625.638.8VL - Foundations of Neural Networks

Applied and Computational Mathematics
Spring 2024


This course will be a comprehensive study of the mathematical foundations for neural networks. Topics include feed forward and recurrent networks and neural network applications in function approximation, pattern analysis, signal classification, optimization, and associative memories.Prerequisites: Multivariable calculus, linear algebra

Expanded Course Description

This course introduces the concepts of Neural Networks (Deep Learning) with emphasis on their derivation and underlying mathematical theory. Topics include the mathematical theory of learning in neural networks, feed-forward neural networks, convolutional neural networks, recurrent neural networks, deep learning optimization, regularization, unsupervised methods, generative adversarial networks, model assessment, and ethical issues in neural networks. Students will gain experience in formulating models and implementing algorithms using Python. Students will need to be comfortable with writing code in Python to be successful in this course. At the end of this course, students will be able to implement, apply, and mathematically analyze a variety of neural networks when applied to real-world data. Course Note(s): Although students will have coding assignments, this course differs from other EP neural network courses in that the primary focus is on the mathematical foundations underlying the algorithms.


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Zerotti Woods


Course Structure

The course materials are divided into 14 modules each roughly corresponding to a week of study for the course.  These modules can be accessed by clicking Modules on the left menu of the Canvas course page and will typically be comprised of several components.  These components include

Students are encouraged to preview all sections of the module before starting.  Most modules run for a period of seven (7) days, exceptions are noted on the Course Outline page.  Students should regularly check the Calendar and Announcements for assignment due dates and any changes or modifications of the course.

Course Topics

Course Goals

This course covers mathematical principles that serve as a basis for the field of Deep Learning. Emphasis in this course will be on formulating mathematical problems that can be solved with Neural Networks, understanding which Neural Networks are appropriate for different data sets, and proper uses of Neural Networks to explore real world problems.

Course Learning Outcomes (CLOs)



Deep Learning, by Ian Goodfellow 

Other Materials & Online Resources

Optional As noted above, additional reading assignments and materials will be provided in the various Course Content pages either as links to download pdf files or links to other websites.

Required Software


You will need access to a recent version of Python. Anaconda is an open source python distribution platform that contains all packages and libraries that will be needed for this course.

Student Coursework Requirements

Student assignments are due according to the dates in the Calendar and Assignments items in the corresponding modules.

I generally 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.

It is expected that each student participate in all lectures. All lectures will be recorded so in the event that a student must be absent, the lecture recording will be posted.

This course will consist of the following basic student requirements:

Homework 18%

  • 6 Assigned Homework Assignments
Discussion Post for Weekly Research Paper 12%
  • Read assigned research and discuss with classmates

Group Research Assignment 20%

  • Proposal of final project with selected dataset.
  • Grade will come from a mixture of peer review and instructors review.

Final Project 40%

  • Students will be placed in groups on the first day of class.
  • Project code base must be submitted. 10%
  • Oral presentations (instructor review) 10%
  • Peer Review (from within group) 10%
  • Peer review from class on oral presentation. 10%

Individual Research Paper 10%

  • Each student will be choose a foundational research paper. They will do a recorded presentation on the findings and topics of the researc

Grading Policy

A grade of A indicates achievement of consistent excellence and distinction throughout the course—that is, conspicuous excellence in all aspects of assignments and discussion in every week.

A grade of B indicates work that meets all course requirements on a level appropriate for graduate academic work. These criteria apply to both undergraduates and graduate students taking the course.

EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10).

Score RangeLetter Grade
100-98= A+
97-94= A
93-90= A−
89-87= B+
86-83= B
82-80= B−
79-77= C+
76-73= C
72-70= C−
69-67= D+
66-63= D
<63= F

Course Policies

Homework will be assigned for the first half of the course. It will be due BEFORE the beginning of class. Students are encouraged to discuss with other students about the HW assignments. Late assignments are not accepted with very little exception. 

Final presentations will be done during finals week. Each group will have twenty five minutes to present with a five minute question and answer period. Students in the audience along with the instructor will give formal feedback on every presentation.

Students have a responsibility to assist in peer reviewing. This is an essential component to the course and students are expected to participate during each presentation.

Multivariate calculus, linear algebra (e.g. EN.625.252), and probability and statistics (EN.625.603 or similar course). Students should also be comfortable with reading and writing mathematical proofs.

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 (https://ep.jhu.edu/student-services/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. 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 Student Disability Services at Engineering for Professionals, 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 following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

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.