Math 2568: Linear Algebra
Spring 2025
Course Description: Matrix algebra, vector spaces and linear maps, bases and dimension, eigenvalues and eigenvectors, and applications.
Course Objectives: At the completion of this course, students will be able to:
1. Solve systems of linear equations
2. Manipulate and reduce matrices
3. Define (abstract) vector spaces
4. Understand linear transformations between vector spaces
5. Compute determinants, eigenvalues, and eigenvectors
6. Describe similarity transformations and diagonalizability
Modality:
The course will be taught through recorded video lectures posted on Carmen.
Assignment Weights:
Problem Sets 30%
Midterm 1 20%
Midterm 2 20%
Final Exam 30%
Your grades will be recorded on Carmen and your final grade will be curved. This makes it impossible to give an exact course-to-letter-grade correspondence before all coursework is completed, but I am available to give a rough idea of how your grade is shaping at request.
Problem Sets:
There will be 12 homework assignments throughout the semester. These assignments will be given weekly with some exceptions (for example, no assignment is due the first week).
Generally, Problem Sets will consist of multi-step problems that emphasize problem-solving strategies and clear writing. All necessary work must be shown to receive credit for a response. Students are welcome to work together in small groups on these, but all must write up their own solutions.
Exams:
There will be two Midterm exams and one Final Exam.
Exam Date Time
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Midterm 1
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Fri, February 7
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TBA
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Midterm 2
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Fri, March 21
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TBA
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Final Exam
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TBA
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TBA
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Coursework Submission and Formatting:
All coursework (i.e. Problem Sets and Exams) will be submitted on Gradescope. In order to facilitate online grading, your work must be submitted as a single pdf file with pages selected.
There are many ways to make your file a single pdf; some things to keep in mind follow:
□ If you are using a tablet and stylus, make sure to export the file as a pdf. The
“Notability” app is a suggested tool, as it makes this process simple and immediately exports the file in the desired format.
□ If you are using pen(cil) and paper, scan your work as a pdf file. This can be achieved
with a smart phone (e.g. on the “Notes” app on iOS, there is a “Scan documents” function that works well for this).
□ If you end up with a sequence of photos of your work, this can still be salvaged by an online pdf converter. Free versions of these are numerous and easy to find; simply
Google “(your file format) to pdf converter” and you will find many operational tools.
Make sure you knowhow to perform this process before submitting your first assignment (and
certainly before the first Midterm!). If you are in doubt of this, please reach out; we can figure it out over e-mail, during Office Hours, or during a scheduled meeting if necessary.
Errors in the submission process will be viewed as late submissions and thus incur grading penalties, along with possible delays and errors in the grading process.
Late Submissions:
A Problem Set submitted late but within 24 hours of the deadline will receive a 30% grading penalty. Submissions made after this will receive no credit.
Late submissions to Exams will receive no credit.
Working Together:
Group work on Problem Sets is not only acceptable, but also encouraged! (Keep in mind you must still write up your own solutions, though)
However, working together on Exams is considered academic misconduct.
Internet Solutions, Calculators, and other Electronic Resources:
The internet is a perfectly good resource for Problem Sets insofar as there is no plagiarism. However, relevant material beyond those explicitly said to be permitted may not be accessed during exams. This includes calculators and online matrix tools.
Tentative Schedule:
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Week
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Mon
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Wed
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Fri
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1 (of Jan 6)
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Intr. & 1.1
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1.1
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1.2
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2 (of Jan 13)
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1.2
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1.3
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1.5
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3 (of Jan 20)
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MLK Day
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1.6
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1.6
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4 (of Jan 27)
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1.7
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1.7
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1.7
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5 (of Feb 3)
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1.9
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1.9
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Midterm 1
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6 (of Feb 10)
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2.1
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2.2 & 2.3
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2.3
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7 (of Feb 17)
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3.2/5.2
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3.3/5.3
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3.3/5.3
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8 (of Feb 24)
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3.3
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3.4/5.4
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3.4
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9 (of Mar 3)
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3.4/5.4
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3.5/5.5
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3.5/5.5
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10 (of Mar 10)
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Spring Break
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11 (of Mar 17)
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3.6/5.6
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3.6/5.6
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Midterm 2
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12 (of Mar 24)
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3.7/5.7
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3.7/5.7
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3.7/5.7
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13 (of Mar 31)
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4.1
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4.2 & 4.3
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4.2 & 4.3
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14 (of Apr 7)
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4.4
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4.4
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4.5 & 4.6
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15 (of Apr 14)
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4.5 & 4.6
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4.7
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4.7
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16 (of Apr 21)
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4.7
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