Mathematics 101: Building a Solid Foundation

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

41 students enrolled

What Will I 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.

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 is the target audience?

- 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.

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Curriculum For This Course

30 Lectures

04:14:09
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Lecture 1: Introduction
30 Lectures
04:14:09

Lecture Contents: Instructor Bio, Course Objectives, Course Overview

Preview
03:04

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 2: Numbers & Symbols

09:38

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 3: Working with Numbers

07:13

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 4: The Four Basic Operations - Adding

03:59

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 5: The Four Basic Operations - Subtracting

04:11

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 6: The Four Basic Operations - Multiplying

07:39

This lecture will cover the following:

- using the multiplication tables backwards
- getting comfortable with short division
- using the above to handle long division

Lecture 7: The Four Basic Operations - Dividing

09:01

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 8: What are Primes, Factors, & Multiples?

10:21

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 9: Understanding Negative Numbers

07:17

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

Preview
10:33

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 11: The In-Betweens as Fractions

09:03

This lecture will enable you to:

- add & subtract fractions
- multiply & divide fractions

Lecture 12: The Four Basic Operations on Fractions

10:37

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 13: Powers - Exponential Growth & Decay

06:39

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 14: Scientific Notation & The Power of 10

10:33

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 15: What are Roots & Logarithms?

08:49

This lecture will cover the following:

- understanding percentages, proportions, & ratios
- converting between percentages, decimals, fractions & ratios
- calculating percentages of quantities

Lecture 16: Understanding Percentages, Proportions & Ratios

10:26

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 17: Introducing Algebra, Variables, & Algebraic Expressions

08:56

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 18: Introducing the Concept of Equations

10:43

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 19: Points, Lines, Rays, & Angles

11:17

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 20: A Basic 2-D Shape - The Triangle

07:13

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 21: Another Basic 2-D Shape - The Circle

04:27

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 22: Characteristics of 2-D & 3-D Shapes

06:26

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 23: Understanding Polygons & Polyhedra

10:31

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 24: Introducing a Geometrical Theorem - The Pythagoras

05:24

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 25: Getting Familiar with Trigonometry

10:33

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 26: Geopositioning with Coordinates

07:50

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 27: The Visual & Numerical Relationships - Graphs

12:36

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 28: Making Sense of Data - Statistics

15:01

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 29: What Are the Odds - Probability

06:50

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

Lecture 30: A Picture is Worth... - Graphs & Charts

07:19

About the Instructor