﻿ JRD: Math 240

2021 March 18,

# Math 240: Probability

Carleton College, Winter 2021, Joshua R. Davis, , Anderson 238, x4095

## Introduction

Probability is a beautiful subject of pure mathematics. It has applications to many other disciplines: statistics, physics, computer science, finance, etc. (And there's gambling.)

This is a first course in probability. Approximately half of the course is discrete and the other half continuous. We do some simulations and other exercises using the statistics software R. The prerequisites are Math 120 or Math 211. Talk to me if you are concerned about your background.

The course materials are

• Introduction to Probability by Blitzstein and Hwang, 2nd edition. This text is used in many, but not all, sections of Math 240 at Carleton.
• Classwork lists many of the problems that we study in class.
• R Instructions help you run R/RStudio either in a web browser or on your own computer.
• Here are the exams from this term.
• Here are the exams from my fall 2019 version of this course, with quartiles (75th, 50th, and 25th percentiles).
• Here are the exams from my fall 2018 version of this course.

Because the COVID-19 pandemic makes things unpredictable, the details of the course are subject to revision. We all need to be empathetic and flexible. Anyway, here is my tentative plan.

Our class meets in Zoom during period 3A (MonWed 11:30-12:40, Fri 11:10-12:10). This synchronous lecture/discussion is recorded, so that students in distant time zones (for whom Carleton's morning is the middle of the night) can watch it asynchronously. All other students are expected to participate synchronously.

Office hours are held in Zoom; see the Moodle page for the Zoom link. The official times are Sun 4:15-5:00 PM, Mon 7:00-7:45 AM, Tue 7:45-8:30 PM, Thu 2:10-2:50 PM. Additionally, my CS 311 office hours are Sun 3:30-4:15 PM, Tue 7:00-7:45 PM, Thu 1:30-2:10 PM. I will talk to you in CS 311 office hours, if there are no CS 311 students waiting. No appointment is needed for office hours; just drop in. If you cannot attend office hours, then e-mail me to ask for an appointment, listing several times at which we could meet. I teach 1A and 3A, so don't bother trying those.

## Responsibilities

The following elements contribute to your numerical grade. There is no logistical reason to limit the exams to 70 minutes. My intent is to give you enough time that you can relax, but not so much time that you neglect to study before the exam.

• Participation (5%): If class time is the middle of the night for you, then you are not expected to attend class synchronously; we make other arrangements. Otherwise, you are expected to attend every class meeting promptly, and to participate in the discussion and group work. You can make up for a deficiency in class participation by talking with me in office hours or generally demonstrating effort and interest.
• Homework (5%): Assignments are mostly problem sets. Occasionally you are asked to do some calculations in R. Although homework itself counts for not much of your grade, it has a huge effect on your exams.
• Exam A (30%): The first exam occurs about 1/3 of the way through the term.
• Exam B (30%): The second exam is given about 2/3 of the way through the term. It is cumulative but focused on recent material.
• Exam C (30%): The final exam is given at the end of the course. It is cumulative but focused on recent material.

Numerical grades are converted to letter grades only at the end of the term. There are no predetermined percentages (90%, 80%, 70%, etc.) required for specific grades (A, B, C, etc.), because I cannot write problems that are so precisely and reliably tuned. Instead, I assign letter grades by comparing students' scores to the course goals. Roughly speaking, a student who meets most of the goals earns a B. A student who meets almost all goals — and sometimes exceeds them — earns an A. A student who demonstrates effort but meets only a few of the goals earns a C. Students, for whom I have insufficient evidence of learning and effort, might earn grades below C.

An advantage of this system is that students are not in competition with each other. Also, students don't suffer when I accidentally write a difficult exam. The disadvantage is that you cannot compute your own grade. Send me e-mail, if you want me to estimate your current grade for you.

The College's accreditation says that a 6-credit course is 150 hours of work. That's about 15 hours per week or 5 hours per class meeting. Those 5 hours break down into about 1 hour for class itself and 4 hours for homework, reading, studying, etc. If you find yourself spending much more time than this, then talk to me.

## Standards for Work

On homework, you are encouraged to figure out the problems with other students. However, you should always write/type your solutions individually, in your own words. You may not copy someone else's work or allow them to copy yours. Presenting someone else's work as your own is an act of academic dishonesty. The College requires me to report you, if I suspect that you have not upheld its Academic Integrity standards.

Writing is not just for English and history majors. Written and oral communication skills are essential to every academic discipline and are highly prized by employers. In this course, your written work is evaluated both for correctness and for presentation.

Homework is assigned nearly every day, and you are expected to attempt the problems immediately. However, to give you some flexibility, homework is collected only once a week. Depending on time constraints in any given week, perhaps not all of your homework will be graded. In order to ensure full credit, do all of the assigned problems.

## Special Accommodations

During the term, you have one free pass to hand in a week's batch homework late, no questions asked. Simply hand in your late batch when the next batch is due, writing "Late Pass Used" prominently at the top of the late batch. If you need to submit another late batch, then submit it whenever you can, and notify me by e-mail when you do. Depending on the grader's schedule, it may or may not be graded, but I want to know what you're doing.

If some medical condition affects your participation in class or your taking of exams, let me know in the first week of class. You may need to make official arrangements with Disability Services.