BMCC MAT315Syllabus - this is a syllabus PDF

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Borough of Manhattan Community College City University of New York Department of Mathematics

Linear Algebra MAT 315 Instructor: Dr. David Allen Office: N599T Phone: 212-220-8000 ext: 7994 Office Hours: Wednesday 10am-noon, Friday 8am-9am and by appointment. E-mail: [email protected] Credits: 3 credits

Catalogue Description: The 2011-2014 bulletin pg.62 states that MAT 206 is a course that ”…covers matrices, determinant systems of linear equations, vector spaces, eigenvalues and eigenvectors, Boolean Algebra, switching circuits, Boolean functions, minimal forms and Karnaugh maps.” Prerequisite: Intermediate Algebra and Trigonometry (MAT 056) or the equivalent with the departmental approval.

Required Text and Supplementary Materials: LINEAR ALGEBRA WITH APPLICATIONS, FIFTH EDITION, Otto Bretscher, PEARSON.

ISBN-10:

0321796977

SUPPLEMENTAL TEXTBOOK (ISBN-10: 0387962050) An Introduction to Linear Algebra by Lang (1997)

COURSE OUTLINE/REMARKS: This course will be a combination of the standard modes of learning and teaching. This includes traditional lecture as well as presentations and collaborative learning. Problem sessions will be in an integral part of the course and it is important for each student to contribute, this means that one must study and keep up. The Professor can and WILL call students to the board to present a problem or discuss a construction at any time without giving prior notice. Ultimately the student is responsible for working on the homework problems, hence, the Professor will not give the answers to questions, but rather hints that serve to guide the student to the solution. Keep in mind that the only way to learn mathematics is to do mathematics (i.e., work on problems). It is not unusual for students to spend a lot of time working on problems that appear in the textbook or assigned during class.

GRADING CRITERIA1: Exam I* (See note (ii) below)

35%

Exam II*

35%

Final Exam

37%

Attendance/in-class participation

10%

Quizzes (three at six percent each):

18%

Note (i): Students will be given approximately one week’s notice before an exam or quiz is administered and these announcements will be made in class. Homework assignments are due one week after being assigned unless stated otherwise. Additional details pertaining to the quizzes and exams such as expectations and the use of technology etc. will be provided during the semester. Note (ii): For grading purposes, only the highest grade from Exam I or Exam II will be recorded. For example, if a score of 80 is earned on exam I and a score of 90 is earned on Exam II, then the 90 will be recorded and the 80 is dropped. If a student misses Exam I, then it is automatically dropped and s/he must take Exam II. If a student does not take Exam I and Exam II, then s/he automatically loses that percent of the course grade. Other Resources: The Math Lab is located in room S535 and its phone number is: 212-220-1366. The lab contains many resources the student may find useful including: tutors, calculators and software to name a few. Additional details can be found on the Mathematics Department website: http://www.bmcc.cuny.edu/math/

1

Parts of the syllabus may change at any time for any reason with or without notice.

Use of Technology: A graphing calculator—TI83 is not required but this technology will assist with various calculations.

College Attendance Policy At BMCC: The institution’s attendance policy as stated in the 2011-2014 bulletin pg. 91 is as follows: “The maximum number of absence hours is limited to one more class hour than the contact hours as indicated in the BMCC college catalogue. For example, you may be enrolled in a four hour class that meets four times a week. You are allowed five hours of absence, not five days. In the case of excessive absence, the instructor has the option to lower the grade or assign an “F” or “WN” grade. “

Attendance is a critical element to being successful in this course. Please make every effort to attend all classes and in the in case that a class must be missed, then please get the notes from a classmate, read over them and schedule an appointment during an office hour to discuss any questions you may have on the missed material.

Academic Adjustments/Students with Disabilities : The Office of Accessibility can arrange accommodations for students with disabilities. It is located in room N360 and its phone number is: 212-220-1264. Additional information and forms can be obtained via the website: http://www.bmcc.cuny.edu/accessibility/index.jsp. Students seeking such accommodations should also contact the professor to ensure timely arrangements and coordination.

BMCC Policy on Plagiarism: The institution’s policy on plagiarism as stated in the 2011-2014 bulletin pg. 99 is as follows: “Plagiarism is the presentation of someone else’s words, ideas or artistic/scientific/musical/technical work as one’s own creation. A student who copies or paraphrases published or online material, or another person’s research, without properly identifying the source(s) is committing plagiarism.” “Plagiarism violates the ethical and academic standards of our college. Students will be held responsible for such violations, even when unintentional.” Please understand that plagiarism is taken very seriously by many organizations, academic ones included. If the student is unsure about referencing procedures and protocols, then please seek advice from faculty and/or library personnel. Outline of Topics: (From Web Syllabus). Please note that the order may vary TOPICS Linear Equations in Linear Algebra Systems of Linear Equations

Row Reduction and Echelon Forms Vector Equations The Matrix Equation Ax=b Solution Sets of Linear Systems Applications of Linear Systems Linear Independence Introduction to Linear Transformations The Matrix of a Linear Transformation Matrix Algebra Matrix Operations Inverse of a Matrix Characterizations of Invertible Matrices Partitioned Matrices Matrix Factorizations Introduction to Determinants Properties of Determinants Cramer's Rule, Volume, and Linear Transformations Vector Spaces and Subspaces Null Spaces, Column Spaces, and Linear Transformations Linearly Dependent Sets: Bases The Dimension of a Vector Space Rank Change of Basis Eigenvalues and Eigenvectors Eigenvectors and Eigenvalues The Characteristic Equation Diagonalization Eigenvectors and Linear Transformations Orthogonality and Least- Squares Inner Product, Length, and Orthogonality Orthogonal Sets

Orthogonal Projections The Gram-Schmidt Process Least Squares Problems Symmetric Malices and Quadratic Forms Diagonalization of Symmetric Matrices Quadratic Forms...