# Math 150 Linear Algebra

NOTE: This course begins August 23. Until then, the information here is subject to change. The final syllabus will be distributed and posted at the start of class.

### Course Information

Meeting Times: Monday, Wednesday, Thursday, and Friday, 11:00 - 11:50 am

Location: Hirt 209 (Main Lab on Thursdays)

Office Hours: TBD

Prerequisite: Math 170

Location: Hirt 209 (Main Lab on Thursdays)

Office Hours: TBD

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. After learning the basic principles and theory of each topic, we will reinforce the material using the open source mathematics software SAGE. Through a series of lab experiments, you will also gain familiarity with the programming language Python. 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, LU factorization, vector spaces and subspaces, the four fundamental subspaces, projections, determinants, eigenvalues and eigenvectors, symmetry, singular value decomposition, linear transformations, and applications.

Topics will include vectors and vector arithmetic, solutions of linear systems, LU factorization, vector spaces and subspaces, the four fundamental subspaces, projections, determinants, eigenvalues and eigenvectors, symmetry, singular value decomposition, 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 Sage programs to perform computations related to all of the above topics.

### Required Materials

**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.

### Textbook Homework

Suggested homework problems for each section can be found in the attached table.

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. You should plan to spend a significant amount of time on the homework. It is expected that you spend approximately 8-12 hours per week studying the material outside our class meetings, according the the typical 2-3 hour per credit rule of thumb.

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 attempted.

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. You should plan to spend a significant amount of time on the homework. It is expected that you spend approximately 8-12 hours per week studying the material outside our class meetings, according the the typical 2-3 hour per credit rule of thumb.

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 attempted.

### Assignments

In addition to the homework in the textbook, you will be periodically be given other problems to work on and submit. These will be more conceptual problems that explore the definitions and theorems we'll see in class, as opposed to formulas and calculations. Your work should display proper notation and use of mathematical language.

### Quizzes

You will be given quizzes on the material regularly. Keeping up with the suggested textbook homework will ensure that you are prepared for the quizzes, which will feature problems very similar to those in the homework. The dates for quizzes is provided in the schedule below; note that exact topics covered on a quiz is subject to change. Any changes will be announced in class.

Quiz grades will not be based strictly on whether or not you found the correct answer. Your work must also be written clearly, and with proper notation, to receive full credit.

Make up quizzes will only be given for excused absences.

Quiz grades will not be based strictly on whether or not you found the correct answer. Your work must also be written clearly, and with proper notation, to receive full credit.

Make up quizzes will only be given for excused absences.

**All make ups must be completed before the graded quizzes are returned to the class; this will typically be the next class meeting.**### Exams

We will have two midterm exams. Use of notes, textbooks, calculators, electronic devices, or other materials will not be permitted during an exam. If you will not be able to attend class for a scheduled exam, please let me know

*before*the exam is scheduled. Make up exams will be given for excused absences only.- Midterm 1: Wednesday, October 4
- Midterm 2: Wednesday, November 15

**TBD**### Final Grades

Your final grade will be calculated as follows:

**Quizzes:**20% (lowest quiz grade is dropped)**Assignments:**15%**Labs:**15%**Midterm Exams:**30%**Final Exam:**20%

F | D | D+ | C | C+ | B | B+ | A |

0-59 | 60-64 | 65-69 | 70-77 | 78-83 | 84-89 | 90-93 | 94-100 |

### Learning Differences

In keeping with college policy, any student with a disability who needs academic accommodations must call Learning Differences Program secretary at 824-3017, to arrange a confidential appointment with the director of the Learning Differences Program during the first week of classes.

### Mercy Mission

This course supports the mission of Mercyhurst University by creating students who are intellectually creative. Students will foster this creativity by: applying critical thinking and qualitative reasoning techniques to new disciplines; developing, analyzing, and synthesizing scientific ideas; and engaging in innovative problem solving strategies.

## Schedule

The exact topic covered on a particular date is subject to change. Exams and quizzes will be given on the day they are scheduled, though the sections appearing on a quiz may differ. Announcements will be made in class regarding any schedule changes.

Date | Topic | Notes |