SLR 511F: 10 MATHEMATICAL IDEAS EVERYONE SHOULD KNOW and their everyday applications in the real world

COURSE OUTLINE: PROPOSED TOPICS #1-10

1. The far reaching consequences of very simple algebra and algebraic equations.

2. FAMOUS EASY-TO-UNDERSTAND problems

3. The simplest ideas in probability, statitics and finance (gambling, risk management, compound interest, life insurance, futures, etc.)

4. Numbers and their interesting quirks, computer computation

5. Cryptography (e.g. MasterCard security), bar codes, etc.

6. Chaos theory and how it is used

7. The concept of a proof (proof types and false proofs)

8. The mathematics of Social Choice (voting systems, etc.)

9. Geometry and art, topology, GPS, etc.

10. Fractals and Mandelbrot sets

A very brief history will accompany each topic but the emphasis will be on everyday applications. No specialized knowledge is required

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SOME REFERENCES

1. http://cms.math.ca/ Canadian Mathematics Society

2*. http://www.ams.org/mathweb/ Math on the Web, AMS & MAA

3. http://www.univie.ac.at/future.media/moe/einfuehrung.html Maths Online

4. http://www.bbc.co.uk/learning/subjects/maths.shtml BBC math learning resources

5. "50 Mathematical Ideas you really need to know", A. J. Crilly, Quercus, UK

(Chapters $6.00)

6*. "For All Practical Purposes, Mathematical Literacy in Today’s World",

S. Garfunkel, ed., COMAP,Freeman & Co., NY, ISBN: 0 7167 3817 1

(excellent but expensive at Amazon.ca $71.29)

7. "The Story of Mathematics", A. Rooney, Indigo Books (Chapters $5.00)

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SESSION #1. INTRODUCTION and OUTLINE OF THE TOPICS #1-10

TRY these few problems which came out of SESSION #1

PROBLEM 1. (Algebra) Solve 6x − 2 = 1 for x

PROBLEM 2. (Algebra) Solve the SYSTEM OF EQUATIONS 2x − 3y = 0, x + y = 5 for x and y

PROBLEM 3. (Probability) 2 balls are drawn at random from a hat containing 2R and 3W balls. What is the probability of EXACTLY ONE W ball being chosen?

PROBLEM 4. (Probability) Try the Birthday Problem with just 3 people.

PROBLEM 5. Given that every EVEN number can be written as “2n” for some integer n and every ODD number can be written as 2m+1 for some integer m , PROVE the THEOREM that the product of an EVEN and ODD number must be ODD

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