Course:  Math 18

Title:  Linear Algebra

Lecture:  MWF 8:00--8:50am in Ledden Auditorium

Discussion Sections:
A01: Thursday 8:00--8:50 am, AP&M 2301 with Veera Palacharla
A02: Thursday 9:00--9:50 am, AP&M 2301 with Veera Palacharla
A03: Thursday 10:00--10:50 am, AP&M 2301 with Alice Chan
A04: Thursday 11:00--11:50 am, AP&M 2301 with Alice Chan
A05: Thursday 12:00--12:50 pm, AP&M 2301 with Alice Chan
A06: Thursday 1:00--1:50 pm, AP&M 2301 with Alice Chan

Credit Hours: 4 units

Prerequisite: Math 3C, 4C, 10A, 20A, or test equivalent

Catalog Description:Matrix algebra, Gaussian elimination, determinants. Linear and affine subspaces, bases of Euclidean spaces. Eigenvalues and eigenvectors, quadratic forms, orthogonal matrices, diagonalization of symmetric matrices. Applications. Computing symbolic and graphical solutions using Matlab. Students may not receive credit for both Math 18 and 31AH.


  • Linear Algebra and its Applications, 5th edition, by Lay, Lay and McDonald. International edition is acceptable, as homework from the book won't be turned in. Similarly, the 4th edition text seems to be very close to the 5th edition. If you do not have the 5th edition, you will need to get the (book) homework problems from another student who does. You will NOT need the MyMathLab code, as we will NOT be using it for homework. Reading is REQUIRED.
  • I-clicker 2: We will use these daily.

Course Outcomes: By the end of the course, you should be able to show understanding and mastery of the subject material

  • by performing calculations, including knowing which tools to use in which circumstances
  • by clearly explaining concepts, processes, definitions and theorems.
For this course, the main subject material is
  • systems of linear equations (mathematical interpretations of systems, row reduction, solution sets, as matrix equations, linear independence)
  • linear transformations (as matrices, vector spaces, null spaces, column spaces, bases, dimension, rank, change of basis)
  • determinants
  • eigenvalues and eigenvectors (characteristic equation, diagonalization)
  • orthogonality, length, the Gram-Schmidt process and QR-factorization
  • the least-squares problem.

In addition, students should improve their ability to learn mathematics from a textbook and to explain mathematics to others.

I will focus my teaching, homework and tests on these subjects and outcomes.

How this course will be run: For your benefit, this course will not be run in a traditional lecture format. Here is how a usual pre-lecture, lecture and post-lecture will proceed.

  • Pre-lecture: You will read the sections to be covered for the lecture. Some tips for reading are below, and you are responsible for material in the assigned reading whether or not it is discussed in the lecture.

    By midnight before lecture, you will complete a short reading quiz on TritonED. These quizzes will count as part of your iClicker grade and will have infinite tries. These questions are meant to be fairly easy, to check if you did the reading, and to find potential misunderstandings you have.

  • Lecture: "Lecture" will begin with a discussion of any points from the reading quiz that I feel students had problems with or are particularly important.

    In "lecture," I will discuss various important ideas from the sections, and will ask questions about and from the reading assignment. You will discuss these questions and ideas with other students. iClickers will be used for these questions, and will count for a (small) portion of your grade.

    I will NOT lecture on the entire section. If you do not do the reading, the lecture will not cover everything you need to know, since I will assume that you have at least a cursory understanding of the material in the textbook.

  • Post-lecture: You will complete homework and discussion section problems on the material from class and the textbook.

Tips for reading:

  • Reading a math textbook is not like reading a history textbook. A quick read-through will do very little, if anything, for you. You need to understand each paragraph before continuing on. Your understanding will increase as you spend time thinking about what you read.
  • The language and terms used are important! An important part of learning the math is learning the terms used, their definitions, why those definitions were chosen, and the idea behind the terms. This is also incredibly important when trying to communicate and explain math. Language is a huge part of mathematical thinking.
  • Allow yourself plenty of time. When I read new math, I expect to spend an average of 15 minutes a page, though sometimes it can take much longer than that.
  • Remove distractions. Turn off your cell phone. Turn off your computer. Hide in the corner of the library. Even short distractions ruin your focus. Research shows that multitasking does not work, and, in fact, those who think they are better at it are actually worse at it.
  • The Practice Problems at the end of each section in the book are useful in self-evaluating your understanding.
  • If you continue to have difficulty understanding the material after spending time trying to read and understand it on your own, my office hours and the TAs' office hours are a good way to get additional help.

Discussion sections: Discussion sections will not be a time to ask questions about the homework, as they are in most classes. Instead, they will be run as follows:

  • You will be split, more or less at random, into groups of 3-4.
  • You will be assigned the roles of manager, skeptic and recorder. These roles will be explained on the assignment sheets.
  • You will work as a group on assigned problem(s) from sections we have covered in class.
  • Your group's answer for one of the questions will be written down and submitted to by the end of the section. (Bring your cellphone.) The first few will be graded by your TA so that you can learn the quality expected on an exam. After the first midterm, they will be graded (quickly) by the homework grader.
  • The grade is half participation (so 5 points out of 10). Thus, an answer that gets 7/10 points is of a quality that would get 2/5 points on an exam.
  • These assignments will be a small portion of your grade.

Additional resources: The following are some recorded lectures for linear algebra from other universities. These are not the only examples, but may help you in understanding the material. However, these lectures are not based on the same textbook we are using, so the organization is different.

Calculators: A calculator is not needed or expected for this class. If you use one, a TI-83 or TI-84 (or similar model) suffices for this course, as would any more powerful calculator (such as a TI-89). The calculator should be used only as an aid in learning concepts, not just as a means of computation. Note: The use of calculators will not be permitted during exams.

iClicker: iClickers are required for this class. We will use them daily. Make sure to register your clicker on via tools => i>clicker Student Registration.

Gradescope: All standard homework assignments will be turned in via

  • Your login is your university email, and your password can be changed here. The same link can be used if you need to originally set your password.
  • Assignments should be in a single pdf file before being uploaded, or as a picture for each question.
  • Hand written files can be scanned to be uploaded. High resolution is not required. However, make sure your files are legible before submitting.
  • Most word processors can save files as a pdf.
  • There are many tools to combine pdfs, such as here.
  • All grading, including the midterms and final, will be done on Gradescope. Regrade requests must be sent via Gradescope.
  • If you have not yet been added to the course, the Gradescope entry code is M452Z9.

Homework: Homework exercises will be assigned each Monday on the course homework page and they are due on the subsequent Monday by 8 am, i.e., before class. There will usually be three problems that you will turn in each week.

In addition to the required homework, I will give more suggested problems. These will not be turned in, but you should to do them if you want to succeed in the class. The graded problems will likely not be enough practice to be able to do the required calculations quickly enough for a test.

MATLAB assignments: You have five MATLAB assignments and a MATLAB quiz that count for a total of 10% of your course grade (the assignments count for 5%, and the quiz counts for 5%).

Midterm Exams: There will be two midterm exams, one given on Monday, Oct 17 and the other on Monday, Nov 7 during class (see the course calendar). No calculators will be allowed during the midterm exams. You may bring one 3x5 notecard with as many notes as you can write onto it. Students will not be allowed to take makeup midterm exams. If you will miss an exam for an excellent reason, please contact me as soon as possible so that we can make arangements.

Final Exam: The final exam will be held at the following time:

  • 8:00am--10:59am Monday, December 5th (See the course calendar.)
No calculators will be allowed during the midterms or during the final exam. You again get ONE 3x5 card.

Grading: Assignment grades will be posted on Gradescope and/or TritonED. Your term grade will be based on the scores of the homework, iClicker questions, MATLAB assignments, two midterms and one final exam. Your term grade will be the highest of the following:

  • (5% iClicker and reading quizzes) + (5% discussions) + (10% MATLAB) + (15% HW) + (17.5% Midterm) + (17.5% Midterm) + (30% Final)
  • (5% iClicker and reading quizzes) + (5% discussions) + (10% MATLAB) + (15% HW) + (20% best Midterm) + (5% worst Midterm) + (40% Final)
I will not determine a curve until after the final exams have been graded. However, I generally curve the exams so that the class average for each is somewhere between 75 to 85%. As a warning, my raw test scores are often low, by design. Make sure to look at the class average before despairing.

Academic Dishonesty: Academic dishonesty is considered a serious offense at UCSD. Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university. It is in your best interest to maintain your academic integrity.

Accomodations: Students with special needs or disabilities must provide an Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities (OSD) as soon as possible. Please call OSD at 858-534-4382 or visit for more information