Math 235 : Introduction to Linear Algebra

Fall 2017

This is the course-wide webpage. Please consult your section webpage for additional information.


Students needing an override in order to enroll in the course should contact the course chair Matthew Dobson with the following information: (1) sections of the course which conflict with other courses from your academic schedule, and (2) preferred section of the course. (Unfortunately, in order to keep the sections balanced we cannot guarantee that you will be assigned to your preferred section.)


235.1. Arie Stern Gonzalez, MWF 9:05AM--9:55AM.
235.2. Aaron Gerding, MWF 11:15AM--12:05PM.
235.3. Inanc Baykur, TuTh 2:30PM--3:45PM.
235.4. Aaron Gerding, TuTh 1:00PM--2:15PM.
235.5. Alexei Oblomkov, TuTh 10:00AM--11:15AM.
235.6. Alexei Oblomkov, TuTh 8:30AM--9:45AM.
235.7. Matthew Dobson, MWF 1:25PM--2:15PM.

Textbook and Online homework

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

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

Online homework and quizzes will be assigned through MyMathLab by your instructor.

Syllabus and weekly schedule

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

The schedule below gives the topics from the course text to be covered each week. (This is only a guideline, and may be modified by your instructor as necessary.)

9/5--9/8: 1.1 Systems of linear equations; 1.2 Row reduction and echelon forms; 1.3 Vector equations.

9/11--9/15: 1.3 (continued); 1.4 The matrix equation Ax=b; 1.5 Solution sets of linear systems.

9/18--9/22: 1.7 Linear independence; 1.8 Introduction to linear transformations.

9/25--9/29: 1.9 The matrix of a linear transformation; 2.1 Matrix operations.

10/2--10/6: 2.2 The inverse of a matrix; 2.3 Characterizations of invertible matrices.

10/9--10/13: 3.1 Introduction to determinants; 3.2 Properties of determinants.

10/16--10/20: 3.2 (continued); 3.3 Cramer's rule, volume, and linear transformations; 4.1 Vector spaces and subspaces.

10/23--10/27: 4.2 Null spaces, column spaces, and linear transformations; 4.3 Linearly independent sets and bases.

10/30--11/3: 4.4 Coordinate systems; 4.5 The dimension of a vector space.

11/6--11/10: 4.6 Rank; 5.1 Eigenvectors and eigenvalues.

11/13--11/17: 5.1 (continued); 5.2 The characteristic equation.

11/20--11/24: Thanksgiving break.

11/27--12/1: 5.3 Diagonalization; 5.5 Complex eigenvalues.

12/4--12/8: 6.1 Inner product, Length, and Orthogonality; 6.2 Orthogonal sets.

12/11--12/12: 6.3 Orthogonal projections; 6.4 The Gram--Schmidt process.


There will be two midterm exams and a final exam. Past exams are available here.

Midterm 1 will be on Thursday, Oct 12th, 7-9pm.
Locations, by section number. Section numbers are listed above if you are unsure:
1: HAS0138
2: HASA0124
3: ELABII0119
4: HASA0126
5: GSMN0064 (Goessmann)
6 GOES0020 (Goessmann)
7: HAS0134

Practice Midterm 1
Alexei has kindly provided a solution set for the practice midterm Practice Midterm Solutions

Midterm 2 will be on Tuesday, Nov 14th, 7-9pm.
Locations, by section number. Section numbers are listed above if you are unsure:
1: HAS0138
2: HASA0124
3: Is in two rooms.
Students with last names A-L GSMN0151
Students with last names M-Z GSMN0152
4: HASA0126
5: ILCS131
6 ILCS240
7: HAS0134

Practice Midterm 2
Practice Midterm 2 Solutions

Final exam will be Monday, Dec 18th, 10:30am-12:30pm in Boyden Gym.

Practice Final
Full solutions are available on the webpage of Professor Alexei Oblomkov

You are allowed one 8.5" x 11" sheet of notes (both sides). 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 the course chair Matthew Dobson at least one weeks' written notice for a midterm exam and at least two weeks' written notice for the final exam. Other make-up exams (for example due to medical emergencies) will be handled by your section instructor. Make-up exams will not be given to accommodate travel plans.


Your course grade will be computed as follows: First midterm exam 25%; Second midterm exam 25%; Final exam 25%; Homework, quizzes, and class participation 25% (determined by your section instructor).

Grades will be assigned to course percentages according to the following scale:

A : 90--100
A- : 87--89
B+ : 84--86
B : 80--83
B- : 77--79
C+ : 74--76
C : 70--73
C- : 67 -- 69
D+ : 64 -- 66
D : 57 -- 63
F : 0 -- 56

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.

This page is maintained by Matthew Dobson