Office: LN-2218, Phone: 777-2465, Email: alex@math.binghamton.edu, Office Hours: MWF 1:10 - 2:10 and by appointment.
Class meeting times and locations:
MWF 10:50 - 11:50 in SW - 231
Th 10:05 - 11:30 in SW - 231.
``Advanced Linear Algebra'' by Steven Roman, Second Edition, Graduate Texts in Mathematics, Springer, New York, 2005.
We will cover most of Part I: Basic Linear Algebra, consisting of Chapters 1 - 10, if time allows. The topics covered should include: Vector spaces over any field, subspaces, sums, direct sums, intersections, spanning sets, independence, basis, dimension, coordinates, linear transformations, matrix representing a linear transformation with respect to a pair of bases, kernel, range, injective, surjective, bijective, invertible, the dimension theorem, transition matrices, equivalence of matrices representing the same transformation with respect to different bases, operators on V, similarity, invariant subspaces, quotient spaces, isomorphism theorems, linear functionals, dual spaces, dual bases, adjoint operators, eigenvalues, eigenvectors, diagonalization of operators, characteristic polynomials, determinants, geometric and algebraic multiplicities, Jordan canonical form, rational canonical form, inner product spaces in real and complex cases, orthogonality, projections, Gram-Schmidt theorem, unitary, normal, and self-adjoint operators, spectral theorems.
Exam 1: Feb. 28, 2008.
Exam 2: Apr. 3, 2008.
Exam 3: May 1, 2008.
Final Exam: Monday, May 12, 11 AM - 1 PM, FA-212.
There will be 3 ``hourly'' exams (actually 1 hour and 25 minutes) during the semester and 1 Final Exam (2 hours long) during the scheduled Finals period. The hourlies will be worth 100 points each, and the (2-hour) Final Exam will be worth 150 points. The contents of each exam will be determined one week before the exam. The Final Exam will be comprehensive, covering the whole course. ANYONE UNABLE TO TAKE AN EXAM SHOULD CONTACT THE PROFESSOR AHEAD OF TIME TO EXPLAIN THE REASON. A MESSAGE CAN BE LEFT AT THE MATH DEPT OFFICE (777-2147) OR ON PROFESSOR FEINGOLD'S VOICEMAIL (777-2465) OR SENT TO HIS EMAIL ADDRESS. NO ONE SHOULD MISS THE FINAL!
Practice Exams may be posted here. The practice exams below were designed for the course when taught from a different textbook, so the material covered may not correspond exactly to our exams this semester. The contents of these practice exams should still be relevant and worth your study.
A practice Exam 1 and its solutions can be found by clicking on the indicated link.
A practice Exam 2 and its solutions can be found by clicking on the indicated link.
A Another Exam 2 from spring 2007 and its solutions can be found by clicking on the indicated link.
A practice Exam 3 and its solutions can be found by clicking on the indicated link.
A Another Exam 3 from spring 2007 and its solutions can be found by clicking on the indicated link.
A Final Exam from spring 2007 and its solutions can be found by clicking on the indicated link.
Exams and their solutions will be posted here after they are given and graded. These will be very useful to correct your mistakes and to prepare for the final.
Exam 1 and its solutions can be found by clicking on the indicated link.
Exam 2 and its solutions can be found by clicking on the indicated link.
Exam 3 and its solutions can be found by clicking on the indicated link.
Each exam will be curved, giving each student a letter grade as well as a number grade, and the Total of all points earned will also be curved. The letter grades on the exams indicate how a student is doing, and will be taken into consideration in making the curve for the Totals. The course grade will be determined by the curve of Total points earned. Only borderline cases will be subject to further adjustment based on Homework. Any cases of cheating will be subject to investigation by the Academic Honesty Committee of Harpur College.
For each section of material covered there will be an assignment of problems from the textbook. They will be due one week from the day they are assigned (or the next scheduled class meeting after that if there is a holiday). Late assignments will be accepted at the discretion of the Professor. Assignments will be examined by a grader, who will record the fact that an assignment was attempted, and give some feedback on how selected problems were done. MOST QUESTIONS ABOUT PROBLEMS SHOULD BE ASKED OF THE PROFESSOR AT THE BEGINNING OF CLASS. DO NOT DEPEND ON THE GRADER TO FIND AND CORRECT YOUR MISTAKES. The number of homeworks attempted will be considered as a factor in determining your course grade if you are a borderline case in the Total curve.
Class attendance is required at both the lectures and the discussion sessions, and sleeping in class does not count as being there. Lectures can be interrupted at any time for questions. At the start of each class be ready to ask questions about homework problems or about the previous lecture. I hope there will be a substantial amount of participation by the students, and I want to create an atmosphere where you all feel very free to ask questions and make comments. If anyone feels that I have not answered a question clearly, completely, and with respect and consideration for the student who asked it, I want you to let me know about it immediately so I can correct the problem. You can do this in class or in my office hours, verbally or in writing, on paper or by email, or by whatever means makes you most comfortable, but with enough detail that I understand what you think I did wrong. It will be too late to help if you only tell me at the end of the course when I do a Student Opinion of Teaching survey.
The material is a combination of theory and calculation, and it is necessary to understand the theory in order to do sensible calculations and interpret them correctly. There is a significant difference between training and education, and I feel strongly that our goal at this university is to educate you, not just to train you to do computations. Theory is not presented to impress you with my knowledge of the subject, but to give you the depth of understanding expected of an adult with a university education in this subject. I will try to give you the benefit of my 37 years of experience teaching mathematics at the university level, but it will require your consistent concentrated study to master this material. While much learning can take place in the classroom, a significant part of it must be done by you outside of class. Using the book, class notes, homework exercises, only you can achieve success in this course. Students who do not take this course seriously, who do not take the advice I give, are not likely to be rewarded at the end. I am here to help and guide you, and I also make and grade the exams to judge how much you have learned, but grades are earned by you, not given by me. Exams will be a combination of theory questions and calculations appropriate for a course of this level.
Homework assignments will be made in class, and will be posted here.