MATH 203 Linear Algebra (3) Spring 2023
203-03 (20962) 11:00-11:50am MWF MAYBANK HALL 223
203-01 (20374) 1:00-1:50pm MWF MAYBANK HALL 113

last change: April 6, 2023

Tom Kunkle, 327 RS Small, kunklet@cofc.edu, (843)953-5921 (office), (843)766-0943 (home).
Hours: M 9:00-10:00am, Tu 3:10-4:10pm, W 10:00-10:50am, F 12:00-12:50pm, or by appointment.
Warning: I can only hold limited office hours on exam days. Please study and get your questions to me before the day of the exam.
I'm happy to meet at other times that fit your schedule, if I'm available. Here's what my week looks like.
Linear Algebra and Its Applications, 6th edition, David C. Lay, Pearson. ISBN-13: 9780135851258
There are no other required materials for this course.
This is probably the best introductory linear algebra book available. If you use it only as source of exam problems, you're cheating yourself. Read it, and as you do, follow along with the author with paper and pencil.
If it becomes necessary for me to change any part of this syllabus, you'll always find its most current version at https://kunklet.people.cofc.edu/ Look for the last change date at the top of this document, and the description of changes at the bottom.
A passing grade in MATH 120 or permission of instructor
Note: The number of exams and quizzes, their dates and their point values may change in the event of an emergency, e.g., the college changing its schedule or delivery of classes during the semester due to weather or contagion.
We'll have three (3) 50-minute midterm exams, a 2-hour final exam, and weekly quizzes. All exams will be in-person and closed-book: no notes, books, calculators, electronic devices, etc.
Every exam will have at least one problem asking you to prove or explain something in writing. Look for problems like these in the homework.
Although basic ideas we learn in this course can appear on multiple exams or quizzes, each weekly quiz will be based primarily on material covered since the time of the previous exam or quiz, and, each midterm exam will be based primarily on material covered since the previous midterm. Our final exam will be weighted slightly toward material covered after the last midterm but will otherwise be cumulative. Unless I tell you otherwise, you should assume that any topic of this course could appear on the final. When in doubt, please ask me.
Each of the midterm exams is worth 100 points, the final exam is worth 150 points, and the weekly in-class quizzes are worth 30 points altogether. Minimum required scores for letters grades are
A (90%)
A- (87%)
B+ (83%)
B (80%)
B- (77%)
C+ (73%)
C (70%)
C- (67%)
D+ (63%)
D (60%)
D- (57%)
I won't drop any exams, but if you do better on the final exam than on your worst midterm exam (excluding any on which you received a grade reduction for an honor code violation), I'll raise that (one) midterm exam score by averaging it with your final exam (percentage) score. Then, at the end of the semester, I'll calculate your course grade two ways--based on the percent you earned of the 450 possible exam points, and again based on the percent you earned of the 480 possible exam and quiz points--and give you whichever letter grade comes out higher.
Here are the exams and solutions from the last time I taught this class under a format similar to this semester's. Since course content, exam dates, and the order of topics can change from one semester to the next, these exams might not always cover the material you should be studying for your exams. You can see exactly which sections are represented on these old exams by searching in the solutions for the word "Source." math department sample final exams
Calculators will be excluded from all exams and quizzes but will be useful in some of the exercises. I think all TI calculators have many useful built-in matrix functions. When you want a symbolic calculator, WolphramAlpha.com does everything. For those of you who are interested in programming, Octave is a very good free clone of MATLAB, the leading linear algebra software. I managed to install a fully functioning Octave on my Mac using Homebrew.
Caution: Overreliance on calculators will leave you unprepared for the exams.
I strongly encourage you all to attend class every day. Good attendance is a necessary first step towards a good grade. If you're absent on a non-exam day, I'll assume that you have a good reason for missing and will not require an excuse; however, I am unable to reteach the class to everyone who misses a day. Instead, I encourage you to catch up using the text, the videos and notes I've prepared for you, and notes from a classmate, if possible. Try homework for the day you miss, and then bring questions to me in my office. See Make-up Policy for absences on exam days.
Only students officially registered (graded or auditing) for this course may attend class. During the week following the drop/add deadline, the professor will verify student enrollments in this course. Any student appearing on the class roll but determined not to have attended the class even once will be removed, except for cases where a student is absent because of quarantine or isolation due to COVID-19
Exams:
If you must miss an exam, I expect you to make every effort to contact me as soon as possible. Do not delay. Out of fairness to your classmates, I can allow you a make-up exam only if I determine that your absence at exam time and every reasonable time until the make-up is excusable. If you've never seen a doctor for an illness causing you to miss the exam, it might be difficult for me to allow you a makeup. An unexcused exam will be given the grade zero, probably causing you to fail the course.
Quizzes:
At the end of the semester---starting from the date of the last in-class quiz and ending on the last day of final exams---I'll allow you to make up at most two (2) quizzes that you've missed for any reason. These makeups can only be used to replace quizzes that you've missed due to absences, not simply low scores. The topic of the makeup quizzes can be from anything we've covered during this semester and will be taken outside of class at a mutually convenient time. I'll drop your two (2) lowest quiz scores (after any makeups) before computing your quiz average.
Attend every class, practice lots of homework, and read the book!
After each class, do as many of the assigned problems as possible. There will be a short time to ask questions about these at the beginning of the next class. If you run into dificulty, really try; don't flit from one unsolved problem to the next.
Don't just do the homework until you get the right answer, but practice homework problems until you can work through them reliably on an exam. Practice reading the instructions on homework problems. If you are able to do the homework only after looking at some answers in the back to figure out what the question is asking, then you're not prepared for the exams.
Begin extra studying at least a week in advance for the tests. Rework old problems that could appear on the test. Write and rewrite a special set of notes that summarize in your own words the important facts for the test. Include in these notes the different types of problems appearing in the homework and the steps you follow to solve each type. For example, here are the notes written by an A student while studying for the first test in MATH 111 Precalculus.
Here are some review notes I wrote to help you study for the exams. I go over these notes in the videos found here. These notes aren't meant to take the place of the text and lectures.
All class announcements, your exam and quiz grades, and any course materials not found on the syllabus and will be available on Oaks, the College's learning management system. For technical problems with Oaks, please contact the IT Help Desk at 843.953.5457 or studentcomputingsuport@cofc.edu.

This is a list of all the problems worth doing in each section we'll cover. I won't collect these, but you should be doing them daily.

"5-25" means at least the odd numbered problems between 5 and 25, inclusive, and preferably the even numbered problems as well.
"5-25(x15,18)" means problems 5-25, excluding 15 and 18.
* indicates a challenging but worthwhile problem.
** indicates a very challenging problem for your enjoyment only. I won't put a ** problem on an exam, and, unless it's a slow day, I probably won't have time to do one in class.
[17] means to do problem 17 if time allows us to cover this topic in class. Ask me if you're not sure.
"2.sup" refers to the supplementary exercises at the end of Chapter 2.

1.1: 1-16, 19-35, 37, 39-42, 43*, 44*.
1.2: 1-4, 7-15, 19-40(x28), 45.
1.3: 1-35b, 36ab, 41**,42**.
1.4: 1-4, 7-15, 17-46(x38).
1.5: 1-13, 15, 19-22, 23*, 24*, 27-36(x29,30,33,34), 41-52(x49).
1.7: 1-26(x22), 27*, 28-31, 32*, 33-38, (39-44)*, 45, 46.
1.8: 1-29(x18,27), 32**, 35, 36*, 39-31, 42**.
1.9: 1-12, 13*, 14*, 15-40, 43.
1.sup: 1-25, 29-48(x34,41,43,47,48).
2.1: 1-30(x14), (31-33)*, 35, 36.
2.2: 1-29(x15,16,22), 39-48(x46).
2.3: 1-7, 11-38(x33), 41, 42, 45, 46.
2.sup: 1-17, 18*, 19, 20*, 21-24, 29-31.
3.1: 1-14, 19-42.
3.2: 1-21, 24, 25, 27-46(x36,44).
3.3: 1-16, 18-24.
3.sup: 1-20, 21**, 25, 26.
4.1: 1-36(x4,25,32).
4.2: 1-40(x37), 41*, 42*, 43-45.
4.3: 1-34, 35*, 39, 40, 41*, 42*, 43.
4.4: 1-23(x19,20), 24*, 27, 28, 29*, 30*, 31-36.
4.5: 1-30, 31*, 32*, 33-40, 41*, 42*, 43-50.
4.sup: 1-25(x19,21,24), 27.
5.1: 1-33, 34*, 35, 37, 38, 39*, 40*.
5.2: 1-17, 18*, 19*, 20-30, 31**, 32.
5.3: 1-27, 28*, 29-34, 37*, 38.
5.4: 1-24, 25*.
5.5 1-16, (17-20)*,23-26.
5.sup 1-21, (22-25)*.
6.1: 1-20, 21*, 22*, 23-31, 32*, 33* (Hint: the set of all such vectors is the null space of what matrix?) 34-39.
6.2: 1-14, 17-37.
6.3: 1-18, 21-29, 30*.
6.sup: 1-13, 14* (Hint: try a 3x2 matrix.), 15-16.
See CofC calendars and exam schedules for potential storm makeup days.
Content of exams and quizzes refers to topics in their order of appearance on this Schedule. For instance, "Exam 1 (1.1-1.9)" means all questions on Exam 1 will be selected from 1.1, 1.2, 1.3, 1.4, 1.5, 1.7, 1.8, 1.9.
W 1/11 ( 1 ) : 1.1
F 1/13 ( 2 ) : 1.1, 1.2
M 1/16 :holiday
W 1/18 ( 3 ) : 1.2
F 1/20 ( 4 ) : 1.3 Quiz 1 (1.1-1.2)
M 1/23 ( 5 ) : 1.4
W 1/25 ( 6 ) : 1.4, 1.5
F 1/27 ( 7 ) : canceled
W 2/1 ( 9 ) : 1.7
M 2/6 ( 11 ) : Q&A
W 2/8 ( 12 ) : Exam 1 (1.1-1.8)
F 2/10 ( 13 ) : 1.9 Why is rotation linear?, 2.1 slide
M 2/13 ( 14 ) : 2.1, 2.2
W 2/15 ( 15 ) : 2.2, 2.3 slide
F 2/17 ( 16 ) : 2.3 Quiz 4 (2.1-2.2)
M 2/20 ( 17 ) : 3.1
W 2/22 ( 18 ) : 3.2
F 2/24 ( 19 ) : 3.3 Quiz 5 (2.3-3.2)
M 2/27 ( 20 ) : 4.1
W 3/1 ( 21 ) : 4.1, 4.2 writing subspace proofs
F 3/3 ( 22 ) : 4.2 Quiz 6 (3.3,4.1)
M 3/6 :holiday
W 3/8 :holiday
F 3/10 :holiday
Express II classes begin Mar 13. Mar 24 is the last day to withdraw from this course with a grade of W. 
M 3/13 ( 23 ) : 4.3
W 3/15 ( 24 ) : Q&A
F 3/17 ( 25 ) : Exam 2 (2.1-4.3)
M 3/20 ( 26 ) : 4.4
W 3/22 ( 27 ) : 4.5
F 3/24 ( 28 ) : 4.5 Quiz 7 (4.4)
M 3/27 ( 29 ) : 5.1 Quiz 7 due
W 3/29 ( 30 ) : 5.2
F 3/31 ( 31 ) : 5.3 Quiz 8 (4.5-5.2)
M 4/3 ( 32 ) : 5.3, 5.4
W 4/5 ( 33 ) : 5.4
F 4/7 ( 34 ) : 5.4 Quiz 9 (5.3)
M 4/10 ( 35 ) : 5.5
W 4/12 ( 36 ) : Q&A
F 4/14 ( 37 ) : Exam 3 (4.4-5.5)
M 4/17 ( 38 ) : 6.1
W 4/19 ( 39 ) : 6.2
F 4/21 ( 40 ) : 6.3 Quiz 10 (6.1-6.2)
M 4/24 ( 41 ) : Q&A
W 4/26 ( 42 ) : Q&A
F 4/28 ( 43 ) : Final Exam 203-03: 10:30am-12:30pm, 203-01: 1-3pm.

The Center for Disability Services/SNAP is committed to assisting qualified students with disabilities achieve their academic goals by providing reasonable academic accommodations under appropriate circumstances. If you have a disability and anticipate the need for an accommodation in order to participate in this class, please connect with the Center for Disability Services/SNAP. They will assist you in getting the resources you may need to participate fully in this class. You can contact the Center for Disability Services/SNAP office at 843.953.1431 or at snap@cofc.edu. You can find additional information and request academic accommodations at the Center for Disability Services/SNAP website. Currently, SNAP requires students to schedule alternate testing arrangements at least one week before the exam date.
This introductory linear algebra course is intended for students majoring in the mathematical, natural, or social sciences. We'll cover systems of linear equations and their solutions, row reduction, matrix algebra and inverse matrices, determinants and Cramer's rule, vector spaces, linear transformations, linear independence and spanning sets, eigenvectors, eigenvalues, diagonalization, and the basics of orthogonality. For more details, see the list of sections below and our text.
By the end of the course, students should be able to
  1. Solve a linear system by row reduction and express the solutions in parametric vector form.
  2. Find the dimensions and bases of the null-, column-, and row-space of a matrix
  3. Determine the linear independence of a set of vectors.
  4. Perform basic vector and matrix arithmetic.
  5. Determine the invertability of a given matrix, and compute the inverse by row reduction and Cramer's Rule;
  6. Compute determinants by row reduction and by row or column expansion;
  7. Determine whether a subset of a given vector space is a subspace.
  8. Translate fluently between the desciption of a linear transformation and its representation as matrix multiplication;
  9. Find the eigenvalues of 2 by 2 and triangular matices, the eigenspaces of matrices with given eigenvalues, and the diagonalization of such matrices.
  10. Compute lengths and inner products of vectors in ℝn and their projection onto a span of orthogonal vectors;
  11. Demonstrate understanding of the definitions and theorems of introductory linear algebra by using them to write logically and grammatically correct proofs.
This course can be used to satisfy some requirements of the undergraduate mathematics degree program, for which there are also some standard goals; students will:
  1. use algebra, geometry, calculus and other track-appropriate sub-disciplines of mathematics to model phenomena in mathematical terms;
  2. use algebra, geometry, calculus and other track-appropriate sub-disciplines of mathematics to derive correct answers to challenging questions by applying the models from the previous Learning Outcome; and
  3. write complete, grammatically and logically correct arguments to prove their conclusions.
These outcomes will be assessed on the final exam.
As members of the College of Charleston community, we affirm, embrace and hold ourselves accountable to the core values of integrity, academic excellence, liberal arts education, respect for the individual student, diversity, equity and inclusion, student centeredness, innovation and public mission. Congruent with these core values, the College of Charleston expects that every student and community member has a responsibility to uphold the standards of the honor code, as outlined in the Student Handbook. In pursuit of academic learning, you are expected to reference the work of other scholars, and complete your own academic work, while utilizing appropriate resources for assistance. Any acts of suspected academic dishonesty will be reported to the Office of the Dean of Students and addressed through the conduct process. Your adherence to these practices and expectations plays a vital role in fostering a campus culture that balances trust and the pursuit of knowledge while producing a strong foundation of academic excellence at the College of Charleston. Any questions regarding these expectations can be clarified by your instructor.
If in-person classes are suspended, I'll announce a detailed plan for a change in modality to ensure the continuity of learning. All students must have access to a computer equipped with a web camera, microphone, and Internet access. Resources are available to provide students with these essential tools.
Changes:
1/29: revised Schedule after 01/26 cancelation.
2/01: revised Schedule and topics Exam 1.
2/10: added Why is rotation linear? 2_1slides
2/15: 2_3slides
3/2: Added this guide to writing subspace proofs to Schedule.
3/24: Quiz 7 is take-home, due Mar 27.
3/27: slides 5.1, 5.2
3/29: assigned problems in 5.1-5.3.
4/6: assigned problems for all remaining sections.