LINEAR ALGEBRA SYLLABUS Fall 2014 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 Gillet 205
Course Webpage: https://sites.google.com/site/professorsormani/teaching/linalg-f14
Google "Professor Sormani" then select "Teaching" then select "Linear Algebra"
Instructor : Professor Sormani
Webpage: https://sites.google.com/site/professorsormani/ Email: sormanic@gmail.com
Office: Gillet 200A Office Hours: 5:00-5:30pm & 7:45-8:15pm 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.
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: On the first meeting of most weeks there will be a quiz on problems similar to the homework due that day. This includes problems which involve proofs.
Projects: There will be one long term project assigned on an application related to your career interests.
Grading: Quizzes (20%), Projects (20%), Midterm Exam (20%), Final Exam (40%) or do only one part of the 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 (Wed 9/3) (this is a review for many students)
HW: Ch 1 Part II Read pages 34-43 Do exercises: p40/ 1.1-1.6, 1.9 and p46/ 2.11, 2.12, 2.14, 2.15
Please email me your name, major, career plans and a photo before Monday
Lesson 2: Solving Linear Systems (Mon 9/8) Quiz I on Vectors in Euclidean Space
HW: Ch 1 Part I.1 Read I.1 Do exercises: p11/ 1.17, 1.18, 1.29, 1.30, 1.35,
Lesson 3: Solving Linear Systems with Matrices (Wed 9/10)
HW: Ch 1 Part I.2 Read I.2 Do exercises: p20/ 2.17, 2.18, 2.19, 2.21, 2.22, 2.25, 2.26, 2.27
Lesson 4: Homogeneous Linear Systems (Mon 9/15) Quiz II on Solving Linear Systems with matrices
HW: Ch 1 Part I.3 Read I.3 Do exercises: p32/ 3.14, 3.15, 3.16, 3.18, 3.20, 3.23
Lesson 5: Cauchy-Schwartz (Wed 9/17)
HW: Ch 1 Part II.2 Read II.2 and do exercises 2.17-2.21 (these have proofs, submit for extra credit)
Lesson 6: Reduced Echelon Form (Mon 9/22) Quiz III on Solving Linear Systems (Lehman Closed Wed 9/24)
HW: Ch 1 Part III Read III.1-III.2 Do exercises: p 54/1.8, 1.9, 1.10, 1.16, p62/2.10ab, 2.10, 2.18a,,2.20, 2.23
Lesson 7: Vector Spaces (Mon 9/29) Quiz IV on Reduced Echelon Form
HW: Ch 2 I.1-I.2 Read Ch 2 I.1 Do exercises: p 86: 1.17, 1.21, 1.22, 1,28/a,d, 1.36, 1.37, 1.42; Read Ch 2 I.2: Do p97 2.22, 2.27;
Lesson 8: Linear Independance(Wed 10/1)
HW: Ch 2 II.1 Do HW: p 97/2.20a, 2.24 a,c, 2.25, 2.28, 2.46 Read Ch 2 III.1 Do p110/ 1.20, 1.22b, 1.26, 1.30, 1.32, 1.37.
Lesson 9: Basis and Dimension (Mon 10/6) Quiz V on Vector Spaces (Ch 2 I.1)
HW: Ch 2 III.1-III.2 Read III.1 Do p118/ 1.18, 1.19, 1.23 , 1.29, 1.32, 1.35, Read III.2 Do p125/ 2.16, 2.17, 2.18, 2.26,
Lesson 10: Review for Midterm (Wed 10/8) (Lehman closed Mon 10/13)
HW: Read Ch 2 III.3 and do 3.16, 3.17, 3.18, 3.19, 3.20, 3.21, 3.31
Review Ch 1- Ch 2 focussing on the material on the five quizzes and the definitions in Chapter 2 III.1-III.3 (will have proofs and short answers)
Lesson 11: Midterm Exam on Chapters 1-2 (Wed 10/15)
HW: (Choose a Topic Section for your Project Part I: See p 64, 66, 71, 144, 146, 150 and 156)
Lesson 12: Isomorphisms (Mon 10/20) Submit topic choice for Project Part I
HW: Ch 3 Read I.1/ do 1.12, 1.14, 1.15a, 1.16, 1.19, 1.21, 1.22, 1.28, and prep to retake vector spaces quiz on Wednesday
Lesson 13: Homomorphisms (Wed 10/22) (retake Quiz V on Vector Spaces, max score 80 percent)
HW: Ch 3 Read I.2/ do 2.9, 2.13, Read II.1/ do 1.18, 1.19 a, 1.20, 1.22, 1.26, 1.30, 1.32 ab, 1.34, 1.39 (this hw counts as Quiz VI due 10/27)
Lesson 14: Range and Null Space (Mon 10/27) hand in take home Quiz VI on Isomorphisms and Homomorphisms
HW: Ch 3 Read II.2/ do 2.21-2.24, 2.27, 2.31, 2.33, 2.34, 2.38
Lesson 15: Linear Maps and Matrices (Wed 10/29)
HW: Ch 3 III.1-III.2: starting at p208 study 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 11/3) Quiz VII on Range and Null Spaces of maps defined by matrices
HW: No need to read Ch 3 IV.1/ just do 1.8, 1.10, 1.14, 1.15, 1.16, 1.17, No need to read Ch 3 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 11/5) (Withdrawal Deadline: 11/6)
HW: Do Ch 3 IV.2/ 2.25, 2.26, 2.29, 2.32, 2.37 Read Ch 3 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 Register for Hackathon 2014 before Nov 7 (this will count as your project 1 if you participate)
Lesson 18: Inverses (Mon 11/10) Quiz VIII on Matriz Multiplication
HW: Read Ch 3 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 11/12)
HW: Continue with Ch 3 IV.4 homework assigned during Lesson 18, work on project.
Hackathon 2014 Nov 14 6pm - Nov 15 9 am Register here to participate. Participants may skip Project 1.
Lesson 20: Matrix Equivalence and Column Reduction (Mon 11/17) Quiz IX on Inverses
HW: Ch 3 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 11/19)
HW: Ch 3 VI.1 p 255 defn 1.1 Ex 1.2-1.3 do 1.6, 1.7, Ch3 VI.2 read all/ Do 2.10, 2.11, 2.12 Ch 3 Topic: Geometry of Linear Maps read 290-292, Do p294/1, 2, 3, 5 (choose Project Part II topics from end of Chapter 3)
Lesson 22: Determinants (Mon 11/24) Submit Project Part I and choice of topic for Project Part II
HW: Ch 4 I.2-I.3 Read all of Ch 4 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 11/26)
HW: Read Ch 4, II-III and Cramers Rule. Do p348/1.8 p355/1.11-1.15,1.24, p359/2,4
Lesson 24: Complex vector spaces (Mon 12/1) Quiz X on Determinants
HW: Review Ch 2, Read Ch 5 I.1-I.2 Read and do exercises and proofs on this the SOS webpage.
Lesson 25: Similar Matrices, Eigenvalues and Eigenvectors (Wed 12/3)
HW: Ch 5 II.1-3: Read II.1 Do 1.4, 1.10, 1.11,1.12, Read II.2 Defn 2.1, Ex 2.2, Ex 2.3 Reac all of II.3 Do 3.20, 3.21, 3.22, 3.23, 3.24, 3.28, 3.31, 3.35, 3.41,
(students who do not do part II of the project will have their quizes count as 30 percent of the grade and project count as 10%)
Lesson 26: Orthonormal Matrices (Mon 12/8) Quiz XI on Eigenvalues and Eigenvectors
HW: Ch 3 Topic Orthonormal Metrices
Lesson 27: Review of Quizzes VI-XI (Wed 12/10)
HW: Practice for final and complete course projects
Lesson 28: Review for Final (Mon 12/15) Course Project Part II due (students who do not do part II of the project will have their quizes count as 30 percent of the grade and project count as ten percent).
HW: Practice problems for the final will be assigned from the textbook
Final during Finals Week (Dec 22 6:15-8:15 pm Gillet 205)
Department of Mathematics and Computer Science, Lehman College, City University of New York