LINEAR ALGEBRA SYLLABUS Fall 2015 Professor Sormani
MAT313 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.
Meeting Times: 6:00-7:40 pm Mon/Wed
Course Webpage:
https://sites.google.com/site/professorsormani/teaching/linalg-f15
Google "Professor Sormani" then select "Teaching" then select "Linear Algebra"
Instructor : Professor Sormani Email: sormanic at@ gmail.com
Webpage: https://sites.google.com/site/professorsormani/
Office: Gillet 200A Office Hours: 5:30-6:00 pm & 7:45-8:15 pm Mon/Wed
Grading Policy
Expectations: Students are expected to learn both the mathematics covered in class and the mathematics in the textbook.
Completing homework is part of the learning experience. Learning to learn from a book is a crucial life skill.
Homework: Approximately four hours of homework will be assigned in each lesson and due on the first meeting of each week.
The solutions to the homework are provided on the textbook website so check your work before submitting it. Come to office
hours before class if you are unsure. Homework assignments will be listed on the course webpage (below).
Quizzes: Quizzes will be randomly given in any lesson at any time based upon problems simila to the homework due that day or earlier
in the week. This includes problems which involve proofs. Missed quizzes can be taken during office hours for a max score of 80%
Projects: There will be two projects assigned on applications related to your career interests.
Midterm: A missed midterm can be taken later for a max score of 80%,
Final: A missed final is an incomplete in the course only if one already has a passing average.
Grading: Quizzes (20%), Projects (20%), Midterm Exam (20%), Final Exam (40%) or do only one project for 10% and your quizes count for 30%.
Materials, Resources and Accommodating Disabilities:
Textbook: Linear Algebra, a free textbook by Jim Hefferson with answers to exercises
Tutoring: Please come to office hours for assistance with this advanced course.
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 Outcomes
1. Learn to prove theorems. Students should be able to observe connections between different topics in the
course description above, especially systems of equations, matrices and vector spaces.
2. Learn to perform calculations. Students must learn how to perform calculations in different settings.
They should be comfortable doing algebra on matrices, solving systems of linear equations and working with vectors.
Math Major Outcomes incorporated into MAT313
A. Perform numeric and symbolic computations
B. Construct and apply symbolic and graphical representations of functions
C. Model real-life problems mathematically
E. State and apply mathematical definitions and theorems
F. Prove fundamental theorems
Department of Mathematics and Computer Science, Lehman College, City University of New York
Schedule: (the schedule is subject to change)
Lesson 1: Vectors in Euclidean Space (Mon 8/31) (this is a review for many students)
HW: Ch One Read Part II.1 Do 1.1-1.6, 1.9 Read Part II.2 Do 2.11, 2.12, 2.14, 2.15
Note the pages assigned are the numbers in the book not the pages of the pdf file.
Note that if you go to the contents and click on Chapter 1 Part II it takes you right to the correct place.
Please email me your name, major, career plans and a photo before Monday
Lesson 2: Solving Linear Systems (Wed 9/2)
HW: Ch One Part I.1 Read I.1 Do exercises: One.I.1/ 1.17, 1.18, 1.29, 1.30, 1.35,
Research Opportunity with a stipend (meets on Fridays)
Lesson 3: Solving Linear Systems with Matrices (Wed 9/9) (Lehman Closed Mon 9/7 Labor Day)
HW: Ch One Part I.2 Read I.2 Do exercises: One.I.2/ 2.17, 2.18, 2.19, 2.21, 2.22, 2.25, 2.26, 2.27
Lesson 4: Homogeneous Linear Systems (Th 9/10) warning Thursday meeting
HW: Ch One Part I.3 Read I.3 Do exercises: One.I.3/ 3.14, 3.15, 3.16, 3.18, 3.20, 3.23
Lesson 5: Cauchy-Schwartz (Wed 9/16) (Lehman Closed Mon 9/14 Rosh Hoshanah)
HW: Ch One Part II.2 Read II.2 and do exercises One.II.2/ 2.17-2.21 (these have proofs, submit for extra credit)
Lesson 6: Reduced Echelon Form (Mon 9/21) (Lehman Closed Wed 9/23 Yom Kippur)
HW: Ch One Part III Read III.1-III.2 Do exercises: One.III.1/ 1.8, 1.9, 1.10, 1.16, p62/2.10ab, 2.10, 2.18a,,2.20, 2.23
Lesson 7: Vector Spaces (Mon 9/28)
HW: Read Ch Two I.1 Do 1.17, 1.21, 1.22, 1,28/a,d, 1.36, 1.37, 1.42; Read Ch Two I.2: Do p97 2.22, 2.27;
Lesson 8: Linear Independance(Wed 9/30)
HW: Ch Two II.1-II.2 Do 2.20a, 2.24 a,c, 2.25, 2.28, 2.46 Read Ch Two III.1 Do 1.20, 1.22b, 1.26, 1.30, 1.32, 1.37.
Lesson 9: Basis and Dimension (Mon 10/5)
HW: Ch Two III.1-III.2 Read III.1 Do 1.18, 1.19, 1.23 , 1.29, 1.32, 1.35, Read III.2 Do 2.16, 2.17, 2.18, 2.26,
Lesson 10: Review for Midterm (Wed 10/7) (Lehman closed Mon 10/12 Columbus Day)
HW: Read Ch Two III.3 and do 3.16, 3.17, 3.18, 3.19, 3.20, 3.21, 3.31
Review Ch One- Ch Two: be sure to be able to solve systems and find reduced echelon forms and be sure to know the definitions in Chapter 2 III.1-III.3 and to be able to prove any of the ten parts of a Vector Space as well as prove statements about the dot product
Lesson 11: Midterm Exam on Chapters 1-2 (Wed 10/14)
HW: (Choose a Topic Section for your Project I: See p 64, 66, 71, 144, 146, 150 and 156)
Lesson 12: Isomorphisms (Mon 10/19)
HW: Read Ch Three.I.1 do 1.12, 1.14, 1.15a, 1.16, 1.19, 1.21, 1.22, 1.28,
Lesson 13: Homomorphisms (Wed 10/21)
HW: Read Ch Three I.2 do 2.9, 2.13, Read Ch Three II.1/ do 1.18, 1.19 a, 1.20, 1.22, 1.26, 1.30, 1.32 ab, 1.34, 1.39
Hackathon b4nycsh.splashthat.com October 24 9am-9pm at 25 Broadway NY NY, participation can count as one project!
Lesson 14: Range and Null Space (Mon 10/26)
HW: Read Ch Three II.2 do 2.21-2.24, 2.27, 2.31, 2.33, 2.34, 2.38
Lesson 15: Linear Maps and Matrices (Wed 10/28)
HW: Ch Three III.1-III.2: Read Ch Three III.1 particularly studying Ex 1.9-Ex 1.11, Do 1.12, 1.13, 1.14, 1.22, 1.27, 1.30; Read over III.2 but do not worry about any basis except the standard basis/ Do 2.13, 2.17, 2.22 Most important is to understand transformations defined by matrices.
Lesson 16: Matrix Multiplication (Mon 11/2) sub
HW: No need to read Ch Three IV.1/ just do 1.8, 1.10, 1.14, 1.15, 1.16, 1.17, No need to read Ch Three IV.2 just read defn 2.3, ex 2.4, ex 2.5, ex 2.0, ex 2.10, /do 2.14, 2.15,
Lesson 17: Permutation Matrices and Row Reduction Matrices (Wed 11/4) sub
HW: Do Ch Three IV.2/ 2.25, 2.26, 2.29, 2.32, 2.37 Read Ch Three IV.3/ do 3.24, 3.25, 3.26, 3.27, 3.28, 3.29, 3.30, 3.34, 3.35, 3.38, 3.40, 3.41, 3.42, 3.43
Lesson 18: Inverses (Mon 11/9)
HW: Read Ch Three IV.4/ Do 4.12, 4.13, 4.14, 4.20, 4.30, 4.32, 4.33, find the inverse of a 2x2 matrix in general
Lesson 19: Inverses and Determinants of 2x2 Matrices (Wed 11/11) Matrix Mult Quiz today (already graded on my door!)
HW: Continue with Ch Three IV.4 homework assigned during Lesson 18, work on project.
Lesson 20: Matrix Equivalence and Column Reduction (Mon 11/16) Range Rank Null Space Nullity of a Matrix Quiz today
HW: Ch Three V.2 Read Defn 2.3, Thm 2.6, Ex 2.7 / Do p 262 2.10, 2.11, 2.14, 2.15, 2.19, 2.20, 2.23
Lesson 21: Projections, Gram-Schmidt and Geometry of Linear Maps (Wed 11/18) Inverse quiz today
HW: Ch Three VI.1 p 255 defn 1.1 Ex 1.2-1.3 do 1.6, 1.7, Ch Three VI.2 read all/ Do 2.10, 2.11, 2.12 Ch Three Topic: Geometry of Linear Maps read 290-292, Do p294/1, 2, 3, 5
(choose Project II topics from end of Chapter 3)
Lesson 22: Determinants (Mon 11/23) Submit Project I and choice of topic for Project II
HW: Ch Four I.2-I.3 Read all of Ch Four I.2 Do 2.8, 2.9, 2.10, 2.13, Read all of Ch 4 I.3 Do 3.17, 3.18, 3.30, 3.33,
Lesson 23: Geometry of Determinants and Similar Matrices (Wed 11/25)
HW: Read Ch Four II.1 and do 1.8 Read Ch Four III.1 and do 1.11-1.15,1.24, Read Cramer's Rule and do 2,4
Lesson 24: Complex vector spaces (Mon 11/29)
HW: Review Ch Two, Read Ch Five I.1-I.2 Read and do exercises and proofs on this the SOS webpage.
Lesson 25: Similar Matrices, Eigenvalues and Eigenvectors (Wed 12/2)
HW: Read Ch Five II.1 Do 1.4, 1.10, 1.11,1.12, Read Ch Five II.2 focusing on Defn 2.1, Ex 2.2, Ex 2.3 Read Ch Five II.3 Do 3.20, 3.21, 3.22, 3.23, 3.24, 3.28, 3.31, 3.35, 3.41,
Lesson 26: Orthonormal Matrices (Mon 12/7)
HW: Read Ch 3 Topic Orthonormal Metrices
Lesson 27: Extra Lesson for Catchup (Wed 12/9)
HW: Practice for final and complete course projects
Lesson 28: Review for Final (Mon 12/14) Course Project II due (no lateness allowed if not submitted today then quizzes count for 30%)
HW: Practice problems for the final will be assigned from the textbook
Extra Lesson if needed on Wed 12/16 (only needed if a lesson has been cancelled)
Final during Finals Week (Dec 21): 6:15-8:15 pm in Gillet 205
Department of Mathematics and Computer Science, Lehman College, City University of New York