LINEAR ALGEBRA SYLLABUS Fall 2016 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 in Gillet 205
Course Webpage:
https://sites.google.com/site/professorsormani/teaching/linalg-f16
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 similar 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%
Midterm Exam: 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 (30%), Midterm Exam (30%), Final Exam (40%)
Materials, Resources and Accommodating Disabilities:
Textbook: Linear Algebra, a free textbook by Jim Hefferon 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: (Mon 8/29) Vectors in Euclidean Space (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: (Wed 8/31) Solving Linear Systems
HW: Ch One Part I.1 Read I.1 Do exercises: One.I.1/ 1.17, 1.18, 1.29, 1.30, 1.35,
No Lehman classes on Labor Day (Mon 9/5)
Lesson 3: (Wed 9/7) Solving Linear Systems with Matrices
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: (Mon 9/12 Eid al-Adha) Cauchy Schwartz (students who miss class for Eid al-Adha may come to office hours for this)
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 5: (Wed 9/14) Homogeneous Linear Systems
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 6: (Mon 9/19) Reduced Echelon Form
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: (Wed 9/21) Vector Spaces
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: (Mon 9/26) Linear Independance
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: (Wed 9/28) Basis and Dimension
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,
No Lehman Classes on Rosh Hoshanah (Mon 10/3) Extra Office Hours during class time
Lesson 10: (Wed 10/5) Review for Exam I
Lesson 11: (Thursday Meeting 10/6) Matrices and Rank
HW: Read Ch Two III.3 and do 3.16, 3.17, 3.18, 3.19, 3.20, 3.21, 3.31
No Lehman classes Columbus Day (Mon 10/10) or Yom Kippur (Wed 10/12)
Lesson 12: (Mon 10/17) Midterm Exam on Chapters One-Two (similar to the quizzes)
Lesson 13: (Wed 10/19) Isomorphisms
HW: Read Ch Three.I.1 do 1.12, 1.14, 1.15a, 1.16, 1.19, 1.21, 1.22, 1.28,
Lesson 14: (Mon 10/24) Homomorphisms
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
Lesson 15: (Wed 10/26) Range and Null Space
HW: Read Ch Three II.2 do 2.21-2.24, 2.27, 2.31, 2.33, 2.34, 2.38
Lesson 16: (Mon 10/31) No meeting for Halloween (extra review at end of course will be scheduled)
Lesson 17: (Wed 11/2) Linear Maps and Matrices
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 18: (Mon 11/7) Matrix Multiplication
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 19: (Wed 11/9) Permutation Matrices and Row Reduction Matrices
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 20: (Mon 11/14) Inverses
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 21: (Wed 11/16) Inverses and Determinants of 2x2 Matrices
HW: Continue with Ch Three IV.4 homework assigned during Lesson 18,
Lesson 22: (Mon 11/21) Matrix Equivalence and Column Reduction
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 23: (Wed 11/23) Projections, Gram-Schmidt and Geometry of Linear Maps
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
Lesson 24: (Mon 11/28) Determinants
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 25: (Wed 11/30) Geometry of Determinants and Similar Matrices
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 26: (Mon 12/5) Complex vector spaces
HW: Review Ch Two, Read Ch Five I.1-I.2 Read and do exercises and proofs on this the SOS webpage.
Lesson 27: (Wed 12/7) Similar Matrices, Eigenvalues and Eigenvectors
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 28: (Mon 12/14) Orthonormal Matrices
HW: Read Ch 3 Topic Orthonormal Metrices
Extra Review Session (Wed 12/12) to make up for Halloween
Final Monday Dec 19 6:15-8:15 pm
Department of Mathematics and Computer Science, Lehman College, City University of New York
FOR NOW ON YOU MAY ONLY RETAKE A QUIZ ONCE AND ONLY AFTER YOU DEMONSTRATE TO ME THAT YOU HAVE COMPLETED AT LEAST FIVE HW PROBLEMS RELATED TO THE QUIZ.