Fall 2019 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 attend class and regularly 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.)

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] 9/2 - 9/9: 1.1 Systems of linear equations; 1.2 Row reduction and echelon forms; 1.3 Vector equations.

[Week 2] 9/9 - 9/13: 1.3 (continued); 1.4 The matrix equation AX=B; 1.5 Solution sets of linear systems.

[Week 3] 9/16 - 9/20: 1.7 Linear independence; 1.8 Introduction to linear maps.

[Week 4] 9/23 - 9/27: 1.9 The matrix of a linear map; 2.1 Matrix operations.

[Week 5] 9/30-10/4: 2.2 The inverse of a matrix; 2.3 Characterizations of invertible matrices.

[Week 6] 10/7 - 10/11: 3.1 Introduction to determinants; 3.2 Properties of determinants.

Common Midterm I: Wednesday 10/16 (rooms assigned - see below)

[Week 7] 10/14 - 10/18: 3.2 (continued); 3.3 Cramer's rule, volume and linear maps.

[Week 8] 10/21 - 10/25: 4.1 Vector spaces and subspaces; 4.2 Null space (kernel), column space (image) and linear maps.

[Week 9] 10/28 - 11/1: 4.3 Linearly independent sets and bases; 4.4 Coordinate systems.

[Week 10] 11/4 - 11/8: 4.5 The dimension of a vector space; 4.6 The rank+nullity theorem.

Common Midterm II: 7-9PM Wednesday 11/13 (!!!NOTE THE DATE CHANGE!!! rooms TBA - see below)

[Week 11] 11/11 - 11/15: 5.1 Eigenvectors, eigenvalues and eigenspaces; 5.2 The characteristic equation.

[Week 12] 11/18 - 11/22: 5.3 Diagonalization; 5.5 Complex eigenvalues.

[Week 13] 11/25 - 11/29: Thanksgiving Break!!!

[Week 14] 12/2 - 12/6: 6.1 Inner product, Length and orthogonality; 6.2 Orthogonal sets (if time permits).

[Week 15] 12/9 - 12/13: 6.3 Orthogonal projection; 6.4 The Gram-Schmidt process; 6.5 Least squares (if time permits).

Final Exam: 10:30AM-12:30PM Tuesday 12/17 in Boyden Gym.

Learning Sections

Here are the class times, rooms, and instructors:

30254 MATH 235.1 MWF 9:05-9:55 LGRT 145
Jennifer Li, LGRT 1341, jli@math.umass.edu

30255 MATH 235.2 MW 4:00-5:15 LGRT 121
Rob Kusner, LGRT 1435G and 1535, 545-6022, profkusner@gmail.com

30256 MATH 235.3 TuTh 2:30-3:45 Goessmann 152
30310 MATH 235.4 TuTh 1:00-2:15 Goessmann 152
Mohammed Zuhair Mullath, LGRT 1115J, 545-0864, mmullath@umass.edu

30363 MATH 235.5 TuTh 10:00-11:15 Goessmann 152
Alexei Oblomkov, LGRT 1238, 545-2857, oblomkov@math.umass.edu

30365 MATH 235.6 TuTh 8:30-9:45 LGRT 219
Patrick Dragon, LGRT 122D, 545-0090, dragon@math.umass.edu

30385 MATH 235.7 MWF 1:25-2:15 LGRT 143
Angelica Simonetti, LGRT 1235L, 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. Past exams are available here.

You are allowed one 8.5" x 11" sheet of notes (both sides, in your own handwriting). Calculators and the textbook are not allowed on the exams. You should bring your student ID (UCard) to each exam.

If you have a documented conflict for one of the exams, in order to take the make-up exam you must give your instructor (please cc the course chair Rob Kusner profkusner@gmail.com) at least one week's written notice for a midterm exam and at least two weeks' written notice for the final exam. Your instructor and the course chair will evaluate your request and your instructor will arrange for the make-up. Other make-up exams (for example due to medical emergencies) will be handled directly by your section instructor. Make-up exams will not be given to accommodate travel plans.

Midterm I

The first midterm is scheduled for 7-9PM on Wednesday 10/16/19 at the following locations:

• Marcus 131 for students in 235.3 [ZM], 235.4 [ZM] & 235.7 [AS] only!
• Thompson 104 for students in 235.2 [RK] & 235.6 [PD] only!
• Thompson 106 for students in 235.1 [JL] & 235.5 [AO] only!

Also, an extra-time session (for those with contracts or documented conflicts pre-cleared with your instructor) is scheduled to take place:

• 5-9PM on Wednesday 10/16/19 in Goessmann 151 (proctored by ???)

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 Pat Dragon).

Midterm II

The second midterm is scheduled for 7-9PM on Wednesday 11/13/19 (!!!NOTE THE DATE CHANGE!!!) at the following locations:

• Goessmann 64 for students in 235.2 [RK] only!
• Morrill 2 131 for students in 235.5 [AO] & 235.7 [AS] only!
• Morrill 1N 375 for students in 235.3 & 235.4 [ZM] only!
• ELab II 119 for students in 235.1 [JL] & 235.6 [PD] only!

Again, an extra-time session (for those with contracts or documented conflicts pre-cleared with your instructor) is scheduled to take place:

• 5:05-9:05PM on Wednesday 11/13/19 in LGRT 1234 (proctored by ???)

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 final exam is scheduled for 10:30AM-12:30PM on Tuesday 12/17/19 in Boyden Gym.


If you have a contract with DS, please contact them IMMEDIATELY to schedule your exam there.
They require a week advanced notice, so you must contact them BEFORE Monday 12/9/19

Of course under extraordinary circumstances, your instructor may offer a make-up 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).

Please remember: you are allowed one 8.5" x 11" sheet of notes (both sides, in your own handwriting) for the final exam; calculators and the textbook are not allowed; and you should bring your student ID (UCard).


The four course assessments are equally weighted (25% each): Midterm I; Midterm II; Final exam; Homework, quizzes and class participation (determined by your section instructor).

Course grades correlate to overall course 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. It is also your responsibility to notify Disability Services (normally at least one week in advance) if you wish to take an exam there.

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

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