This course is a mathematical introduction to probability. It also serves to provide the background knowledge for a mathematical statistics course (Math 3321).

Instructor: Andrew Irwin, airwin@mta.ca, 364-2536, Dunn 209.

Class meets Tuesday and Thursday 8:30 - 9:50 in Dunn 106. Some classes will meet in the Dunn 102 computer lab, as announced in class.

Course information (handouts, homework, solutions, textbooks, computer code, and other material) will be distributed on the course Moodle page.

This course consists of a combination of theory, examples, and computer simulation. By the end of the course you should

- be comfortable performing basic probability calculations
- know about the origin and utility of a range of discrete and continuous probability distributions
- have acquired basic skills for computing with probability and performing simulations with the R software package
- be ready for the mathematical theory and examples to be explored in Math 3321 (Statistics)

Both of our textbooks are available for free in electronic form. Printed versions are available at the campus bookstore.

- Grinstead & Snell. 1998. Introduction to Probability (as a PDF). American Mathematical Society. R code for the textbook is available on the course moodle page.
- W Venables et al. 2012. Introduction to R (as a PDF). Many more resources are at www.r-project.org

I suggest buying a printed copy of Grinstead and Snell, but you may find that the electronic version of Venables et al is as useful as the printed version. Solutions to odd numbered problems are available on the book website.

We will be using the software package R throughout the course: in class, in a few labs, and for homework. R will not appear on the tests or exam as these will be written on paper. The software is installed on the computers in the Dunn 102 lab and is available for free to install on your own computer. I suggest you install R and the additional software Rstudio on your own computer. If you have any problems installing the software, please ask for help.

I have two primary reasons for using this software in our course:

- we will use computations and simulations to investigate probability. Having a concise computer-executable notation to perform calculations quickly and easily is a great benefit. Since we use the computer to perform the calculations, we are not restricted to overly simple examples.
- this software is used by thousands of research labs and corporations around the world and has applications well beyond probability and statistics. I hope you will be able to learn to use the software to solve problems of your own in a wide range of application areas.

The software is very easy to start using and most of the examples we use in this course will be quite simple, encompassing only a few lines of code. Despite the brevity of the code, some careful thought will sometimes be require to understand exactly what the computer is doing. R has many commands and add-on packages and even after many years of use, I am still learning more about it each time I start on a new project. I will show you what you need to know in the class, labs, and on the web page, but there are many more resources available on the web. For example, there are many different introductory tutorials and short video tutorials.

We will follow the main text quite closely. Approximately 5 classes will be held in the Dunn 102 classroom as needed. Each lab will have an associated lab assignment to hand in on moodle. There will also be approximately 6 regular problem sets. Since we meet 26 times and have 2 tests, there will be 19 regular classes.

- Discrete probability (2)
- Continuous probability (2)
- Combinatorics (2)
- Conditional probability (2)
- Famous distributions and densities (2)
- Expectation (2)
- Sums of random variables (1)
- Law of large numbers (1)
- Central limit theorem (2)
- Generating functions (2)

- Homework: 13%
- Computer labs: 7%
- Test 1 on Thursday October 4: 20%
- Test 2 on Thursday November 1: 20%
- Exam: 40%

You may find that there are quite a few formulae to remember, especially for the second test and final exam. To ensure you don't make a mistake simply because you don't remember a particular fact, you may prepare and bring to each test and the exam a **single-sided, 8.5x11 page with handwritten notes**.

Grades will be assigned in the course following the guidelines in the Academic Calendar (section 10.8).

Everyone in the course is expected to adhere to Mount Allison's norms for academic conduct (see the Academic Calendar 10.5). This means no cheating (using unauthorized aids). You are encouraged to discuss homework and lab problems with others in the course and with me, but must write your own solutions for evaluation.

A recent article in Slate summed up the problem with cheating in journalism quite nicely and is analogous to our concerns with academic dishonesty at the university

Plagiarism and fabrication are fundamental betrayals of the reader's trust. With plagiarism, an author tries to convince his audience that he has become conversant in a subject through journalistic research, processed that research, and distilled it by turning it into words on paper. Instead, a plagiarist merely takes someone's thoughts or words and presents them as his own. With fabrication, an author tries to convince his audience of something that isn't true, of an event that never happened, or a quote that was never uttered. Fabrication, like plagiarism, betrays the readerâ€”and betraying the reader is the cardinal sin in journalism.

Some interesting thoughts on the broader questions about trust in society and on computer networks in particular are in this interview with Bruce Schneier

Information here goes beyond the scope of the course, but may be of interest to you.

- Style guide for r
- One approach to testing R code through unit testing
- A gallery of graphs and how to make them in R
- A collection of blogs about R
- A site devoted to searching the web for R resources