Math 232 Spring 2018

Math 232: Linear Algebra

Spring 2018

CLASS SCHEDULE AND HOMEWORK

SYLLABUS

Prof. Rafe Jones

Email: rfjones at carleton dot edu
Phone: 507-222-4450
Office: CMC 226
Office Hours:

Monday
Tuesday
Wednesday
Friday
10:00-11:00
10:00-11:00
9:15-10:15, 3:30-4:30
10:30-11:30

Or just stop by and see if I'm around (it helps to make appointment, though it's not strictly necessary). I have a schedule posted on my office door that gives a general idea of my whereabouts.

Class meeting times:
MW 12:30-1:40, F 1:10-2:10 in Weitz 230

Textbook: Linear Algebra with applications, fifth edition, by Otto Bretscher

Carleton college policy on Academic Integrity

Math skills center: a welcoming place where you can drop in any time to get help with math questions; it also functions as a place to study, to do homework, and to meet for one-on-one tutoring. Its hours are Monday-Friday: 8:30am-11pm, Saturday: 2-5pm, and Sunday: 2-5pm and 7-11pm. See the MSC website for more information. Or just stop by!

Grading Rubric for Homework and Exams

Note sheet art contest winners:

This one wins for best header, and best bat:

This one easily had the best snail:

This one gets an award for best abstract seaweed, and best math joke:

This one wins the coveted highest-contrast (e.g. most eye-watering) category:

This one wins for best conceptual decoration:

This one wins for basically being an art-theory class essay prompt (this was the back of the note sheet):

This one wins for most enthusiasm:

This one wins for clearest retrospective realization:

Click here to download Josh Davis' Mathematica notebook on the geometry of some linear transformations of R2 and R3.

Final Exam

The final will be this coming Monday from 3:30-6:00 pm in Weitz 133. There will be a review session on Sunday from 11-12:15 in CMC 206.

The final will be approximately twice as long as the midterms, though you'll have 2.5 hours in which to do it. It will cover everything we've done in the class. The material since the second midterm (the parts of sections 7.4, 4.1, 4.2, and 4.3 that we covered in class) will account for roughly one-third of the exam.

Note Sheet: You will be allowed to have one side of one 8.5 by 11 sheet of notes for the exam. All sheets must be handwritten. You can write anything you like on the sheet -- formulas, examples, mnemonics, your personal linear algebra mantra, etc. No magnifying devices allowed. For those who would like to decorate their sheets or otherwise artistically arrange them: I will post my favorite ones on the course website after the exam.

Review tips:

Do the review problems below. There are a lot of them, but many are routine and won't take you very long. The problems from the sections are all odd, so you can check your answers in the back. Several of the final exam problems will very closely resemble review problems. Note that this is not a comprehensive list of all the kinds of questions that might appear on the final, though all the major ideas of the course are represented in these problems.
To simulate the environment of the exam, set aside 2.5 hours and do these problems: Section 1.1 #19; Section 2.2 #25; Section 3.2 #3; Section 4.1 #5; Section 4.3 #13; Section 6.1 #17; Section 7.3 #13; Section 7.4 #3, 47; and these True/False questions from the end of each chapter: Chapter 1 #22, Chapter 3 #37, Chapter 6 #37; Chapter 7 #21, 39. Note that these are a subset of the review problems below. I will post comments on these problems, so you can see if you're doing them correctly. For comments and solutions, click click here.
For a handout listing some important definitions and computation techniques, click here.
If while doing the review problems there are topics you feel you haven't grasped, consult your class notes and/or the book on that topic. You could also go back over problems on the topic from the homework assignments, reworking problems as necessary.

Review Problems:

Section 1.1 #17
Section 1.2 #9
Section 1.3 #9, 19, 47
Chapter 1 True/False Review questions, #21, 22, 23, 29, 30, 27
Section 2.1 #17, 19, 21
Section 2.2 #5, 25, 27
Section 2.3 #21, 23, 37, 39
Section 2.4 #5, 7, 13, 33, 69, 73
Section 3.2 #1, 3, 27, 29
Section 3.3 #9, 15, 25, 27
Chapter 3 True/False Review questions, #5, 7, 9, 17, 19, 21, 25, 37, 44
Section 4.1 #3, 5, 7, 23, 25, 27
Section 4.2 #3, 25, 27, 49, 53, 63
Section 4.3 #1, 13, 21, 23, 59
Chapter 4 True/False Review questions, #9, 37, 43
Section 6.1 #9, 17, 33, 43
Section 6.2 #7, 17, 37
Section 6.3 #11
Chapter 6 True/False Review questions, #13, 37
Section 7.1 #1, 9, 39
Section 7.2 #3, 9, 19
Section 7.3 #5, 9, 13, 15, 21, 27, 31, 35, 43, 47
Section 7.4 #3, 5, 33, 47, 49
Chapter 7 True/False Review questions, #1, 3, 19, 25, 27, 31, 39, 46, 51

Second Midterm

The second midterm is Monday, May 21, in Weitz 133 (during class time). It will cover Sections 3.3, as well as the material we've discussed about determinants, eigenvalues, eigenvectors, and eigenbases, which roughly corresponds to Sections 6.2, 7.2, and 7.3. The exam will consist of a few computation problems, and a few true-false questions with explanation. To review for the exam, try to do the true/false review questions also without looking at your notes, and be sure to write out a sentence or two explaining your answer for each. If you recognize areas where you aren't sure of yourself, then go back and consult your notes, book, and old homework in order to solidify your knowledge. You can also simulate the exam environment by taking the practice exam below without looking at your notes, and using only 70 minutes.

Some review problems:

Chapter 3 Exercises (pp. 163-165) #1-7, 16, 17, 19, 29, 38, 41, 43, 44, 50.
Chapter 6 Exercises (pp. 308-309), #3, 7, 8, 12, 15, 17, 37, 40, 41.
Chapter 7 Exercises (pp. 382-384), #1, 3, 19, 27, 31, 33, 36, 39, 46, 51, 53.

For solutions to all the true-false questions at the end of each chapter, click here.

For a practice midterm, click here.

For solutions to the practice midterm, click here.

First Midterm

The first midterm is Wednesday, April 25, in class. It will cover Chapters 1 and 2, and Sections 3.1 and 3.2. You should know all the definitions and techniques necessary to do the homework problems. The exam will consist of about 5 problems, each of which is similar in format to one of the homework exercises. There will also be a section of true/false questions, similar to the review exercises below. You'll need to make sure you justify your answers for those, so it's good to get in the habit of writing down a few sentences justifying your answers as you do the exercises below. There is also a practice midterm below, which is similar in format to the actual exam. You'll have the full 70 minutes of class on Wednesday to complete the exam. Good ways to review for the exam include working the review problems below, using the practice exam to simulate an exam environment, reworking any homework problems that you lost points on or feel you didn't fully understand, and reviewing your class notes.

Below are quite a lot of review problems. They are True/False, but they're not necessarily easy! For each problem, you should write down some justification for your answer; for some of them just a sentence will do, while for others you'll need to do a computation, give an example, or make an argument. For instance for #4 from Chapter 1, if you think the answer is false, then you should jot down a system of four equations in three unknowns that is consistent. You should be able to move quickly through the first ones from each chapter, but some of the later ones will require significant thought.

Chapter 1 Exercises (pp. 38-40) #1-27, 31-35, 37, 39, 41-43.
Chapter 2 Exercises (pp. 107-109) #1-11, 18, 19, 21, 23, 27, 30, 34, 35, 36, 40, 43, 47, 53, 49, 50, 53, 57.
Chapter 3 Exercises (pp. 163-165) #6, 7, 9, 13, 14, 18, 20, 22, 25, 27, 29, 37, 41.

For a practice midterm, click here. For solutions to the practice midterm, click here.

For solutions to all the true-false questions at the end of each chapter, click here.

Welcome to the class!

EXAMS

Midterm Exam 1: Wednesday, April 25, in class

Midterm Exam 2: Monday, May 21, in class

Final Exam: Monday, June 4, 3:30-6:00pm

CLASS SCHEDULE AND HOMEWORK

SYLLABUS

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