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.

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.

You will be given take home assignments, usually every week. These assignments will include questions taken directly from the text as well as additional problems related to topics we’ll see in class. Late work will not be accepted. The assignments will be posted on the course website (not Blackboard), along with solutions after assignments are due. Your lowest homework grade will be dropped when calculating your final grade.

In addition to the homework assignments, you will have a weekly lab assignment. These will typically be completed during the lab meetings. If you need additional time on the lab, or if you are absent, the lab work may be completed at home and turned in by Friday of the week the assignment is given. Your lowest lab assignment grade will be dropped when calculating your final grade.

Lab assignments will be completed online through Sage Cloud. You do not need to purchase any software or equipment for the labs, and you are free to use your own computer if you prefer. To work at home, you'll only need an internet connection - no software needs to be installed.

Lab assignments will be completed online through Sage Cloud. You do not need to purchase any software or equipment for the labs, and you are free to use your own computer if you prefer. To work at home, you'll only need an internet connection - no software needs to be installed.

We will have two midterm exams. You will be given an exact list of topics, along with a review sheet, approximately one week before each exam. Use of notes, textbooks, calculators, electronic devices, or other materials will not be permitted during an exam.
**Friday, May 20, 8:00 - 10:00.**

- Midterm 1: Wednesday, March 9
- Midterm 2: Wednesday, April 27

Your final grade will be calculated as follows:

Your letter grade will be determined according to the department grading scale:

**Average of midterm exams:**30%**Average of homework assignments:**30%**Average of lab assignments:**15%**Final Exam:**25%

Your letter grade will be determined according to the department grading scale:

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

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

This schedule will be kept up to date as assignments are given, or if we get behind schedule. Exam dates will not be changed as long as the University is open on those days.

Date | Topic | Noteworthy Events |

Week 1 | ||

Feb 3 | Class Introduction | |

Feb 5 | Vectors and Linear Combinations | |

Week 2 | ||

Feb 8 | Lengths and Dot Products | |

Feb 10 | Matrices | |

Feb 12 | Vectors and Linear Equations | |

Week 3 | ||

Feb 15 | Elimination | |

Feb 17 | Elimination | |

Feb 19 | Rules for Matrix Operations | |

Week 4 | ||

Feb 22 | Inverse Matrices | |

Feb 24 | Inverse Matrices | |

Feb 26 | Transposes & Permutations | |

Week 5 | ||

Feb 29 | Spaces of Vectors | |

Mar 2 | Solutions of \(Ax=0\) | |

Mar 4 | Rank & Reduced Echelon Form | |

Week 6 | ||

Mar 7 | Review | |

Mar 9 | Midterm I | |

Mar 11 | Solutions of \(Ax=b\) | |

Week 7 | ||

Mar 14 | Solutions of \(Ax=b\) | |

Mar 16 | Solutions of \(Ax=b\) | |

Mar 18 | Independence, Basis, Dimension | |

Week 8 | ||

Mar 21-25 | Easter Break | |

Week 9 | ||

Mar 28 | Easter Break | |

Mar 30 | Independence, Basis, Dimension | |

Apr 1 | Orthogonality & Projections | MAA Section Meeting (April 1-2, Gannon U) |

Week 10 | ||

Apr 4 | Determinants | |

Apr 6 | Determinants | |

Apr 8 | Cramer's Rule | |

Week 11 | ||

Apr 11 | Eigenvalues & Eigenvectors | |

Apr 13 | Eigenvalues & Eigenvectors | |

Apr 15 | Diagonalization | |

Week 12 | ||

Apr 18 | Diagonalization | |

Apr 20 | Similar Matrices | |

Apr 22 | Break | |

Week 13 | ||

Apr 25 | Review | |

Apr 27 | Midterm II | |

Apr 29 | SVD | |

Week 14 | ||

May 2 | Markov Matrices | |

May 4 | Linear Transformations | |

May 6 | Linear Transformations | |

Week 15 | ||

May 9 | Linear Transformations | |

May 11 | Linear Transformations | |

May 13 | Review | |

Week 16 | ||

May 16 | Reading Day | |

May 18 | ||

May 20 | Final Exam 8:00 - 10:00 |

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.

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.