MATH 44, section 1 -- Linear Algebra Spring 1999

• Syllabus and Schedule
  • Course Syllabus
    
  • Detailed Schedule
    

• Notes, etc.
  • Solutions for Discussion 1
  • Lecture Notes for class on February 10

• Information on Exams
  • The first exam this semester was held Friday, February 19.
    Review Sheet for Exam 1
  • The second exam this semester was held Friday, March 26.
    Review Sheet for Exam 2
    
  • Solutions for practice True-False questions, Exam 2.
  • The third exam this semester was held on Friday, April 23.
    Review Sheet for Exam 3.
  • Solutions for practice True-False questions, Exam 3
  • The final exam for this class will be held at 2:30 pm on Tuesday, May 11.
    Review Sheet for Final Exam.
    Review Session: Sunday, May 9 at 1:00 pm in HA 412

• Assignments
  • Problem Set 1 -- From Smith: Chapter 2/8,9,10; Chapter 3/2,3,4,10,12,15,16. (Note: In some of these problems you are asked to show that a set W with given sum and scalar multiplication operations is a vector space. If you recognize that the set is a subset of another set V that we already know is a vector space, and the operations on W are the restrictions of the operations on V, then you can use the "shortcut method" we discussed in class on Friday, January 21. It is enough to show that the subset is closed under sums and scalar multiples and contains the zero vector.) Due: Friday, January 29.
  • Discussion 1
  • Problem Set 2 -- From Smith: Chapter 4/2,5,10,11,15,28 (Note: the sum of two subspaces S,T of a vector space V is defined on page 40. Read that and Proposition 4.1.16 and its proof before trying problems 11 and 28); Chapter 5/1,2,4,5,10,11,12. Due: Friday, February 5.
  • Discussion 2
  • Discussion 3
  • Discussion 4
  • Problem Set 3 -- From Smith Chapter 8/11,15,16,19; Chapter 9/1,2,6,7,8; Chapter10/1,2,15. Due: Wednesday, March 17.
  • Problem Set 4 -- Due: Friday, April 9.
  • Problem Set 5 -- From Smith: Chapter 14/1,3,4,5,10,11,12,13,15 -- Due: Friday, April 16.
  • Problem Set 6 (The Final Problem Set!) -- From Smith: Chapter 15/ 1a,c, 2a,c, 4,9; Chapter 16/1a,d,f,2,3a,b,c Due: No later than the end of the day, Wednesday May 5. Announcement: Please omit problem 7 from Chapter 15! The proof of part a ("Bessel's Inequality") uses some ideas we have not discussed; while part b ("Parseval's Identity") is not true as stated(!). (It is true if you assume that {A₁,...,A_n} is an orthonormal basis for V, but not for a general orthogonal set of vectors!)

• Information and Announcements
  

• Related Links
  • One branch of linear algebra grew out of the use of matrices and determinants to study solutions of linear and non-linear equations -- a historical survey of this development.
  • Some biographical information about linear algebra pioneers:
    
    • Augustin Cauchy
    • Arthur Cayley
    • William Rowan Hamilton
    • Charles Hermite
    • Hermann Amandus Schwarz
    • James Joseph Sylvester

Last modified: May 5, 1999