Fall 2020 Math 235: Introduction to Linear Algebra

This is the course-wide webpage with common guidelines for all learning sections. Please consult your section webpage (below) for additional information.

Enrolling and Overrides

Students waiting to enroll in the course should check SPIRE to see if a slot in the desired section opens. If an override is still needed, please wait till AFTER THE FIRST WEEK OF CLASSES to contact your (desired) section instructor, cc'ing the course chair Professor Rob Kusner profkusner@gmail.com with the following information: (1) sections of the course which conflict with other courses on your academic schedule, and (2) your desired section of the course. (Unfortunately, in order to keep the sections balanced, we cannot guarantee that you will be assigned to your desired section.)

Course-wide Videos

We are making a series of our our own short videos to help you learn linear algebra; please watch and think about them before each class!

Syllabus and Weekly Schedule

Math 235 is an introductory course on linear algebra, covering systems of linear equations, matrices, linear maps, determinants, vector spaces, eigenvalues and eigenvectors, and orthogonality.

The schedule below gives the topics from the course text to be covered each week (this a guideline which may be modified by your instructor as necessary):

[Week 1] 8/24: 1.1 Systems of linear equations; 1.2 Row reduction and echelon forms; 1.3 Vector equations.

[Week 2] 8/31: 1.4 The matrix equation AX=B; 1.5 Solution sets of linear systems.

[Week 3] 9/07: 1.7 Linear independence; 1.8 Introduction to linear maps.

[Week 4] 9/14: 1.9 The matrix of a linear map; 2.1 Matrix operations.

[Week 5] 9/21: 2.2 The inverse of a matrix; 2.3 Characterizations of invertible matrices.

[Week 6] 9/28: 3.1 Introduction to determinants; 3.2 Properties of determinants.

Common Midterm I: [7-9PM* Friday 2 October 2020]

[Week 7] 10/05: 3.2 (continued); 3.3 Cramer's rule, volume and linear maps.

[Week 8] 10/12: 4.1 Vector spaces and subspaces; 4.2 Null space (kernel), column space (image) and linear maps.

[Week 9] 10/19: 4.3 Linearly independent sets and bases; 4.4 Coordinate systems.

[Week 10] 10/26: 4.5 The dimension of a vector space; 4.6 The rank+nullity theorem.

[Week 11] 11/02: 5.1 Eigenvectors, eigenvalues and eigenspaces; 5.2 The characteristic equation.

Common Midterm II: [7-9PM* Friday 6 November 2020]

[Week 12] 11/09: 5.3 Diagonalization; 5.5 Complex eigenvalues.

[Week 13] 11/16: 6.1 Inner product, length and orthogonality; 6.2 Orthogonal sets; 6.3 Orthogonal projection; 6.4 The Gram-Schmidt process; 6.5 Least squares solutions (if time permits).

Final Exam: Wednesday 02 December 2020 at 11:30A-1:30P

*This is the preferred time period for most students to take the exam. Additional time periods are available for students with special accomodations or other documented conflicts. Please contact your instructor by email AT LEAST ONE WEEK BEFORE THE EXAM DAY to discuss your particular situation. We strive to be as flexible as possible in these unusual times!

Learning Sections

Here are the class times and instructors:

63125 MATH 235.01 MWF 1:25P (and also...)
Eric Sarfo Amponsah

63126 MATH 235.02 TT 4:00P (and also...)
63227 MATH 235.06 TT 2:30P (and also...)
Jon Simone, jsimone@umass.edu

63127 MATH 235.03 MW 2:30P (and also...)
Rob Kusner, profkusner@gmail.com

63129 MATH 235.04 TT 1:00P (and also...)
63225 MATH 235.05 TT 10:00A (and also...)
Tina Kanstrup

63245 MATH 235.07 MWF 11:15A (and also...)
Angelica Simonetti, simonetti@math.umass.edu

Textbook and On-line Homework

The course text is Linear Algebra and its Applications (5th edition) by David Lay, Steven Lay & Judi McDonald.

MyMathLab is required for this course. An electronic copy of the textbook is included in your purchase of MyMathLab.
Go to www.mymathlab.com and use the Course ID for your learning section (provided by your section's instructor).

On-line homework and quizzes will be assigned through MyMathLab by your instructor. Here are suggestions from Pearson for getting started with MyMathLab.


There will be two midterm exams and a final exam (please see above for their scheduled dates and times).

Past exams are available here.

During our exams, all instructors will be "on-call" via Piazza (and email) to help clarify any confusion about the exam, though under our honor system it is, of course, each student's reponsibility to work on one's own!

Although — during the pandemic — our exams are "open-book," for each exam you are strongly encouraged to prepare a 8.5" x 11" sheet of notes (both sides, in your own handwriting); you will be invited to submit your note-sheet with your exam (for extra credit)!

Midterm I

The topics for the first midterm may include the following sections of the textbook: 1.1, 1.2, 1.3, 1.4, 1.5, 1.7, 1.8, 1.9, 2.1, 2.2, 2.3

Please work through the problems at the end of Chapters 1 & 2 before the exam.

Here are some Midterm I review suggestions (courtesy of an inspiring former instructor, Pat Dragon).

Midterm II

The topics for the second midterm may include the following sections of the textbook: 3.1, 3.2, 3.3, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6

Please work through the problems at the end of Chapters 3 & 4 before the exam.

Here are some Midterm II review suggestions (once again, courtesy of Pat Dragon).

Final Exam

The topics for the final exam may include the following sections of the textbook: 4.5, 4.6, 5.1, 5.2, 5.3, 6.1, 6.2 (and possibly some of 6.3, 6.4, 6.5).

Please work through the problems at the end of Chapters 5 & 6 before the exam.

Here is a Final review (revue?!) (of course, courtesy of Pat Dragon).


The four course assessments are weighted as follows: 20% each for Midterms I, II, and the Final exam; the remaing 40% for homework, quizzes and class participation (as determined by your section instructor).

All students have the option to take the course Pass/Fail – please check SPIRE for the details. In case students elect to take the course for a letter grade, this correlates to overall course performance percentages roughly as follows:

A : 90-100
A-: 86-89
B+: 82-85
B : 76-81
B-: 72-75
C+: 68-71
C : 62-67
C-: 58-61
D+: 54-57
D : 48-53
F : Below 48

Accommodation Policy Statement

UMass Amherst is committed to providing an equal educational opportunity for all students. A student with a documented physical, psychological, or learning disability on file with Disability Services may be eligible for academic accommodations to help them succeed in this course. If you have a documented disability that requires an accommodation, please notify your instructor during the first two weeks of the semester so that we can make appropriate arrangements. Information on services and materials for registering with Disability Services are also available on the Disability Services website.

UMass Amherst's Official Academic Honesty Statement

Since the integrity of the academic enterprise of any institution of higher education requires honesty in scholarship and research, academic honesty is required of all students at the University of Massachusetts Amherst. Academic dishonesty is prohibited in all programs of the University. Academic dishonesty includes but is not limited to: cheating, fabrication, plagiarism, and facilitating dishonesty. Appropriate sanctions may be imposed on any student who has committed an act of academic dishonesty. Instructors should take reasonable steps to address academic misconduct. Any person who has reason to believe that a student has committed academic dishonesty should bring such information to the attention of the appropriate course instructor as soon as possible. Instances of academic dishonesty not related to a specific course should be brought to the attention of the appropriate department Head or Chair. Since students are expected to be familiar with this policy and the commonly accepted standards of academic integrity, ignorance of such standards is not normally sufficient evidence of lack of intent (http://www.umass.edu/dean_students/codeofconduct/acadhonesty/).

!!!DRAFT!!! (Still under reconstruction! :-)

This page is maintained by Rob Kusner profkusner@gmail.com