Syllabus (public companion)
Orientation and course shape — Blackboard is authoritative for graded specifics
This public page is an orientation companion to the syllabus, not the operational syllabus itself. It describes the shape of the course in qualitative terms. It carries no numeric grade weights, no due dates, and no submission rules. For everything that counts toward your grade — exact weights, deadlines, policies, and submissions — Blackboard (the LMS) is authoritative. If this page and Blackboard ever disagree, follow Blackboard.
Course description
Introduction to Probability is a first course in the mathematics of uncertainty. We develop probability as a language for reasoning when outcomes are not known in advance: how to set up a model of a random situation, how to compute the probabilities of events, how to update those probabilities when evidence arrives, and how to describe the behavior of quantities that vary by chance. The course balances a classical foundation with a Bayesian-friendly emphasis on conditioning and updating, and it uses light computer simulation to check and build intuition for the theory.
Who it is for
This course is aimed at students who have college algebra and at least one semester of calculus. Some exposure to statistics is helpful but not required, and no programming experience is assumed — the simulation work is fully scaffolded. It suits students in mathematics, the sciences, computing, data-related fields, and anyone who wants a principled way to reason about risk, evidence, and chance.
Learning outcomes
By the end of the course, a successful student will be able to:
- Construct sample spaces and assign probabilities, and apply the complement, addition, and multiplication rules correctly.
- Compute conditional probabilities and assess the independence of events.
- Use Bayes’ rule to update a probability from a prior and new evidence, and interpret the result.
- Count outcomes systematically and work with discrete random variables, their probability mass functions, expectations, and variances.
- Work with continuous random variables and densities, and use the standard models — binomial, geometric, Poisson, exponential, and normal.
- Describe joint behavior, dependence, covariance, and correlation for paired random quantities.
- State and apply the law of large numbers and the central limit theorem, and demonstrate both through simulation.
- Build, run, and interpret a small probability simulation in R and Quarto, and document it reproducibly.
Weekly rhythm
The course meets three days a week, and each day has a settled role:
- Monday — concept + checkpoint. We introduce the week’s central idea and close with a short, low-stakes checkpoint to surface where the class stands.
- Wednesday — problem + simulation. We work problems together and, on simulation weeks, run code that checks the theory against generated data.
- Friday — quiz + application. A short quiz consolidates the week, and we apply the idea to a fresh context.
This rhythm is the plan; the authoritative weekly schedule, including any shifts, lives in Blackboard.
Assessment shape (indicative — not a contract)
The table below conveys the relative emphasis of each graded category in qualitative terms only. It is not a grading contract: it carries no percentages and no point values, and the actual weights live in Blackboard.
| Category | Rough emphasis |
|---|---|
| Checkpoints | small |
| Quizzes | small |
| Homework | the largest single category |
| Simulation labs | small |
| Midterm | moderate |
| Project | small |
| Final | moderate |
Read this as a picture of where the weight sits: regular homework is the backbone of the grade, the midterm and final each carry moderate weight, and the many smaller pieces — checkpoints, quizzes, labs, and the project — add up around them. For the exact weighting, consult Blackboard.
Software and reproducibility
We use R (through RStudio or Posit Cloud) and Quarto for the simulation strand. Simulation supports the probability reasoning rather than replacing it: you will use it to confirm hand calculations and to build intuition. Every simulation is written so it can be reproduced — a single Quarto file, a fixed random seed, and recorded session information — so that the same code yields the same result. Setup instructions are on the R · Quarto setup page.
AI use (summary)
Generative AI tools may be used as a study aid — to explain a concept a second way, to help debug your own R code, or to quiz yourself. They are not a substitute for doing the reasoning yourself, and they are prohibited on quizzes and exams.
When you use AI on permitted work, include a brief AI Use Note with three parts:
| Field | What to record |
|---|---|
| Tool | which tool you used |
| Purpose | what you asked it to do |
| Verification | how you checked its output yourself |
The Verification field is load-bearing: AI output is a draft to be checked against the course material and your own work, never an answer to be trusted on sight. The full policy lives in Blackboard.
Materials
You will need:
- Introduction to Probability (Grinstead & Snell) — the free primary text, GNU FDL.
- MIT OpenCourseWare 18.05 — a free supplement (CC BY-NC-SA 4.0), used selectively.
- E. T. Jaynes, Probability Theory: The Logic of Science — optional, cited only for orientation.
- Blackboard (the LMS) — for all graded work, dates, and announcements.
- A scientific calculator for in-class quizzes and the exams.
Where things live
Keep the two homes of the course straight:
- Blackboard (the LMS) is the operational home: graded checkpoints, quizzes, homework, labs, the midterm, the project, the final, all due dates, all submissions, and all grades. It is authoritative.
- This public site is the public notes home: weekly notes, labs as study material, resources, and orientation pages. It is ungraded.
This companion exists to orient you. Whenever a graded specific is at stake — a weight, a deadline, a policy — go to Blackboard, which is authoritative.