VANDERBILT UNIVERSITY
Department of Mathematics
Math 194-1: Methods of Linear Algebra
Room SC 1313, MWF 8:10—9:00
Spring 2008, 3 hours credit
Instructor: Daniel Ramras, Ph.D.
Office Phone:
(615) 322-4169
Math Office:
(615) 322-6672
e-mail: daniel.ramras@vanderbilt.edu
Text:
Office: 1408 Stevenson Center
Office Hours: T 4:00-5:30pm, Th 5:10-6:30pm
or by appointment
Linear Algebra with Applications, 7th edition, by Steven J. Leon. Reading the text is an important
part of this course, and students will be expected to read the sections indicated on the syllabus
before class.
Prerequisite and Description: Math 194 is an introduction to Linear Algebra. Students are expected to have
completed a single-variable calculus sequence (e.g. Math 150A-B and either Math 170A or Math 175).
Students should also have completed or be enrolled concurrently in a multivariable calculus course
(e.g. Math 170B or Math 175). If you are not sure that you meet these prerequisites, please contact the
instructor immediately. Students receiving credit for Math 194 will not receive credit for any of the
following: Math 196, Math 204, Math 205a.
The course will address the following topics: Systems of linear equations, matrices, and row reduction
(Chapter 1); Determinants of matrices (Chapter 2); Vector spaces and linear transformations (Chapters
3 and 4); Eigenvalues (Chapter 6); Orthogonality (beginning of Chapter 5). Applications of all of the
above to various problems in science and engineering will also be covered.
Attendance: Consistent attendance will be expected of all enrolled students. Students who miss a class
meeting are responsible for any assignments and announcements made.
Calculators: Calculators will not be used.
Classroom Policy: Students are not allowed to use electronic equipment such as cell phones, music
players, or computers during class. These activities are a disruption to the instructor and students.
Honor Code: All quizzes and exams will be subject to Vanderbilt’s Honor Code. Students will not be
allowed any resources (books, notes, etc.) during quizzes and exams, and must work individually.
Accommodation Procedure: If the student needs course accommodations due to a disability, special
arrangements in case the building must be evacuated, or has emergency medical information that
needs to be shared with the instructor, contact the instructor as soon as possible. The Opportunity
Development Center (2-4705) at Vanderbilt provides services for students with disabilities.
Specific accommodations can be made for students with either physical disabilities or learning
disabilities. Upon receiving appropriate documentation from the student, the Opportunity
Development Center will make arrangements with the instructor for the accommodations.
Complaint Procedure: If at any time during the semester the student wishes to discuss class procedure,
schedule, grades, or any class situation, contact the instructor during regularly scheduled office
hours or via e-mail, as listed above. Any complaint that cannot be resolved directly with the
instructor should be referred to the Director of Teaching (Jo Ann Staples in SC 1332).
Homework: There will be weekly graded homework assignments, due at the start of class on Fridays.
Students should read the text prior to attempting homework problems, as many necessary
techniques and ideas are presented in the text. The lowest homework grade will be dropped.
Tutoring: The Tutoring Services Office of the College of Arts and Science offers free individual tutoring
and other related services. For additional information, see
http://www.vanderbilt.edu/cas/supportservices/tutoringservices/index.php.
In addition, the School of Engineering provides special help for their students. Engineering students
should contact the office of Dean Arthur Overholser (3-3773) in SC 5332.
Quizzes: There will be nine in-class quizzes. Quizzes are given on Wednesdays and will generally cover
the material from the previous three classes (WFM). Each quiz will be worth 12.5 points and will
be given at the start of class. The lowest quiz grade will be dropped.
Exams:
Three 100-point in-class exams will be given during the semester. The date of each exam is
posted on the syllabus. Attendance on these dates is compulsory; otherwise, a grade of zero will
be recorded. Any conflict with an exam date must be reported to the instructor at least a week
prior to the exam date (except in cases of emergency). If an exam is missed and the student has an
excused absence (as defined in the course catalog), a makeup exam will be given during regularly
scheduled office hours.
Extra Credit: Expressing oneself in writing is an important skill, often ignored in technical
courses. Students will have the opportunity to earn extra credit by writing a short paper describing
one of the applications in the text, and explaining its relationship to the course topics.
Final Examination: A 300 point comprehensive final examination will be given on:
Thursday April 24th from 9:00 – 11:00 a.m. in SC ???.
There will not be an alternate final exam time.
Grading Procedure: Each student will have the following six scores. The lowest exam score will be
replaced with (half of) the final exam score (however, scores of zero resulting from unexcused
absences will not be replaced). The total number of possible points for the semester is 800.
Quizzes
100 points
Homework
100 points
Exams 1, 2, and 3
100 points each
Final Exam
300
The instructor will assign final grades for the course.
Grading Questions: Questions concerning the grading of a quiz or exam must be written on separate
paper and presented to the instructor at the start of class the day after the paper is returned (for
example, if an exam is returned on a Wednesday, questions must be submitted by the start of class
Friday.)
Schedule for Math 194-1 (Fall 2007)
Wed Jan 9
Fri Jan 11
1.1: Systems of linear equations
1.1, 1.2: Solving linear systems; row reduction
Mon Jan 14
Wed Jan 16
Fri Jan 18
1.2 continued; applications of row reduction
1.3: matrix algebra and linear systems QUIZ 1 (Add/Drop Deadline)
1.3: Inverses and transposes; applications HW 1 DUE
Mon Jan 21
Wed Jan 23
Fri Jan 25
1.4: Elementary matrices and row reduction
1.4 continued: invertible matrices, computing inverses QUIZ 2
Review of Chapter HW 2 DUE
Mon Jan 28
Wed Jan 30
Fri Feb 1
Exam 1
2.1: determinants
2.2: properties of determinants
Mon Feb 4
Wed Feb 6
Fri Feb 8
3.1, 4.1: vector spaces and linear transformations
3.2, 4.1: Subspaces; column space and nullspace of a matrix QUIZ 3
3.2, 4.2: matrix representation of a linear transformation;
column space and nullspace vs. kernel and image HW 3 DUE
Mon Feb 11
Wed Feb 13
Fri Feb 15
4.2 continued; applications
3.3, 3.4: linear independence, bases, and dimension QUIZ 4
3.3, 3.4 continued HW 4 DUE
Mon Feb 18
Wed Feb 20
Fri Feb 22
EXAM 2
3.5, 4.3: change of basis; similarity of matrices
3.5, 4.3 continued; applications HW 5 DUE
Mon Feb 25
Wed Feb 27
Fri Feb 29
3.6: row and column space; the Rank-Nullity Theorem
6.1: eigenvalues and eigenvectors QUIZ 5
6.1 continued; applications HW 6 DUE
Spring Break; no classes
Mon Mar 10
Wed Mar 12
Fri Mar 14
6.2: Linear differential equations
6.2 continued; applications QUIZ 6
6.3: diagonalization HW 7 DUE (Withdrawal deadline)
Mon Mar 17
Wed Mar 19
Fri Mar 21
6.3 continued; applications
6.4: complex numbers; Hermitian matrices; unitary matrices QUIZ 7
6.4 continued: the Spectral Theorem for Hermitian matrices HW 8 DUE
Mon Mar 24
Wed Mar 26
Fri Mar 28
6.4 continued: normal matrices; the Spectral Theorem for normal matrices
Review for Exam 3 QUIZ 8
Exam 3 HW 9 DUE
Mon Mar 31
Wed Apr 2
Fri Apr 4
6.5: the Singular Value Decomposition
6.5 continued
6.5 continued: applications HW 10 DUE
Mon Apr 7
Wed Apr 9
Fri Apr 11
6.6: quadratic forms
6.6 continued: optimization QUIZ 9
5.1: orthogonality; applications HW 11 DUE
Mon Apr 14
Wed Apr 16
Fri Apr 18
5.2, 3.6 revisited: orthogonal subspaces; Fundamental Subspaces Theorem
5.3: The least squares problem
5.3 continued: applications
Mon Apr 21
Last class: review for final
Thurs Apr 24
Final Exam: 9:00am – 11:00am in SC 1313
Exam Dates:
Exam 1: Friday January 28, 2008
Exam 2: Monday February 18, 2008
Exam 3: Friday March 28, 2008
Final Exam: Thursday, April 24, 2008, 9:00am – 11:00am