Alexandra Popa


PhD student

Mathematics Department

Stony Brook University

Stony Brook, NY 11794-3651, USA

E-mail: alexandra@math.sunysb.edu


Office: S 240 B ( inside the Math Learning Center, basement of the Mathematics building)


Summer office hours: Monday 3 - 4 pm

                        Wednesday 3 - 4 pm

Math Learning Center hours: Wednesday 1 - 3 pm


Summer teaching: MAT 211 Introduction to Linear Algebra

Class meetings: Monday, Wednesday and Thursday 6:00 - 8:15 pm, Physics P 112

First day of classes: June 2, 2008

Last day of classes: July 10, 2008

Midterm exam: June 23, 2008; 6:00 - 8:15 pm; Physics P 112

Final exam: July 10, 2008; 6:00 - 8:15 pm; Physics P112

Grading system: 30% midterm exam, 40% final exam, 30% homework, up to 25% extra credit

SCORE/GRADE CORRESPONDENCE and other information

Grader: Andrew Stimpson stimpson@math.sunysb.edu

Andrew Stimpson's MLC hours: Monday 2 - 6 pm; Thursday 12 - 6 pm

Textbook: Bretscher,Otto, Linear Algebra with Applications, Third Edition, Pearson/Prentice-Hall.

Other references:

  • Birkhoff, Garrett and MacLane, Sauders,A Survey of Modern Algebra, Revised Edition, Macmillan Company

  • Lang, Serge,Linear Algebra, Addison-Wesley Publishing Company,1966

  • Nomizu, Katsumi,Fundamentals of Linear Algebra, McGraw-Hill Book Company, 1966

  • Samelson, Hans,An Introduction to Linear Algebra, 1974, Pure and Applied Mathematics: A Wiley Interscience Series of texts, Monographs and Tracts

  • Smith, Larry, Linear Algebra, Third Edition, Springer

  • Strang, Gilbert, Linear Algebra and Its Applications, Second Edition, Academic Press



All references including the textbook are available at the Math/Physics library. The textbook will (probably) be available for sale at the University Bookstore as well. You may download the exercises from the textbook HERE.


Estimated schedule of lectures

According to the University policy, the final exams will remain with the lecturer. It is your right to see your graded final exam. If you wish to see it, please come in the Math Learning Center, on Friday, July 11, between 8:00 pm and 8:30 pm. Alternatively, please send me an e-mail after September 1, 2008.

THE MANDATORY READING ASSIGNMENTS AS WELL AS THE DEADLINES FOR THESE ARE AVAILABLE HERE . You may use the textbook or other linear algebra references. This will help you follow the lecture and better understand the material.

Extra Credit Policy: There are two ways in which you can add extra points to your total score: by doing the extra credit problems in the homework assignments or by doing the extra credit reading assignments. The extra credit problems should be handed in together with the homework, by the due date. The extra credit problems will count up to 10% of the total score. The reading assignments (which will count up to 15% of the total score) are to be found HERE. Doing a reading assignment also implies that you come to my office and explain the required proof at the blackboard. It is self understood that you will be able to explain any of the basic notions you are using. (For instance: I might give you as an extra reading assignment to prove that any vector space admits a basis; after you show me the proof at the blackboard, I might ask you to explain what a basis of a vector space is.) While explaining some extra credit proof at the blackboard you may not use any material unless otherwise stated in the extra credit reading assignment. The references needed for the extra credit reading assignments are available at the Math/Physics library. Please be advised that within the extra credit (both problems and reading assignments), there is no partial credit! In other words, if the problem you solved is incomplete or has significant errors, you will not receive any credit. Also, if you come to show an extra credit proof, but you are unable to explain one of the fundamental notions you are using, you will not receive any credit either.


Homework Policy: You must hand in the homework by the due date. Late homework will not be graded. Homework assignments will be posted here.You may talk to other colleagues about the homework problems, but you should write your own solutions. Please feel free to ask for my help as well (no later than the due date, if you like your homework to be graded).

Please be advised that solutions with little or no justification (if the case arises) will receive no credit. Also, you are expected to show all your work. (For instance, if some problem requires the computation of a determinant, you do not need to quote the properties you are using, but you will have to show all the stages of your calculations.)


HOMEWORK 1: DUE JUNE 11

APPENDIX TO HOMEWORK 1: HOW TO APPLY THE PRINCIPLE OF MATHEMATICAL INDUCTION

HOMEWORK 2: DUE JUNE 16

HOMEWORK 3: DUE JUNE 26

HOMEWORK 4: DUE JULY 2

HOMEWORK 5: DUE JULY 7

FUNDAMENTAL THEOREM ABOUT THE ORTHOGONAL COMPLEMENT

Exams Policy: The exams will last for 2 hours and 10 minutes. However, the subjects will be made in such a way that a good student can solve them in 1 hour and 45 minutes at the most. The problems in the exam will vary from standard to challenging. The standard problems will be similar to the ones in the homework assignments. It will be clearly indicated (both in the homework assignments and in the exams) what the standard ones are and what are the ones with higher degree of difficulty. The final exam is cumulative, covering all topics presented in class.The midterm exam will cover all topics covered in class by the time of the midterm.

Exams Rules: You must bring your photo ID to the exam. During the exam you are not allowed to use any additional materials (like textbooks or calculators) or to consult your colleagues. Should you have any questions (before or during the exam) please feel free to ask me.

Midterm. The midterm exam will cover all topics covered in class until that time. One of the subjects on the midterm exam will ask you to give some definitions and examples or counterexamples for some fundamental linear algebra concepts; these concepts will be chosen from the following: matrix multiplication, real vector space, span, linear dependence/independence, basis, linear transformation, kernel, image. All the other subjects on the midterm will be problems that vary from standard to challenging. With the exception of the theoretical subject, all the other standard problems on the midterm will be similar to problems in homework assignments 1, 2 and only the sets of problems from 1 to 7 in homework 3. You may wish to familiarize yourself with THE FRONT PAGE OF THE MIDTERM.

MIDTERM SOLUTIONS

Final Exam. The final exam is cumulative covering all the topics presented in class. One of the subjects on the final exam will require that you give some definitions and examples or counterexamples for some fundamental linear algebra concepts; these concepts will be chosen from the following: matrix multiplication, real/complex linear space, span, linear dependence/independence, basis, dimension of a finitely generated linear space, linear transformation, kernel, image, isomorphism, isomorphic/non-isomorphic linear spaces, inner product and norm, orthogonal transformation and matrix, orthonormal basis, the matrix of a linear transformation. One of the subjects on the final exam will be non-standard and have a higher degree of difficulty. With the exception of the theoretical subject and the challenging problem, all the other problems on the final exam will be similar to the standard problems in the homework assignments. In order to approach the last subject succesfully, one has to have in depth understanding of all concepts and results presented in class, to be able to solve any non-standard problem in the homework, to prove any result proved in class, to solve any exercise assigned in class, to prove claims other than those mentioned in class and having a maximum level of difficulty equal to the most difficult results given as homework or presented in class. You may wish to familiarize yourself with THE FRONT PAGE OF THE FINAL EXAM. According to the University policy, the final exams will remain with the lecturer. It is your right to see your graded final exam. If you wish to see it, please come in the Math Learning Center, on Friday, July 11, between 8:00 pm and 8:30 pm. Alternatively, please send me an e-mail after September 1, 2008.

FINAL EXAM PREPARATION GUIDE (the standard subjects)

IMPORTANT NOTE: Please be advised that I will be able to schedule an appointment with you outside my regular office hours only if time permits. If you are the first student asking for a separate appointment for a certain week, I will probably be able to schedule it; if you are the fourth student asking for a separate appointment in the same week I will probably no longer have the time to schedule that.


University Student Conduct Code


DSS ADVISORY: If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Disability Support Services (631) 632-6748 or http://studentaffairs.stonybrook.edu/dss/. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: http://http://www.studentaffairs.stonybrook.edu/dss/ada.