Math 235 : Introduction to Linear Algebra

Spring 2018

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 Paul Hacking 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. Weimin Chen, MWF 1:25PM--2:15PM.
235.2. Paul Hacking, MWF 11:15AM--12:05PM.
235.3. Sean Hart, TuTh 11:30AM--12:45PM.
235.4. Andrew Havens, MWF 12:20PM--1:10PM.
235.5. Aaron Gerding, MWF 10:10AM--11:00AM.
235.6. Liubomir Chiriac, TuTh 2:30PM--3:45PM.
235.7. Liubomir Chiriac, TuTh 1:00PM--2:15PM.
235.8. Taryn Flock, TuTh 10:00AM--11:15AM.
235.11. Mario DeFranco, MWF 9:05AM--9:55AM.

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.)

1/22--1/26: 1.1 Systems of linear equations; 1.2 Row reduction and echelon forms; 1.3 Vector equations.

1/29--2/2: 1.3 (continued); 1.4 The matrix equation Ax=b; 1.5 Solution sets of linear systems.

2/5--2/9: 1.7 Linear independence; 1.8 Introduction to linear transformations.

2/12--2/16: 1.9 The matrix of a linear transformation; 2.1 Matrix operations.

2/20--2/23: 2.2 The inverse of a matrix; 2.3 Characterizations of invertible matrices.

2/26--3/2: 3.1 Introduction to determinants; 3.2 Properties of determinants.

3/5--3/9: 3.2 (continued); 3.3 Volume and linear transformations; 4.1 Vector spaces and subspaces.

3/12--3/16: Spring break.

3/19--3/23: 4.2 Null spaces, column spaces, and linear transformations; 4.3 Linearly independent sets and bases.

3/26--3/30: 4.4 Coordinate systems; 4.5 The dimension of a vector space.

4/2--4/6: 4.6 Rank; 5.1 Eigenvectors and eigenvalues.

4/9--4/13: 5.1 (continued); 5.2 The characteristic equation.

4/17--4/20: 5.3 Diagonalization; 5.5 Complex eigenvalues.

4/23--4/27: 6.1 Inner product, Length, and Orthogonality; 6.2 Orthogonal sets; 6.3 Orthogonal projections.

4/30--5/1: 6.4 The Gram--Schmidt process.


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). 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 Paul Hacking 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.

First midterm exam

The first midterm will be held on Tuesday 2/27/18, 7:00PM--9:00PM, at the following locations:

Sections 1, 2, and 3 (Chen, Hacking, and Hart). ILC N151
Section 4 (Havens). HASA0124
Section 5 (Gerding). HASA0126
Sections 6 and 7 (Chiriac). HASA0020
Section 8 (Flock). HAS0134
Section 11 (DeFranco). GSMN0064

The syllabus for the first midterm is the following sections of the textbook: 1.1, 1.2, 1.3, 1.4, 1.5, 1.7, 1.8, 1.9, 2.1.

Please work through the practice exam here. Solutions to the practice exam are here.

Second midterm exam

The second midterm will be held on Tuesday 4/10/18, 7:00PM--9:00PM, at the following locations:

Section 1 (Chen) HAS0134
Section 2 (Hacking) GOES0020
Section 3 (Hart) FERN0011
Section 4 (Havens) HASA0124
Section 5 (Gerding) HASA0126
Section 6 (Chiriac 2:30PM--3:45PM) HERT0227
Section 7 (Chiriac 1:00PM--2:15PM) HERT0231
Section 8 (Flock) ILC S331
Section 11 (DeFranco) GSMN0064

The syllabus for the second midterm is the following sections of the textbook: 2.2, 2.3, 3.1, 3.2, 3.3, 4.1, 4.2, 4.3, 4.4, 4.5.

Please work through the practice exam here. Solutions to the practice exam are here.

Final Exam

The final exam will be held on Monday 5/7/18, 10:30AM-12:30PM, in Boyden gym.

The syllabus for the final exam is the following sections of the textbook: 4.5, 4.6, 5.1, 5.2, 5.3, 5.5, 6.1, and 6.2.

Please work through the practice exam here. Solutions to the practice exam are here.


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 Paul Hacking