials using the 4-Step Method, Part 1 to 4 : Factoring Polynomials, Part 9 to 12 (The Language of Mathematics IIIb #106-109)
Table of Contents: The Language of Mathematics
Complex Trinomials Part 1 of 4, 4-Step Method (Language of Math #106)
Complex Trinomials Part 2 of 4, 4-Step Method (Language of Math #107)
Complex Trinomials Part 3 of 4, 4-Step Method (Language of Math #108)
Complex Trinomials Part 4 of 4, 4-Step Method (Language of Math #109)
Wednesday, February 15, 2012
Difference of Squares: Solving Equations, a Graphical Representation, Part 1 to 3 (The Language of Mathematics IIIb #102-104)
Since we're on the topic of the "Difference of Squares", I thought it would be worthwhile to use two different methods to delve deeper into the meaning of what it means to solve an equation, both algebraically and graphically.
Difference of Squares: Solving Equations, a Graphical Representation Part 1 (#102)
Difference of Squares: Solving Equations, a Graphical Representation Part 2 (#103)
Difference of Squares: Solving Equations, a Graphical Representation Part 3 (#104)
Tuesday, February 14, 2012
Difference of Squares, Part 1 to 3: Factoring Polynomials, Part 6 to 8 (Language of Mathematics IIIb #99-101)
Table of Contents: The Language of Mathematics
Difference of Squares: Part 1 (Language of Mathematics #99)
Difference of Squares: Part 2 (Language of Mathematics #100)
Difference of Squares: Part 3 (Language of Mathematics #101)
Why We Factor: Introduction to Factoring Polynomials (Language of Mathematics IIIb #105)
Table of Contents: The Language of Mathematics
Lyrics to "El Guillatún" by Horeja, the the track sampled in this video:
English:
Millelche is sad with the tempest
The wheat lies down on the mud
The indians resolve after crying
Talk with Isidro, with God and Saint John
With God and St. John
With God and St. John
The machi walks for the guillatún
Chamal and revoso, trailonco and cultrúm
And even the sick ones of her machitún
Enlarge the rows of that guillatún
Of that guillatún, of that guillatún
The rain that falls and falls again
The indians look at it without knowing what to do
They tear out their hair, they break their feet
Because the harvest is going going to get ruined
It's going to get ruined
The indians gather at a large yard
With the instruments a song broke out
The machi repeats the word sun
And the echo of the field increases her voice
Increases her voice
The king of heavens heard well
Scares away the winds to another region
Undid the clouds and then lied down
The indians cover it with a prayer
With a prayer
The smell of meat and muday can be felt
Cinnamon, orange, bark of quillay
The festival ends with dawn
They saved the chant, the dance and the bread
The dance and the bread, the dance and the bread.
Spanish:
Millelche está triste con el temporal
los trigos se acuestan en este barrial
los indios resuelven después de llorar
hablar con Isidro, con Dios y San Juan.
Camina la machi para el guillatún
chamal y revoso, trailonco y cultrúm,
y hasta los enfermos de su machitún
aumentan las filas de aquel guillatún,
de aquel guillatún, de aquel guillatún.
La lluvia que cae y vuelve a caer
los indios la miran sin hallar qué hacer
se arrancan el pelo, se rompen los pies,
porque las cosechas se van a perder,
se van perder.
Se juntan los indios en una corralón
con los instrumentos rompió una canción,
la machi repite la palabra sol
y el eco del campo le sube la voz, le sube la voz.
El rey de los cielos muy bien escuchó
remonta los vientos para otra región,
deshizo las nubes, después se acostó,
Los indios la cubren con una oración,
con una oración.
Se siente el perfume de carne y muday
canelo, naranjo, corteza e' quillay,
termina la fiesta con el aclarar,
guardaron el canto, el baile y el pan,
el baile y el pan, el baile y el pan.
Music by Horeja
www.facebook.com/horeja
Lyrics to "El Guillatún" by Horeja, the the track sampled in this video:
English:
Millelche is sad with the tempest
The wheat lies down on the mud
The indians resolve after crying
Talk with Isidro, with God and Saint John
With God and St. John
With God and St. John
The machi walks for the guillatún
Chamal and revoso, trailonco and cultrúm
And even the sick ones of her machitún
Enlarge the rows of that guillatún
Of that guillatún, of that guillatún
The rain that falls and falls again
The indians look at it without knowing what to do
They tear out their hair, they break their feet
Because the harvest is going going to get ruined
It's going to get ruined
The indians gather at a large yard
With the instruments a song broke out
The machi repeats the word sun
And the echo of the field increases her voice
Increases her voice
The king of heavens heard well
Scares away the winds to another region
Undid the clouds and then lied down
The indians cover it with a prayer
With a prayer
The smell of meat and muday can be felt
Cinnamon, orange, bark of quillay
The festival ends with dawn
They saved the chant, the dance and the bread
The dance and the bread, the dance and the bread.
Spanish:
Millelche está triste con el temporal
los trigos se acuestan en este barrial
los indios resuelven después de llorar
hablar con Isidro, con Dios y San Juan.
Camina la machi para el guillatún
chamal y revoso, trailonco y cultrúm,
y hasta los enfermos de su machitún
aumentan las filas de aquel guillatún,
de aquel guillatún, de aquel guillatún.
La lluvia que cae y vuelve a caer
los indios la miran sin hallar qué hacer
se arrancan el pelo, se rompen los pies,
porque las cosechas se van a perder,
se van perder.
Se juntan los indios en una corralón
con los instrumentos rompió una canción,
la machi repite la palabra sol
y el eco del campo le sube la voz, le sube la voz.
El rey de los cielos muy bien escuchó
remonta los vientos para otra región,
deshizo las nubes, después se acostó,
Los indios la cubren con una oración,
con una oración.
Se siente el perfume de carne y muday
canelo, naranjo, corteza e' quillay,
termina la fiesta con el aclarar,
guardaron el canto, el baile y el pan,
el baile y el pan, el baile y el pan.
Monday, February 13, 2012
Friday, February 10, 2012
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.
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):
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.
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 to Series I
- Section 2: The Real Number Set
- Section 3: Zero and Infinity
- Section 4: Basic Operations
- Section 5: Prime Numbers
- Section 6: Fractions
- Section 7: Trigonometry
- Section 8: Basic Geometry
- Section 9: Coordinate Geometry
- Section 10: Proofs
- Section 11: Why a Negative and a Negative Makes a Positive
Series II
- Section 1: Exponents and Radicals
- Section 2: Book Recommendations
Series IIIa
- Section 1: Summary of Series I and II, and an Introduction to Series IIIa
- Section 2: Black Holes and Elementary Particles
- Section 3: Techniques for Solving Equations
- Section 4: Solving Equations and Checking Solutions, Examples and Methods
- Section 5: Solving Quadratic Equations: Factoring Techniques
- Section 6: Introduction to Polynomial Functions
Series IIIb
- Section 1: Introduction to Factoring Polynomials
- Section 2: Difference of Squares
- Section 3: Complex Trinomials: Factoring using the 4-Step Method
- Section 4: The Quadratic Formula and The Discriminant
- Section 5: The Let Statement, and Substitution (with Quadratic Formula)
- Section 6: Synthetic Division, Polynomial Long Division, and The Division Statement
- Section 7: The Remainder Theorem and The Factor Theorem
- Section 8: Why Math is Important
- Section 9: Study Tips
Series IVa
- Section 1: Units and Systems
- Section 2: Ratios and Fractions
- Section 3: Units and Ratios
- Section 4: Unit Conversion
Series IVb
- Section 1: Infinity (My Two Infinities)
- Section ??: Miscellaneous
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
Wednesday, February 8, 2012
Saturday, February 4, 2012
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