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

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)




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)




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

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 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 (Math #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 maturedthrough 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.

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

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)


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)


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)


Saturday, February 18, 2012

The Division Statement, a Graphical Representation (The Language of Mathematics IIIb #125)

Table of Contents: The Language of Mathematics

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)


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)


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

Monday, February 13, 2012

Why Do 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.

Introduction to Series IIIb (The Language of Mathematics IIIb #98)

Table of Contents: The Language of Mathematics

Recap of Series I, II, and IIIa (The Language of Mathematics IIIb #97)

Table of Contents: The Language of Mathematics

Thursday, February 9, 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.
  • 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

      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



    Introduction to Ratios, and Their Relationship to Fractions (Language of Mathematics IV #147)

    Table of Contents: The Language of Mathematics

    Systems, SI Units, and a Conversion Table for Colored Squares and Triangles (Language of Mathematics IV #146)

    Table of Contents: The Language of Mathematics

    Units - Introduction and Prerequisites (Language of Mathematics IV #145)

    Table of Contents: The Language of Mathematics

    Introduction to Series IV (Language of Mathematics IV #144)

    Table of Contents: The Language of Mathematics

    Wednesday, February 8, 2012