Teaching Fall 2021 Math6350

Deep learning theory with applications in differential equations and data science

Semester: Fall 2021;

Time: 08/30/2021-12/12/2021, TR 02:20pm-03:35pm;

Location: Phillips 510;

Instructor: Yanxiang Zhao, Phillips Hall 709

Phone: 202-994-0606

Email: yxzhao at email dot gwu dot edu

Office Hour: TR 06:00pm--07:00pm or by appointment

Course Description

This course is aimed at advanced undergraduate and beginning graduate students in mathematics, science and engineering. The goal of this course is to provide a broad entry point to applied data science for students with a basic knowledge in linear algebra, differential equations, scientific computing who are seeking to expand their background to include methods in data science, optimization, dynamical systems and control theory.

Course Recording (University policies)

Use of Electronic Course Materials and Class Recordings:
Students are encouraged to use electronic course materials, including recorded class sessions, for private personal use in connection with their academic program of study. Electronic course materials and recorded class sessions should not be shared or used for non-course related purposes unless express permission has been granted by the instructor. Students who impermissibly share any electronic course materials are subject to discipline under the Student Code of Conduct. Please contact the instructor if you have questions regarding what constitutes permissible or impermissible use of electronic course materials and/or recorded class sessions. Please contact Disability Support Services if you have questions or need assistance in accessing electronic course materials.

The course recordings can be found on Blackboard under the tab of 'Zoom meeting'

Prerequisites

Math 3342: Introduction to Ordinary Differential Equations;
Math 3553: Introduction to Numerical Analysis (or their equivalents or permission of instructor);
Knowledge of a programing language.

Textbook

Primary textbook: Data-Driven Science and Engineering: Machine Learning, Dynamical Systems and Control by Steven L. Brunton and J. Nathan Kutz [link];
Other useful references:
1. Geometric data analysis, beyond convolutions [link];
  - This one is advanced book, with many applications in data science.
2. Mathematical foundations for data analysis [link];
  - This is an undergraduate level textbook with lecture videos.
3. Machine Learning [link];
  - This is a YouTube video collection for the Machine Learning course taught by Andrew Ng.
4. Plenty of textbooks and videos available online.

Learning Outcomes

As a result of completing this course, the students will be able to:

Mathematical Preliminaries: Singular value decomposition, Fourier transforms, Sparsity and compressed sensing;
Machine Learning and Its Applications: Regression, clustering and classification, neural networks and deep learning;
Data-driven Dynamical Systems;
Linear Control Theory.

Average minimum amount of independent, out-of-class, learning expected per week

More than 2/3 of the time you devote to this class should take place outside the classroom (lecture and recitation). Even the best students in the class should plan on spending an average of at least 6 hours a week on homework and other studying. Students who struggle with the material may need to spend more time in order to earn a grade they will find acceptable.

Course Calendar

	Mon	Tue	Wed	Thu	Fri
Week 1	Aug29	Aug30	Aug31	Sep01	Sep02
Week 2	Break	Sep07	Sep08	Sep09	Sep10
Week 3	Sep13	Sep14	Sep15	Sep16	Sep17
Week 4	Sep20	Sep21	Sep22	Sep23	Sep24
Week 5	Sep27	Sep28	Sep29	Sep30	Oct01
Week 6	Oct04	Oct05	Oct06	Oct07	Oct08
Week 07	Oct 11	Oct12	Oct13	Oct14	Oct15
Week 08	Oct18	Oct19	Oct20	Oct21: Midterm	Break
Week 09	Oct25	Oct26	Oct27	Oct28	Oct29
Week 10	Nov01	Nov02	Nov03	Nov04	Nov05
Week 11	Nov08	Nov09	Nov10	Nov11	Nov12
Week 12	Nov15	Nov16	Nov17	Nov18	Nov19
Week 13	Nov22	Nov23	Break	Break	Break
Week 14	Nov29	Nov30	Dec01	Dec02	Dec03
Week 15	Dec06	Dec07	Dec08	Dec09	Dec10
Week 16	Dec13	Dec14	Dec15	Dec16	Dec17

Homework

Homework 01;

Homework 02;

Exams

If you have a legitimate conflict with the test dates and times (such as Student-athletes accommodation and Religious holidays), please contact the instructor as soon as possible, do not wait until shortly (within 24 hours) before the test.
If you miss a test because of an illness, you must inform the instructor before the test, and get a note from your doctor in order to be allowed to make the test up at a later date. Unexplained missed tests will not be excused or allowed to be made up.
Assistance of any type (notes in any form, books, calculator, smartphone apps, etc.) is strictly banned during exams. Using the work of others on exams is strictly prohibited.
One in-class midterm exam is scheduled at Oct 21.
Final exam schedule will be announced later.

Grading

Your course grade will be determined by your cumulative average at the end of the term and will be based on the following scale:

	A	A-	B+	B	B-	C+	C	C-	D+	D	D-
Scale	95%	90%	87%	83%	80%	77%	73%	70%	67%	63%	60%

Your cumulative average will be the following weighted average:

	In-class performance	Midterm	Final
Scheme	30%	30%	40%

Class Policies

University policy on Religious Holidays:

Students should notify faculty during the first week of the semester of their intention to be absent from class on their day(s) of religious observance;
Faculty should extend to these students the courtesy of absence without penalty on such occasions, including permision to make up examinations;
Faculty who intend to observe a religious holiday should arrange at the beginning of the semester to reschedule missed classes or to make other provisions for their course-related activities.

Academic Integrity

Academic dishonesty is defined as cheating of any kind, including misrepresenting one's own work, taking credit for the work of other without crediting them and without appropriate authorization, and the fabrication of information. For the remainder of the code, see: http://www.gwu.edu/~ntegrity/code.html.

Support for Students Outside the Classroom

Disability Support Services (DSS): Any student who may need an accommodation based on the potential impact of a disability should contact the DSS office at 202-994-8250 in the Rome Hall, Suite 102, to establish eligibility and to coordinate reasonable accommodations. For additional information please refer to: http://gwired.gwu.edu/dss/.
University Counseling Center (UCC): The UCC (202-994-5300) offers 24/7 assistance and referral to address students' personal, social, career, and study skills problems. Services for students include: crisis and emergency mental health consultations; confidential assessment, counseling services (individual and small group), and referrals. For additional information please refer to: http://counselingcenter.gwu.edu/.

Security

In the case of an emergence, if at all possible, the class should shelter in place. If the buliding that the class is in is affected, follow the evacuation procedures for the building. After evacuation, see shelter at a predetermined rendezvous location.

Student Responsibilities and Classroom Courtesy:

You are responsible for knowing about all announcements made in class related to homework assignments, exams etc., and for all material covered in class.
Be aware of the University's Code of Academic Integrity, see http://www.gwu.edu/~ntegrity for details. If cases of academic dishonesty arise, whether on homework assignments, quizzes or exams, they will be pursued to their conclusion.
Each student must conduct him or herself in a manner that promotes a positive atmosphere, conveys mutual respect, and creates no distractions, thereby allowing all students to focus on our goal: learning NUMERICAL ANALYSIS. In particular:
cell phones, texting devices, laptops, and all other potentially distracting must be turned off during class;
- cell phones, texting devices, laptops, and all other potentially distracting must be turned off during class;
- everyone should make a serious effort to arrive promptly for the start of class;
- except for serious reasons, once in class everyone should remain in class until the class is over;
- apart from the lecture, students asking the instructor questions, and students responding to the instructor's questions, the class should be silent.

Questions

Everyone is strongly encouraged to ask questions during class, and during office hours! Should you need further assistance, you may consider hiring a tutor (the department keeps a list of tutors; copies are available outside Phillips Hall 739).