685.640.81 - Mathematical Reasoning and Structure for Data Science

Expanded Course Description

This course provides a rigorous mathematical foundation for statistical and algorithmic reasoning essential to modern data science. Students will delve into logic, set theory, combinatorics, linear algebra, probability theory, regression, classification, and clustering methods from first principles, complemented by computational exercises.

Course Structure

Course content is divided into weekly modules, accessible via Canvas. Each module includes lectures, readings, discussions, and assignments. Check the Course Calendar for specific deadlines.

Course Topics

Foundations of Mathematical Reasoning

Data Types and Mathematical Structures

Counting and Combinatorics

Probability Foundations

Random Variables and Distributions

Joint Distributions and Independence

Mathematical Statistics for Modeling

Bayesian Thinking and Simulation

Linear Algebra for Data Models

Linear Models and Least Squares

Logistic Regression and Optimization

Information Theory and Model Complexity

Mathematical Principles of Clustering

Course Goals

By course end, students will:

·        Formulate problems using mathematical structures such as sets, functions, and relations.

·        Analyze regression models through matrix algebra and optimization methods.

·        Apply combinatorial and probabilistic reasoning to data modeling.

·        Understand and utilize frequentist and Bayesian statistical inference.

·        Articulate assumptions and limitations of statistical models clearly and mathematically.

·        Translate mathematical concepts into reproducible computational experiments.

Textbooks

Mathematical Methods in Data Science: Bridging Theory and Applications with Python by Sebastien Roch

Free Copy from the author: https://mmids-textbook.github.io/index.html

Required Software

Python and Jupyter Notebooks with necessary libraries.

Student Coursework Requirements

Item	% of Grade
Weekly Problem Sets and Computational Exercises	50%
Midterm Exam	20%
Final Project	30%

Grading Policy

Assignments are due according to the dates posted in your Canvas course site. You may check these due dates in the Course Calendar or the Assignments in the corresponding modules. I will post grades one week after assignment due dates.

Generally I do not directly grade spelling and grammar. However, egregious violations of the rules of the English language will be noted without comment. Consistently poor performance in either spelling or grammar is taken as an indication of poor written communication ability that may detract from your grade.

Course Policies

Late Work Policy: I highly recommend turning assignments in on time. Late assignments lose 10% if submitted within 24 hours past due date. Another 10% for every 24 hours until 1 week where it will no longer be accepted. Late work not accepted for midterm or final projects unless documented exceptional circumstances are provided.

Student Generative AI (GenAI) Use

Please see video on AI use in module

Academic Policies

Deadlines for Adding, Dropping, and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar. Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course. 

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students. This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Our courses are designed with a proactive approach to accessibility to minimize the need for disability disclosure and accommodation requests, but we recognize that you may need additional support. Students with disabilities (including those with psychological conditions, medical conditions, and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.  For further information or to start the process of requesting accommodations, please contact EP Student Disability Services at ep-disability-svcs@jhu.edu. 

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. For a full description of the code please visit the Student Conduct Code website.

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team (EP-Registration@exchange.johnshopkins.edu) in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.