jamesquinlan/mat220-linear-algebra

Introduction to Linear Algebra

MAT220-Applied-Linear-Algebra

I believe that linear algebra is the most important subject in college mathematics. Isaac Newton would not agree! But he isn’t teaching mathematics in the 21st century. – Gilbert Strang

Course Description

Linear algebra, the study of multivariate linear systems and transformations, is essential prepara- tion for advanced sciences, statistics, and computing. Linear algebra also introduces students to discrete mathematics, algorithmic thinking, a modicum of abstraction, moderate sophistication in notation, and simple proofs. The goal of this course is to introduce students to the theory, techniques, and applications of linear algebra. Some of the topics include systems of linear equations, matrix algebra, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, orthogonality, and the Gram-Schmidt process. Applications may include predator-prey models, economic system equilibrium, Markov chains, traffic flow, balancing chemical equations, and least-squares approximations. Technology will be used to investigate concepts and solve problems.

Learning Outcomes

At the conclusion of this course students will be able to:

• compute with and recognize properties of particular matrices;
• formulate, solve, apply, and interpret properties of linear systems;
• recognize and use basic properties of subspaces and vector spaces;
• determine a basis and the dimension of a finite-dimensional space;
• find the eigenvalues and eigenvectors of a matrix, and use them to represent a linear trans- formation;
• recognize and use equivalent forms to identify matrices and solve linear systems;
• read proofs with understanding; and
• use definitions and theorems to prove basic results in core topics.

Furthermore, MAT220 will help students build mathematical habits of mind by:

• developing their critical thinking and communication skills through activities that teach students how to:

  • state problems clearly,
  • articulate assumptions,
  • understand the importance of precise definitions, and reason logically to conclusions;
  • identify and model essential features of a complex situation, modify models as needed for traceability, and draw valuable conclusions; and
  • use and compare analytical, visual, and numeracy methods;

• linking theory to practice by being exposed to a variety of contemporary applications in mathematics that motivate and illustrate the concepts they are learning, as well as become aware of connections to other fields (both within and outside of mathematics) and learn to apply mathematical concepts to problems in those fields;

• developing mathematical independence and participate in open-ended inquiry;

• operating current technologies; and

• learning to read, interpret, analyze, and write proofs.

Textbook

@book{leon2014linear,
 title={Linear algebra with applications},
 author={Leon, Steven J and De Pillis, Lisette and De Pillis, Lisette G},
 year={2014},
 publisher={Pearson}
}