Linear Algebra Spring 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: 7:50-9:30 pm Mon/Wed
Course Webpage: https://sites.google.com/site/professorsormani/teaching/linalg-s15
Google "Professor Sormani" then select "Teaching" then select "Spring 2015 Linear Algebra"
Instructor : Professor Sormani
Webpage: https://sites.google.com/site/professorsormani/ Email: sormanic@gmail.com
Office: Gillet 200A Office Hours: 6:45-7:45 pm & 9:30-10:00 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.
Homework: Approximately four hours of homework will be assigned in each lesson. The solutions to the homework are provided on the textbook website so check your work. Come to office hours before class if you are unsure. Homework assignments will be listed on the course webpage (below).
Exams: There will be three exams and a final. Exams which are taken late or retaken have a deduction of 20%. It is recommended that on the dates of exams, students do not work in the morning so that they are rested for the exam.
Projects: There will be four projects. Late projects will have a deduction of 20% for being one week late and are not accepted after that.
Grading: Projects (20%), Exam I (10%), Exam II (20%), Exam III (10%), Final Exam (40%)
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 1/28) (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 2/2)
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 2/4)
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 2/9)
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: Review for Exam I on Chapter 1 I-II (Wed 2/11)
HW: Review sample exam given in class.
Lehman Closed 2/16, Lunar New Year Eve 2/18 (no class this week)
Exam I is next week. No office hours this week or before the exam.
Lesson 6: Exam I on Chapter 1 I-II (Mon 2/23)
Exam I file is at the bottom of this page and you should finish the exam for homework due on Mon 3/2.
Lesson 7: Reduced Echelon Form (Wed 2/25)
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 8: Vector Spaces (Mon 3/2)
Project 1 (due 3/9) : 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 9: Linear Independance (Wed 3/4)
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 10: Basis (Mon 3/9)
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 11: Dimension (Wed 3/11)
HW: Read Ch 2 III.3 and do 3.16, 3.17, 3.18, 3.19, 3.20, 3.21, 3.31
Lesson 12: Isomorphisms (Mon 3/16)
HW: Ch 3 Read I.1/ do 1.12, 1.14, 1.15a, 1.16, 1.19, 1.21, 1.22, 1.28,
Lesson 13: Linear Maps (Wed 3/18)
Project 2 (due 3/25): 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
Lesson 14: Range and Null Space (Mon 3/23)
HW: Ch 3 Read II.2/ do 2.21-2.24, 2.27, 2.31, 2.33, 2.34, 2.38
Lesson 15: Matrices (Range, rank, null space and nullity) (Wed 3/25)
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 3/30) (Retake Exam I 8:30-10pm today)
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 4/1)
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
Project 3 (due 4/13): find the reduced Echelon form, check for linear independence of the columns of the original matrix, range, null space, and nullity for the matrices on Page 54 1.10 abcd and 1.11 ab then do page 230 2.14 abcd and 2.15abcd . See lessons 14-17 for examples. Email me your answer to the first problem to be sure you are doing things correctly before continuing.
Lehman Closed for Spring Recess Mon 4/6 and Wed 4/8
Lesson 18: Inverses (Mon 4/13)
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: Review for Exam II on Chapter Two I, II, III and Chapter Three I-IV (Wed 4/15) and a Quiz counting as the retake of Project II (can earn 100% not multiplied by .8) check if a map is one to one, onto, and linear being very careful with the use of the = sign in a proof (only put = between things already shown to be =).
HW: Verify a space is a vector space, verify vectors are linearly independant, verify a map is a linear map, find the range, rank, null space and nullity of a matrix, multiply matrices, multiply permutation matrices quickly, find the inverse of a matrix, verify the inverse of a matrix.
Lesson 20: Exam II on Chapter Two I, II, III and Chapter Three I-IV (Mon 4/20)
Project 4 (due 5/18): Choose an application project from the Topics at the end of Chapters 2 and 3 (except Geometry of Linear Maps)
Lesson 21: Determinants (Wed 4/22)
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,
Exam II was returned today in class, it can be found on my office door along with an answer key. Email me to know your progress in class.
Lesson 22: Professor is Sick today (Mon 4/27). Students may work on Project IV in class.
Lesson 23: Geometry of Determinants, Similar Matrices and Complex Vector Spaces (Wed 4/29)
HW: Read Ch 4, II-III and Cramers Rule. Do p348/1.8 p355/1.11-1.15,1.24, p359/2,4
HW: Review Ch 2, Read Ch 5 I.1-I.2 Read and do exercises and proofs on this the SOS webpage.
Lesson 24: Similar Matrices, Eigenvalues and Eigenvectors (Mon 5/4)
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, To evaluate this course, go to your Lehman email to obtain your SETL login information.
Lesson 25: Review for Exam III on Chapter Four I-III and Chapter Five I-II (Wed 5/6)
HW: Practice finding determinants of matrices using various methods and finding eigenvectors and eigenvalues of matrices (see HW above) (Retake Sections of Exam II 8:30-10pm on 5/6 (the topics will be the same but the problems are not necessarily similar))
EXTRA OFFICE HOURS 5/7 6-9 PM TO MAKE UP FOR ABSENCE ON 4/27
Lesson 26: Exam III on Chapter Four I-III and Chapter Five I-II (Mon 5/11) There were 8 problems on Exam III. Only problems 4, 6 and 7 counted towards the Exam III grade. The rest counted as extra credit if the overall performance was high. Problem 4 was to find the determinant of a matrix two ways. Problem 5 was to find the evalues of a matrix. Problem 6 was to find the evector of a matrix given the evalue. Students must know how to complete the entire exam correctly before the final. As there is no time to schedule a retake of Exam III during the semester, students who need the retake will have three problems on the final (which will be similar to these problems) count as the retake of Exam III (times .8) and also separately contribute to the final exam grade.
Lesson 27: Eigenvalues of Linear Maps between Vector Spaces (Wed 5/13)
HW: Review all three exams and practice similar problems. Hand in Project IV and any Extra Credit work on Mon 5/18 (no resubmission or lateness allowed).
Lesson 28: Review for Final (Mon 5/18 starting at 8:30 pm)
Final during Finals Week Wed May 20 8-10 pm (students may stay until 11pm)
Department of Mathematics and Computer Science, Lehman College, City University of New York