Why the abstraction of mathematics is so fundamental

250,907 views

Where did the word "Algebra" and its underlying ideas come from

67,092 views

The general idea behind the word 'abstract'

43,865 views

Bridging algebra and geometry. What makes linear equations so linear.

39,254 views

Introduction and examples of variables, expressions and equations

117,293 views

Introduction to basic algebraic equations of the form Ax=B

1,184,242 views

slightly more complicated equations

474,070 views

Equations with the variable on both sides.

337,930 views

Solving linear equations with variable expressions in the denominators of fractions

543,253 views

Solving linear inequalities.

351,447 views

Graphing linear equations

263,607 views

Getting a feel for slope and y-intercept

248,338 views

Figuring out the slope of a line

275,674 views

Second part of determining the slope of a line

145,919 views

Part 3 of slope

110,416 views

Determining the equation of a line

188,235 views

Using the "Graph of a line" module to understand how a line's graph changes when its slope or y-intercept is changed.

119,879 views

Introduction to averages and algebra problems involving averages.

148,462 views

Adding sums of consecutive integers

132,092 views

Taking a percentage of a number.

207,845 views

Growing a quantity by a percentage

108,288 views

Finding the full price when you know the discount price

85,643 views

Slightly harder percent problems

87,050 views

systems of equations

146,574 views

What a ratio is. Simple ratio problems.

148,754 views

A slightly more involved ratio problem with algebra

72,202 views

More advance ratio problem with algebra.

51,672 views

An alternate solution to the advanced ratio problem in the last video.

30,063 views

Basic ratio problems. (from KhanAcademy.org)

117,669 views

More advanced ratio problems

62,176 views

Age word problems

158,431 views

Second set of age word problems

74,284 views

Part 3 of the presentation on age word problems

73,889 views

(Ax+By)(Ax+By)

87,718 views

factoring quadratics

168,921 views

Introduction to i and imaginary numbers

58,657 views

Calculating i raised to arbitrarily high exponents

38,314 views

i as the principal square root of -1

32,171 views

Introduction to complex numbers. Adding, subtracting and multiplying complex numbers.

254,407 views

Dividing complex numbers. Complex conjugates.

143,665 views

Introduction to using the quadratic equation to solve 2nd degree polynomials

189,926 views

2 more examples of solving equations using the quadratic equation

129,132 views

Solving a quadratic by completing the square.

220,484 views

Deriving the quadratic formula by completing the square.

106,678 views

Solving quadratic inequalities using factoring

94,043 views

How to solve a quadratic inequality. Visual intuition of what a quadratic inequality means.

64,784 views

An introduction to functions.

274,548 views

More examples of solving function problems

198,301 views

Even more examples of function exercises. Introduction of a graph as definition of a function.

114,209 views

An example of a functions problem submitted by a youtube viewer

84,394 views

Figuring out the domain of a function

187,666 views

Proof of the logarithm property: log a + log b = log ab

113,657 views

Proofs of the logarithm properties: A(log B) = log (B^A) and log A - log B = log (A/B)

58,197 views

Proof of the logarithm property log_a (B) = (log_x (B))/(log_x (A))

38,492 views

Dividing one polynomial into another

77,157 views

What are conic sections and why are they called "conic sections"?

130,275 views

Introduction to the Circle

77,906 views

Introduction to the ellipse.

82,514 views

Introduction to the hyperbola

76,760 views

Continuation of the intro to hyperbolas

42,086 views

Part 3 of the intro to hyperbolas

35,249 views

Part 1 of identifying and graphic conic sections

49,393 views

Part 2 of identifying and graphing conic sections

28,731 views

Let's identify (and graph) a couple of more conics!

27,013 views

Calculating the foci (or focuses) of an Ellipse.

65,693 views

Introduction to the foci (focuses) of a hyperbola

41,439 views

Proof of the hyperbola foci formula

23,143 views

Introduction to partial fraction expansion

129,025 views

A more complex problem

65,434 views

Dealing with repeated factors

46,272 views

Parabola as the locus of all points equidistant from a point and a line

90,918 views

Finding the focus and directrix of a parabola

42,248 views

Algebra word problem involving two bicycles passing each other.

38,319 views

Fun algebra word problem involving a train passing a bike.

21,116 views

Trains passing at different rates.

36,999 views

3 people overtaking each other at different rates

24,499 views

Fun word problem that is almost a brain teaser.

28,268 views

Not quite a brain teaser but fun nonetheless!

31,181 views

Two ways to solve a rational inequality (or an inequality involving a fractional expression)

40,081 views

Slightly harder rational inequality problem

21,685 views

Finding the coefficients of a third degree polynomial given 2 roots and the y-intercept

26,000 views

Figuring out the formula for fixed mortgage payments using the sum of a geometric series

23,053 views

Introduction to Function Inverses

73,503 views

Function Inverse Example 1

73,207 views

Function Inverses Example 2

36,424 views

Function Inverses Example 3

32,505 views

Understanding direct and inverse variation

31,039 views

Examples of variables varying directly and inversely

15,005 views

Even and odd functions

28,885 views

A possible reason why even functions are called "even" and odd functions are called "odd"

13,842 views

Getting comfortable with evaluating newly defined function operators

24,112 views

Proving an expression for the sum of all positive integers up to and including n by induction

36,099 views

Another way to prove the expression for the sum of all positive integers up to and including n

8,100 views

Setting up proportions to solve a word problem

29,073 views

Examples of how to convert basic repeating decimals to fractions

30,130 views

Converting more interesting repeating decimals to fractions

18,367 views