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SMS  Enrichment Topics (for Secondary Schools)

  An Introduction to Cryptology (3 hours)
  Combinatorial Games (3 hours)
  Fractals (3 hours)
  A Fun Introduction to Mathematical Modelling with Graphs (3 hour)
  Graph Coloring (3 hours)
  Logical Puzzles (3 hours)
  The Mathematics of Lottery (3 hours)
  The Mathematics of Sudoku (1-3 hours)
  The Power and Pitfalls of Probability Theory (3 hours)
icon  Probability Through Games (3 hours)
icon  What are the Odds? (3 hours)
  Problem Solving (3 hours)
  What Is Mathematics? (1 hour)

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Topic: Combinatorial Games
Duration:

3 hours

Format:

Lecture & hands-on

Description: This is one of our most successful modules in terms of student response. It consists of a series of hands-on games and puzzles. While the students have fun with these games, they learn how certain ideas from combinatorial mathematics – graph theory, tiling, and symmetry -- provide the underlying principles of their solutions.
Topic: An Introduction to Cryptology
Duration:

3 hours

Format:

Lecture & hands-on

Description: This module introduces the students to the art and science of secret codes. Beginning with the mathematical background (modular arithmetic), the students are taught how to encrypt and decrypt messages using the shift, transposition, and affine ciphers. The module concludes with a Cryptology Tour of Singapore in which the students must decrypt the secret messages which will lead them to a tourist attraction in Singapore.

Topic: Fractals
Duration:

3 hours

Format:

Lecture & hands-on

Description: This module introduces students to some of the exciting mathematics behind some of the most stunningly beautiful images in mathematics -- fractals.
The concept of complication (and beauty) arising from infinite iteration of simple operations will be reinforced through the Iterated Function System (IFS). This is an important result of Michael Barnsley and is useful in modeling nature. Students will be able to appreciate its power by using the IFS to model trees, leaves, mountains and etc.

Topic: What Is Mathematics?
Duration:

1 hour

Format:

Lecture

Description: Mathematics has been called “the language of the universe” and “the ultimate testimony to the ingenuity of the human mind”. Yet, most students associate mathematics with dry number/formula crunching or a bag of ad hoc tricks for irksome problems. In this workshop, rather than concentrating on specific mathematical theories or techniques, we will try to take a peek at the nature of mathematics.

Topic: Logical Puzzles
Duration:

3 hours

Format:

Lecture & hands-on

Description: This module gives the students the chance to work in groups to crack some of our mind-boggling logical puzzles. Students will be asked to present their arguments to their peers. These logical puzzles serve to illustrate some problem-solving techniques and also that mentally challenging problems can be fun too.

Topic: Problem Solving
Duration:

3 hours

Format:

Lecture & hands-on

Description: This is one of the most popular modules. Some techniques of problem solving will be introduced, namely using pictures, working backwards and case-by-case analysis. After a preliminary understanding of some examples, students are broken into groups and given different sets of problems to solve.
These problems will reinforce the problem solving techniques covered. Competition is introduced to see which team comes up with all the solutions in the shortest period of time.

Topic: Graph Coloring
Duration:

3 hours

Format:

Lecture & hands-on

Description:

Motivated by the Four Colour Map Problem, the concepts of a graph, its colouring and chromatic number are introduced. While the problem of evaluating the chromatic number of a graph is very difficult in general, an efficient algorithm for finding its upper bound is presented. Applications of colouring to the time-tabling problem and traffic phasing problem are finally mentioned.


Topic: The Mathematics of Sudoku
Duration:

1 or 3 hours

Format:

Lecture (& hands-on)

Description:

Sudoku is a logic puzzle where you are given a 9×9 grid made up of nine 3×3 blocks. The goal is to place the numbers 1 through 9 into the cells in such a way that each row, column and box contains each number exactly once. Some of the cells are given, and this is done in such a way that there is a unique way to fill in the remaining cells. The puzzles can be of varying levels of difficulty. They can be easy enough to appeal to anybody, while a mathematician will immediately be fascinated by the more fiendish puzzles and start thinking about algorithms. Some of the techniques for solving this puzzle will be discussed and participants will solve some puzzles together.


Topic: A Fun Introduction to Mathematical Modelling with Graphs
Duration:

3 hours

Format:

Lecture & hands-on

Description:

The Theory of Graphs dates back to 1736 when the great Swiss Mathematician Leonhard Euler devised an innovative approach to solve the problem involving seven bridges in Konigsberg. Graph theory has come a long way since then. In this workshop, I will give a brief introduction to mathematical modeling using Graphs and demonstrate how several real life and recreational puzzles / problems can be modeled and solved.


Topic: Mathematics of Lottery
Duration:

3 hours

Format:

Lecture & hands-on

Description:

This module introduces the students to critical thinking in daily lives by introducing concepts of probability through the use of lotteries. Using the 4D lottery game and related hands-on exercises, students will learn how probability estimation and some of the common misconceptions in lotteries. The module provides an opportunity for students to learn about mathematics through a relevant contemporary social issue and concurrently diminishes the likelihood of the development of addictive behavior.


Topic: The Power and Pitfalls of Probability Theory
Duration:

3 hours

Format:

Lecture & Discussion

Description:

Probability is an interesting mathematical subject in that it has so many potential applications in real problems. I will show you some successful applications in medicine and surveys as well as some unsuccessful ones, and will teach you some ideas on how to tell them apart in future situations.


Topic: Probability Through Games
Duration:

3 hours

Format:

Lecture & Discussion

Description:

A gambler’s dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Today, probability is a thriving mathematical area and has many potential applications in real problems. In this talk, we give an introduction to important concepts and selected famous problems in probability. Through simple and fun activities, it is hoped that participants will be able to gain insights and appreciation of these problems and concepts.


Topic: What are the Odds?
Duration:

3 hours

Format:

Lecture & hands-on

Description:

The term "odds" is used widely to describe and predict uncertain events. We will look quite carefully at this idea through the more familiar notions of population proportions and probabilities. A variety of examples from epidemiology and sports will be used to illustrate the ideas.