Textbook: Linear Algebra, A Geometric Approach, 2nd Edition by Shifrin & Adams. Macmillan Higher Education ISBN: 9781429215213

Calculator: The use of calculators or computers in order to perform routine computations is encouraged in order to give students more time on abstract concepts.  Most ACC faculty are familiar with the TI family of graphing calculators. Hence, TI calculators are highly recommended for student use. Other calculator brands can also be used.  Your instructor will determine the extent of calculator use in your class section.

Other Technology: Access to a webcam and microphone are required for this course. Eligible students can check out required technology at https://www.austincc.edu/students/student-technology-services

Textbook: Linear Algebra, A Geometric Approach, 2nd Edition by Shifrin & Adams. Macmillan Higher Education ISBN: 9781429215213

1. Solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion.
2. Carry out matrix operations, including inverses and determinants.
3. Demonstrate understanding of the concepts of vector space and subspace.
4. Demonstrate understanding of linear independence, span, and basis.
5. Determine eigenvalues and eigenvectors and solve eigenvalue problems.
6. Apply principles of matrix algebra to linear transformations.

Demonstrate understanding of inner products and associated norms

The course objectives of Linear Algebra are:

(1) To use mathematically correct language and notation for Linear Algebra.

(2) To become computational proficiency involving procedures in Linear Algebra.

(3) To understand the axiomatic structure of a modern mathematical subject and learn to construct simple proofs.

(4) To solve problems that apply Linear Algebra to Chemistry, Economics and Engineering.

The topics that will enable this course to meet its objectives are:

(i) the basic arithmetic operations on vectors and matrices, including inversion and determinants, using technology where appropriate;

(ii) solving systems of linear equations, using technology to facilitate row reduction;

(iii) the basic terminology of linear algebra in Euclidean spaces, including linear independence, spanning, basis, rank, nullity, subspace, and linear transformation;

(iv) the abstract notions of vector space and inner product space;

(v) finding eigenvalues and eigenvectors of a matrix or a linear transformation, and using them to diagonalize a matrix;

(vi) projections and orthogonality among Euclidean vectors, including the Gram-Schmidt orthonormalization process and orthogonal matrices;

(vii) the common applications of Linear Algebra, possibly including Markov chains, areas and volumes, Cramer's rule, the adjoint, and the method of least squares;

(viii) the nature of a modern mathematics course: how abstract definitions are motivated by concrete examples, how results follow from the axiomatic definitions and are specialized back to the concrete examples, and how applications are woven in throughout. This course will present various "characterization" theorems (eg. characterizing isomorphic finite-dimensional vector spaces by their dimension and characterizing invertible matrices by various criteria);

(ix) basic proof and disproof techniques, including mathematical induction, verifying that axioms are satisfied, standard "uniqueness" proofs, proof by contradiction, and disproof by counterexample.