Mathematics 101: Building a Solid Foundation

Name: Mathematics 101: Building a Solid Foundation
Rating: 4.2 (36 reviews)

Overcome your lingering fear of math with this personal tour guide to clearly lead you through the maze of math skills

Created byGurmeet Grewal

Last updated 4/2016

English

What you'll learn

At the end of my course, you will be able to apply the concepts & techniques learned to work out basic math problems from adding numbers, figuring out that most dreaded value of x, to calculating the odds of Team Go winning the cricket match while helping you get past any lingering fear you may feel toward math in general. So whether you are an adult or a student, or whether you have always been daunted by numbers at work, school, or in everyday life, you won't find a better way of overcoming your nervousness about numbers & learning to enjoy making the most of mathematics.

Course content

1 section • 30 lectures • 4h 14m total length

Lecture 1: Introduction3:04
Lecture Contents: Instructor Bio, Course Objectives, Course Overview
Lecture 2: Numbers & Symbols9:38
This lecture will cover the meaning & use of some of the symbols common in mathematics, their classifications & characteristics, the use of the real number line in visualizing numbers, the four basic operations in mathematics, other symbols used in mathematics, & the three lesser used operations.
Lecture 3: Working with Numbers7:13
This lecture will cover the meaning & use of the place-value grid, writing out numbers in expanded form & in words, rounding numbers & making approximations, & the meaning & use of the concept called the order of operations.
Lecture 4: The Four Basic Operations - Adding3:59
This lecture will cover the following:

getting the handle on adding with simple numbers
understanding the concept of “carrying over” with larger numbers
using shortcuts for adding numbers in your head
Lecture 5: The Four Basic Operations - Subtracting4:11
This lecture will cover the following:

understanding that subtraction is the opposite of addition
understanding what is “borrowing” & how to use it
using shortcuts for subtracting numbers in your head
Lecture 6: The Four Basic Operations - Multiplying7:39
This lecture will cover the following:

understanding the concept of multiplication
using tips to memorize the multiplication tables
getting a handle on multiplying long numbers
Lecture 7: The Four Basic Operations - Dividing9:01
This lecture will cover the following:

using the multiplication tables backwards
getting comfortable with short division
using the above to handle long division
Lecture 8: What are Primes, Factors, & Multiples?10:21
This lecture will cover the following:

understanding prime numbers & why they are so important
being able to tell when one number is divisible by another
knowing how to break a number down into its basic components
finding the Greatest Common Factor (GCF) & the Least Common Multiple (LCM)
quickly checking numbers for divisibility without remainders
Lecture 9: Understanding Negative Numbers7:17
This lesson will help you understand:

what negative numbers mean & how to interpret them
when negative numbers are useful
how to use the “number line” to understand negative numbers
how to carry the four basic operations with negative numbers
Lecture 10: The In-Betweens as Decimals10:33
This lesson will cover the following:

interpreting decimals such as 0.0897
understanding the concept of carrying & borrowing when adding & subtracting decimals
understanding the concept of moving the decimal point when multiplying & dividing
understanding the concept of rounding relative to decimals
Lecture 11: The In-Betweens as Fractions9:03
This lecture will cover the following:

interpreting fractions
being able to tell when two fractions are the same
interpreting top-heavy fractions
converting between fractions & decimals
Lecture 12: The Four Basic Operations on Fractions10:37
This lecture will enable you to:

add & subtract fractions
multiply & divide fractions
Lecture 13: Powers - Exponential Growth & Decay6:39
This lecture will cover the following:

the meaning of powers & the role they play in mathematics
the significance of powers in expressing exponential growth
the mathematics behind powers
Lecture 14: Scientific Notation & The Power of 1010:33
This lecture will cover the following:

the meaning of the power of 10 & the scientific notation
expressing numbers using the power of 10
understanding the metric system of measurement relative to the power of 10
expressing numbers in the standard form
Lecture 15: What are Roots & Logarithms?8:49
This lecture will cover the following:

understanding what roots are & what they are useful for
understanding logarithms & what they actually mean
switching between the language of powers, roots, & logarithms
Lecture 16: Understanding Percentages, Proportions & Ratios10:26
This lecture will cover the following:

understanding percentages, proportions, & ratios
converting between percentages, decimals, fractions & ratios
calculating percentages of quantities
Lecture 17: Introducing Algebra, Variables, & Algebraic Expressions8:56
This lecture will cover the following:

the meaning of letters when they appear in equations & formulas
translating real-life situations into algebraic expressions
using the rules for working with algebra to solve equations
Lecture 18: Introducing the Concept of Equations10:43
This lecture will cover the following:

using variables in equations
understanding what equations are
using the balanced-scale method for solving equations
re-arranging terms in an algebraic equation
understanding the role of the inequality symbol in the validity of algebraic expressions
Lecture 19: Points, Lines, Rays, & Angles11:17
This lecture will cover the following:

understanding the concept of points, lines, & rays in mathematics
classifying, measuring, & drawing angles
what do angles at a point mean
understanding the meaning of opposite angles & their properties
what parallel lines are & the associated Laws of Corresponding & Alternate Angles
Lecture 20: A Basic 2-D Shape - The Triangle7:13
This lecture will cover the following:

identifying the different types of triangles based on their sides & angles
understanding the rationale behind a triangle’s angles
understanding how to calculate a triangle’s area
Lecture 21: Another Basic 2-D Shape - The Circle4:27
This lecture will cover the following :

identifying the parts of a circle & how they are related
understanding what the Greek letter symbol called pi is
learning how to calculate the area of a circle
Lecture 22: Characteristics of 2-D & 3-D Shapes6:26
This lecture will cover the following:

understanding the relationship between length, area, & volume of 2-D & 3-D shapes
learning to calculate the areas & volumes of 2-D & 3-D shapes
understanding the rationale behind the units used for area & volume
Lecture 23: Understanding Polygons & Polyhedra10:31
This lecture will cover the following:

understanding the characteristics & parameters of regular polygons
briefly introducing the world of regular polygons from 3-sided shapes to shapes of 10^100 sides
understanding the meaning of solid geometry
getting acquainted with the only 5 regular polyhedra also known as the Platonic solids
Lecture 24: Introducing a Geometrical Theorem - The Pythagoras5:24
This lecture will cover the following:

understanding the meaning of Pythagoras’ theorem
applying the theorem to work out lengths theoretically
applying the theorem to work out lengths in the real world
understanding the meaning of Pythagorean triples
Lecture 25: Getting Familiar with Trigonometry10:33
This lecture will cover the following:

understanding the meaning of trigonometry
applying trigonometry principles to understand another aspect of triangles
understanding how to apply the correct trigonometric function when faced with a problem
Lecture 26: Geopositioning with Coordinates7:50
This lecture will cover the following:

understanding the meaning of axes on a 2 dimensional plane & 3 dimensional space
understanding the meaning of coordinates
understanding how to calculate distances on a coordinate plane
Lecture 27: The Visual & Numerical Relationships - Graphs12:36
This lecture will cover the following:

how to plot a line on a coordinate plane given two or more points
understanding that a line can be represented as an equation
how to plot a line from a given equation
how to measure the slope of a line
what the generalized equation y = mx+c means relative to a straight line
Lecture 28: Making Sense of Data - Statistics15:01
This lecture will cover the following:

what the two meanings of statistics are
what the difference between qualitative & quantitative data is
what the measures of central tendency are & knowing the difference between them
how outliers can distort the statistics of a data set understanding quartiles & interquartile ranges in interpreting data
Lecture 29: What Are the Odds - Probability6:50
This lecture will cover the following:

what probability is & how it is measured
what it means when the probability or likelihood of an event is given
understanding the properties of two types of outcomes i.e. independent & mutually exclusive outcomes
working out the probabilities of these two outcomes
Lecture 30: A Picture is Worth... - Graphs & Charts7:19
This lecture will cover the following:

what bar graphs & pie charts are
how to interpret bar graphs & pie charts
how to convert raw data into graphs & charts

Requirements

As this course can act as a springboard to intermediate levels, or a refresher for some, a very rudimentary knowledge of mathematics may be necessary, & other than that, there are no prerequisites as it covers the very basics of the subject. A scientific calculator will be needed for some lectures, for example, roots & logarithms, & trigonometry.

Description

For those who get jittery whenever anything faintly related to math is brought up, think that math is difficult, confusing, dull or just plain scary, then this course is your ideal companion. It covers all the basics from the four arithmetical operations, fractions, decimals, to probability & statistics, leading you clearly & surely towards a greater understanding of this fascinating subject. Even apparently daunting concepts are explained simply, with the assistance of useful diagrams, & with a refreshing lack of jargon. It has 30 lectures in video format totaling 4.25 hours. The contents of the lectures are pre-formatted & presented consistently with no delivery pauses, so there is no waiting time involved in writing out a particular concept or problem on a white board which is the norm with many such courses. It starts out with the concept of numbers, then onto the four basic operations of addition, subtraction, multiplication, & division, onto primes, factors, & multiples, negative numbers, fractions, decimals, powers, scientific notation, roots, logarithms, percentages, proportions, ratios, algebra, equations, lines & angles, 2-D & 3-D shapes, polygons & polyhedra, geometry, trigonometry, coordinates, graphs, statistics, probability, & finally to charts. To test your level of understanding of the concepts learned from each lecture, resources in the form of problems for each of the subject-related topics are available in the Question & Answer & Practice makes Perfect downloadable documents. This course is unique in the sense that it starts out with the most fundamental concept, that is numbers, & gradually builds upon each topic so that by the end of Lecture 30, a coherent perspective of the fundamentals of mathematics is formed while helping you get past any aversion you may feel toward the subject in general.

Who this course is for:

The target audience is a student who wants a solid understanding of the basics of mathematics as a springboard to intermediate levels, an adult who wants to improve skills in arithmetic, fractions, decimals, percentages, algebra, geometry, trigonometry, & so on for when he/she has to use math in the real world, & someone who wants a refresher so he/she can help another person (e.g. a sibling or child) understand math. The intention of this course is to rekindle the basic workings of mathematics in your mind, whether you are a high school, college, or university graduate or even a career-minded professional whose mathematical thought processes have declined over the years, with a focus on getting you to confidently depend on your inherent mathematical skills.