Week 1
Introductions, Modelling, and Linear Models

⦿ Wednesday Part 1: Introductions

Introducing the course

The Official Course Outline.

Frequently Asked Questions. A friendlier, "just the facts" companion to the official course outline.

Introducing ourselves

We should also start to get to know each other. It seems only fair that I go first, so here is more than you probably wanted to know about me. (Optional reading. Provided in case you're curious.)

You may not be wondering about me, but I am very interested in who you are. Don't worry I respect your privacy, and won't require you to tell me much about you, but there are a few things it would be helpful to know to teach you. And the more I know about you the better I can support you. So tell me a little bit about yourself and your mathematical experiences by filling out this Start-up Survey on Moodle.

Exercises

First exercise: Send me an email message, fill out a brief survey, and (possibly) buy a calculator. Easy-peasy. The details are here: Exercise set 1.1

⦿ Wednesday Part 2: Mathematical Modelling

Mathematical Modelling: The Process Pencast 3:09|PDF

Problem → Model → Manipulation → Solution → Interpretation

Warm-up Problems Pencast 6:45|PDF

A couple of artificial puzzle problems.

Pet Biscuits Pencast 11:17|PDF

Another puzzle problem, but that will turn out to be "just like" a real-world problem.

Sony's Secret Pencast 8:11|PDF

The real-world problem that is "just like" the puzzle problem above. Model forms are powerful because they are reusable in many domains.

Mathematics is the language of patterns Pencast 19:53|PDF

One definition of mathematics is "the language humans have created for describing patterns". Here we go looking for patterns in lists of numbers. And meet Carl Friedrich Gauss as a boy.

Exercises

Hopefully the material above has warmed up your math muscles. To find out give the problems in Exercise set 1.2 a try and then check your work against the solutions.

These should be review problems drawing on your past mathematical experience, but if you get stuck don't hesitate to email me or see me after class.

⦿ Friday: Linear Models

Examples of linear models Slide Show

You will probably encounter far more linear models than any other kind. They are everywhere! Here are some examples, with a bit of commentary.

Four Forms of Linear Models Pencast 14:41|PDF

You will encounter linear relationships described using 1) the English language (watch for "for every"), 2) tables of number pairs, 3) graphs, and 4) equations. Here's a brief review of these four forms and how to translate between them.

Review: Solving Systems of Equations Pencast 8:40|PDF

Two methods: Substitution and Elimination. Most students have more experience with substitution, but elimination will generalize to working with matrices next week...

Existence and Uniqueness of Solutions (in 2D) Pencast 15:40|PDF

Two big questions: 1) Can a system have more than one solution? 2) Can a system have no solutions?

Solving 3 equations in 3 unknowns Pencast 9:02|PDF

Most students have more experience with substitution, but elimination will generalize to working with matrices next week, so we solve this system using elimination.
Three equations in three unknowns is as many as one ever wants to do by hand. For this size, and definitely for larger systems, a computer is your friend.

Existence and Uniqueness of Solutions in 3D PDF

Exercises

If you're comfortable with the topics above you're ready to try the problems in Exercise set 1.3. Don't forget to check your work against the solutions.

All the exercises in one place

Exercise Set 1.1 (No solutions because they're not those kinds of exercises.)

Exercise Set 1.2: Problems and Solutions.

Exercise Set 1.3: Problems and Solutions.

Assignment

The first assignment is posted. Due by 1 pm next Friday (January 12).

Remember if you get stuck don't hesitate to see me after class or email me.