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--- people:kargin:math471_spring2025 [2025/10/18 20:38]
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+++ people:kargin:math471_spring2025 [2026/01/19 13:48] (current)
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-Syllabus
+====== Math 571: Advanced Probability — Spring 2026 ======
+===== Binghamton University =====
-==== Math 471 Advanced Probability. Spring 2026.====
+**Instructor:** Vladislav Kargin \\
-Binghamton University
+**Office:** WH-136 \\
+**Meeting time and location:** TR 8:00–9:30 AM, WH 329 \\
+**Office hours:** TR 10:00–11:00 AM
-  * Instructor: Vladislav Kargin
+----
-  * Office: WH-136
-  * Meeting time and location: TR -- 8:00-9:30AM -- WH 329
-  * Office hours: Wednesday -- 12-1:30pm
-** This course is a 4-credit course, which means that in addition to the scheduled lectures/discussions,
+This course is a 4-credit course, which means that in addition to the scheduled lectures/discussions, students are expected to do at least 9.5 hours of course-related work each week during the semester. This includes things like: completing assigned readings, participating in lab sessions, studying for tests and examinations, preparing written assignments, and other tasks that must be completed to earn credit in the course.
-students are expected to do at least 9.5 hours of course-related work each week during the
-semester. This includes things like: completing assigned readings, participating in lab sessions,
-studying for tests and examinations, preparing written assignments, completing internship or
-clinical placement requirements, and other tasks that must be completed to earn credit in the
-course. **
-=== Prerequisite ===
+----
+===== Prerequisite =====
 Probability Theory (MATH 501)
-=== Description ===
+===== Description =====
+This course is an introduction to the advanced concepts of probability theory. It covers topics such as: Measure theory, Probability spaces, Random variables, Conditional Expectations, Stochastic processes, Martingales, Limit Theorems, Large deviations.
-This course is an introduction to the advanced concepts of probability theory. It covers topics such as: Measure theory, Probability spaces, Random variables, Conditional Expectations, Stochastic processes, Martingales, Limit Theorems, Large deviations
 The course is intended for students who have a strong foundation in probability theory.
+===== Recommended Text =====
+Durrett, //Probability: Theory and Examples//, 5th edition. PDF available at [[https://services.math.duke.edu/~rtd/PTE/PTE5_011119.pdf|PTE]]
-=== Recommended Texts ===
+===== Lecture Notes =====
+Instructor's lecture notes will be provided and posted on Piazza.
-Durrett "Probability: Theory and Examples" 5th edition, pdf available at [[https://services.math.duke.edu/~rtd/PTE/PTE5_011119.pdf|PTE]].
+===== Communication =====
+We will use Piazza ([[http://piazza.com/|piazza.com]]) for communication. All announcements will be sent to the class using Piazza.
+----
+===== Class Structure and Participation =====
-=== Piazza===
+Each class session is divided into two parts:
-We will use Piazza ("http://piazza.com/") for communication. All announcements will be sent to the class using Piazza.
+**Student-led segment (30–45 minutes):** Students take on rotating roles to present and critically examine the day's material.
+**Lecture segment (45–60 minutes):** Instructor extends the material, addresses misconceptions, and covers additional applications.
-=== Homework Policies ===
+==== Roles ====
-Weekly sets. I fully grade two or three problems (announced after submission); the other count for completion. Solutions must be concise (≤1 page/problem) and list the named results used (e.g., “DCT + UI”).
+Each session involves:
-Starting HW2, the solution for these problems must be typed in LaTeX, typeset to pdf and submitted by the due date. 3 late-day tokens total for the term; beyond that late work is not accepted.
-Rubric for a HW problem:
+  * **Presenters (2 students):** One states definitions, notation, and theorem statements; the other outlines the proof and provides an example.
-= correct & clear; 3 = essentially correct (minor gap); 2 = right idea with major gap; 1 = meaningful progress; 0 = off-track. +0.5 exposition bonus possible (capped at 4).
+  * **Skeptics (2 students):** One checks correctness and catches errors; the other proposes counterexamples when assumptions are weakened.
+  * **Scribe (1 student):** Records theorem statements, key proof steps, questions raised, and instructor additions. Notes should NOT include names—they are learning material, not meeting minutes. Submit within 24–48 hours; instructor reviews and shares with everyone.
+  * **Observers (3 students):** Participate in discussion and ask questions; may be called on for examples or perspectives.
- I may invite you to brief board checks on your own solutions; these verify understanding and may adjust the HW score slightly.
+==== Role Assignments ====
-You may discuss ideas, but write your own solutions.
+  * Sunday evening: Instructor announces which pairs are presenters and skeptics for Tuesday and Thursday, and which results will be covered.
+  * Within-pair role assignment: Students decide among themselves or flip a coin at the start of class.
+Students are expected to pre-read the assigned material before each class.
+----
-=== Exam ===
+===== Homework Policies =====
-There will be one in-class midterm (open-book/no-web) and a final take-home exam with a brief (~10-12 minutes) oral follow-up. I will choose one of your solutions and ask a few “why does this step hold? / where does the hypothesis bite?” questions. Final is cumulative.
+Weekly problem sets. I fully grade two or three problems (announced after submission); the others count for completion. Solutions must be concise (≤1 page per problem) and list the named results used (e.g., "DCT + UI").
+**Format:** Starting HW 3, solutions must be typeset in LaTeX and submitted as PDF. Non-LaTeX submissions will be returned without grading.
+**LaTeX resources:** Homework templates will be posted on Overleaf. Students should create a free account at [[https://www.overleaf.com/|Overleaf]].
-=== Grading ===
+**Submission:** Submit via Gradescope as PDF by the due date.
-  * Homework (45%)
-  * Midterm exam (15%)
-  * Final write-up (30%)
-  * Final follow-up (10%)
+**Late policy:** 3 late-day tokens total for the term; beyond that, late work is not accepted.
+**Rubric:**
+  * 4 = correct & clear
+  * 3 = essentially correct (minor gap)
+  * 2 = right idea with major gap
+  * 1 = meaningful progress
+  * 0 = off-track
+  * +0.5 exposition bonus possible (capped at 4)
+I may invite you to brief board checks on your own solutions; these verify understanding and may adjust the HW score slightly.
-/*
+You may discuss ideas, but write your own solutions.
-=== Project ===
-You are supposed to prepare a project for this course and make a presentation on the project.
-The project should cover some topic in probability theory. You can choose your own topic. It might be a topic, which is not covered by the lecturer, or it might be a recent paper in a mathematical journal.
-You are supposed to give a 30-minute presentation on the topic, which should be a lecture to your fellow students. You may choose to do a blackboard lecture or a slide presentation, as you prefer.
-You presentation will be graded on the following criteria:
-    • Clarity: Your presentation should be clear and easy to understand.
+----
-    • Engagement: Your presentation should be engaging and interesting.
-    • Answering questions: You should be able to answer questions from the audience about your topic.
+===== Exams =====
+**Midterm:** One in-class exam (open-book, no internet). Thursday, March 5, 2026.
-<h2>Data Analysis Contest</h2>
+**Final:** Take-home exam with a brief (10–12 minutes) oral follow-up. I will choose one of your solutions and ask "why does this step hold?" / "where does the hypothesis matter?" questions. The final is cumulative.
-<p>Students will compete against each other in a Data Analysis Contest. The competition will begin on Tuesday, Feburary 20 and can be completed in teams of 2 &ndash; 4 members. Grades will be based upon a progress report and a final report (one per team) as well as the contest results. Further details about the contest along with specific grading criteria will be given in a separate document and discussed in class.</p>
-*/
+----
+===== Grading =====
+^ Component ^ Weight ^
+| Homework | 40% |
+| Participation (presenter/skeptic/scribe) | 10% |
+| Midterm exam | 15% |
+| Final write-up | 25% |
+| Final oral follow-up | 10% |
+----
-=== Tentative schedule ===
+===== Schedule =====
-| Midterm | TBA |
+^ Event ^ Date ^
-| Final Exam | TBA, as scheduled by the University|
+| Classes begin | Tuesday, January 20 |
+| Midterm | Thursday, March 5 |
+| Spring break | March 28 – April 6 |
+| Last day of classes | Wednesday, May 6 |
+| Final exam | As scheduled by the University |

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