Syllabus for MAT 313- Elements of Linear Algebra

MAT 313:Elements of Linear Algebra

4 hours, 4 credits. Vector spaces, systems of linear equations, determinants, linear transformations, and matrices. PREREQ: MAT 176. With Departmental permission, MAT 176 may be taken as a COREQ.

Location: Gi 205 MW 11:00-12:40

Instructor: Robert Schneider

Contact Info:

• email: robert.schneider@lehman.cuny.edu
• web page: comet.lehman.cuny.edu/schneider/
• office hours: M,W 9:30 - 10:40 Gillet 211+ by appoinment - administrative meetings

Review Session - Monday May 20 -- 11:00 Go to Gi 205 and we can move elsewhere if it is taken

Final Wed May 22- 11:00 Gi205 - 2 hours covering material from both tests

Grading Policy:

• Midterm and Endterm 40%- two one hour exams
  • first exam -Mon April 8 - 1 hour
    • row reduce matrix to identity and find inverse
    • row reduce matrix to form with some 0 rows - find null space and vectors not in null space together form basis
    • rules of matrix multiplication and addition (including dot product)- possible simple proof of a rule
    • use of commutativity of inverse to do problems like page 90 12,13
    • mystery
  • second exam Wed May 15
• Final: 40%-- May 22 11:00 in Gi 205 -- Combination of two tests- 2 hours
• Homework: 20%
• extra credit will be given for various projects and exceptional class comments

Course Objectives:

• understand fundamental theorems and assumptions underlying linear algebra
• prove some of the fundamental theorems
• apply appropriate theorems from linear algebra to a problem

Materials, Resources and Accommodating Disabilities:

• textbook: Introduction to Linear Algebra Fourth Edition; Gilbert Strang;Wellesley-Cambridge Press;978-0-9802327-1-4;2009
  
• Linear Algebra course by Strang including lecturesetc; free from MIT
• Homeworks and exams with solutions for course given at MIT-- how he organizes things
• Specific Website for this fourth edition
• Accommodating Disabilities:  Lehman College is committed to providing access to all programs and curricula to all students.  Students with disabilities who may need classroom accommodations are encouraged to register with the Office of Student Disability Services.  For more info, please contact the Office of Student Disability Services, Shuster Hall, Room 238, phone number, 718-960-8441.

Course Calendar:

We will try to cover the material in Chapters 1-6 of the book at a speed appropriate for maximal understanding and retention.

• Introduction to Linear Algebra before Ch 1
  • I will try to give a preview of important concepts in a little different way than Strang. We will redo it his way in Ch1
  • problems from class and
    • pg 8: 2,3,4,7,15 due Jan 30
    • pg19: 1,2,3,4 due Feb 4
  • Hopefully this session wont take more that 1.5 weeks
  • Due Feb 11
    • pg 8-9: 8,16,17,18,19
    • pg 19 7a,c,d;9,10,12,18,19
  • HW from class
    • Show addition by vectors is the same as addition by algebra for vectors. Consider obtuse angles.
    • Show that the dot product (inner product) is the same vectorially and algebraically when one of the vectors is along the x axis. Consider obtuse angles.
    • Show that if A,B are two by two matrices and v is a 2X1 matrix then A(Bv) = (AB)v where we are using matrix multiplication (associativety) (extra credit)
  • HW due Feb 18
    • Read through Ch 1 and first two sections Ch2
    • pg 40,41 1,2,4,9-12,15-20,22
  • HW due Feb 25
    • read 2.3
    • pg pg 51 1-5; pg 53 11, In 12,13,14 do what book asks but then work with Gauss-Jordan to solve by row reducing to identity. Can you see what the inverses are when they exist?
  • HW due March 6
    • Read to page 70
    • p51 1,3,5,11a,12,13
    • p63 1,2,3,4,12,13,16,18
    • p75 1,2,3,4,5.6.7d
    • Consider the equations
  • x+2y=4; 3x+5y=7
  • -2x-3y=5; 4x-7y=8
  • x+y=5; -x-y=3
  • In each equation try use the method of Gauss-Jordan keeping track of the matrices that do row operations to find the inverse of the appropriate matrix to solve the equations. If the method fails explain why. Once you can find the inverse solve the equations just using matrix multiplication when the right hand side is a general 2x1 vector.
  • Before the test Read to pg 88
    • pg 77-78 13,16,17,20
    • p89 6,10,12 (use that if there is a right inverse then there is a left inverse and hence an inverse),13 (use same thm),22,23,27
  • HW due April 22: Read 3.1,3.5
    • pgs127-129 1,2,3a,4,5,6,9,10,11
    • p178: 1,2,3,5,6,8,11,12,13,14
  • HW due May 1
    • p 129-130: 19,20,22,23,26
    • p178: 15,16,18,20,21,22

Final Exam: The Final Exam will be given during Finals Week on Wed May 22 from 11:00 to 1:00 in Gi205 (regular room).

 

Department of Mathematics and Computer Science, Lehman College, City University of New York