LINEAR ALGEBRA SYLLABUS Fall 2017 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-f17
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. Up to three quizzes can be retaken during office hours within two weeks for a max score of 80%.
Midterm Exam: A midterm can be retaken for a max score of 80% within two weeks.
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 8/28) 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 page 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 8/30) 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,
Lehman has no classes on Mon 9/5
Lesson 3: (Wed 9/6) Solving Linear Systems with Matrices (Quiz 1 on Lines and Quiz 2 on Solving Linear Systems)
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 9/11) Homogeneous Linear Systems (Quiz 3 on Solving Linear Systems with Matrices)
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: (Wed 9/13) Cauchy Schwartz and Proofs (Quiz 3 on Solving Linear Systems with Matrices)
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: (Mon 9/18) Vector Spaces and Proving (Quiz 4 on Basic Proofs)
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;
Lehman has no classes on 9/20 (students may meet to work on Vector Spaces together)
THE SOLUTIONS TO QUIZ 4 were emailed to the class. If you did not receive them them email me.
Lesson 7: (Mon 9/25) Linear Independance (Practice Quiz on Vector Spaces)
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 8: (Wed 9/27) (Quiz 5 on Vector Spaces) (Retake old quizzes as needed in class today)
HW: Read Ch Two III.1 Do 1.20, 1.22b, 1.26, 1.30, 1.32, 1.37.
Lesson 9: (Mon 10/2) Basis and Dimension (Quiz 6 on Linear Independence postponed)
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: (Wed 10/4) Reduced Echelon Form (Quiz 6 on Linear Independence)
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
Lehman has no classes on Mon 10/9 (students may meet to study)
Lesson 11: (Wed 10/11) Midterm Exam on Chapters One-Two (Problems like those on Quizzes 1-4 and 6, and also a Reduced Echelon Form question )
Study Complex vector spaces on your own: Read and do exercises and proofs on this the SOS webpage.
HW: Review Ch Two, Read Ch Five I.1-I.2
Lesson 12: (Mon 10/16) Matrices and Rank (Quiz 7 on Complex Numbers)
HW: Read Ch Two III.3 and do 3.16, 3.17, 3.18, 3.19, 3.20, 3.21, 3.31
Lesson 13: (Wed 10/18) Isomorphisms (Retake Quiz 5 on Vector Spaces)
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 10/23) Homomorphisms (Quiz 8 on Matrices and Rank)
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 10/25) Range and Null Space (Practice quiz on Homomorphisms)
HW: Read Ch Three II.2 do 2.21-2.24, 2.27, 2.31, 2.33, 2.34, 2.38
Lesson 16: (Mon 10/30) Linear Maps and Matrices (Quiz 9 on Homomorphisms)
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 17: (Wed 11/1) Matrix Multiplication (Quiz 10 on Rank Range Nullspace and Nullity of a Matrix)
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 18: (Mon 11/6) Permutation Matrices and Row Reduction Matrices (Quiz 11 on Matrix Multiplication)
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 19: (Wed 11/8) 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 20: (Mon 11/13) Projections, Gram-Schmidt and Geometry of Linear Maps (Quiz 12 on Finding Inverses of Matrices)
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 21: (Wed 11/15) 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 22: (Mon 11/20) Geometry of Determinants and Similar Matrices (Quiz 13 on Determinants: know all three methods)
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 23: (Wed 11/22) Sodoku and Derivatives (catch up on old hw)
Lesson 24: (Mon 11/27) 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 and practice finding eigenvalues and eigenvectors: 3.20, 3.21, 3.22, 3.23, 3.24, 3.28, 3.31, 3.35, 3.41, see the solutions manual for help.
Lesson 25: (Wed 11/29) Barycenters with Guest Speaker Prof Ndaiye
Lesson 26: (Mon 12/4) Symmetric and Ortgogonal Matrices (Quiz 14 on finding Eigenvalues and Eigenvectors)
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 27: (Wed 12/6) Power Iteration (Retakes for Quiz 9, 10, 11, 12 or 13 in office hours today)
HW: Read Ch 3 Topic Orthonormal Metrices, Read wikipedia on power iteration
Lesson 28: (Mon 12/11) Review for the Final (Retakes for Quiz 14 in office hours today) Photos of the Review
The Final will have problems exactly like those on the quizzes. There is no sample final.
Final during Finals Week: Mon Dec 18 6:15-8:15 pm in 305. Students may stay afterwards until 9:15 pm.
Department of Mathematics and Computer Science, Lehman College, City University of New York