# Math 150 Linear Algebra - FALL 2020

## Class Resources and Handouts

Course Syllabus
Pre-Semester Review Material

## Jump to...

Moodle Information
Course Schedule
Final Grade Information
COVID-19 Information
University Policies and Services

### Course Information

Meeting Times: Monday, Tuesday, Wednesday, and Friday, 2:00 - 2:50 pm
Location: CAE 208
Office Hours: Monday 10-11, Tuesday 3-4, Wednesday 12-12:45, Thursday 8-9 and 2-3:30
Prerequisite: Math 170

### Course Description

This is a one semester course in linear algebra with computer applications. We will be covering the following topics: matrices and matrix properties, vectors and vector spaces, linear systems, and linear transformations. The class lectures will focus primarily on definitions and theory, with some simple calculations being performed without the aid of a computer. We will also have time dedicated to implementing the ideas learned in class using the open source numerical computation software Scilab. Many of these lab experiments will focus on applications of linear algebra to other areas of mathematics and other fields, including data science.

Topics will include vectors and vector arithmetic, solutions of linear systems, Gaussian elimination, inner products, vector spaces and subspaces, the four fundamental subspaces, determinants, eigenvalues and eigenvectors, symmetry, linear transformations, and applications.

### Objectives

On successful completion of the course, students should be able to:
• describe the solution(s) of a system of linear equations, or be able to decide that one does not exist.
• be able to perform arithmetic operations on vectors and matrices, where defined.
• calculate the determinant of a matrix, and understand its significance.
• define a vector space and determine whether a set is a vector space.
• find the basis and dimension of a vector space.
• define and describe the four fundamental subspaces.
• define and identify linear maps.
• define and compute eigenvalues and eigenvectors.
• explain the geometric effect of a linear transformation on 2-dimensional spaces.
• produce and utilize simple computer programs to perform computations related to all of the above topics.

### Required Materials

##### Textbook
Linear Algebra and its Applications, by David Lay, Steven Lay, and Judi McDonald, 5th Edition. No other supplies are required for the course. You will not need to purchase any software, access codes, or supplementary material with the text. Older editions may be used, but are discouraged (the fourth and fifth editions are quite different). A rental or electronic version is fine - you will not need to bring your book to class.
##### Online Resources
We'll be making use of two learning platforms this semester: Blackboard and Moodle. On Blackboard, you'll find notes and videos for all sections of the course, as well as important course announcements and your current grades.

### Moodle

Moodle is a Learning Management System, similar to Blackboard, that allows for flexible mathematics based quizzes. We will be using Moodle for all quizzes and for additional course resources. There is no fee for using Moodle.
Sign in to Moodle here!

#### Accessing Moodle

At the beginning of the semester, you will receive an email (delivered to your Mercyhurst email address) with information on enrolling in the Moodle course. You will be required to create a password. Be sure to keep this password safe, and do not share your login information with other students in the course.

There is a mobile app available for Moodle, but it is not recommended for use in this course. A computer (desktop or laptop) or tablet is strongly preferred, using the Moodle website as opposed to the app.

If you already have a Moodle account and would like to use it rather than the new one generated for you, just let me know. You can link the course to any existing account.

#### Question Styles

The quizzes and exams you'll take on Moodle are based on homework problems from the textbook. Some questions are multiple choice, and others will require you to enter a numerical answer. When necessary, specific instructions will be provided with a question. Questions will be asked one at a time, so you can focus on each individual question as you work.

#### Time Restrictions

You will be required to finish each quiz within 90 minutes. Any work you have completed will be submitted at the end of this period, even if you have not finished the assessment.

Each quiz and can only be submitted during its availability window. You will have a 24 hour period, from 12 am until 12 pm, in which to complete the quiz on the dates in this syllabus.

Please note that once you begin a quiz, you will be required to complete it within the given time period or before the end of the availability window, whichever comes first. For instance, if you begin a quiz at 11 pm, you will only have 1 hour to finish. Be sure to allow yourself enough time to finish each assessment before you begin.

### Labs

While understanding the theory and mechanics of linear algebra is critical to truly applying it, the majority of the calculations we'll do by hand'' in class are actually done by a machine in the real world.

To help balance these two sides of linear algebra, we'll use most of our Tuesday class meeting time to explore applications and see how a computer algebra system (CAS) can make our work easier and faster.

In particular, we'll be experimenting with SAGE, an incredibly powerful and open source (free) CAS based on the Python programming language.

You will not have any required lab assignments for this course. Instead, consider the lab meetings as a kind of show and tell'' for linear algebra. We'll see how to make predictions with biological important, how linear algebra can be used to solve some games and puzzles, and how data science (a fast growing and important field) relies on linear algebra. And, if there's a certain application you're interested in, please let me know so I can make sure it is mentioned.

You will not need any supplies for these lab meetings. If you have a laptop, you are welcome to bring it and follow along or experiment on your own.

### Textbook Homework

Suggested problems from the textbook for each section we will cover appear in the table below. Your work will not be collected. However, actually working through these problems is the key to your success in this class. Attending every class is not enough; mathematics can only be learned through practice. It is expected that you spend approximately 8-12 hours per week studying the material outside our class meetings, according to the typical 2-3 hours per credit rule.

Most of the problems will have solutions in the back of the textbook. Make sure to check your work. The exams will be based primarily on these problems.

Stay up to date with homework, and get help if you cannot understand a problem after trying it on your own. Do not ignore a problem that you are struggling with. If you are having trouble with a topic, please come talk to me during office hours, ask questions in class, or seek help from a classmate. You are expected to try to work on all problems on your own first; when coming to my office, be prepared to show me what you've already tried.

 Section Problems 1.1 1, 3, 7, 9, 11, 13, 15, 17, 19, 21, 23, 24, 26 1.2 1, 5, 7, 9, 11, 13, 15, 19 1.3 1, 5, 9, 11, 13, 15, 19, 23 1.4 1, 5, 7, 9, 11, 13, 15, 21, 25, 37 1.5 1, 3, 5, 7, 9, 11, 33, 35 1.7 1, 3, 5, 7, 9, 11, 15-20, 21, 29, 31 1.8 1, 3, 5, 9, 11, 13, 15, 17 1.9 1, 3, 9, 15, 17, 19, 21, 37 2.1 1, 3, 5, 7, 9, 11, 12, 15, 23, 27 2.2 1, 3, 5, 7, 9, 17, 18, 29, 31, 33 2.3 1, 3, 5, 7, 9, 13, 15, 23, 33 3.1 1, 3, 5, 9, 11, 13, 19, 21, 23, 37, 41 3.2 15, 17, 19, 21, 23, 25, 27, 29, 33, 35, 37, 39 3.3 1, 3, 5, 7, 19, 21, 23, 27 4.1 1, 3, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 18, 21 4.2 1, 3, 5, 7, 9, 11, 23 4.3 1, 3, 5, 7, 9, 15, 19, 21 4.5 1, 3, 5, 7, 9, 11, 13, 15, 17, 25 4.7 1, 7, 9 5.1 1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 24 5.2 1, 3, 5, 7, 9, 13, 15, 21 5.3 1, 5, 7, 9, 11, 21, 27 5.5 1, 3, 5 6.1 1, 3, 5, 7, 9, 11, 15, 17, 19, 23, 25, 27

### Quizzes

Keeping up with the homework will ensure that you are prepared for the quizzes, which will feature problems very similar to those in the homework as well as more conceptual questions about the topics you'll see each week.

There is a total of 11 quizzes scheduled for the semester. Your lowest quiz grade will be dropped, including a missed quiz. Each quiz will be available for a 24 hour period (midnight to midnight) on Moodle as shown in the course schedule. You'll know your quiz grade as soon as you're finished with it, but the correct answers will not be visible until the quiz has closed.

Before you can get started with a graded quiz, you'll need to complete a Quiz Tutorial on Moodle. This ungraded quiz (that will not test your mathematical knowledge) will help you get acquainted with the quiz layout and how to enter your responses.

You will have 90 minutes to complete each quiz from the time you begin, so please be sure that you allow time to finish a quiz before starting. You can sign off and return to Moodle after starting a quiz, but your time will end after 90 minutes from when you first accessed the quiz. You will only have one chance to take each quiz, and will not be able to change your responses after submitting. You will not be required to submit any written work for your quizzes.

### Exams

There will be three midterm exams given throughout the semester, according to the semester schedule. The material on the exams will be similar to topics covered on quizzes and homework. All exams should be considered cumulative; each exam will include some material from the previous exams.

### Final Grades

##### Basis of Final Grade
Up to 500 points are available to earn throughout the semester, as follows:

 300 points Midterm Exams Three exams, 100 points each 200 points Quizzes Eleven quizzes, 20 points each, lowest quiz grade dropped
##### Grading Scale
 Grade F D D+ C C+ B B+ A Percentage 0-59 60-66 67-69 70-76 77-79 80-86 87-89 90-100 Points 0 298 333 348 383 398 433 448

### Course Policies and Suggestions

On successful completion of the course, students should be able to:
• If you are struggling with a topic, please come to office hours as soon as possible. Tutoring for this course can not be expected through our usual department tutors, but it may be possible to arrange private assistance. Don't let yourself fall behind!
• There are other linear algebra textbooks available in the library and in my office. Due to book prices, you may not want to invest in a second book, but it can be helpful to have alternate sources or see topics explained in other ways. There are two recommended textbooks available free online:
• I do not have a "no electronics" policy, and I'd prefer not to implement one. Please try to remember to mute all devices during lecture, and use devices in a way that does not distract other students in the class.

## Schedule

 Date Topic Notes

## COVID-19 Information

This is sure to be an unprecedented semester! While we cannot know what the next few months will bring, we must all work together to keep our campus community safe and healthy.

Below is some information regarding policies of the University (in italics) as well as comments, suggestions, and requests that pertain to our class specifically.

#### Face Masks

As per the COVID-19 Prevention, Mitigation, and Response Policy, Mercyhurst University is requiring that all members of the campus community wear a cloth or disposable face covering over their nose and mouth when on campus. Please refer to the policy for specific details as to where and when face coverings are required. Students may use their own face coverings or those provided by the University. A student in need of a face covering should email covid19@mercyhurst.edu or call 814-824-3600 to find the nearest location where face coverings are available. The University’s Mask/Face Coverings Policy will be enforced in this class.

I will have a few disposable masks with me in case you need to borrow one, but please understand that these supplies are limited.

#### Sanitation and Safety

In keeping with the COVID-19 Prevention, Mitigation, and Response Policy, students are expected to use hand sanitizer and to wipe down their desks using disinfectant wipes when they enter and exit the classroom. Classrooms have been provided with sanitizer and disinfectant wipes for student and faculty use.

#### Eating and Drinking in Classrooms

In light of the COVID-19 situation, Eating is not permitted in classrooms, labs, or other academic spaces. A water bottle or cup with a lid, and straw preferably, is permitted to be used in classrooms and labs to help prevent a student from becoming uncomfortably parched. Masks should be pulled only slightly away from the bottom of the face to take a quick drink and immediately replaced to covering the mouth and nose.

#### Class Dismissal, Congestion Prevention

In keeping with the COVID-19 Prevention, Mitigation, and Response Policy, faculty members and students should take steps to avoid crowding outside of classrooms, in hallways, and any enclosed area in university buildings. All rooms will be designated with signs indicating maximum capacity for specific instructional use. These must always be adhered to. Students waiting to enter classrooms or exiting classrooms should always maintain a minimum of 6 feet of distance from others. Class time endings may be adjusted when necessary to minimize overcrowding or congestion.

#### Seating Chart

In compliance with federal and state regulations, the University must be able to conduct contact tracing if there is a positive test or an outbreak; therefore, seating charts are mandatory for all in-person classes. Students will be required to sit in the same seat in the classroom each time they attend class. The seating chart will be available for review for purposes of contact tracing.

#### Paper Sharing Policy

We will not be exchanging paper this semester. Supplemental materials will be distributed and made available electronically. Assignments and exams will be submitted electronically as well. You are welcome to bring your own paper to class to take notes, but you may not pass paper to a classmate or to me.

#### Attendance, Missed Class

Attendance at all classes is expected. However, it is important that students and course instructors adhere to the university’s COVID-19 mitigation policies and strategies. As such, a student who misses class due to illness or suspected illness within the context of those policies will not be penalized and will be provided sufficient means to make up any missed course content or work and remain actively engaged in the class.

The word "attendance" has a broader definition than usual this semester. While attending class is certainly preferred, please do not feel obligated to come if have any potential symptoms. I plan to record all class meetings via Zoom, and those recordings will be available on Blackboard throughout the semester. You can also join and participate in the live Zoom meeting. If you're not up to joining in, watch the meeting and the associated pre-recorded video lectures when you're able to.

If you are unable to attend class (or join the live Zoom meeting) for more than a few days, please let me know as soon as possible. I am happy to work with you in building a plan that allows you the time off you need without risking your academic progress.

#### Potential Class Changes

It is my hope that we remain able to meet in person as scheduled for the entire semester. However, there is a very good chance that our plans will change, and without much notice.

Mathematics students are a rare breed, which this semester is a good thing: it means that our class is small enough to safely meet in person! It is my hope that we remain able to meet in person as scheduled for the entire semester. However, there is a very good chance that our plans will change, and without much notice.

Our highest priority (even above learning about determinants and vector spaces) is to remain healthy and safe. We will all need to remain responsible, flexible, and understanding to make this semester a success, and I have full confidence that we will be able to achieve that goal.

## University Policies and Services

#### ADA and Learning Differences

Mercyhurst University is committed to making reasonable accommodations for qualified students, and employees with disabilities as required by law. Individuals seeking an accommodation for a disability must submit a written request outlining the specific accommodation request being made. Supporting documentation may also be required. To request an accommodation, contact Alice Agnew, Director of Equal Opportunity Programs, 311 Egan Hall, aagnew@mercyhurst.edu, 814-824-2362.

#### Title IX Information

Mercyhurst is committed to providing an environment free from sex discrimination, including sexual harassment and sexual violence. Please refer to the Title IX – Sexual Respect button on the HUB for more information. If you would like to file a sexual misconduct complaint, please contact Mercyhurst Title IX Coordinator Alice Agnew, 311 Egan Hall, aagnew@mercyhurst.edu, 814-824-2362. Please be aware that in compliance with Title IX educators must report incidents of sexual assault/harassment, stalking, and domestic/dating violence. If you disclose any of these situations in class, in papers, or to me personally, I am required to report it to the Title IX Coordinator (or any of the Deputy Title IX Coordinators).

#### Academic Honesty

Students are required to uphold academic integrity throughout the course. In particular, plagiarism of any sort, unauthorized collaboration on exams, quizzes and other assignments, and other incidences of academic dishonesty will be handled according to the policies set forth in the Student Handbook.

#### Course Evaluations

Near the end of the semester, you will be asked to complete an online course evaluation. The evaluation will be completed in class during the last two weeks of the semester using any laptop, tablet, or mobile device. The response tool allows you to note aspects of the course that helped you learn, as well as aspects that might be modified to help future students learn more effectively. You will receive an email letting you know when the evaluation window for our class is open. Please note that these course evaluations are anonymous and instructors do not see the results until after the grades for the course are submitted.