This page contains information specific to section 2 of Math 235. Please see the syllabus on Moodle for the common guidelines and topics schedule followed by all sections of Math 235.

Instructor: Jonathan Simone

Email: jsimone@umass.edu

Class Meetings:
MWF 11:15am-12:05pm on Zoom (link in Moodle)

Office Hours (Zoom link in Moodle):
W 1:30-2:30
Th 3:30-4:30
and by appointment



Class Structure:

Class Prep Videos: Before every class meeting you will be required to watch one or more videos introducing the material to be discussed in class. The links to these videos can be found in the schedule below. Note that the schedule is regularly updated and subject to change.

Class Meetings: Class meetings will be conducted on Zoom. You can find links to the meetings on Moodle. During class, we will discuss any questions you have on the material from the videos and then work on problems. Some of these problems will appear on written homework (see below).



Textbook and Online Homework:

The course text is Linear Algebra and its Applications (5th edition) by David Lay, Steven Lay & Judi McDonald. Online homework will be administered through MyMathLab. An electronic copy of the textbook is included in your purchase of MyMathLab.

Follow the instructions here to sign up for MyMathLab. Due dates are subject to change throughout the semester. Please stay up-to-date on all upcoming due dates.



Written Homework:

There will be biweekly written homework assignments due roughly every other week. Completed assignments are to be uploaded to gradescope no later than midnight. You will receive an email inviting you to register to gradescope during the first couple of weeks of classes.

Most homework problems will be a subset of problems completed in class. Your homework solutions should be written neatly and concisely. In particular, if you wrote solutions to a problem in your class notes that appears on the written homework, you should rewrite you solution along with all of you other written homework solutions (i.e. do not submit your class notes).

You may work on your own or collaborate with others on these assignments. If you choose to collaborate, be sure to write your solutions in your own words---solutions should not be simply copied from collaborators.



Piazza:

Everyone enrolled in Math 235 will be added to a single Math 235 Piazza account. Feel free to take advantage of the message board to ask your peers questions about linear algebra topics, homework, logistics, etc.

Note: If you have a question for me, please email me directly, as I may not regularly check Piazza.



Exams:

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

Midterm 1: March 4
Covers Sections 1.1-1.5, 1.7-1.9, 2.1

Midterm 2: April 8
Covers 2.2, 2.3, 3.1-3.3, 1.4-4.3

Final exam: TBA
Covers TBA



Grading:

Written Homework: 10%
Online Homework: 30%
Midterm 1: 20%
Midterm 2: 20%
Final: 20%



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/).

Chegg, Discord and other online help resources: Seeking answers from any website is a clear violation of the academic honesty policy, while submitting course materials to these sites or similar ones is a violation of the instructor’s copyright. Instructors may be monitoring such websites throughout the semester.



Disability Services Accommodations:

The University of Massachusetts Amherst is committed to making reasonable, effective and appropriate accommodations to meet the needs of students with disabilities and help create a barrier-free campus. If you have a disability and require accommodations, please register with Disability Services (161 Whitmore Administration building; phone 413-545- 0892) to have an accommodation letter sent to your faculty. Information on services and materials for registering are also available on their website.



Schedule and Class Prep Videos: (to be regularly updated)

You can find even more videos on the video page.

Class Meeting Sections Covered Class Prep Videos
2/1 1.1 a) Systems of Equations (5:18)
b) Geometry of Linear Systems (8:39)
c) Augmented Matrices of Linear Systems (5:01)
2/3 1.1, 1.2 a) Solving Systems using Matrices (12:24)
b) Reducing Rob's Favorite Matrix to Echelon Form (16:49)
c) Solving the System Associated to Rob's Favorite Matrix (7:36)
2/5 1.2 a) Infinitely Many Solutions and Free Variables (13:58)
b) A Remark on Consistency (4:46)
2/8 1.3
Required Video:
Vectors, Linear Combinations, and Spans (28:37)
Recommended Videos:
a) Building Intuition: Linear Combinations and Chess I (8:30)
b) Building Intuition: Linear Combinations and Chess II (14:57)
c) Building Intuition: Combos and Carbs (14:47)
2/10 1.4
Required Video:
Multiplication and Matrix Equations (17:35)
Recommended Videos:
a) Multiplication: Motivation and Definition (8:41)
b) Multiplying Matrices and Vectors: Row-Vector Rule (11:38)
c) Matrix Equations (13:02)
2/12 1.5
Required Video:
Homogeneous Systems (16:49)
Recommended Videos:
a) Example: Ants and Anti-Ants I (7:04)
b) Example: Ants and Anti-Ants II (11:01)
2/15 1.7 Linear Independence (24:23)
2/17 1.8 Linear Transformations (18:22)
2/19 1.9
Required Videos:
a) The Standard Matrix of a Linear Transformation (14:32)
b) 90° Counterclockwise Rotation of R2 (7:27)
Recommended Videos:
a) Using Rotations of R2 to Prove Trig Identities (6:10)
b) Rotations of R3 (7:05)
2/22 1.9 One-to-one and Onto Transformations (17:28)
2/26 2.1 Matrix Operations (18:10)
3/1 2.2
Required Video:
Matrix Inverses (22:46)
Recommended Video:
Elementary Matrices and the Proof of the Matrix Inverse Algorithm (12:58)
3/3 Review
3/5 2.3 a) Invertible Linear Transformations (9:53)
b) Invertible Matrix Theorem (19:07)
3/8 3.1 a) Intro to Determinants (19:08)
b) Cofactor Expansions and Triangular Matrices (14:37)
3/10 3.2 The Effect of Row Operations on Determinants (6:48)
3/12 3.2 Determinant of Invertible Matrices and Properties of Determinants (11:16)
3/15 3.3 a) Cramer's Rule (15:47)
b) The Adjugate and a formula for the Inverse of a Matrix (14:48)
3/17 3.3 a) Interpreting Determinants as Areas and Volumes (21:53)
b) Linear Maps and Determinants (6:19)
3/19 4.1 Introduction to Vector Spaces (14:45)
3/22 4.1 continued Introduction to Vector Spaces (14:45)
3/24 4.2 Null Spaces, Column Spaces, and Linear Transformations (9:26)
3/26 4.3 Linear Independence and Bases (14:33)
3/29 4.4 Coordinate Systems (10:26)
3/31 4.5 Dimension of Vector Spaces (11:59)
4/2 4.5 Dimension of Vector Spaces (11:59)
4/5 4.6 Row Space and Rank (9:17)
4/7 Review
4/9 5.1 Intro to Eigenvalues and Eigenvectors (16:07)
4/12 5.1, 5.2 a) Eigenspaces (9:07)
b) The Characteristic Equation (10:12)
4/16 5.2 Eigenvalues and Determinants (10:28)
4/19 5.3 Diagonalization (21:36)
4/20 5.3 Diagonalization (21:36)
4/21 5.5 Complex Eigenvalues (8:40)
4/23 5.5 Complex Eigenvalues (8:40)
Supplemental Videos Chapter 5 (Optional) a) Markov Chains I (23:11)
b) Markov Chains II (15:24)
4/26 6.1 Inner Product (Dot Product) on Rn and Orthogonal Vectors (13:10)
4/28 6.2 Orthogonal Projections (22:14)
4/30 6.3 Orthogonal Decomposition Theorem (13:52)
5/3 6.4 The Gram-Schmidt Process (18:46)