MATH 6397 Mathematics of Data Science
Tue, Thu 10-11:30, Room: S 115
This is a course of mathematics exploring foundational and theorical concepts underlying the development and applications of intelligent systems and deep learning
algorithms. The emphasis of the course will be theoretical aspects. The aim of the course is to provide the necessary background to start a graduate research project in this emerging area of investigation.
Topics of the course include: statistical learning theory, Support Vector Machines, geometry of high-dimensional data,
manifold learning, dimensionality reduction, expressive power of neural networks, generalization in neural networks, convolutional neural networks.
This is class is targeted to graduate students interested in mastering theoretical tools underlying machine learning and data science.
Even though algorithmic aspects of the topics will not be ignored and exploration of algorithmic issues will be assigned for
individual or group projects, this course will not duplicate existing courses on machine learning or data science offered in
the Computer Science Department that are focused on algorithmic implementation and computation.
Homework and student assignments
Student evaluation is based on two assignments: (i) class participation and (ii) final project.
(i) Class participation: Every week, I will assign simple proofs or numerical tests or literature searches.
(ii) Final project: It requires the critical reading of one or more fundamental research papers in an area closely related to topics of the course.
I will select the papers in coordination with the students and will provide assistance during the senester. Please, note that they will be mathematically challenging papers that it would be unrealistic to critically read in a few day but will require a serious study.
I will set up several deadlines during the semester to verify the completion of a number of intermediate objectives
finalized to the preparation of a written report and a 15-to-20 min in-class presentation.
Suggested topics with related papers are listed here. This file will be periodically updated.
Please follow the deadlines and instructions given in this document for the preparation of your project:
Instructions and timeline.
Please, use the following Latex template to submit your reports:
Report Latex template
Delivery of the final project report is scheduled by April 7. Presentation instructions and presentation calendar is given
here (to be updated).
List of lecture notes (to be updated):
Class overview: Class overview
Lecture set 01: MDS_1
Lecture set 02: MDS_2
Lecture set 03: MDS_3
Lecture set 04: MDS_4
Lecture set 05: MDS_5
Bibliographical References (to be updated)
- This course brings together mathematical tools not usually presented in a single course, for the purpose of solving problems arising in different fields related to the analysis of data.
I will be selecting material from several sources including:
- 1. Mathematics of Data Science, by A. S. Bandeira, A. Singer, T. Strohmer available free online
- 2. Foundations of Data Science, by Blum, Hopcroft and Kannan’s available free online at
It includes material on the Curse of Dimensionality and various topics in machine learning.
- 3. The Elements of Statistical Learning by Hastie, Tibshirani and Friedman, Springer 2017. The authors have made this book freely available on the website
This classical treatise covers a broad range of topics in statistical learning theory and neural networks.
- 4. Understanding Machine Learning: From Theory to Algorithms by Shai Shalev-Shwartz and Shai Ben-David, Cambridge University Press 2014. Authors made the book available for personal use
- 5. Deep learning theory lecture notes by Matus Telgarski, available here
Thses notes include a detailed analysis of the approximation properties of neural networks.
- 6. Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges by Michael M. Bronstein, Joan Bruna, Taco Cohen, Petar Veličković, which is available
here. Related material can be found at the following webpage
- 7. Deep Learning with PyTorch by Stevens, Antiga and Viehmann. The authors have made this book freely available
It is a practial manual to implement deep learning algorithms in Pytorch - for those students more interested into the numerical/applied side.
Students are encouraged to visit the University’s COVID-19 website for important information including diagnosis and symptom protocols, testing, vaccine information, and post-exposure guidance.
Please check the website throughout the semester for updates. Consult the
Excused Absence Policy for information regarding excused absences due to medical reasons
Please, regularly consult
COVID-19 Updates and Resources
by the Provost Office for the most updated information.
Here is the current
University protocols about COVID reporting and exposure.
Data suggests that vaccination remains the best intervention for reliable protection against COVID-19. Students are asked to familiarize themselves with pertinent vaccine information, consult with their health care provider.
The University strongly encourages all students, faculty and staff to be vaccinated.
Excused Absence Policy
Regular class attendance, participation, and engagement in coursework are important contributors to student success. Absences may be excused as provided in the University of Houston
Undergraduate Excused Absence Policy for reasons including: medical illness of student or close relative, death of a close family member, legal or government proceeding that a student is
obligated to attend, recognized professional and educational activities where the student is presenting, and University-sponsored activity or athletic competition. Under these policies,
students with excused absences will be provided with an opportunity to make up any quiz, exam or other work that contributes to the course grade or a satisfactory alternative.
Please, when it is possible, inform the instructor in advance so that appropriate arrangements can be made for the make up evaluation.
Please read the Consult the
Excused Absence Policy for details regarding reasons for excused absences, the approval process, and extended absences.
Additional policies address absences related to military service, religious holy days, pregnancy and related conditions, and disability.
Reasonable Academic Adjustments/Auxiliary Aids:
The University of Houston complies with Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, pertaining to the provision of reasonable academic adjustments/auxiliary aids for disabled students. In accordance with Section 504 and ADA guidelines, UH strives to provide reasonable academic adjustments/auxiliary aids to students who request and require them. If you believe that you have a disability requiring an academic adjustments/auxiliary aid, please contact the Justin Dart Jr. Student Accessibility Center (formerly the Justin Dart, Jr. Center for Students with DisABILITIES).
Recording of Class:
Students may not record all or part of class, livestream all or part of class, or make/distribute screen captures, without advanced written consent of the instructor. If you have or think you may have a disability such that you need to record class-related activities, please contact the Justin Dart, Jr. Student Accessibility Center. If you have an accommodation to record class-related activities, those recordings may not be shared with any other student, whether in this course or not, or with any other person or on any other platform. Classes may be recorded by the instructor. Students may use instructor’s recordings for their own studying and notetaking. Instructor’s recordings are not authorized to be shared with anyone without the prior written approval of the instructor. Failure to comply with requirements regarding recordings will result in a disciplinary referral to the Dean of Students Office and may result in disciplinary action.
Resources for Online Learning:
The University of Houston is committed to student success, and provides information to optimize the online learning experience through our
Power-On website. Please visit this website for a comprehensive set of resources, tools, and tips including: obtaining access to the internet, AccessUH, and Blackboard; requesting a laptop through the Laptop Loaner Program; using your smartphone as a webcam; and downloading Microsoft Office 365 at no cost. For questions or assistance contact UHOnline@uh.edu.
Please check and use your Cougarnet email for communications related to this course. To access this email, login to your Microsoft 365 account with your Cougarnet credentials.
Academic Honesty Policy:
High ethical standards are critical to the integrity of any institution, and bear directly on the ultimate value of conferred degrees. All UH community members are expected to contribute to an atmosphere of the highest possible ethical standards.
Maintaining such an atmosphere requires that any instances of academic dishonesty be recognized and addressed. The
UH Academic Honesty Policy
is designed to handle those instances with fairness to all parties involved: the students,
the instructors, and the University itself. All students and faculty of the University of Houston are responsible for being familiar with this policy.
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Per the UHS Sexual Misconduct Policy, your instructor is a “responsible employee” for reporting purposes under Title IX regulations and state law and must report incidents of sexual misconduct (sexual harassment, non-consensual sexual contact, sexual assault, sexual exploitation,
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Please note that the instructor may need to make modifications to the course syllabus. Notice of such changes will be announced as quickly as possible through
your official cougarnet email.