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math304:spring2020
Linear Algebra - Math 304
Spring 2020 - Course Coordinator: Prof. Alexander Borisov
| Sec | Instructor | Office | Phone | Email(*) | Meets | Room |
|---|---|---|---|---|---|---|
| 1 | Alexander Borisov | WH-109 | 777-2764 | borisov | MWF:8:00-9:30 | SL-302 |
| 2 | Casey Donoven | WH-202 | 777-2982 | cdonoven | MWF:8:00-9:30 | WH-G002 |
| 3 | David Biddle | WH-126 | biddle | MWF:9:40-11:10 | AA-G021 | |
| 4 | Charles (Matt) Evans | WH-380 | evans | MWF:11:20-12:50 | LH-12 | |
| 5 | David Biddle | WH-126 | biddle | MWF:11:20-12:50 | AA-G021 | |
| 6 | Alex Feingold | WH-115 | 777-2465 | alex | MWF:1:10-2:40 | SL-302 |
| 7 | Thomas Kilcoyne | WH-336 | kilcoyne | MWF:2:50-4:20 | LH-12 | |
| 8 | Thomas Kilcoyne | WH-336 | kilcoyne | MWF:4:40-6:10 | LH-12 |
(*): Each email address in this table is of the form xxx@math.binghamton.edu but that should happen automatically if you just click on the link.
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.
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.
Important: Syllabus Adjustments due to the Coronavirus Epidemic
Syllabus Addition for MATH 304, due to the Online Instruction Mode
The following changes will be implemented in all sections of MATH 304, effective 03/19/2020.
1) Instead of the regular classes, the instructors will be holding online office hours, using Zoom or alternative software. These online office hours will be held during the regular instructional times. Additional online office hours may be scheduled as needed. In addition to the recommended textbook reading, there will be links to videos posted online. You are responsible for learning the material on your own, and using the online office hours to clarify any questions that you may have.
2) Instead of the in-class quizzes you will be getting homework assignments, through WebWork, MyCourses, or other system, at your instructor's discretion. These assignments are on top of the regular WebWork homework, and they will differ by section and may have shorter deadlines.
3) Midterm examinations and final examination will be conducted in a various remote formats, depending on the section. Your instructor will provide you with the details.
4) Since we are unable to hold a common in-class final examination, the one-letter-grade rule from the original syllabus will not apply.
5) It is your responsibility to inform your instructor of any circumstances that hinder or jeopardize your participation in the course, including any computer-related issues. The instructors and the course coordinator will do their best to help you learn and have a successful semester.
Consider the current situation, as unfortunate as it is, as an opportunity to develop a valuable skill of learning independently. It is, actually, one of the main goals of college education, much more important than any specific knowledge in any course.
Textbook
``Linear Algebra” by Jim Hefferon, Third Edition, available as a free download here:
Linear Algebra by Jim Hefferon.
Students can also buy a cheap printed version from the link on the author's 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 Schedule
Only the Final Exam will be common to all sections, but we expect each section will administer other exams on the same day, three times during the semester, as follows:
Exam 1: February 17 or 19 (depending on section)
Exam 2: March 18 This Exam will have to be given online since all classes March 17, 18 have been cancelled.
Exam 3: April 22 or April 24, depending on your section. This Exam will have to be given online.
Final Exam: Thursday, May 7, 8:00-10:00 AM, will be given online.
Arrangements for online exams will be announced soon. It is your instructor's responsibility to find a way to administer such exams, get the results and return the graded exam results.
Grade Distribution and Policies
The course total will be determined as follows:
Homework: 5%
Quizzes: 20% (the number and scope to be determined by your instructor)
Exam 1, 2, and 3: 15% each
Final Exam: 30%
The general grade cutoffs are going to be the following:
90% A; 80% B; 70% C; 60% D; and proportional cutoffs for A-,B+,B-,C+, and C-.
These cutoffs may be relaxed at the end of the semester, and may also differ a bit from section to section.
This rule from the original syllabus will not apply: (Additionally, the following one-letter-grade rule will apply: the grade in the course cannot exceed the grade on the final examination by more than one letter grade. For example, if you get a grade of B- on the final, the highest grade you can get in the course is A-. Note that the rule only works one way: even if you get an A on the final, you may still, theoretically, fail the course. The purpose of this rule is to bring some uniformity to the grading, considering that each section will have their own exams, quizzes, and cutoffs.)
Homework
Online homework will be done using WebWork. The server address is
https://webwork.math.binghamton.edu/webwork2/304Spring2020/
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 xyzw77@binghamton.edu then your username: xyzw77 and your password: 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.
Besides the online 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 paramount to your success in the course.
Expected workload outside of the classroom
This class is scheduled to meet three times per week for 90 minutes each time. In addition to attending all classes, you should expect to need 8 to 10 hours per week outside of the class meetings to study the material and do homework.
Expected behavior in class
During classes all students are expected to behave according to university rules. Your instructor makes the final decisions about what to allow in the classroom, regarding in particular cell phone and laptop use, and food and beverage consumption. If you have any temporary of permanent needs that may necessitate an exception, it is your responsibility to discuss the matter with your instructor in advance.
Disability Information
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.
Announcements
January 22 First Day of Classes: After meeting your instructor you should have been given this webpage address to check for the syllabus and instructions. Step 1: Read the entire syllabus, including the detailed syllabus for your section. Step 2: Set up your WebWork account for doing homework assignments. Step 3: Attend all classes and keep up with all homework corresponding to your section lectures.
February 11: Prof. Borisov will hold a review for all MATH 304 students on Sunday, Feb. 16, at 1:00-3:00 pm, in LH-14. The review session will be based entirely on student's questions, the posted sample exams or any other sources.
March 16: Today the administration announced that all classes (in person and online) have been cancelled for March 17 and 18, so that online only classes will begin March 19. That prevents having the scheduled March 18 Exam 2 in class. Each instructor will tell their students how Exam 2 will be handled.
March 30: Lectures of Prof. Feingold (Section 6) recorded on Panopto as well as written lecture notes are available through links on his webpage: Feingold Section 6 Webpage. These recordings are 90-minute class lectures presented online including interactions with students, and the written lecture notes are copies of the pages shown during the lectures.
Tentative Schedule
Unless otherwise specified, the Text is the Jim Hefferon's book and the exercises are from there, in the format “Chapter:Section.Subsection.ProblemNumber”. It is subject to change and adjustment at your instructor's discretion. NOTE: The Problems are for practice only and are not to be turned in. There will be separate weekly GRADED HOMEWORK through WebWork. Many of the examination problems will be similar to these practice problems and/or the WebWork problems.
| Week | Dates | Topics | Text | Problems |
|---|---|---|---|---|
| 1 | Jan 22, 24 | Introduction, preview, examples; linear combination | Ch. 1, I.1 | 1:I.1.17,1.19,1.21 |
| Gaussian elimination (reduction) | Ch. 1, I.1 | 1:I.1.22,24,27,32 | ||
| 2 | Jan 27-31 | (Augmented) matrix of a system, solution set | Ch. 1, I.2 | 1:I.2.15,16,17,18,20,23 |
| Logical statements, basic constructions, quantifiers | A-1, A-2 | |||
| Induction (informal), sets, functions | A-3, A-4 | |||
| 3 | Feb 3-7 | 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 | ||
| 4 | Feb 10-14 | 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 (skip proofs of 2.5, 2.6) | Ch. 1, III.2 | 1:III.2.11,14,20,21,24 | ||
| Review for Examination 1 | Ch. 1; Appendix | Sample_1,Answers_1; Sample_2,Answers_2; Sample_3,Answers_3 | ||
| 5 | Feb 17-21 | Examination 1 | Jan 22 – Feb 14 | |
| Matrix operations, including the transpose. Linear system as a matrix equation | Matthews 2.1 | 3:III.1.12,13,14,15 | ||
| Linear maps (transformations) given by matrices | Matthews 2.2 | 3:III.1.18; 3:III.2.17,30 | ||
| 6 | Feb 24-28 | Vector spaces: definition, examples | Ch. 2, I.1 | 2:I.1.17,18,19,21,22,29,30 |
| Subspaces. Span | Ch. 2, I.2 | 2:I.2.20,21,23,25,29,44 | ||
| Linear independence | Ch. 2, II.1 | 2:II.1.20,21,24,27 | ||
| 7 | Mar 2,4 | Properties of linear independence | Ch. 2, II.1 | 2:II.1.28,29,31,32 |
| Basis of a vector space | Ch. 2, III.1 | 2:III.1.18,19,20,21,22,23,24,28,29,32 | ||
| – | Mar 6 | No class | Winter Break | |
| 8 | Mar 9-13 | Dimension of a vector space | Ch. 2, III.2 | 2:III.2.16,17,18,19,22,23,26,29 |
| Column space, row space, rank | Ch. 2, III.3 | 2:III.3.17,18,19,20,21,23,29,32,39 | ||
| Range space and null space | Ch. 3, II.2 | 3:II.2.21,23,24,26,31,35 | ||
| 9 | Mar 16-20 | Review for Examination 2 | Sample_1,Answers_1; Sample_2,Answers_2; Some_Practice_Problems, Answers | |
| Examination 2 | Feb 19 – Mar 16 | |||
| 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 | ||
| 10 | Mar 23-27 | Elementary matrices. Row reduction using elementary matrices | Ch. 3, IV.3; CDTW Ch. 2, 2.3 | 3:IV.3.24,25,34; 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) | ||
| 11 | Mar 30-Apr 3 | Linear maps (transformations) between general vector spaces | Ch. 3, II.1 | 3:II.1.18,19,20,25,26,28 |
| Matrix of a linear transformation, matrix of the composition, inverse | Ch. 3, III.1, IV.2 | 3:III.1.12,14,15,18,19,20,21,22,26,29 Matrix_of_Transformation_1 | ||
| Change of basis, similar matrices | Ch. 3, V.1, V.2; Ch. 4, I.1 | 3:V.1.7,9,10,11; 4:I.1.5,8,11,13,14 Matrix_of_Transformation_2 Matrix_of_Transformation_3 Matrix_of_Transformation_4 Similar_Matrices | ||
| – | Apr 4-12 | No Class | Spring Break | |
| 12 | Apr 13-17 | 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.3.23,26,27,28,29,30,33 Eigenvectors_1 Eigenvectors_2 Eigenvectors_3 Eigenvectors_4 Eigenvectors_5 | ||
| Diagonalization of matrices | Ch. 5, II.2, II.3 | 5:II.3.21,32,35,40,41,44 Diagonalization_1 Diagonalization_2 Diagonalization_3 Diagonalization_4 Diagonalization_5 Diagonalization_6 | ||
| 13 | Apr 20-24 | Review for Examination 3 | Sample_1, Answers_1; Sample_2, Answers_2; Sample_3, Answers_3 | |
| Examination 3 | Mar 20 – Apr 20 | |||
| 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.2,10,11,12; Orthogonal_1 Orthogonal_2 Orthogonal_3 Orthogonal_4 | ||
| 14 | Apr 27-May 1 | 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 the Final Examination | ||||
| 15 | May 4 | Review for the Final Examination | Sample exams 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 | |
| Thu. May 7 | 8:00-10:00 am GW 69EX | Cumulative Final Exam |
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Syllabi from previous semesters
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:
math304/spring2020.txt · Last modified: 2020/08/21 17:45 by borisov