Administrative details for MATH 3120 — Linear Algebra (Spring 2026)

Course Description

This course is an introduction to the ideas and techniques of linear algebra with an emphasis on understanding linear systems, matrices as transformations, vector spaces, and applications. We will balance computational methods with geometric insight and selected applications relevant to the sciences, engineering, data analysis, and computation.

Topics include solving linear systems, matrix algebra, determinants, eigenvalues and diagonalization, vector spaces and subspaces, linear transformations, orthogonality, least squares approximation, and singular value decomposition.

Required Text

W. Keith Nicholson, Linear Algebra with Applications (Open Edition, Vretta–Lyryx, 2023). This book is open access and may be obtained at no cost:

Free online version (CC-BY-NC-SA): https://collection.bccampus.ca/textbooks/linear-algebra-with-applications-2023-a-d-vretta-lyryx-inc-446/

The text includes extensive examples and exercises. We will use selected sections of this text to support lecture and homework, and other chapters as reference.

Course Topics and Textbook Sections

We will primarily cover the following material from Nicholson (2023):

Linear Systems and Matrices

• Ch. 1 (Systems of Linear Equations)
• Ch. 2 (Matrix Algebra and Linear Transformations)

Determinants and Eigenstructure

• Ch. 3.1–3.5 (Determinants, Eigenvalues, Diagonalization; selected applications)

Vector Geometry and Subspaces

• Ch. 4 (Vector Geometry; selected sections)
• Ch. 5 (Subspaces, Span, Independence, Dimension, Orthogonality, Rank, Least Squares)

Abstraction and Linear Maps

• Ch. 6 (Vector Spaces — core ideas)
• Ch. 7 (Linear Transformations — kernel, image, isomorphisms)

Orthogonality and Data

• Ch. 8 (Orthogonal Complements, Projections, QR Factorization, SVD, PCA)

(Sections not listed here may be used as supplementary reference or optional reading at the instructor’s discretion.)

Provisional Exam Schedule

We will have three in-class exams. Each exam will be preceded by a review day in class. The provisional dates are as follows:

• Exam 1: Monday, February 23 25
  Linear systems; matrix algebra; linear transformations
• Exam 2: Monday, March 23 30
  Determinants; eigenvalues; diagonalization; vector spaces
• Exam 3: Monday, April 27
  Orthogonality; least squares; SVD/PCA

Exact dates will be confirmed once the official Penn academic calendar is finalized.

There is no separate final exam during the registrar’s final exam period.

Grading Policy

Your course grade will be based on the following components:

• In-Class Exams (70%)
  There will be three in-class exams. The highest exam score will count for 30% of your final grade, and the other two exam scores will count for 20% each.
  Exams are cumulative in spirit, with emphasis on material covered since the previous exam. The third exam emphasizes synthesis and later topics, but strong performance on any exam is rewarded.
• In-Class Work (10%)
  Periodic short in-class activities, typically completed in small groups. These activities are designed to support understanding, discussion, and engagement. They are graded primarily on participation and serious effort.
• Writing Assignments (10%)
  Short writing assignments focused on explaining, interpreting, or reflecting on key ideas from the course. These assignments emphasize clarity of thought and conceptual understanding rather than formal derivations.
• Homework / Practice (10%)
  Regular homework assignments are intended primarily as practice and preparation for class and exams. Homework is graded for completion and coherence rather than correctness.

Final letter grades will be assigned using a standard grading scale, with adjustments made as appropriate to reflect overall course performance.

Academic Integrity

Students are expected to uphold the University of Pennsylvania’s standards of academic integrity in all aspects of this course, including homework, in-class work, writing assignments, and exams. You are responsible for ensuring that all work you submit reflects your own understanding and effort.

Course activities are designed to help you learn the material; they are most effective when you actively work through problems yourself, even when using outside help. Seeking assistance from classmates, course materials, or other resources is encouraged where appropriate, but copying solutions or submitting work you do not understand undermines the learning process and is not permitted.

All suspected violations of academic integrity will be handled in accordance with the University’s policies. Students are expected to be familiar with the Penn Academic Integrity Policy, available at:
https://catalog.upenn.edu/policies/pennbook/academic-integrity/

Policy Notes

• Collaboration on homework is encouraged where indicated; all submitted work must reflect the student’s own understanding.
• Exams must be taken at the scheduled times unless excused for documented University-approved reasons.
• Late homework, regrade requests, and other course policies will be posted on Canvas.