Friday, October 19, 2012

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.

Monday, April 30, 2012

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

      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

    Series II

      Section 1: Exponents and 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.

    Friday, April 20, 2012

    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.

    Sunday, April 15, 2012

    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).

    Friday, April 13, 2012

    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

    II. Personal Finance

      Section 1: Time Management

    III. Food and Farming

      Section 1: Community Supported Agriculture, CSA

    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

    IX. Film and Music (Sight and Sound)

        - In the works

    X. Science and Technology

      Biology:
      Physics:

    XI. Construction and Engineering

        - In the works

    XII. Miscellaneous


    Monday, April 9, 2012

    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


      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


    Image of Tree Menu


    From Series I Tree Menu - The Language of Mathematics

    Thursday, April 5, 2012

    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)



    Thursday, March 22, 2012

    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)



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

    Table of Contents: The Language of Mathematics

    Wednesday, March 21, 2012

    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

      Section 1: Exponents and Radicals
      Section 2: Book Recommendations


    Image of Tree Menu

    From Series II Tree Menu - The Language of Mathematics

    Tuesday, March 6, 2012

    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

      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


    Image of Tree Menu

    From Series IIIa Tree Menu - The Language of Mathematics

    Monday, March 5, 2012

    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 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



    Sunday, March 4, 2012

    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)



    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 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 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.