Math 221 - Introduction to Linear Algebra

Basic Information

• Matthias K. Gobbert, Math/Psyc 416, (410) 455-2404, gobbert@math.umbc.edu,
  office hours: MW 03:00-04:00 or by appointment
• Classes: room SOND 103, MW 04:00-05:15 p.m.; please see the detailed schedule for more information.
• Prerequisites: a grade of C or better in Math 151 or Math 155, or instructor approval
• Required textbook: David C. Lay, Linear Algebra and Its Applications, third edition, Addison-Wesley, 2003 (or updated printing 2006). Associated webpage: http://www.laylinalgebra.com This webpage makes available Chapter 1 and some other information in PDF-files, in case you have not obtained the textbook at this point!
• Grading policy:
  

  Homework	Quizzes	Test 1	Test 2	Test 3	Participation	Final Exam
  10%	5%	20%	20%	20%	5%	20%

  • The homework problems are listed on the homework page. Working the homework is vital to understanding the course material, and you are expected to work both the recommended and required problems; but turn in only the required problems, some of which will be graded. The homeworks are due at the beginning of class on the dates listed.
  • The quizzes will generally be unannounced and brief. They are combinations of individual and group quizzes administered in class. Both types of quizzes are designed to provide you with quick feedback on your understanding of the material and to generate class discussion.
  • The graded participation component rewards your professional behavior and active involvement in all aspects of the course. Examples of expected professional behavior include attending class regularly, reading assigned material when requested, cooperating with formal issues such as submitting requested material on time, and participating actively in class, specifically in group work.
  • The tests and the final exam are traditional in-class exams; to help you focus on what is relevant, they are closed-book, closed-notes, and no calculators/computers allowed. See the detailed schedule for the dates of the exams and their coverage.
  Late assignments cannot be accepted under any circumstances due to the organizational difficulties associated with the communcation with the grader; but a sufficient number of homework and quiz scores will be dropped in order to avoid penalizing infrequent absences. Additional details or changes will be announced as necessary. Announcements may be made in class, by e-mail, or in Blackboard. You are responsible for checking your UMBC e-mail address sufficiently frequently.
• Blackboard is a course management system that allows for posting and communicating among registered participants of a course. To log in, I suggest to go to myUMBC and then use the Blackboard link on the left. Then look for this course under "My Courses". We will actively only use the "Course Documents" area. The worked-out examples and some additional notes for selected sections are organized by chapters and sections following the textbook. The PDF files of the lectures for each class will be posted in additional folders. I will also use Blackboard to send e-mail to the class, which goes to your UMBC account by default. Therefore, you must either check your UMBC e-mail regularly or have the mail forwarded to an account that you check frequently.

Course Description

This course will develop both a proficiency with the terminology and calculation techniques of Linear Algebra and with the underlying concepts and their use to solve problems. This approach reflects the fact that it is both the calculation techniques and the fundamental concepts, including the language of Linear Algebra itself, that are ubiquitous in the application areas.

Learning Goals

• understand and remember the key ideas, concepts, definitions, and theorems of the subject. Examples in this course include linear dependence and independence, the concept of a vector space, eigenvalues and eigenvectors, and the rank theorem. --> This information will be discussed in the lecture. You will apply and use them on quizzes, homework, and tests.
• be able to apply mathematical theorems and computational algorithms correctly to answer questions, and interpret their results correctly, including potentially non-unique solutions or breakdowns of algorithms. Examples include choosing among several theorems that help decide if a matrix is diagonalizable and the algorithm for row reduction that is non-unique in its steps and that may break down, and we need to know how to interpret these breakdowns. --> The group discussions, homework, and tests address these skills.
• appreciate the power of mathematical abstraction and understand how mathematical theory is developed. The classical example of mathematical abstraction in this class is the axiomatic definition of a vector space which is done in abstract generality after observing that the axioms hold true concretely for vectors in the special case of Rⁿ. --> These integration goals will be supported by the lectures.
• be able to communicate orally by discussing mathematical ideas and algorithms with the instructor as well as other students. --> Group discussions and quizzes will contribute to this goal.
• be able to communicate in writing effectively by using the notation and terminology of the subject correctly. --> Homework, group quizzes, and tests will give you feedback.

Course Details

• Detailed schedule
• Homework assignments
• General policies and procedures including grading guidelines
• Example of a lecture using a tablet laptop and taped with voice-over

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