Math History: videos, tutorials and helps

Chapter 1:

converting to Babylonian numbers

Chapter 2:

Method of False Position (example)

Finding the sides of a rectangle given its area and semi-perimeter (example)

Chapter 3:

Proving formulas with triangular numbers (#1) part 1: finding the formula; part 2: proving algebraically; part 3: showing geometrically

Chapter 4:

Solving equations geometrically after the manner of Euclid (problem 2)

Euclid's method for greatest common denominators (problem 3)

Verifying Archimedes propositions about cones and spheres using modern formulas (problem 4)

Video presentation project assignment.

My example and explanation for chapter 5 problem 1. Part 1, Part 2

Chapter 5:

Solving a problem in the manner of Diophantus (problem 1) Part 1, Part 2

Solving a problem in the manner of Brahmagupta (problem 2)

Completing the square in 2 ways: way 1, way 2 (problem 4)

Chapter 6:

Solving some of Alcuin's problems using the method of false position and bar diagrams.

Some hopefully useful background about your Fibonacci number problems part 1, part 2

Chapter 7:

Cardin's process for finding roots of a cubic equation: intro, example 1, example 2

The written out details for the cubic

Chapter 8:

Descartes method for finding tangent slopes: example, more comments (for the general case)

A random youtube video (not mine) on Newton's method of finding roots that looks pretty good.

Chapter 9 helps:

The problem of points

An induction example, used to prove the connection between combinations and Pascal's triangle

Conditional probability

Bernoulli's formula

Chapter 10 helps:

Using the prime factorization to find the factors and the sum of the factors of a whole number in an organized way (pg 462)

Using modular arithmetic to find remainders of powers of numbers. Part 1; Part 2; Part 3

Note: you will get a remainder of 1 by the 6th power for most of the assigned problems. The one exception, is that you need to continue to the eight power of 3 in problem c

Chapter 11:

Not directly helps for the homework, but this is more-or-less my usual lecture about hyperbolic geometry, so if you understand this, it should help make sense of some of the homework problems. Email if there are specific points you get stuck on and need additional help. Part 1, part 2, part 3

Chapter 12:

Countably infinite

The rational numbers are countable

The real numbers are uncountable