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

John C. Clements, Dalhousie University, SLR Kelowna

email: john.clements@dal.ca

(Is this how you feel about Mathematics? - most do.)

** 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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