# Math 304-06: Linear Algebra

## Fall 2021

To the main 304 course site for Fall 2021.

#### Teacher

Thomas Zaslavsky
Office: WH-216
Email: zaslav@math.binghamton.edu

#### Office hours

My regular office hours are M, W, F, 1:00-2:30. You do not need an appointment. If I'm not in my office, I am probably nearby and will be back shortly...
Also by appointment at other times.

#### Face coverings

Your face mask is required to cover both nose and mouth and to be on at all times during class. That means no eating. You will not be allowed in class if you don't follow this rule. I'm sure I don't have to explain why.

### Course description

#### Syllabus

The textbook is Linear Algebra, Fourth Edition, by Jim Hefferon. A free e-book is available. You can order a cheap print copy for around \$22.

For the list of topics and sections covered, see the main 304 site.

#### Course goals

Develop theoretical and computational skills in basic linear algebra.

I will not cover everything in lectures; you have to learn a lot by reading for yourself.

I encourage you to form study groups. Discussion with other students is a big part of learning math.

I expect everyone to read the assigned sections carefully before the lecture.

Supplementary topics are found in our special supplement.

#### Homework assignments

The homework is on WebWork (see the main 304 site). You are supposed to do the homework. I highly recommend the problems in the textbooks (see the main 304 page for the list). I do encourage you to work together. That does not include looking up solutions on line (or off line), not even at Khan Academy, whose solutions often are not good. If you find a solution on line, DO NOT USE IT. I know from experience that using outside resources tends to lower your grade. Instead, email me or see me in person.

Webwork recommended problems

For Test 1: Sets 1, 3, 4 ##1-6, 6.

For Test 2: Sets 4, 5, 7, 8.

For Test 3: Sets 9-11 and part of 12.

For Final Exam: Set 12, Basic 1 and 2 (as reminders of early September) if you have not done them.

#### Schedule

The times are approximate. We are not exactly following the textbook in class, although we are hewing close to it.
• August–early September: Chapter 1, Section I (omit proof of Lemmas 3.6-7). Also, the appendix on logic and sets and functions (omit mathematical induction).
• 9/10–17: Chapter 1, Section II.
• Matrix multiplication: Ch. 3 Section IV.2: 2.3-6, 2.8-13. Recommended Ex. 2.14-17.
• 9/20–22: Chapter 1, Section III (much of this is review).
• 9/22–24: Chapter 2, Section I.
• 9/27–10/1: Chapter 2, Section II.
• 10/4: Chapter 2, Section II, and review.
• 10/6: Test 1. Coverage: Ch. 1 and 2 (except Section III) and matrix multiplication. Also see the supplement.
• 10/8–13: Chapter 2, Section III.
• 10/18–22: Chapter 3, Sections II-III.
• 10/22–31: Chapter 3, Sections III-IV. (Section IV is partly review.) Also CDTW Section 2.3. WebWork Sets 4, 5, 7, 8.
• 11/1: Chapter 3, Section V.
• 11/1: Review.
• 11/3: Test 2. Coverage: Ch. 2 and 3 (assigned parts).
• 11/5–8: Chapter 3, Section V. Basis change for simplifying matrices.
• 11/8–12: Determinants. Chapter 4, Sections I.1-2, II, III. (Optional reading, if interested: Cramer's Rule for the inverse matrix.)
Note that we are taking the definition of the determinant to be the Laplace expansion in row 1 (Theorem III.1.5 in Ch. Four). We are skipping the book's definition (to make more time for eigenvalues).
• 11/12–15: Complex numbers. Readings in Matthews Sections 5.1-6.
• 11/15–29: Eigenvalues et al. Readings in Matthews Sects. 6.1-2; Hefferon Ch. 5, Section II.3.
• 11/29–12/3: Diagonalization. Hefferon Ch. 5, Section II (all).
• 12/3–10: Orthogonality. Projection. Hefferon Ch. 3, Section VI. Orthogonal (or "orthonormal") matrices. Reading in Matthews, pages 130, 132.
• 12/11: Review session in WH 100E, 1-3 p.m.

#### Quizzes

There will be many short quizzes. There are no make-up quizzes. There will be quizzes approximately weekly, usually on Friday. The past quizzes are available here:
Quiz 1 | Quiz 2 | Quiz 3 | Quiz 4 | Quiz 5 & Solutions | Quiz 6 & Solutions | Quiz 7 solution | Quiz 8 solution | Quiz 9 | Quiz 10 | Quiz 11 | Quiz 12 & Solutions

#### Exam dates and coverage

See the main course page. Details will appear.
• Exam 1: Wednesday, Oct 6. Coverage: Everything we have done up to that time, including class, textbook readings and exercises, and Webwork.
• Test 1 and solutions.
• Grade guide: A (80+), B (65-79), C (50-64), D (45-49), F (0-44).
• Exam 2: Wednesday, Nov 3. Coverage: Ch. 2 and 3.
• Test 2 and solutions.
• Grade guide: A (79+), B (64-78), C (50-63), D (44-49), F (0-43).
• Exam 3: Monday, Dec 6. Coverage: Everything we covered since the last exam (eigenvalues and eigenvectors of matrices and linear transformations, diagonalization, and also change of basis and some orthogonality).
• Test 3 and solutions.
• Grade guide: A (84+), B (68-83), C (50-67), D (45-49), F (0-44).
• Final Exam: Monday, Dec 13, 2021, 8:05-10:05 p.m. in GW 69EX. Coverage: The entire course, including orthogonality.

#### Exam policy

See the 304 course site. Notably:
• University PHOTO ID is required to take all exams.
• No electronics are allowed during exams or quizzes.

### Classroom behavior

Always turn your cell phone to silent before entering the classroom. No cell phone use is allowed except for classwork, such as consulting the textbook. If you do use your phone otherwise, I may confiscate your device for the rest of the class.

To the main 304 course site.