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MATH UN2010 – Linear Algebra

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Course Description

MATH UN2010 covers matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, and selected applications. The course also provides an introduction to writing mathematical proofs.

MATH UN2010 or MATH UN2015?

MATH UN2010 – Linear Algebra emphasizes theoretical foundations, abstract reasoning, and mathematical proofs. It is intended to prepare students for upper-level mathematics courses.

Students who prefer a greater emphasis on applications and practical problem solving should consider MATH UN2015 – Linear Algebra and Probability. MATH UN2015 is recommended for students in engineering, technology, the natural and life sciences, the social sciences, economics, and related fields.

Mathematics majors and joint mathematics majors must take MATH UN2010. Students may not receive credit for both MATH UN2010 and MATH UN2015.

Prerequisite

MATH UN1201 – Calculus III, or the equivalent, is strongly recommended.

Textbook

Otto Bretscher, Linear Algebra with Applications, 5th edition. See the publisher’s page.

Sample Syllabus

The sequence and selection of topics may vary by instructor.

  1. Linear Equations
    • Introduction to linear systems
    • Matrices, vectors, and Gauss–Jordan elimination
    • Solutions of linear systems
    • Matrix algebra
  2. Linear Transformations
    • Introduction to linear transformations and their inverses
    • Linear transformations in geometry
    • Matrix products
    • Inverse linear transformations
  3. Subspaces of Rn and Their Dimensions
    • Image and kernel of a linear transformation
    • Subspaces of Rn
    • Bases and linear independence
    • Dimension of a subspace
    • Coordinates
  4. Orthogonality and Least Squares
    • Orthogonal projections and orthonormal bases
    • Gram–Schmidt process and QR factorization
    • Orthogonal transformations and orthogonal matrices
    • Least squares and data fitting
  5. Determinants
    • Introduction to determinants
    • Properties of the determinant
    • Geometric interpretations of the determinant
    • Cramer’s rule
  6. Eigenvalues and Eigenvectors
    • Diagonalization
    • Finding the eigenvalues of a matrix
    • Finding the eigenvectors of a matrix
  7. Symmetric Matrices and Quadratic Forms
    • Symmetric matrices
    • Quadratic forms
    • Singular values

Help Room

See the 406 Mathematics Help Room schedule.

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