625.252.82 - Linear Algebra and Its Applications

Course Structure

The course materials are divided into modules which can be accessed by clicking Course Modules on the course menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

• Linear Systems
• Linear Transformations
• Matrix Algebra
• Subspaces
• Determinants
• Eigenvalues and Eigenvectors
• Eigenvectors and Linear Transformations
• Orthogonality and Least Squares
• Symmetric Matrices and Quadratic Forms

Course Goals

The main goal of the course is to see the beautiful interplay between geometry and basic algebra that allows to solve many fundamental problems in finite-dimensional linear spaces.

Course Learning Outcomes (CLOs)

• Use algebraic skills essential for the study of systems of linear equations, matrix algebra, vector spaces, eigenvalues and eigenvectors, orthogonality and diagonalization, and least-squares method.
• Use spatial reasoning and geometric properties to solve problems and visualize solutions in two- and three-dimensional settings as well as conceptually extend these results to higher dimensions.
• Critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra.
• Synthesize mathematical statements, ideas, and results by using correct mathematical definitions, terminology, and symbols

Textbooks

Lay, D. C. et al (2016). Linear Algebra and its Applications (5th ed.) Pearson Education.

ISBN-13: 9780321982384

Textbook information for this course is available online through the appropriate bookstore website: For online courses, search the MBS website.

Student Coursework Requirements

It is expected that each module will take approximately 8-11 hours per week to complete. Here is an approximate breakdown:  online lectures (3 hours per week), reading the assigned sections of the texts (approximately 2–3 hours per week), and assignments (approximately 3–5 hours per week).

This course will consist of the following basic student requirements:

Homework

Homework assigned for each week. Your lowest homework grade will be dropped.

Exams

There will be 2 mid-term exams.  There will be a cumulative final exam the last week of class. All exams are due by end of day Sunday of the exam week.  Follow all directions as stated in each exam module.

In addition to counting as the final, if higher than any individual exam, the final exam will replace the lowest exam score. For example:

• If you score a 60 on exam 1, a 70 on exam 2, and an 80 on the final, the 80 replaces the 60 on exam 1.
• If you score a 60 on exam 1, a 70 on exam 2, and an 50 on the final, your exam 1 and 2 score do not change.

Quizzes

There will be a short online quiz each week. There are two attempts at the quiz and the questions are pulled randomly during each attempt.  The higher of the two attempts counts for the grade. Your lowest quiz grade will be dropped.

Discussion Forums

For modules with a discussion forum, post your initial response to the discussion by Thursday night and respond to at least two classmates by end of day Sunday. The lowest discussion grade is dropped. 

Projects

There are group projects in this course that will focus on problem solving and mathematical communication.  See each project direction sheet in the course for more details. 

Grading Policy

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 Evaluation

Your final grade for the class will be given as a weighted average with the weights given as follows:

- Discussion Forums: 10% (lowest grade dropped)

- Homework: 10%   (lowest grade dropped)

- Quizzes: 15%  (lowest grade dropped)

- Projects: 15%

- First midterm: 15%

- Second midterm: 15%

- Final exam: 20% 

In addition to counting as the final exam, the final will replace a lower midterm grade if applicable. 

Student Generative AI (GenAI) Use

This course follows the EP Guidance on Student Generative AI and is designated as a YELLOW (Restricted / Guided Use) course. Generative AI tools may be used in limited ways to support learning, but they may not replace your own reasoning or problem-solving. All submitted work must reflect your independent understanding, and you are responsible for ensuring that your use of AI complies with both this policy and university academic integrity standards.

Tools such as ChatGPT, Claude, and Gemini may be used for conceptual clarification, generating practice problems, or improving the presentation of your own work (e.g., grammar or LaTeX formatting). You may also use AI to help identify errors in your reasoning after making a genuine attempt. However, you may not use AI to generate solutions, proofs, or substantive parts of graded assignments, nor may you use it on assessments intended to measure your individual understanding unless explicitly permitted.

Any use of generative AI must be disclosed. You are required to include a brief statement identifying the tool used, the purpose of its use, and how it contributed to your work, along with representative prompts where appropriate. Failure to disclose AI use will be treated as a violation of academic integrity.

You are expected to critically evaluate any AI-generated content, as such tools may produce incorrect or misleading results. You must be able to explain and justify all aspects of your submitted work. The instructor reserves the right to request clarification or verification of authorship. In all cases, generative AI may assist your learning, but it may not substitute for your own intellectual effort.

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.