Math: Why it Matters

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Math Why it Matters
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Why Math?
Whats the use of all this?
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Math in the News
Unique Team of Mathematicians, Physicians, and
Public Health Specialists Established To Help
Tackle Infectious Diseases, SARS
Spiral Waves Break Hearts New Research Stresses
the Importance of Communication Between Cardiac
Cells
Mathematicians team up with Lockheed Martin to
develop computer tracking systems
Mathematicians solve problems for businesses
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Why Math?

• Mathematics is fundamentally entrenched in the
  world
• It is integral to many different disciplines
• Advanced math is becoming more relevant to
  todays society

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High School Topics
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Fractals
Fractals
- geometrical figures that are generated by
starting with a very simple pattern that
grows through the application of a set of rules
,
Mandelbrot's fractal geometry provides a
mathematical model for many complex forms found
in nature such as shapes of coast lines,
mountains, galaxy clusters, and clouds. Here,
both the trees and the clouds are actual fractals

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Digital Mobility
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Fun Games
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Maths in Real Life

• Fundamental notion in CS Algorithm
• What is an Algorithm?
• Informally a recipe for computing something
• Formally a finite sequence of instructions for
  correctly solving a computational or mathematical
  problem in a finite amount of time
• Examples of algorithms
• Numerical Finding the GCD of two numbers
• Semi-numerical Sorting a deck of cards
• Linguistic Checking and correcting the grammar
  of a text
• Specialized -Rendering a space ninja in a video
  game -Optimizing the price
  of a stock option

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Maths in Real Life

• OK, so wheres the math?
• Algorithms are described in terms of mathematical
  and logical instructions
• Math helps you analyze (and hopefully improve!)
  the running time of your algorithms
• Where do we need fast algorithms?
• Graphics and Games
• E-Commerce
• Aerospace
• Energy

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Undergraduate Topics
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Graduate School Research
Exploring the fourth dimension The Hyperspace
Structures

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Filtering out the Noise
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Filtering Out the Noise
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Optimal Pricing

• Question Why did the person sitting next to you
  in an airplane pay a different price for her
  seat?
• Answer Because airlines apply methodologies
  known as Revenue Management and Pricing
  Optimization

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Optimal Pricing

• The problem Selling the right product to the
  right customer at the right price and the right
  moment
• Used in industries with
• Limited capacity
• Perishable inventory
• High fixed costs and low marginal costs
• That includes airlines, telecoms, rail, car
  rental, hotels, etc

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Optimal Pricing

• Sub-problems and research areas
• Demand estimation (statistics)
• Customer behaviour modelling (econometrics)
• Capacity management (operations research)
• Price and revenue optimization (operations
  research)
• Research perspectives
• Still an open field, no definitive solution yet
• Lots of interest from the industry (funding!)

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Profiles
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Paul Gauthier

• Paul Gauthier

2002 Rank 31 in 40 under 40 richest people
(Fortune Magazine)2001 Rank 19 1999 Rank 21
Wealth 132 million (2002)Age
31Birthplace Halifax, Canada Education B.S.
Dallhousie University (Computer science)
Creator of the Internet search engine The
head and co-founder of one of the world's most
dynamic software firms - The Inktomi, the
products of which are search engine and network
caching systems
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Student Stories
Math

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Alejandro Garcia

• Research Assistant,
• Bank of Canada, Monetary and Financial Modeling
  Division.
• Job Description Conduct research on the
  financial sector and to assist with development
  of monetary policy and financial stability.
  Specifically, gather economic data and create
  models and conduct econometric analysis.
• Education Undergraduate Economics (Universidad
  de los Andes) and Applied Quantitative
  Information Technology Program (Western). Master
  of Economics (Carleton University)

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Alejandro Garcia

• Favourite thing about my job The learning
  environment and the emphasis on research.
• Most Important educational skills Economic
  intuition, from my degree in Economics.
  Computations skills to help me program models,
  linear algebra for econometric analysis and
  calculus to help me understand the solution
  techniques that are used in the types of models
  that my group works with.

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How do I further my education?

• While youre an undergrad
• Workshops
• Seminars
• Research collaborations (Summer internships)
• Graduate Studies

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What can I do after?

• Many Future Options
• Teaching
• Pure Research
• Applied Research
• Implementation (taking applied research and
  getting it to work in real situations)

Mathematicians are everywhere!
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What sort of support is out there?

• MITACS www.mitacs.ca
• PIMS www.pims.math.ca
• CRM www.crm.umontreal.ca
• Fields Institute www.fields.utoronto.ca
• Your local career services office
• Your math department

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Questions?

• Merci Beaucoup pour ton temps!