Problem of the Week
Hilton Memorial Lecture
(*): To send an email to your instructor, click on the link in the Email column of the table.
If a section has its own detailed syllabus webpage, a link to that page will be provided under the Instructor column of the table above.
Each instructor should provide their students with a Zoom link to the recurring class meetings which begin on Friday, Feb 12, and end on Monday, May 17, 2021.
Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.
``Linear Algebra” by Jim Hefferon, Fourth Edition, available as a free download here:
Linear Algebra by Jim Hefferon.
On can buy a cheap printed version and access more free resources at the textbook's official website.
Here are also some additional books that students and instructors may find helpful.
A First Course in Linear Algebra by Robert A. Beezer
Elementary Linear Algebra by K.R. Matthews
Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron
Exam 1: The week of March 8-12.
Exam 2: The week of April 12-16.
Exam 3: The week of May 10-14.
Final Exam: Tuesday, May 25, 8:00 - 10:00 AM Online.
Remote format of the course requires steps to combat academic dishonesty and to protect the honest students from unfair competition. Details about how quizzes and exams will be administered so as to achieve that goal will be announced by your instructor. Your instructor may decide to use: (1) Limited time to answer each question, (2) Visual observation of you during the exam through Zoom, (3) Oral exams in place of, or in addition to, written exams. Some advice about preparing for oral exams is available through the following link:
The course total will be determined as follows:
Exam 1: 20%
Exam 2: 20%
Exam 3: 20%
WebWork Homework (common for all sections): 5%
Final Exam: 15%
At the end of the course, your grade in the course will be determined by your instructor based on your course total and the following approximate scale. (Borderline cases will be decided by other factors such as attendance or participation.)
A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 55%, C- 50%, D 45%
Online homework will be done using WebWork. The server address is
For students, your WebWork account username is the pre@ portion of your binghamton.edu e-mail account. Your initial password is the same as the username. For example, if your Binghamton e-mail account is email@example.com then your username is: xyzw77 and your initial temporary password is: xyzw77
Make sure to change your password as soon as possible to a secure password, and save that choice where it will not be lost.
Important: Besides the WebWork homework sets, you should do problems from the book, as selected by your instructor, see an approximate schedule below. This part of the homework will not be graded, but it will be important to your success in the course.
You are expected to spend about 12.5 hours per week on average for this class, including participation in Zoom lectures, watching instructional videos, solving homework problems (graded and ungraded), reviewing the material, and preparing for the tests. Expect the work load to be higher than average in the weeks before the exams.
During online classes all students are expected to participate in a way that maximizes their learning and minimizes disruptions for their classmates. Your instructor has the final word on the use of video and audio in the general Zoom sessions, break-out rooms, and online office hours. If you have any concerns, limitations, or circumstances, please communicate with your instructor to find the most appropriate solution.
For all graded assignments and exams, you are not allowed to use any help not explicitly authorized by your instructor. This includes, but is not limited to, problem-solving websites, notes, help from other people, etc. All instances of academic dishonesty will be investigated, penalized, and referred to the appropriate University officials for maximal possible punishment. In other words, don't even think of trying to cheat.
If you fall behind in class, or need extra help to learn the material, talk to your instructor as soon as you can. They should be able to help you and also point you to other resources. We also encourage you to talk to your classmates, and, in particular, to form informal study groups to prepare for the exams.
If you have a disability for which you are or may be requesting an accommodation, please contact both your instructor and the Services for Students with Disabilities office (119 University Union, 607-777-2686) as early in the term as possible. Note: extended time for the examinations may not automatically apply to the interview-style exams, but we will work with you to provide reasonable accommodations that are appropriate for your situation.
The table below contains suggested problems from sections of our textbooks (Heffron or Matthews) in the format “Chapter:Section.Subsection.ProblemNumber”. Your instructor may suggest other problems or exercises. These problems are for practice only and are not to be turned in. There will be graded homework assignments given through WebWork which should be done in the order indicated by your instructor. Instructional videos linked below are supplementary material, not intended to replace the regular lectures. The order in which material is presented in class meetings will be determined by your instructor, and may not precisely follow the order in our textbooks.
|Introduction, preview, examples; linear combination||Ch. 1, I.1||1:I.1.17,19,21|
|Gaussian elimination (reduction)||Ch. 1, I.1||1:I.1.22,24,27,32|
|(Augmented) matrix of a system, solution set||Ch. 1, I.2||1:I.2.15,16,17,18,21,25|
|Basic logic: statements, connectives, quantifiers||Appendix|
|Set theory, general functions||Appendix|
|Homogeneous and non-homogeneous systems (no formal induction in Lemma 3.6)||Ch. 1, I.3||1:I.3.15,17,18,20,21,24|
|Points, vectors, lines, planes||Ch. 1, II.1||1:II.1.1,2,3,4,7|
|Distance, dot product, angles, Cauchy-Schwarz and Triangle Inequalities||Ch. 1, II.2||1:II.2.11,12,14,16,17,21,22|
|Gauss-Jordan reduction, reduced row echelon form||Ch. 1, III.1||1:III.1.8,9,10,12,13,14,15|
|Linear combination lemma, uniqueness of RREF (no proofs of 2.5, 2.6)||Ch. 1, III.2||1:III.2.11,14,20,21,24|
|Review||Ch. 1; Appendix||Student's_Guide; Sample_Problems; Solutions|
|Matrix operations, including the transpose. Linear system as a matrix equation||Matthews 2.1||3:III.1.13,14,15,16|
|Linear maps (transformations) given by matrices||Matthews 2.2||3:III.1.19; 3:III.2.12,17,30|
|Vector spaces: definition, examples||Ch. 2, I.1||2:I.1.17,18,19,21,22,29,30|
|Linear maps between vector spaces||Ch. 3, II.1||3:II.1.18,19,20,22,24,25,26,28|
|Subspaces. Span||Ch. 2, I.2||2:I.2.20,21,23,25,26,29,44,45|
|Linear independence||Ch. 2, II.1||2:II.1.21,22,25,28|
|Properties of linear independence||Ch. 2, II.1||2:II.1.29,30,32,33|
|Basis of a vector space||Ch. 2, III.1||2:III.1.20,21,22,23,24,25,26,30,31,34|
|Dimension of a vector space||Ch. 2, III.2||2:III.2.15,16,17,18,19,20,21,24,25,28|
|Column space, row space, rank||Ch. 2, III.3||2:III.3.17,18,19,20,21,23,29,32,39|
|Range space and Kernel (Null space)||Ch. 3, II.2||3:II.2.21,23,24,26,31,35|
|Review||Student's_Guide; Sample_Problems; Solutions|
|Invertible matrices: definition, equivalent conditions; inverse matrix||Ch.3, IV.4||3:IV.4.13,14,15,16,17,18,19,26,29 InvertibleMatrices_1 InvertibleMatrices_2 InvertibleMatrices_3 InvertibleMatrices_4 InvertibleMatrices_5|
|Elementary matrices. Row reduction using elementary matrices||Ch. 3, IV.3; CDTW Ch. 2, 2.3||3:IV.3.24,25,32 ElementaryMatrices_1 ElementaryMatrices_2 ElementaryMatrices_3|
|Determinant of a matrix, properties||Ch. 4, I.1, I.2||4:I.1.1,3,4,6,9; 4:I.2.8,9,12,13,15,18 Determinants_1 Determinants_2 Determinants_3 Determinants_4 Determinants_5 Determinants_6|
|More on Determinants||Ch. 4, II.1, III.1||4:III.1.11,14,16,17,20,21,22 Determinants_7(Cramer) Determinants_8(Adjoint)|
|Matrix of a linear transformation, matrix of the composition, inverse||Ch. 3, III.1, IV.2||3:III.1.13,17,18,19,21,23 Matrix_of_Transformation_1|
|Change of basis, similar matrices||Ch. 3, V.1, V.2; Ch. 5, II.1||3:V.1.7,9,10,12; 5:II.1.5,8,11,13,14 Matrix_of_Transformation_2 Matrix_of_Transformation_3 Matrix_of_Transformation_4 Similar_Matrices|
|Complex numbers||Matthews 5.1–5.6||Matthews 5.8.1,2,5,6,7,9 Complex_Numbers_1 Complex_Numbers_2 Complex_Numbers_3 Complex_Numbers_4 Complex_Numbers_5|
|Eigenvectors, eigenvalues, eigenspaces for matrices and linear operators. Characteristic polynomial||Matthews 6.1, 6.2; Ch. 5, II.3||5:II.3.23,24,25,26,27,28,29,30,31 Eigenvectors_1 Eigenvectors_2 Eigenvectors_3 Eigenvectors_4 Eigenvectors_5|
|Diagonalization of matrices||Ch. 5, II.2, II.3||5:II.3.22,33,36,46 Diagonalization_1 Diagonalization_2 Diagonalization_3 Diagonalization_4 Diagonalization_5 Diagonalization_6|
|Orthogonal and orthonormal bases of $R^n$ and its subspaces; orthogonal matrices||Ch. 3, VI.1, VI.2||3:VI.1.6,7,17,19; 3:VI.2.10 Orthogonal_1 Orthogonal_2 Orthogonal_3 Orthogonal_4|
|Orthogonal complement of a subspace, orthogonal projection||Ch. 3, VI.3||3:VI.3.11,12,13,14,26,27 Complements_1 Complements_2 Complements_3 Complements_4 Complements_5|
|Gram-Schmidt process; orthogonal diagonalization of matrices||Ch. 3, VI.2||3:VI.2.13,15,17,18,19,22 GramSchmidt_1 GramSchmidt_2 OrthogonalDiagonalization_1 OrthogonalDiagonalization_2|
|Review for Final Exam||Student's_Guide; Sample_Book_Problems; Sample_Problems; Solutions|
IMPORTANT: Please note that the sample exams below are traditional written exams. Our interview-style exams will focus more on understanding and less on calculations.
Sample_1,Answers_1; Sample_2,Answers_2; Sample_3,Answers_3
Being cumulative, Examination 2 will cover all the material of Examination 1 as well as additional topics:
Sample_1,Answers_1; Sample_2,Answers_2; Some_Practice_Problems, Answers
Examination 3 and Final Examination
Being cumulative, Examination 3 and Final Examination will cover all the material of Examinations 1 and 2 as well as additional topics:
Sample_1, Answers_1; Sample_2, Answers_2; Sample_3, Answers_3
The following sample exams are traditional cumulative final exams. They are adapted, with permission, from the collection of Dr. Inna Sysoeva
Sample_1, Answers_1; Sample_2, Answers_2; Sample_3, Answers_3; Sample_4, Answers_4; Sample_5, Answers_5
The syllabus for Math 304 in Fall 2020 is available through this link:
The syllabus for Math 304 in Fall 2019 is available through this link:
The syllabus for Math 304 in Fall 2019 is available through this link:
The syllabus for Math 304 in Spring 2019 is available through this link:
Math 304 Syllabus for Spring 2019
The syllabus for Math 304 in Fall 2018 is available through this link: