Syllabus

Instructors:

Professor: Alexander Strang (alexstrang@berkeley.edu)
TAs: Andrew Thein, Nathan Peng Kuo, Tara Kulshrestha, Wayland La, William Lee
Tutors: Henry Liev, Jake Dalton Thiry, Tiffany Yu, Yvonne Ye

Contact:

Email: data89@berkeley.edu
Ed: https://edstem.org/us/courses/92899/discussion

All regular course communication will use Ed. You may post there privately. For urgent or personal issues (e.g. exceptions or accommodations) please use the course email.

Office Hours:

Professor: Tuesdays 2:00 - 4:00 pm, by reservation a week in advance from the course calendar for up to five students. In Evans 305.
TA: Monday noon - 5:00 pm, Friday 10:00 am - noon in Warren.

Class Outline:

Course Description:

How do we reason about data using mathematical models of random events? This course will complement the computational and conceptual toolkit students develop in Data 8. Students will build mathematical and graphical problem-solving skills needed for upper-division courses in data science. The course will rehearse key analytic competencies commonly demanded in probability applications including techniques of summation and integration, function approximation, visualization, and optimization, while offering a focused introduction to essential multivariate concepts explored in intermediate and advanced data science courses. It will fold this practice into a narrative motivated by the introduction to reasoning with uncertainty provided by Data 8, while also providing a basic foundation in probability.

Course Objectives:

Data 89 will introduce students to analytic and graphical methods that will be further developed in the upper-division data science courses. The course will develop a focused selection of calculus topics, in single and multiple variables, as motivated by a probability context. The probability narrative is tailored to bridge students’ prerequisite inferential experience (Data 8 or Stat 20) to the probability competencies expected in their upper division courses (equivalents to Data 100, Data 140, Data 102). The course will emphasize four key skills: computing chances, calculating expectations, finding critical points, and visualizing functions in univariate and multivariate contexts. The course will help students translate between analytical conclusions, graphical reasoning, and qualitative reasoning by highlighting the parametric dependency of answers to problem context. Practicing these links will help students sharpen their mathematical intuition.

Student Learning Outcomes:

By the end of the course students will be able to:

Name and apply the rudiments of probability (axioms and algebra rules)
Reason with multiple random variables (relate joint, marginal, and conditional distributions; define dependence and independence; measure association through covariance and correlation)
Identify, manipulate, and transform the distributions of random variables (identify distributions from generating processes, distinguish density from mass, compute the distribution of combinations and functions of random variables)
Define expectations and relate to concentration phenomena
Compute chances and expectations from distributions by summation and integration, with an emphasis on techniques of summation and integration (single and multiple on finite and infinite domains; close infinite series)
Visualize functions of single and multiple variables and understand parametric dependency (monotonicity, convexity, comparison of asymptotic rates, linearization, Taylor approximation, relate gradients to level sets)
Find conditional and unconditional maxima of functions of single and multiple variables (identify modes of distributions and M-estimators; use Lagrange multipliers)
Reason with and change coordinates (Cartesian coordinates, vector spaces, polar coordinates, and symmetries)

A topical calendar is available here.

Prerequisites:

Fluency with calculus 1. Satisfied by:

Math 51/1A, N1A, 16A, or 10A. We recommend Math 51/1A.

Introduction to inferential reasoning and thinking with uncertainty. Satisfied by:

Data 8 or Stat 20

Experience working with Jupyter notebooks and Python programming using the datascience module. Satisfied by:

Data 8 or CS 61A or Data 88C. We recommend Data 8.

Class Procedure:

Meeting Times:

Lecture: Tuesday/Thursday 11:00 am - 12:30 pm, Li Ka Shing 245

Discussion: Wednesdays, 10:00 am - 3:00 pm, by section.

Materials (Textbook):

The course will use an online, course-specific text posted as course notes.

Outside Resources:

Calculus: Early Transcendentals by James Stewart
Data 88S Textbook by Ani Adhikari

Announcements and Communication:

All announcements will be posted on Ed. Regular course communication will happen there. If you need to contact us directly regarding an urgent or individual issue, please email us at data89@berkeley.edu. Please use this email for all course related emails that can be addressed by the course staff. Please email before posting privately on Ed.

WeI do not promise to answer communications outside of regular work hours, so please try to make sure you send your messages with appropriate lead time.

Policies:

Lecture Attendance:

Attendance is expected and encouraged, but will not be tracked. Lecture recordings will not be released automatically, and will be delivered only on request. We may provide worksheets in some lectures to help you organize your notes. Otherwise, we expect all students to attend with notetaking materials (pen and paper or notebook, ipad). We will only allow typed notes (laptop use) on request.

Recording Policy:

Based on our experience in many classes, we strongly believe that the virtue of lecture is the live, regular, segmented format. We will do our best to make live lecture worth attending. It is very hard to learn any college level subject without regular, incremental practice. Lecture should not be crammed at 1.5x speed, nor back to back to back.

We also strongly encourage you to make friends in class and to share notes. All of the lecture content is also available in course reading. If you do miss a class, and are unsure what to read, ask the course staff. All worksheets will be posted at the time of lecture.

Discussion Attendance:

Discussion attendance is expected. You must attend your assigned section. Discussion worksheets will be collected to track course participation and will graded for completion and attendance. All discussion worksheets will be designed to help you complete your HW.

Technology Use in Lecture:

Please refrain from using laptops during class. You may take notes on a tablet, or bring a notebook and write in it!

If you need or want to use a laptop for legitimate purposes, you will be given the opportunity to submit a petition to use your laptop. To request an exemption to the policy, complete laptop exemption form by the Thursday at class time, on the first week of class.

If you are a DSP student with note-taking accomodations please contact us so we can arrange a note taker for you.

Late Work Policy:

We will not accept late work without advance notice and only in clearly extenuating circumstances. Please make an effort to submit assignments on time, before the Gradescope deadline. Email us if you face valid extenuating circumstances and cannot submit on time. Do not expect an extension unless it is explicitly granted. Note that, by design, the grading policy allows HW and discussion drops without penalty. We will not grant late submission until you have missed at least 2 HW submissions. Since assignments are graded on completion, you are welcome to submit partially finished work to document your participation.

LLM and AI use:

We can’t police the use of AI for HW, so we won’t. Moreover, some uses of AI are productive. So you are welcome to use it.

However, we strongly advise against using it as a crutch, and suggest you attempt problems on your own first, or with peers. You cannot learn to problem solve by reading solutions. It is your responsibility to take ownership of your practice and study. If you do not master the problems presented in the HW, you will not be prepared for the quizzes. If you do, then you will be well prepared and will not need to spend much additional time studying.

If you find you are relying on AI, or complete the HW but struggle on quizzes, come talk to us so we can help you work out a plan to practice more productively.

Accommodations and Communication:

We cannot address all issues, particularly on late notice. However, we will do our best to accommodate your needs. Legitimate issues arise, and you are welcome to advocate for your benefit. The earlier we are aware of issues, the better we can respond. We are happy to provide appropriate accommodations as long as they are fair to the class.

Accommodations here do not refer to DSP accommodations, but rather extenuating circumstances on particular assignments. All DSP accommodations will be provided as is the student’s right by law.

Activities and Assignments:

The following course components will be designed to 1. [exposit] provide exposition and reference, 2. [construct] provide hands-on practice, 3. [form] evaluate proficiency, 4. [sum] evaluate mastery.

1. Reading: Readings will be suggested for each lecture in a weekly guide posted in advance. Each reading will be associated with a discussion thread on Ed for questions. We strongly suggest that you complete the reading before lecture and before attempting practice problems.

2.a Discussion Problems: Each discussion section will be used to solve practice problems. Discussion sessions will mix guided practice with group work. Discussion worksheets will be due at the end of discussion and checked for completion. They will be returned in the next session.

2.b Homework Assignments: Homework will be assigned weekly. Homework should be submitted to Gradescope. Homework will be graded on a completion basis. Homework will be due at 5 pm on Monday the week after posting. Discussion problems will be selected to help you complete your HW.

3. Quizzes: You will complete 7 quizzes over the semester. Quizzes will be held on Wednesdays and Thursdays through the Computer Based Testing Facility (CBTF). Students will sign up for their own quiz slot with the CBTF. We will contact you with directions for quiz scheduling. Quizzes will focus on problems adapted from HW.

4. Exams: As below. Written exams (2 midterms, 1 cumulative final) will evaluate mastery of the course material.

Exams and Final:

Exams: The course will include two midterm exams (non-cumulative) and one cumulative final. They will be held outside of class. The midterm exams will not be cumulative, however, the skills taught in the beginning of the course will be needed for tasks demanded at the end. Midterms will run for 110 minutes. The final will run for 170 minutes.

The exams will be administered on Mondays from 7:00 - 9:00 pm of weeks 6 and 12 (spring break inclusive). The exam dates are Monday February 23rd and Monday April 6th.

Clobber Policy: If we are given advance notice that you must miss an exam, then we may grant a clobber. If a student is excused from a midterm exam, their exam score will be estimated via regression at the end of the course from their final exam score in a way that does not help or hurt their final grade on average. This method, which assigns them the average score on the missed exam among people who received the same or very similar scores on the final, takes into account variability in exam difficulty.

Final: The final exam will be a cumulative written exam held outside of class. The final exam will be Thurs, 5/14/26 from 8-11 am.

Grades:

Grade Breakdown:

Per the division of assignment roles outlined above, your grade will not be based on a weighted average of components. Instead, you need to participate (i.e., do the work), demonstrate proficiency across most topics (i.e., perform sufficiently well on most quizzes), and show mastery in the exams (weighted to emphasize your best exam).

Mechanism: Letter grades will be assigned via the standard scale, excepting specific adjustments (see below). Grades will be computed as follows:

Participation and Effort (Discussion + Homework): Completion percentage for discussion worksheets and HW, weighted 60% HW completion average, 40% discussion participation average.
- Your final grade will be restricted to lie in specific letter bins conditional on the fraction of the assigned materials you complete. These bins are:
  - If you complete >= 80% ……….. then your letter grade will be between [C+ and A+]
  - If you complete [70%, 80%] …… then your letter grade will be between [D+ and A]
  - If you complete [60%, 70%] …… then your letter grade will be between [F and B+]
  - If you complete [40%, 60%] …… then your letter grade will be between [F and C]
  - You must submit at least 40% of the course work to pass.
- All homework must be submitted on time barring DSP extensions.
- We will not drop any HW or discussion, though, with at least 12 HW and discussion, you may miss 2 HW and 2 discussions while maintaining over 80% completion.
- Homework will be graded on completion, and should be treated as practice problems for your quizzes. All discussion worksheets will be designed to help you complete your homework. Problems that are eligible for completion grading will be marked. Discussion worksheets need not be fully completed to receive full credit, as not all sections may progress as far during their 50 minute block.
Proficiency (quizzes):
- Your final grade will be restricted to lie in specific letter bins conditional on your quiz average. These bins are:
  - [80% to 100%] quiz average ……. then your letter grade will be in [B and A+]
  - [75% to 80%] quiz average ..…… then your letter grade will be in [B- and A+]
  - [70% to 75%] quiz average ..…… then your letter grade will be in [C+ and A]
  - [65% to 70%] quiz average ..…… then your letter grade will be in [C and A-]
  - [60% to 65%] quiz average ..…… then your letter grade will be in [C- and B+]
  - [55% to 60%] quiz average ..…… then your letter grade will be in [D+ and B]
  - [50% to 55%] quiz average ..…… then your letter grade will be in [D and B-]
  - [45% to 50%] quiz average ..…… then your letter grade will be in [D- and C+]
  - You must earn at least a 45% quiz average to pass the class.
- We will outline the scope for each quiz a week in advance.
- Every student who attempts a quiz and receives less than an 90% after the is eligible for a retake. Please do not register for a retake if you earned more than an 90% on your first attempt. By the scheme described above, quiz averages above an 90% all earn the same final grade bracket.
- If you retake a quiz, then your quiz grade will be set to the better of your two attempts, capped at 90% to respect retake eligibility. Students who miss a quiz and communicate with staff may be granted eligibility for the retake.
- Students who miss the original quiz without explanation are not eligible for retakes. Students who miss for an excused reason, may be granted eligibility for the retake. In this case, their retake score is not bounded above by an 90%.
- Retakes will be similar but not identical to the original quiz. Watch for directions on scope and suggestions for study. Problems will be semi-randomized.
- A quiz may be dropped in extenuating circumstances. Do not assume a drop applies unless granted.
Mastery (exam): Your exam average will be computed with weights: 50% to your final, 35% to your better midterm, and 15% to your worse midterm.

Final Grade:

Your grade will equal your exam average, floored at the larger of the two letter grade floors set by participation and proficiency, and bounded above by the smaller of the two letter grade caps set by participation and proficiency.

You must score higher than a 50% on at least one exam to pass the course. Any student who scores less than a 50% on all three exams will fail the course. If you are concerned, after the first or second exam, that you are not prepared to pass the course, come talk to us.