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)