Math 2130 (Fall 2022):
Linear Algebra for Non-Mathematics Majors

[course policies] [homework] [notes] [video] [feedback] [canvas]

About this course

Welcome to Linear Algebra for Non-Mathematics Majors! This is a linear algebra class focussed on matrix methods, calculations, and applications. The main difference between this class and Linear Algebra for Mathematics Majors is that we focus here on an intuitive — as opposed to mathematically rigorous — conceptual understanding; rigorous mathematical proofs are expected in Math 2135 but are not expected here.

Contact information

You may also contact me anonymously.

Office hours

My office is Room 204 in the Math Department. My office hours sometimes change, so I maintain a calendar showing the times I will be available. Some of my office hours will be held over Zoom, so please check the calendar before trying to find me. You can find the Zoom link on Canvas. I am often in my office outside of those hours, and I'll be happy to answer questions if you drop by outside of office hours, provided I am not busy with something else. I am also happy to make an appointment if my office hours are not convenient for you.

Syllabus

The following are the main topics of this course and a rough schedule of when we will get to them. Depending on time constraints, we may or may not cover some of the ones at the end.

Textbook

The following is the textbook for this course:

Gilbert Strang. Introduction to linear algebra, 5e.

One reason I chose this textbook is because there are plentiful supplementary materials available online through MIT's OpenCourseWare, both for you and for me to rely upon.

The textbook also has its own homepage, including a link to the solutions manual.

There are a number of online videos, and some complete courses, about linear algebra. I will likely assign a few from the following series:

3blue1brown. Essence of linear algebra.

These videos are not a substitute for our lectures and textbooks, but they do give useful visual intuition for a lot of what we are doing. You may also enjoy some of 3blue1brown's other mathematical videos.

Prerequisites

Officially Math 2300 (Calculus 2) is required as a prerequisite, but calculus will only be used in a few special applications. For the most part, the only background that is strictly required is high school algebra.

Course goals

We will learn quite a few definitions, theorems, and algorithms in this class. The following list is meant to give an idea of the different levels of mastery you can achieve with them. The letters should also give a rough idea of how those levels of mastery will correspond to a final grade.

  1. Execute an algorithm correctly in familiar situations.
  2. Reproduce statements of definitions and theorems. Execute an algorithm correctly in novel situations.
  3. Recognize situations where a definition or theorem does or does not apply. Appreciate subtleties and edge cases in definitions, theorems, and algorithms. Identify opporunities to use an algorithm.
  4. Use multiple ideas in the same problem. Understand how an algorithm works. Transform problems into forms suitable for application of an algorithm or theorem. Identify opportunities to use linear algebra in other contexts.

For example, one of the most important things we will learn in this class is the Gaussian elimination algorithm for putting a matrix in row echelon or reduced row echelon form. Here is an idea of how I might interpret the above criteria for the Gaussian elimination algorithm:

  1. Find the reduced row echelon form of a matrix when given one.
  2. Use the Gaussian elimination algorithm to compute the column space, null space, and determinant of a matrix.
  3. Recognize situations that where Gaussian elimination can provide useful information. Convert problems to forms suitable for the use of Gaussian elimination.
  4. Apply the idea behind Gaussian elimination in novel situations. Explain why Gaussian elimination can be used to compute the column space, null space, or determinant.

Homework

Homework will be assigned with every lecture. It will be collected in the subsequent lecture, but daily assignments will be graded only on completion. The only graded work in this class are the bi-weekly exams and problem sets.

The goal of homework problems is to provide practice with the concepts we encounter in class. It is an opportunity to think through the topics we discuss in class, to identify gaps in your understanding, and to fill those gaps — before you are evaluated on a graded problem set or in-class exam. In order to encourage you to go through this process of self-evaluation and -improvement, these daily problem sets will be graded on completion. I will not be able to give you feedback on every daily homework problem, but I will be happy to give you feedback if you ask me specifically about a problem.

You do not have to submit every problem that has been assigned. You can and should skip problems you find too easy or too difficult to be useful. Please let me know if you are finding our homework problems too easy to too difficult.

You should plan to spend approximately 3 hours between lectures on the class. Not all of this should be spent on homework problems: I recommend spending only 1 to 1.5 hours on homework problems, even if this means you do not finish all of them. In the remaining time, you should do the reading assignment for the next lecture and review past lectures and readings.

Expectations

You should plan to spend 9 hours per week on this class, not including lecture. It will also be necessary to supply independent motivation as not all of the work you need to do for this class will be collected, or even assigned. It is also essential to recognize early when you are struggling with a concept and discuss it with me.

Above all, you must engage actively with the material as we learn it. If you are studying actively, you will have questions. Use this principle to measure whether you are actively engaged.

Do not expect every problem to follow the pattern of a problem you have seen before! Very few problems will be a matter of applying a standard procedure to a standard kind of problem. Expect problems that give you a solution and ask what you can deduce about the original problem, or give you partial information and ask you what partial information you can conclude about the solution. After all, computers can crank out solutions to linear algebra problems much faster than you or I ever will. We want to understand how to find the places where linear algebra can be useful, how to turn the problems we encounter into linear algebra problems, and how to interpret the solutions that linear algebra gives us. To borrow a phrase from another linear algebra course, we want to understand the crank, not just turn it.

Academic honesty

I encourage you to consult outside sources, use the internet, and collaborate with your peers. However, there are important rules to ensure that you use these opportunities in an academically honest way.

  1. Anything with your name on it must be your work and accurately reflect your understanding.
  2. Expect plagiarism to be treated severely. Deliberate plagiarism will be reported to the Honor Code Office.

To avoid plagiarism, you should always cite all resources you consult, whether they are textbooks, tutors, websites, classmates, or any other form of assistance. Using others' words verbatim, without attribution, is absolutely forbidden, but so is using others' words with small modifications. The ideal way to use a source is to study it, understand it, put it away, use your own words to express your newfound understanding, and then cite the source as an inspiration for your work.

The particular format for your citations is not important, provided that they indicate what the source was and they provide sufficient information for a reader to find the source. Textual references should therefore be specific (include a page number, for example). Internet references should have a working URL.

Questions

Do you have a question or comment about the course? The answer might be in the course policies, on this page. If your question isn't answered in the course policies, please send me an email. Or, if you prefer, you may send me a comment anonymously.

Grading

Your final grade will be determined from 3 components:

Component Contribution Dates
Daily homework (completion) 10% Daily
Problem sets / take-home exams 40% 2 Sep, 30 Sep, 28 Oct, 2 Dec
In-class quizzes / exams 30% 16 Sep, 14 Oct, 11 Nov
Final exam 20% 11 Dec (Section 3)
13 Dec (Section 5)

Up to 5 missed daily homework assignments will be forgiven. Missed problem sets and missed exams may be addressed through the revisions policy described below.

The scoring on these assessments will be based on the goals listed above. Notably, your score will not always be a simple sum of point values from each problem, but will instead be my overall assessment of the degree to which you have achieved the course's goals on the relevant topics.

Missed exams and problem sets will be addressed using the revision policy. No problem set or exam grades will be dropped, apart from those replaced by revisions.

Revisions

At the end of the semester, I would like for your final grade to reflect your mastery of the course material. Exams and problem sets do not always measure this optimally, so you will be allowed to revise your scores by the following process: 1) decide which score you wish to revise; 2) identify the topics that were assessed (for example, from the course outline) and put these in a list to be handed in with your revision (you may want to clear your list with me before going on to the next step); 3) find or devise a list of problems that you can use to demonstrate your mastery of those topics (you should discuss these with me to make sure the problems you have chosen will give you adequate opportunity to demonstrate your mastery of the relevant topics); 4) solve those problems and submit your solutions to me. I will assign a replacement grade based on your submission.

As a practical matter, I insist that your revisions be submitted within two weeks of the return date of the original assignment. This is meant to prevent an influx of revisions at the end of the semester, when I will not have time to look at all of them, and to ensure that you receive the benefit of doing a revision in time for it to be relevant to the rest of the course. Revisions will not be allowed for Problem Set 4 or the Final Exam because of their timing at the end of the semester.

In your revision, be sure to include all of the following:

  1. a cover page indicating which assessment you wish to revise, a list of the topics addressed in that assessment, and a brief description of how your problems address those topics; making this list will require studying the original exam or problem set;
  2. a list of problems and solutions covering the topics named above; you must find or create these problems yourself — new solutions of the problems from the original exam or problem set will not be accepted!
  3. a list of all sources you consulted in preparing your revision (see the section on academic honesty).

Please make sure your submissions are complete and follow these guidelines. Revisions that do not follow these rules will be returned, ungraded.

Special accommodations, CoViD-19, classroom behavior, and the honor code

The Office of Academic Affairs officially recommends a number of statements for course syllabi, all of which are fully supported in this class.

If you need special acommodation of any kind in this class, or are uncomfortable in the class for any reason, please contact me and I will do my best to remedy the situation. You may contact me in person or send me a comment anonymously.