Video Series: Introduction to Higher Mathematics

I’ve been searching lately for videos on introduction to higher mathematics and I found one series which is particularly easy to follow and with excellent explanation. The video series is titled Introduction to Higher Mathematics by Bill Shillito.  The series discusses the topics like logic, set theory, relations and functions, modular arithmetic, etc. which are  needed before taking a mathematics  course. I have already watched seven of these videos and I highly recommend them especially for Grade 12  and undergraduate students who are planning to take or already taking  mathematics and computer science courses and related fields.

Below are the titles of the videos in the series..  » Read more

How Probability Can Be Used to Design Games of Chance

One of the origins of of probability as a field in mathematics was solving games of chance. The famous correspondence between Fermat and Pascal in 1654 was one of the earliest accounts on how to use mathematics formally in order to solve a fair game of chance.

In this post, we are going to design a game that will demonstrate the power of probability. We will use probability to create a game that looks like as if it favors the player, while in reality, it favors the casino. Although most casino games actually obviously favor the casino, the game below is a bit more conservative (or should I say ‘deceptive.’)

The dice to be used in the game below is the standard 6-sided die whose number of dots are from 1 to 6. This means that the smallest possible sum is 1 + 1 = 2 and the largest possible sum is 6 + 6 = 12. Below are the instructions on how to play the game.  » Read more

One to One Correspondence and Hilbert’s Grand Hotel

In the Understanding Hilbert’s Grand Hotel, we have discussed the brilliant schemes of a hotel manager in accommodating finite and infinite number of guests in a hotel with infinite number of rooms, where each room was occupied by one guest. In other words, the hotel was fully occupied. In this post, I will explain the mathematics behind these schemes. To be able to understand the explanation, it his highly recommended that you read first the post in the link above.

Finite Number Of Guests

In the Grand Hotel problem, during the first night, a guest arrived. The hotel was full, so there was no room available. However, to accommodate the new guest, the manager requested the guest in Room 1 to move to Room 2, the guest in Room 2 to move to Room 3, the guest in Room 3 to move to room 4 and so on. This means that each guest had to move to the room whose number is 1 higher than the the current room number. This leaves the Room 1 vacant.

Now, how is this possible? » Read more

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