Linear Algebra: Math 110
Fall 2001, MWF 8-9 in 3 Evans
Announcements
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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.
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Statistics for the final exam: out of 120 points, min 35, 1st quartile 50, median 68, 3rd quartile 82, max 115.
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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.
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Syllabus (with a small correction).
Homework
Problems with * are suggested, for your study only.
- 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.
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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*.
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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*.
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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)".
Syllabus
Professor: Michael Anshelevich, 1063 Evans.
Office hours: Tu 11-12, F 2-3. The office hours for my other class are M 11-12, W 2-3. You are welcome to come by then, but the students from the other class have priority.
Text: Friedberg, Insel, and Spence, Linear Algebra, 3rd ed.
Prerequisites: Math 54. Some topics you should be familiar with: mathematical induction and the basics of complex numbers, solving systems of linear equations, determinants.
Course outline:
- 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.
Exams: We will have two in-class midterms, the 1st one on September 26th, the 2nd one on October 24th. The final exam is on December 13th, 8-11. No make-up exams will be given. If, under exceptional circumstances, you need to miss one of the midterms, the score from the other midterm will substitute for it.
Homework: weekly, due on Wednesdays. There will be problems you need to turn in, and other problems for extra study. No late homework will be accepted; the lowest score will be dropped. You are encouraged to work together, but you must each turn in your own work.
Grading: Homework 20%, each midterm 20%, final 40%.
Comments: In this course you will learn new material, even though you have already seen most of the topics in Math 54. However, unlike in that course, we will put serious emphasis on proofs. An important component of this course is learning to give rigorous proofs, in particular learning what it means to prove a mathematical statement. The hope is that, by the end of the course, the need for precision will become apparent, and precision in your mathematical reasoning second nature...