Math 4305, Fall 2019

Instructor:        Prof. Wing Suet Li
Office:              Skiles 237B
Office Hours:   M, W 3pm - 4pm, after class, and by appointment.
Email:              li@math.gatech.edu
Lectures:          M, W 4:30-5:45pm, Skiles 255
Textbook:         Linear Algebra with Applications, the 5th edition, Bretscher
Course webpage: http://people.math.gatech.edu/~li/Math4305B_Fall2019.html

Special aid:
Students with disabilities or other special needs that require classroom accommodation or other arrangements must let the instructor know at the beginning of the semester.

Course information:

• Topics: Linear algebra in R^n, standard Euclidean inner product in R^n, general linear spaces, general inner product spaces, least squares, determinants, eigenvalues and eigenvectors, symmetric matrices, see http://www.math.gatech.edu/courses/math/4305
  
• Prerequisites: MATH 1502 OR MATH 1512 OR MATH 1555 OR MATH 1504 ((MATH 1552 OR MATH 15X2 OR MATH 1X52) AND (MATH 1522 OR MATH 1553 OR MATH 1554 OR MATH 1564 OR MATH 1X53))

General policies:

• Calculators are not allowed in quizzes and exams.
  
• Attendance: Attendance at all lectures is required. If you miss a lecture, it is your responsibility to catch up on the topics that you missed.
  
• If a student is found responsible through the Office of Student Integrity for academic dishonesty on a graded item in this course, the student will receive a score of zero for that assignment, and the final grade for the course will be further reduced by one letter grade.
  

Homework:

• Doing homework and completing after the lectures and completing the reading assignments before the lectures are essential in learning the material. The home work will be collected, however, the grading is done based on completeness. The quiz questions will be directly chosen from teh homework questions and the midterm exam questions will be similar to the homework problems. Hence, for a successful completion of the course, it is absolutely necessary to work out these questions yourself.
  
• Collaboration, study groups, etc. are strongly recommended when you work through the reading and the homework assignments. The quizzes and tests are individual activities. Collaboration or usage of unauthorized aid (books, notes, phones, computers, etc) will result in zero grade for the whole quiz or test.
  

Grading:

• Grading will be based on homework, quizzes, Midterm 1, Midterm 2 and final: 
  
•                            Homework 5% 
  
•                            Quizzes: 15%   
  
•                            Midterm 1: 20%      
  
•                            Midterm 2: 20%     
  
•                            Final: 40%
• Homework is collected on due date at the beginning of the class and graded based on completeness.
• There will be four quizzes. The lowest quiz score will be dropped.  The quizzes are obligatory; if you do not show up, you will be assigned zero grade for that quiz. there are NO MAKE-UPS for quizzes.
• There will be two in-class midterm tests. The final is comprehensive. The tests and the final are obligatory. Make-ups will be available only for very serious reasons (e.g. documented health reason) or official travels. In case you have a foreseeable serious reason to miss any of hte tests, please let me know in advance.
  
• All quizzes and exams are closed book and closed notes. Calculators are not allowed in quizzes and exams.
  
• The final letter grades will be based on the overall average at the end of the semester, according to the following scheme: 88% or above -- at least an A, 78% or above -- at least a B, 65% or above, at least a C, 50% or above, a D, and scores below 50% will not be curved up to pass. 
  

Honor Code:
The strength of the university depends on academic and personal integrity. In this course, everyone must be honest and truthful. Violations include cheating on exams, plagiarism, improper use of the internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty and unfair competition. Ignorance of these rules is not an excuse.

All students at Georgia Tech are expected to adhere to the Academic Honor Code.  In particular, I expect that you will not attempt to cheat or violate the above policies during quizzes and exams. Transgressors will receive a zero on the exam and will be reported to the Office of Student Integrity.



Exams and Quizzes Schedule:

• Quizzes: There will be 4 quizzes which will be based on the homework materials. Each quiz will take about 20-30 minutes.
  
• Quiz 1: Wednesday Sep 4
  
• Quiz 2: Wednesday Sep 18
  
• Quiz 3: Wednesday Oct 23
  
• Quiz 4: Wednesday Nov 6
  
• Midterms: There will be 2 midterms.
• Midterm 1: Wednesday Oct 2
  
• Midterm 2: Wednesday Nov 13
  
• Final: Wednesday Dec 11, 2:50PM-5:40PM

 
Tentative Schedule:
  [B]:   Linear Algebra with applications, by Otto Bretscher, 5th ed. All homework problems are from [B] unless otherwise stated.

 

Date	Topic	Homework and Remarks
Aug. 19	Review: linear systems and solving linear systems by using elementary row operations (Reading assignment: Ch. 1 of [B].)	Due 8/26: p.5 # 9, 15, 19 p.18 #7, 9, 18, 35, 37 p.34 #34, 35, 36, 37, 49, 55, 57, 59.
Aug. 21	Matrix as linear transformation ([B] Sec. 2.1, 2.2)	Due 9/4: p.53 # 5, 7, 11, 37, 36 p.71 #7, 10, 11, 19-23 p.85 #34, 35, 39, 48, 61, 63 p.97 #5, 15, 30, 31, 39, 41.
Aug. 26	Linear transformation (cont.) ([B] Sec. 2.3, 2.4)
Aug. 28	Linear independence, linear span, and subspace. ([B] Ch. 3)
Sept. 4	Image and Kernel of a linear transformation ([B] Ch. 3)	Quiz 1, covers Ch. 1 and Ch. 2 of [B].
Sept. 9	Basis, dimension, and coordinates  ([B] Ch. 3)
Sept. 11	Linear transformation again ([B] Ch. 4)
Sept. 16	Linear transformation again ([B] Ch. 4)
Sept. 18	Linear transformation again ([B] Ch. 4)	Quiz 2, covers Ch. 3
Sept. 23	Orthogonal bases and orthogonal projections ([B] Sec. 5.1)
Sept. 25	Gram-Schmidt Process and QR factorization ([B] Sec. 5.2)
Sept. 30	Orthogonal transformations ([B] Sec. 5.3)
Oct. 2	Midterm 1	Covers Ch. 1, 2, 3, 4, and Sec. 5.1.
Oct. 9	Least squares and data fitting ([B] Sec. 5.4)
Oct. 14	Inner product spaces ([B] Sec. 5.5)
Oct. 16	Determinants ([B] Ch. 6)
Oct. 21	Eigenvalues and eigenvectors ([B] Ch. 7)
Oct. 23	Complex eigenvalues ([B] Ch. 7)	Quiz 3, covers Ch. 5
Oct. 28	Diagonalization (and the lack of diagonalization) of matrices  ([B] Ch. 7)
Nov. 4	On dynamical systems and stability ([B] Ch. 7)
Nov. 6	Symmetric matrices ([B] Sec. 8.1)	Quiz 4, covers Ch. 7
Nov. 11	Quadratic forms ([B] Sec. 8.2)
Nov. 13	Midterm 2	Covers Ch. 5, 6, 7.
Nov. 18	SVD, singular value decomposition ([B] Sec. 8.3 and notes)
Nov. 20	SVD (cont.)
Nov. 25	Review
Dec. 2	Review
Dec. 11	Final Exam, 2:40p, - 5:30pm