Announcements

• Grades have been posted to Bearfacts. I am not sure when they will be available; email me if you want to know yours. Exams have been turned in at the main Math office, 970 Evans, you may see them in my presence or three weeks into the next term.
• Statistics for the final exam: out of 120 points, min 35, 1st quartile 50, median 68, 3rd quartile 82, max 115.
• I will not have detailed solutions for the exam, so here are a few comments on it. Most people said that a unitary operator may only have eigenvalues +-1; that is not true, they may be other complex numbers of absolute value 1. The set {x+y+z=1} is not a subspace of R^3, even though it is a plane. All the eigenvalues of a self-adjoint operator are real, while this is not the case for a normal non-self-adjoint operator, so they cannot have the same characteristic polynomial. In the problem about the nilpotent matrix, a number of people proved that the matrix is not diagonalizable, and then started the solution to the other part of the problem by assuming that the matrix is diagonalizable... Exactly one person got problem 6 right. Solution: we are given (n+1) polynomials in an (n+1)-dimensional space. Since for each of them, p(1) = 0, they don't span the whole space. Therefore they are linearly dependent.
• There are errors in the textbook. The errata for the various printings are available here. If you find errors in homework problems, please bring them to my attention.
• Syllabus (with a small correction).

Homework

• Homework 14.
  • Read sections 6.6, 7.1, 7.2.
  • Problems without * are due on December 5. Section 6.6: 1*, 2, 3*(corresponding to 2(a)), 4, 7. Section 7.1: 1*, 2(a,c), 3(corresponding to 2(a,c)), 5*, 7(a,b,c).
• Homework 13.
  • Read section 6.5, start 6.6.
  • Problems without * are due on November 28th. Section 6.5: 2(a,c), 5(a,c,e), 7*, 12, 13*, 21(a,b).
• Homework 12.
  • Read section 6.4-6.5, start 6.6.
  • Problems without * are due on November 21th. Section 6.4: 1*, 2(a,b), 3, 5, 6*, 8, 13*, 16. Section 6.5: 1*, 3, 4, 9, 11, 16*.
• Homework 11.
  • Read section 6.3, start 6.4.
  • Problems without * are due on November 14th. Section 6.3: 1*, 2(a,c), 3(b), 6, 7, 8, 11*, 12*, 14, 16*, 17*, 19.
• Homework 10.
  • Read section 6.2, start 6.3.
  • Problems without * are due on November 7th. Section 6.2: 1*, 2(a,c), 3, 4, 7, 8*, 10, 11*, 13*, 15, 19.
• Homework 9.
  • Read section 6.1, start 6.2.
  • Problems without * are due on October 31st. Section 6.1: 1*, 2, 5, 8, 9, 11, 12*, 13, 17, 19*, 20*, 22(a,c), 22*(b,d, conclusion).
• Midterm II.
  • Statistics: out of 50 points, min 14, 1st quartile 21, median 26, 3rd quartile 28, max 36.
• Homework 8. This assignment was not graded.
  • Read sections 5.3-5.4.
  • Problems without * are due on October 24th. Section 5.3: 7*, 10(a), 13, 15, 19*. Section 5.4: 1*, 2, 4, 6(a,b,c), 9, 10, 17*, 19*.
• Homework 7.
  • Read sections 5.2-5.3.
  • Problems without * are due on October 17rd. Section 5.2: 7, 8*, 10, 12, 13, 14(b), 17*, 19. Section 5.3: 1*, 2(b,d,e), 3, 5*, 6.
• Homework 6.
  • Read sections 5.1-5.2.
  • Problems without * are due on October 10rd. Section 5.1: 1*, 3(b,c), 4, 5, 8*, 9, 11, 14, 15, 21*, 22*. Section 5.2: 1*, 2(d), 3(a,b).
• Homework 5.
  • Read section 2.6. Review chapters 3,4, especially the sections with assigned problems and section 4.4.
  • Problems without * are due on October 3rd. Section 2.6: 1*, 2, 3, 8*, 9*. Section 3.2: 1*, 5(a,c), 6(a,b). Section 3.4: 1*, 2(a,f), 6*, 7. Section 4.2: 1*, 13, 21, 23*. Section 4.3: 1*, 9, 11.
• Midterm I.
  • Statistics: out of 50 points, the 1st quartile was 28, median 38, 3rd quartile 42.
• Homework 4. This assignment was not graded.
  • Read sections 2.4-2.6, appendix A.
  • Problems without * are due on September 26th. Section 2.3: 1*, 3, 4(a,b), 8*, 9, 10, 11, 12*. Section 2.4: 1*, 2, 4*, 5, 7, 14*, 15. Section 2.5: 1*, 2(b,c), 4, 6*, 8, 9.
• Homework 3.
  • Read sections 2.1-2.4 and the Appendices as needed.
  • Problems without * are due on September 19th. Section 1.3: 23. Section 1.6: 29. Section 2.1: 1*, 3, 9, 10, 13, 17*, 18*, 21*, 28*. Section 2.2: 1*, 2(a,c,e,f), 3, 5(a,b,c,d), 7*, 8*, 11*.
• Homework 2.
  • Read sections 1.4-1.6, 2.1.
  • Problems without * are due on September 12th. Section 1.4: 1*, 3, 6, 7, 10*. Section 1.5: 1*, 3*, 5, 7, 12, 14, 17*. Section 1.6: 1*, 2(a,c), 4, 12, 14, 21*, 23*.
  • More misprints: in Problem 1.6.12, the second equation should read "2 x_1 - 3 x_2 + x_3 = 0".
• Homework 1.
  • Read sections 1.1-1.6.
  • Problems without * are due on September 5th. Section 1.2: 1, 2, 7*, 9, 11*, 18, 21. Section 1.3: 1*, 5, 8*(a,d,e,f), 10, 11, 12, 13*, 20*.
  • In problem 1.2.21, the definition of addition should read "(v_1, w_1) + (v_2, w_2) = (v_1 + v_2, w_1 + w_2)".

• Vector spaces: general theory and examples.
• Linear transformations, matrices, and the relationship between them.
• Determinants: a brief review.
• Eigenvalues, eigenvectors, and diagonalization.
• Inner product spaces.
• Special classes of operators.
• Jordan canonical form.