Course Syllabus
Course: MATH 2270
Division: Natural Science and Math
Department: Mathematics
Title: Linear Algebra
Semester Approved: Spring 2023
Five-Year Review Semester: Fall 2027
End Semester: Fall 2028
Catalog Description: Linear algebra is a study of systems of linear equations, matrices, vectors and vector spaces, linear transformations, eigenvalues and eigenvectors, and inner product spaces. This class is required for students majoring in mathematics and many areas of science and engineering.
Semesters Offered: Fall, Spring
Credit/Time Requirement: Credit: 3; Lecture: 3; Lab: 0
Prerequisites: MATH 1210
Justification: This class is required for students majoring in mathematics, computer science, as well as many branches of engineering, physics, and chemistry. The material from this course provides a foundation and problem-solving tools for students entering science-related fields. Linear Algebra is also recommended in some allied fields. Linear algebra concepts are common in advanced math and science contexts. This course is fully transferable to all Utah public higher education institutions (Utah State University, University of Utah, Weber State University, Southern Utah University, Dixie State University, Utah Valley University, Salt Lake Community College) as well as Brigham Young University.
Student Learning Outcomes:
Students will know and be able to use principles of matrix operations. Students will be able to perform (by hand and with technology, as appropriate) row operations and matrix arithmetic operations. For example, students will be able to convert a linear system to a matrix equation and solve it. Student learning of these concepts will be assessed through homework, quizzes, activities, presentations, and/or exams.
Students will understand and be able to perform desired operations on vectors in 2-, 3-, and n-dimensions. Students will be fluent in vector arithmetic including dot product. Students will also be able to determine whether a given set of vectors forms a basis for a vector space. Student learning of these concepts will be assessed through homework, quizzes, activities, presentations, and/or exams.
Students will understand and apply inner products to vector spaces. Students will apply inner products in situations such as the Gram-Schmidt Process, least squares approximation, and change of basis problems. Student learning of these concepts will be assessed through homework, quizzes, activities, presentations, and/or exams.
Students will compute eigenvalues and eigenvectors (by hand and with technology, asappropriate). Students will apply eigenvalues and eigenvectors by diagonalizing matrices (where possible). Student learning of these concepts will be assessed through homework, quizzes, activities, presentations, and/or exams.
Content:
Through class discussion, class activities, lecture, and practice in homework and/or projects, students will learn the concepts below. * Systems of linear equations and their solutions * Matrix arithmetic * Determinants* Vector arithmetic * Vector spaces and linear transformations * Inner product spaces* Gram-Schmidt Process* Least squares approximation * Eigenvalues and eigenvectors, including matrix diagonalizationInstructors are encouraged to foster an environment where different correct approaches to problems are considered and appreciated.
Key Performance Indicators:
Student learning may be evaluated using:
Homework 10 to 25%
Quizzes 0 to 15%
Activities / Presentations 0 to 15%
Midterms 30 to 50%
Final Exam (comprehensive) 15 to 30%
Representative Text and/or Supplies:
Anton, Howard, Elementary Linear Algebra, current edition, John Wiley & Sons, Inc.
Pedagogy Statement:
The AAC&Us high impact practices are proving to be of value to students of all backgrounds; be that learning preferences, ethnicity, gender or socioeconomic levels. Based on that knowledge teachers of this course regularly use many teaching/learning methods such as group work, discussion, lecture, online sources for both learning and homework, group and individual presentations, and traditional paper and pencil homework that allows students to demonstrate their learning.
Instructional Mediums:
Lecture
Maximum Class Size: 30
Optimum Class Size: 24
