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Math 312: Linear Algebra | Spring 2013 |
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Faculty: Dr. Aaron M. Silberstein
Telephone: (215) 898-5794
email: aaronsil AT math.upenn.edu
Office Hours: Monday 1-2 (and also by appointment) in DRL 4C3Grader: Shanshan Ding
Telephone: (215) 898-5793
email: shanshand AT math.upenn.edu
Office Hours: (and by appointment) in DRL 4C11Linear Algebra is at the heart of many diverse applications of mathematics. Our goal is to present both the major ideas and technical skill.
To be successful in this course, you should be present for all class meetings and plan to take good notes.Text: Otto Bretscher Linear Algebra with Applications, 5th edition, Pearson (2012).
*NOTE:* This is a new edition (Dec. 2012). It is also available in a binder--ready version, which is the same book but is three-hole punched. It is the full text, same paper quality but a lot less expensive. The net price to the Bookstore is $81.00, so retailing for approximately $108.00 vs. the hardbound net price at 124.50 and retail price of $166.00.
The ISBN for the binder-ready version is: 0321796942 The hardbound ISBN is: 0321796977
Penn's Bookstore (and probably online sources) should have both versions.
REMARK: Can you manage with the old edition? Since I have not yet seen the new edition, I can't answer with complete confidence. While surely 90% of the book will be very similar, there will likely be new sections added and additional problems at the end of each section-- so the numbering of the problems will be altered.
You can certainly manage with the old edition, but some scrambling might be needed. My own vote: use the old edition.Note that a Blackboard site has been arranged for the course. You may find it useful for communication.
Prerequisites & Review Material: Math 240 or equivalent.
To remove rust from your background I suggest doing the linear algebra problems from recent Math 240 Final ExamsSyllabus
Prof. Kazdan taught this course last semester: Math 312 Fall 2012.
The version this semester will be a bit different. In particular, in order to do more applications of linear algebra to real-life problems we will cover the material in Chapters 1-3 of the text more quickly. It is largely a review of material in Math 240.Some References: books, articles, web pages
Notes:
Some Applications Using Linear Algebra
Matrices as Maps and Symmetries
Linear maps from R2 to R3 are just linear equations.
Homework and Exams from Dr. Jauregui's Section of Math 312, Fall 2012.
Some Maple Examples
A large collection of Linear Algebra Problems
The letter F
Basis, span, etc.
The kernel of Lu := u''+4u
Dual spaces
Midterm 1
Midterm 1 Solutions
Minimal Polynomials
Homework Assignments:
- Set 0 (This will not be collected.)
- Set 1 Due: Friday, January 18, at 1 pm in Shanshan's mailbox.
- Set 2 Due: Friday, January 25, at 1 pm in Shanshan's mailbox in the math office (not in her office).
- Set 3 Due: Friday, February 1, at 1 pm in Shanshan's mailbox in the math office (not in her office).
- Set 4 Due: Friday, February 8, at 1 pm in Shanshan's mailbox in the math office (not in her office).
- Set 5 Due: Friday, February 22, at 1 pm in Shanshan's mailbox in the math office (not in her office).
- Set 6 Due: Friday, March 1, at 1 pm in Shanshan's mailbox in the math office (not in her office).
- Set 7 Due: Friday, March 15, at 1 pm in Shanshan's mailbox in the math office (not in her office).
- Set 8: Bretscher, Exercises: Section 6.2, Exercises 6, 17, 13, 23, (Suggested: 26, 45). (Suggested: Section 6.3, Exercises 24, 48.) Section 7.1, Exercises 18-21, 24-29 (these two sets of problems should be considered one problem). Due: Friday, March 29, at 1 pm in Shanshan's mailbox in the math office (not in her office).
- Set 9: Bretscher, Exercises: Section 7.1, Exercises 1, 3, 5, 7, (Suggested: 9, 11, 13), Chapter 6 true or false exercises (pp. 308-9): Exercises 3, 6, 7, (Suggested: 8, 9, 20). (Justify your answers!). Problem: Professor Dennis Gaitsgory at Harvard was teaching linear algebra while a graduate student in Jerusalem, as he wrote here. He knows his linear algebra very well, but missed a crucial aspect of the problem he was teaching. Let M be the n×n matrix given by writing down the numbers in order, left-to-right, top-to-bottom (as Prof. Gaitsgory wrote as an example for his linear algebra class). What is the dimension of the image of M? For which n will M have determinant zero? Due: Friday, April 5, at 1 pm in Shanshan's mailbox in the math office (not in her office).
- Set 10: Bretscher, Section 7.2, Exercises 1, 3, 5, 7, (Suggested: 9, 11, 13), 23. Section 7.6, Exercises 1, 3, 5, 7, 9. Due: Friday, April 12, at 1 pm in Shanshan's mailbox in the math office (not in her office).
- Set 11: Bretscher, Section 7.5, Exercises 1, 3, 5, 7, 9, 11, 13, (Suggested: 15, 28, 45). Chapter 7, True or false exercises: 1, 3, 5, (Suggested: 35). Due: Friday, April 19, at 1 pm in Shanshan's mailbox in the math office (not in her office).
Exams: There will be two in-class exams and a Final Exam. You may always use one 3"×5" card with handwritten notes on both sides
- Exam 1: Wed. Feb. 13, 11:00-11:50
- Exam 2: Wed. March 20, 11:00-11:50 [Solutions].
- Final Exam: Wed. May 1, 12-2 in DRL A1. Mean score: 277. Median score: 280. Std. dev: 23.
How grading worked: I calculated your final grade via the rubric I had written at the beginning of the course, putting on my "Neutral Arbiter of Grades from the Numerical Criteria I Spelled Out at the Beginning of the Semester" hat. Then, I put on my "Student's Advocate" hat and asked: was there anything that I could see from your performance that indicates that the grade you had been assigned was lower than it should have been? This could be insightful comments in class or office hours (both mine and Shanshan's), completed and correct bonus problems, or a sense that a given exam/midterm score was anomalously low. I then increased your grade to the largest extent that I could justify without being unfair to your peers. As that is, I will not entertain requests to raise your grades - I already did that to the extent justifiable.