Linear Algebra

MTH 21

Pedro Morales-Almazan MWF 9:20-10:25
Humn Lecture Hall (Zoom)

Linear Algebra is the study of systems that change in proportion to their inputs. Most applied systems present a linear behavior, which makes Linear Algebra very important in physics, engineering, biology, chemistry, and computer science.


  • Solve systems of linear equations
  • Identify vector spaces
  • Apply matrix and vector algebra
  • Express linear systems using vectors and matrices
  • Use eigenvalues and eigenvectors to describe a system
  • Improve time management
  • Organize critical thinking
  • Develop studying skills
  • Build connections between mathematical thinking and real-life situations
  • Structure working strategies
  • Utilize team work
  • Stregthen reading and writing skills




Messages and announcements will be done using Canvas. When you need to contact your instructor or TA, please use Canvas as email messages will NOT be replied. This is to make communication more efficient, so we can correctly identify your section and other important information.


We will use Piazza for questions regarding HW, exams, lectures, etc. This tool is great for collaboration and to write math. It is difficult to type math in an email or in Canvas, so use Piazza for all content related questions!

office hours

If you have any questions, don't forget to go office hours via Zoom.
Pedro Morales T 10-11am, T 1-2pm, W 1-2pm
David T 1:30-2:30pm
Malachi Th 2-3pm
Jennifer W 2-3pm, Th 9-10am
Leland Th 10-11am
Spencer T 11:30am-1:30pm


For anything else, you can reach your instructor or TA using email, but please use this as the LAST method of communication.


Our book is: Elementary Linear Algebra by Bruce Cooperstein. The book is available in Canvas

SGT, MSI and ACE are additional resources that can help you with class. You are highly encourage to attend to these.

We will use edfinity for class HW.


The grade will be divided into three compnents:

  • Homework and Classwork
  • Participation
  • Exams

These three add to more than 100% of the total grade. In this way, even if you miss some components, your grade will not get affected.

Grades will be assigned using the +/- system.

Homework and Classwork (57%)

Pre-Class (8%)

These are short assignments and reflections that you will complete on Canvas. There will be a Pre-Class assignment per lecture. These will be due at the end of each week. Try to complet them as soon as posisble to avoid accummulating work.

We are dropping the lowest 6 preclass in order to account for any abscences or issues.

In-Class (7%)

We will have group Activities during lecture time to be completed in groups. The Activities are applications of the concepts seen in class. This can be completed in groups of at most 4 and sent using Gradescope. In-Class Activities will be available in Canvas and will be due by the end of the week.

We are dropping the lowest 3 inclass Activities in order to account for any abscences or issues.

Post-Class (10%)

Each week you will have an Online Homework assignment due Sunday at midnight . It will cover the content addressed the previous week.

We are dropping the lowest 3 Post-Class in order to account for any abscences or issues.

Section (8%)

Each Section day you will have different Activities to work on. These Activities will be worked in groups. The Activities will be completed on Canvas.

We are dropping the lowest 3 section grades in order to account for any abscences or issues.

Project (24%)

You will have three application projects. These can be worked on groups of at most 5 members. Each project is independent of the others and you can switch or keep groups.

  • 01-Project: Flow in Networks
    April 17th
  • 02-Project: Error Correcting Codes
    May 8th
  • 03-Project: Markov Chains
    May 29th

Participation and attendance (18%)

Participation (5%)

This consists in class attendance via Zoom and questionaries in Canvas.

Discussion (8%)

Once a week there will be a Discussion topic in Canvas. Participation in this topic is counted by commenting on the Topic post in Canvas.

Responsibility (5%)

This measures your responsibility, consistency, and engagement with the course. It is computed with your Pre-Class, Section, Activities, Reflections, and participation in SGT, MSI and ACE sessions.

This is computed by the average of:

  • Assignments completed on time (proportion)
  • Assistance to ACE, MSI and/or SGT (at least once)
  • Consistency of assignment grades

Exams (35%)

Exams will be remote, open-notebook, open-book, and calculators are allowed. Avoid using other resources, such as websites or third-party materials, as we don't know how reliable ther are. No makeup exams under any circumstances. Under a valid emergency, one absence could be replaced by the final.

Midterms (20%)

These exams cover the class material. The grade is computed by averaging the exams in the regular fashion.

Midterms will take place during lecture time.

  • Exam 1
    April 24th
    Midterm: Covers Sections 1.1-3.3

  • Exam 2
    May 22nd
    Midterm: Covers Sections 3.4-6.3

Final (15%)

The final is comprehensive.

  • Final
    June 9th

Prerequisite and degree relevance

Systems of linear equations matrices, determinants. Introduces abstract vector spaces, linear transformation, inner products, the geometry of Euclidean space, and eigenvalues. Students cannot receive credit for this course and AM 10.

Prerequisite(s): MATH 11A or MATH 19A or MATH 20A or AM 11A or AM 15A.

Student Code of Conduct

The UC Santa Cruz community includes students, staff, faculty, and others who have a vested interest in the University. As members of an academic community, integrity, accountability and mutual respect are vital pillars of being part of this community. The Principles of Community further illustrate the values and expectations set forth for being a part of this community.

Small Group Tutoring (SGT)

Small Group Tutoring provides a small interactive setting for students to be comfortable to engage in conversations about course material with other students. Each session is led by a current UCSC undergraduate student who has taken the course and done well in it. Tutoring sessions are 1-Hour long and generally have a capacity of 6 students. When students sign up for tutoring, students make a commitment to attend tutoring weekly for the entire quarter. All students can sign up for up to 2-Hours of tutoring a week per couse they are enrolled in.

Academic Excellence (ACE)

ACE is an academic support program dedicated to increasing the diversity of UCSC students earning bachelors' degrees in science, technology, engineering, and mathematics. It is a community of scholars who strive for and commit to academic excellence.

Modified Supplemental Instruction (MSI)

In MSI, you can expect the MSI leader to facilitate cooperative group activities designed to have students work together on the course content. MSI is offered at least three times each week for the entire quarter. The MSI leader is an undergraduate student who took the class, did well, and is trained to facilitate group sessions to focus on you, the students, and what you need to succeed in the course. LSS provides continuous training for MSI leaders to create inclusive spaces for students and facilitate group work effectively. MSI is for everyone and open to all students in class to get extra practice on the things you already know or the things you want to know better. Attendance is voluntary; however, students who attend MSI sessions weekly earn a higher final grade than students who do not participate in MSI.

DRC Accommodations

UC Santa Cruz is committed to creating an academic environment that supports its diverse student body. If you are a student with a disability who requires accommodations to achieve equal access in this course, please submit your Accommodation Authorization Letter from the Disability Resource Center (DRC) to me privately during my office hours or by appointment, preferably within the first two weeks of the quarter.  At that time, I would also like us to discuss ways we can ensure your full participation in the course.   I encourage all students who may benefit from learning more about DRC services to contact DRC by phone at 831-459-2089 or by email at

Inclusivity Statement

We understand that our members represent a rich variety of backgrounds and perspectives. UCSC is committed to providing an atmosphere for learning that respects diversity. While working together to build this community we ask all members to:


  • Is the book required for the class?

    No. The book is a good reference to clarify concepts and to practice more problems.

  • Was there a curve last semester?

    No. We don't do curves in this class.

  • I am going to miss a day of class. What should I do?

    Watch the videos of the class and check the material in Canvas.

  • Can we use calculators on the Exams?


  • This Homework problem is impossible to do without a calculator. What should I do if it's on the Exam?

    If a Homework problem really is impossible to do without a calculator, it won't be on the Exam.

  • What can I do to improve my grade?

    Study. Do Homework. Do not wait until the end of the quarter.

  • Do you drop any grades?

    See the grade description.

  • I need a C to keep my scholarship, what can I do?

    Study. Do Homework. Do not wait until the end of the quarter.

  • I added this class late and missed the first one/two/three Homeworks. Can you accept them late?

    No. We do not accept late Homework for any reason. We drop the lowest Homework scores for just such eventualities.

  • Will there be a curve?


  • What do I have to make on the final to get an A/B/C in the course?

    We use the regular grading system.

  • I sent a math question to my instructor and I didn't get a response. Why?

    Because it's impossible to write math over e-mail. Use Canvas or Piazza regarding questions in the class.

  • Can we use calculators on the Homeworks?


  • Do you give extra credit?

    No but our grade distribution add's up to more than 100%.

  • What is going to be on the exam?

    Everything we have done in class.

  • Why you don’t reply my emails?

    Messages regarding this class must be sent through Canvas or Piazza.