Upon completion of this course, students should be comfortable with the following:
Solve linear systems of equations.
Identify and explain the properties of the vector space ℝn.
Utilize the dot product.
Compute orthogonal projections.
Compute matrix operations.
Explain the properties of the determinant.
Identify and explain the properties of abstract vector spaces.
Calculate and identify the characteristics of a matrix.
Relate linear transformations and matrices and define a linear transformation.
Explain the rank-nullity theorem and its consequences.
Aside from course specific learning objectives, this course aims to help you develop additional skills. These are as follows.
Communication: Express mathematical ideas through verbal and written communication, using appropriate mathematical terminology, while building confidence in utilizing and sharing mathematical ideas
Personal Growth: Develop their mathematical identity and connect mathematics to their personal interests, while considering their own skills and strengths.
Problem Solving & Adaptive Competence: Break down, explain and appreciate mathematical tools, while developing problem solving strategies that can be applied flexibly and creatively across disciplines and outside of academia, and critical thinking skills to identify when different tools will be applicable
Metacognition: Accept mistakes as an integral part of the learning process and utilize misconceptions as moments of growth while reflecting on their learning and studying strategies.
Applications: Break down a physical system in order to formulate the problem mathematically.