625.638.81 - Foundations of Neural Networks
Applied and Computational Mathematics
Fall 2026
Description
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.
Instructor
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
- a Module Content page with general instructions on how to complete the module;
- links to video lecture materials;
- links to online quizzes;
- links to reading assignments and indications of required reading in the text;
- links to pdf formatted module assignments;
- discussion questions.
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
- Overview and Foundations
- Learning in Neural Networks
- Feedforward Neural Networks
- Regularization in Neural Networks
- Convolutional Neural Networks
- Recurrent Neural Networks
- Unsupervised Neural Networks
- Practical Methodology
- Structured Probabilistic Models
- Ethical Considerations
- Generative Models
- Generative Models
Course Goals
Course Learning Outcomes (CLOs)
- Explain the biological and mathematical foundations of neural network models.
- Explain the different types of neural networks and different types of learning models.
- Develop mathematical competence for understanding neural networks
- Explain which types of neural networks are used for which purposes such as in discriminators, classifiers, computation, and a broad range of problems.
- Explain how neural networks are implemented using training algorithms such as the feed-forward, back-propagation algorithm.
- Use computational tools for experimentation leading to new theoretical insights.
- Design, build and train neural networks for practical purposes.
Textbooks
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
Python
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%
|
Discussion Post for Weekly Research Paper 12%
|
Group Research Assignment 20%
|
Final Project 40%
|
Individual Research Paper 10%
|
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 Range | Letter 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.
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
Students with Disabilities - Accommodations and Accessibility
Student Conduct 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.