Spring 2022 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.

Students waiting to enroll in the course should attend class and check SPIRE to see if a slot in the desired section opens. If an override is still needed, please wait till AFTER WEEK 1 OF CLASSES ENDS 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 have created and are updating a series of our our own short videos to help you learn linear algebra; please watch and think about them before each class!

Weekly Reviews in DuBois Library 1206

Our undergraduate SI, Caroline Ye, is holding twice-weekly Math 235 review sessions in the DuBois Library (room 1206) every Tuesday (5:30–6:45PM) and Friday (2:30–3:45PM).

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 - we use Wednesday's date because Wöden is great - this is a guideline which may be modified by your instructor as necessary (especially during the COVID pandemic and with winter weather, when Zoom sessions may need to replace in-person meetings):

[Week 1] 02/02: 1.2 Row reduction and echelon forms; 1.3 Vector equations.

[Week 2] 02/09: 1.4 The matrix equation AX=B; 1.5 Solution sets of linear systems.

[Week 3] 02/16: 1.7 Linear independence; 1.8 Introduction to linear maps.

[Week 4] 02/23: 1.9 The matrix of a linear map; 2.1 Matrix operations.

[Week 5] 03/02: 2.2 The inverse of a matrix; 2.3 Characterizations of invertible matrices.

Common Midterm I: [7-9PM* Thursday 03 March 2022]

[Week 6] 03/09: 3.1 Introduction to determinants; 3.2 Properties of determinants.

!!!!!!!!!!!!!!!!!!!!SPRING BREAK!!!!!!!!!!!!!!!!!!!!

[Week 7] 03/23: 3.2 (continued); 3.3 Cramer's rule, volume and linear maps.

[Week 8] 03/30: 4.1 Vector spaces and subspaces; 4.2 Null space (kernel), column space (image) and linear maps.

[Week 9] 04/06: 4.3 Linearly independent sets and bases; 4.4 Coordinate systems; 4.5 The dimension of a vector space.

[Week 10] 04/13: 4.6 The rank+nullity theorem; 4.7 Change of bases (if time permits).

Common Midterm II: [7-9PM* Tuesday 12 April 2022]

[Week 11] 04/20: 5.1 Eigenvectors, eigenvalues and eigenspaces; 5.2 The characteristic equation.

[Week 12] 04/27: 5.3 Diagonalization; 5.5 Complex eigenvalues.

[Week 13] 05/04: 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: Tuesday 10 May 2022 in Totman Gym 10:30AM–12:30PM

*This is the preferred time period for most students to take the exam. Additional time periods (see below) 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:

MATH 235-01 MWF 1:25-2:15 (and also...)
Arie Stern Gonzalez, stern@math.umass.edu

MATH 235-02 TT 1-2:15 (and also...)
Eric Sarfo Amponsah, sarfoamponsah@math.umass.edu

MATH 235-03 MW 2:30-3:45 (and also...)
Mithun Thudiyangal, mthudiyangal@math.umass.edu

MATH 235-04 TT 10-11:15 (and also...)
Mithun Thudiyangal, mthudiyangal@math.umass.edu

MATH 235-05 MWF 12:20-1:10 (and also...)
Arie Stern Gonzalez, stern@math.umass.edu

MATH 235-06 MW 4-5:15 (and also...)
Tina Kanstrup, tkanstrup@math.umass.edu

MATH 235-07 TT 1-2:15 (and also...)
Rob Kusner, profkusner@gmail.com

MATH 235-08 MWF 9:05-9:55 (and also...)
Cristian Rodriguez, rodriguez@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. Here's a link to readable .pdf of the the first two chapters.

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 (each instructor has posted a .pdf step-by-step guide from the publisher).

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.

Our exams are expected to be in-person, but if COVID requires us to go-remote, we'll likely use GradeScope again, and all instructors will be "on-call" via Piazza (and email) to help clarify any confusion about the exam. Under our honor system it is, of course, each student's reponsibility to work on one's own!

Before each exam you are strongly encouraged to prepare a single 8.5" x 11" notesheet (both sides, in your own handwriting) which you can bring to the exam (you may be asked to turn the sheet in with your exam, so please write your name on it)!

Calculators and the textbook are not allowed on the exams. Remember to 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 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 Thursday 03/03/22 at the following locations:

• Mahar 108 for students in 235-01 [ArS], 235-03 [MiT], 235-04 [MiT], 235-05 [ArS], 235-08 [CrR] only!
• Marcus 131 for students in 235-02 [ESA], 235-06 [TiK], 235-07 [Rob] only!

Also, an extra-time session (for those with DS contracts or documented conflicts pre-cleared with your instructor) is scheduled to take place:
• 5:15-9:15PM on Thursday 03/03/22 in Goessmann 151 or 152 (proctored by ESA or Kader or Rob).

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 (and possibly some of 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 second midterm is scheduled for 7-9PM on Tuesday 04/12/22 at the following locations:

• ISB 135 for students in 235-02 [ESA], 235-06 [TiK], 235-07 [Rob] only!
• Mahar 108 for students in 235-01 [ArS], 235-03 [MiT], 235-04 [MiT], 235-05 [ArS], 235-08 [CrR] only!

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

• 5:15-9:15PM on Tuesday 04/12/22 in Goessmann 151 or 152 (proctored by Eric or Kader).

The topics for the second midterm may include the following sections of the textbook: 2.3, 3.1, 3.2, 3.3, 4.1, 4.2, 4.3, 4.4, 4.5 (and possibly some of 4.6 & 4.7). [Mathematics builds on a foundation of earlier material, so you should focus on these sections, but of course it's good to have understood earlier material as well. The section(s) in parentheses will not be on this exam, but you're welcome to study them!]

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).

Also, our SI, Caroline Ye, will host a Midterm II Review session 3-5pm Sunday 4/10/2022 in the Integrative Learning Center: ILC S240.

Final Exam

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 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).

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.

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/).