Prof. Vladimir Dobrushkin
Department of Mathematics

MTH215 (Introduction to Linear Algebra )

Vladimir A. Dobrushkin,Lippitt Hall 202C, 874-5095,

Math 215 will detailed study of finite dimensional vector spaces, linear transformations, matrices, determinants and systems of linear equations.

MTH215, section 03, TR 12:30 - 1:15 pm Rodman Hall, 109

TEXTBOOK: "Linear Algebra and Its Applications, 5th Ed", by David C. Lay, Steven R. Lay, Judi J. McDonald, 2015. ISBN-13: 978-1118233788

Course Objectives and Goals:
Linear algebra is a branch of mathematics that studies systems of linear equations, vector spaces, linear transformations, and the properties of matrices. Students will be able to apply the concepts and methods of linear algebra that play an essential role in mathematics and in many technical areas of modern society, such as computer science, engineering, physics, environmental science, economics, statistics, business management and social sciences.

Prerequisite: C- or better in MTH131, MTH142, or equivalent.

Learning Outcomes: At the end of the course the student should be able to:

  1. solve a linear system of equations by using row operations;
  2. represent linear systems in different formats;
  3. compute basis vectors and determine linear independence of vectors;
  4. write general solutions to linear systems;
  5. perform matrix and vector operations (addition, subtraction, multiplication, scalar multiplication, and dot product);
  6. compute the inverse of matrix;
  7. compute rank and null space of a matrix;
  8. work with linear transformations;
  9. work within vector spaces and subspaces;
  10. compute determinants;
  11. compute eigenvalues and eigenvectors;
  12. use technology to analyze methods and perform calculations;
  13. communicate effectively in written form mathematical ideas and conclusions, by stating in a complete, clear, concise, and organized manner steps, calculations, solution strategy, conclusions, and when appropriate, interpreting results in practical or applied terms.

Makeup Policy: Makeup exams may be scheduled in the event you are unable to attend exams under the following conditions. See University Manual sections 8.51.10 to 8.51.14 for guidelines. Students that miss course work (not exams) under the same the conditions mentioned above will be given an opportunity to make up the course work.

  • If your reason for missing the exam as scheduled is (i) a University sanctioned event for which verifiable documentation can be provided, (ii) a responsibility to an employer that cannot be rescheduled (with documentation from your employer), or (iii) Religious holidays, then you must inform your instructor 48 hours in advance of the exam and provide documentation if requested. Makeup exams will be scheduled after the actual exam, and preferably before the class period when exams are to be handed back, but no later than one week after the original date.
  • If the reason for missing the exam as scheduled is due to (i) illness (with verifiable documentation from a medical provider if requested), or (ii) an emergency (with appropriate documentation if requested), then you must contact your instructor within 24 hours of the exam. Makeup exams may be scheduled no later than a week after the original date, unless the illness or emergency precludes this, in which case we will follow the University Manual sections 8.51.10 to 8.51.14.
  • Failure to notify your instructor within 7 calendar days of your absence will result in a 0 for the exam, see section 8.51.14 University Manual.

Homework will be assigned after each section. Each day we will spend time going over examples, quizzes, and homework problems. You are responsible for all problems assigned, see Course Calendar for a list of problems associated with each chapter. Quizzes will be given almost every class in the weeks without exams. Quiz problems are from homework problems and examples given in class with number changes. There are no makeup quizzes. I'll drop one quiz grade.

Attendance is a vital and necessary part of this course. While there is no formal attendance policy, we cover a lot of information at a rapid pace; missing a class will result in a large amount of material missed. Students are responsible for all missed work, regardless of the reason for absence. It is also the absentee's responsibility to get all missing notes or materials.

Calculators and Software:
A Texas Instruments graphing calculator is required. Technology will play an important role in this course and we will make extensive use of graphing calculators; sure to bring your graphing calculator to each class. Octave online:

Mathematica Projects:
In this course we will use the Mathematica computer algebra system (CAS), which is available in computer labs at URI. The Mathematica projects are created to help you learn new concepts. Mathematica is very useful in visualizing graphs and surfaces in three dimensions. Matlab commercial software is also available at engineering labs. Its free version is called Octave. A student can also use free CASs: SymPy (based on Python), Maxima, or Sage.

Weather phone number:  (401) 874-snow or 874-7669.

Help With Your studies and homework:
Tutors are available at both the Providence and Kingston campuses. Walk-in tutoring for math is located in Lippitt Hall. There is a no appointment needed in the Lippitt Hall tutoring center. It is a place where you can work with tutors and other students in this and other math courses. Support is provided for all math courses up to MTH 244. Be sure to bring your book, notes, and questions with you. The tutoring center is a great place to study with classmates and friends, prep for exams, and review the material covered in lecture. Check with them for specific hours. Also, you can make individual appointments with me. For this, contact me by phone, e-mail, or ask me during class. I may help you with questions during office hours, or at other times by appointment. Also, I will try to answer questions sent by electronic mail as promptly as possible. Students who require accommodations and who have documentation from Disability Services (874-2098) should make arrangements with me as soon as possible.
The Academic Enhancement Center provides Weekly Tutoring Groups program that has replaced Supplemental Instruction.

The nation is experiencing widespread influenza-like illness. If any of us develop flu-like symptoms, we are being advised to stay home until the fever has subsided for 24 hours. So, if you exhibit such symptoms, please do not come to class. Notify me your instructor of your status, and we will communicate through the medium we have established for the class. We will work together to ensure that course instruction and work is completed for the semester.

The Centers for Disease Control and Prevention have posted simple methods to avoid transmission of illness. These include: covering your mouth and nose with tissue when coughing or sneezing; frequent washing or sanitizing your hands; avoiding touching your eyes, nose, and mouth; and staying home when you are sick. For more information please view or . URI Health Services web page, , will carry advice and local updates.

Civility Policy: .
The University of Rhode Island has adopted a civility policy regarding disruptive classroom behaviors. Disruptive behaviors are defined as behaviors that interfere with the learning and/or teaching process. Disruptive behaviors in the classroom include inappropriate talking during lectures or class discussions or in any manner interfering with other student's ability to have a quality learning experience. Students who engage in disruptive behavior will receive one warning without penalty. Continued incidents of disrupting the class will result in the initiation of removal procedures or the loss of a letter grade. Disruptive behaviors include cell phone and pager use. Cell phones and pagers must be turned off, silent, and out of sight during classes, and you should not be checking for calls or messages during class (including "texting"). Common sense and common courtesy should govern classroom civility.

Grading Incomplete (URI regulations): .

  • 8.53.20. A student shall receive a report of "Incomplete" in any course in which the course work has been passing up until the time of a documented precipitating incident or condition, but has not been completed because of illness or another reason which in the opinion of the instructor justifies the report. An instructor who issues a grade of "Incomplete" shall forward a written explanation to the student's academic dean.
  • 8.53.21. The student receiving "Incomplete" shall make necessary arrangement with the instructor or, in the instructor's absence, with the instructor's chairperson to remove the deficiency. This arrangement shall be made prior to the following midsemester for the undergraduate student and within