Place and time: UNIV 117, TR 7:30-8:45 (section 126) and TR 9:00-10:15 (section 127).
Instructor: Paul VanKoughnett
Email: pvankoug AT purdue DOT edu
Office Hours: Tuesday 1-3, Wednesday 1:30-2:30, or by appointment, in MATH 842. (You're also welcome to drop by if my door is open. I'll typically be around Monday afternoon through Thursday afternoon.)
Course contents: Systems of linear equations, finite dimensional vector spaces, matrices, determinants, eigenvalues and eigenvectors.
Textbook: Penney, Linear Algebra: Ideas and Applications, 4th edition. I will be assigning homework out of the textbook, so you need access to this textbook (in this edition!) to do the right problems. However, you don't need a physical copy, and if you prefer to learn from a different book or resource, there are a million options out there!
Here is the first practice midterm. For other review, do questions in the book from chapters 1 and 2. Try to do each problem in as many possible ways as you can -- everything we've learned so far is connected to everything else. You should particularly focus on sections 2.2 and 2.3, which we've had less homework for.
Here are solutions to the practice midterm.
(This is all subject to change.)
| Date | Sections covered | Homework due | Notes |
| 1/13 | Syllabus and 1.1 | Intro to vectors, matrices, and linear dependence. | |
| 1/15 | 1.1 | Quiz 1 today in class. | Linear combinations, linear dependence and independence, and span. Definition of a vector space. Assigned Homework 1, due next Thursday. |
| 1/20 | 1.2 | Systems of linear equations, and encoding them as matrices. | |
| 1/22 | 1.3 | Homework 1 due today. Quiz 2 in class. | Gaussian elimination: row-echelon and reduced row-echelon forms. Assigned Homework 2, due next Friday. |
| 1/27 | 1.3 | Solution spaces in parametric form. Counting solutions to systems of equations: number of variables = rank + dimension of solution space. | |
| 1/29 | 1.3-1.4 | Homework 2 due tomorrow. Quiz 3 in class. | Subspaces. Writing systems of equations using matrix multiplication. The column space of a matrix. Assigned Homework 3, due next Thursday. |
| 2/4 | 1.4 | The null space, and the translation theorem. | |
| 2/6 | 2.1 | Homework 3 due today. Quiz 4 in class. | Testing for dependence using the dependency equation. Expressing spans in simpler ways. Assigned Homework 4, due next Thursday. |
| 2/11 | 2.1 | ||
| 2/13 | 2.2 | Homework 4 due today. Quiz 5 today in class. | Assigned Homework 5, due next Thursday. |
| 2/18 | |||
| 2/20 | Homework 5 due today. Quiz 6 today in class. | ||
| 2/25 | Exam review | ||
| 2/26 | Midterm 1 | ||
| 2/27 | 3.1 | Homework 6 assigned. No quiz. | Linear transformations. Every linear transformation can be represented by a matrix. Lots of examples. |
| 3/3 | 3.2 | Composition of linear transformations is represented by matrix multiplication. | |
| 3/5 | 3.2-3.3 | Assigned Homework 7, due next Thursday. No quiz. | More about matrix multiplication. Introduced the inverse of a linear transformation. |
House rules: You can call me Paul. I'm a postdoc in the math department, which is like a temporary faculty position on the way (hopefully!) to a tenure-track professorship. I do research on algebraic topology, which has to do with encoding high-dimensional shapes in linear algebra and using it to classify and study their properties. So I think linear algebra is pretty important, and I hope you will too!
If you're confused about something, chances are someone else is. So ask a question rather than keeping it to yourself -- you'll be doing them a favor. You'll be doing me a favor too, helping me decide what to spend time on.
I expect you to come to class. If you need to miss a day or come in late, it's not a big deal -- just get notes from someone else. I'd rather you didn't sleep in class -- you'd be better off sleeping at home -- so if you feel yourself nodding off, just get up, leave the room, walk around a little bit, and come back when you feel ready.
I expect you to read the relevant sections in the book. Or, if you can find a different resource that covers the same material, you can use that instead. The most important thing is that you spend time thinking about the material, formulating questions, and doing practice problems.
Grade calculation: Grades are calculated out of 600 points, made up of 200 points for the final exam, 100 points for each of 2 midterms, 150 points for the homework, and 50 points for in-class quizzes.
Quizzes: There will be a 5-minute, 1-question quiz at the end of class every Thursday. The point of this is just to make sure that everyone's on the same page.
Homework: There will be a homework assignment due every Thursday -- mostly problems from the book, possibly with one or two I write myself. There are two ways you can turn this in: (1) hand it to me in class; (2) put it in my mailbox in the math department main office on the 8th floor (under the name "VanKoughnett"). If you want to hand it in to my box, make sure you get it in before 5 PM, when the office closes.
Late homework will generally not be accepted. If you need an extension, ask me before the homework is due.
In high school, your math homework usually took the genre of "calculations" -- sequences of numbers or symbols, linked by equals signs, or successive transformations of the same equation. If you go on to take more math classes, you may start writing "proofs", which are, among other things, paragraphs of mostly English text with some symbols sprinkled in. This class is somewhere in between -- while some problems are still just calculations, some will require you to build a logical argument and explain it in words and sentences. If you go on to work as a scientist or engineer, this is what most of the mathematical writing you read and produce will be like, whether it's a technical specification for a machine part or a statistical analysis of a set of data.
Here are some pointers on how to do this kind of writing effectively:
Exams: There will be two midterms and a final.
There will be no make-up exams except in extremely unusual circumstances -- please talk to me as soon as possible if you think you might be in such circumstances.
Accomodations for students with disabilities: Purdue University strives to make learning experiences accessible to all participants. If you anticipate or experience physical or academic barriers based on disability, you are encouraged to contact the Disability Resource Center at: drc@purdue.edu or by phone: 765-494-1247. In this mathematics course, accommodations are managed between the instructor, student and DRC Testing Center. If you have an accommodation memo from the DRC, come see me as soon as possible so we can discuss your accommodation.
Diversity and inclusion: Purdue's official nondiscrimination policy statement applies to this class. In the context of a math class, what this means is: racism, sexism, homophobia, etc. against your fellow students will not be tolerated; I hold myself to the same standard as your instructor, and in particular I will evaluate you in a nondiscriminatory way; and if something comes up in class that's making it difficult for you to learn and focus on math, I hope you'll feel comfortable talking to me about it. Let's all remember that we're learning some difficult, abstract math, and it's going to be a struggle, and if we're doing things right we'll probably be confused most of the time. For the purposes of this class, we're all in the same struggle, and I hope we can spend our time here supporting each other rather than dragging each other down.