Mathematics:

A framework for a few or a tool for everyone?

​

Classes for the third age

Teacher: Prof. Angioletta Iavasile

​

**

​

Paris, 27 - 28 June 2012

​

__________________________________________________________________

Math lectures for elderly people given at University of Molise in Campobasso, Italy, from March till May 2012

Goals

1. To promote an aware utilization of computer technologies for people not used to.
2. To show applied math as a simple and useful discipline.

__________________________________________________________________

Topics and goals

From the decimal numeric system to the binary one

​

• To learn how it is possible to use only two digits, 0 and 1, to represent every number.

Implementation:

• Students did practical exercises converting numbers from the decimal system to the binary one and vice versa.
• During lessons, light bulbs were used to represent binary numbers:

​

light off = 0 light on = 1

​

​

Because of its straightforward implementation in digital electronic circuitry, the binary system is used internally by almost all modern computers.

​

The topic is very important to understand how the computer works.

All students were very interested.

__________________________________________________________________

Topics and goals

Prime numbers and computer security

​

• Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
• There are infinitely many primes.
• Primes are used in computer security, such as in public-key cryptography.

​

Example: RSA (Rivest-Shamir-Adleman) algorithm

​

RSA is an algorithm for public-key cryptography, based on the presumed difficulty of factoring large integers. RSA is considered secure: it is believed that only finding the prime numbers of the public key is possible to decrypt the message and factoring a very big number has prohibitive running times.

​

The topic helped to understand the mathematics beneath important computer security techniques.

__________________________________________________________________

Topics and goals

The Fibonacci sequence and the Golden Ratio

​

• The Fibonacci sequence consists in numbers following the integer sequence:� 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …�the first two numbers are 0 and 1, and each subsequent number is the sum of the previous two.
• It relates to the golden ratio: two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.
• Many applications in architecture.

Example: Notre Dame in Paris

​

The golden ratio is found in the design of Notre Dame in Paris. The west façade contains many examples of the golden ratio measures that enhance the harmony of forms, as shown in the next slide.

__________________________________________________________________

​

A Golden Ratio application in architecture

​

The west façade of

Notre Dame in Paris

​

__________________________________________________________________

A picture of the classroom

__________________________________________________________________

Thank you for your attention!

EURelations EEIG

Address: Via Mazzini 129/D - 86100 Campobasso, Italy

Phone and Fax: +39 0874 484804

Email: info@eurelations.eu