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Office Rm. Blocker 614A, Telephone (979)862-3257

E-mail: kuchment@math.tamu.edu, Home Page: /~kuchment

**Sections:**500 and 200 (honors)**Time:**TR 9:35 - 10:50 am**Room:**BLOC 121**Textbook:**I. M. Gelfand,*Lectures on Linear Algebra*, Dover, ISBN-10: 0486660826?, ISBN-13: 978-0486660820.

This is a small and cheap wonderful book that can be easily purchased through Amazon, Dover, or other booksellers.**Regular office hours:****TR 1 - 2 pm, Rm. Blocker 614A, no appointment is needed**.

.**Additional office hours**can be**arranged by appointment**

Linear algebra is a mathematical topic of great elegancy and enormous importance. Proficency in it is required in any area of mathematics - analysis, algebra, geometry, etc., as well as applications - from physics to biology, economics, engineering, ... you name it.

The Math 423 class assumes the prior knowledge of some basics of linear algebra from the classes like Math 304 or Math 323.

Starting with a brief going through the basics, which are assumed to be known: concerning vector spaces, bases, Gauss elimination, and matrices, we will progress to a variety of more advanced topics and applications. These, time permitting, will include duality of spaces and operators, bilinear and quadratic forms, various important matrix decompositions, Euclidean and unitary spaces, various classes of matrices (self-adjoint (Hermitian), normal, orthogonal, unitary, positive definite, etc.), spectra, resolvents, eigenvectors and generalized eigenvectors, normal forms, functions of matrices, some numerical analysis topics. Time permitting, we might also cover relations to differential equations, quantum mechanics, and linear programming.

Students who attend the "stacked" Honors sub-section 200, will have to address somewhat more advanced topics and will get different homeworks, quizzes, midterms, and finals.

** This is a rigorous, proof-based course**, which means that close attention will be paid
to students' ability to write mathematical statements and proofs mathematically
and grammatically correctly.

MATH 304 or MATH 323, or instructor's content.

- Participation - 5% of the grade.
- Weekly home assignments or quizzes - 20%.
- Two mid-term exams - 25% each.
- Final exam - 25%

Dates | # of sessions | Topic | Weekly HW | Exams |

2 | Overview of Linear Algebra. Sections 1, 9, 10 | HW1, Q1 | ||

4 | Euclidean vector spaces. Sections 2, 3, 5 | HW2 | ||

4 | Bilinear and quadratic forms. Sections 4-7 | HW3 | ||

February 23rd | 1 | Exam 1 | ||

2 | Complex Vector Spaces, Unitary spaces, Section $8. | Q2, March 2nd | ||

2 | Subspaces | HW4 | ||

4 | Various classes of operators. The spectral theorem. Ch. II + notes. | HW5, 6 | ||

Variational approaches, SVD, etc. Ch. II + notes. | HW 7 | |||

1 | Relations to quantum mechanices | |||

Functions of matrices and ODEs | ||||

April 4th | 1 | Exam 2 | ||

Jordan form. Ch. III | HW8 | |||

Tensors. Ch. IV | ||||

May 4th | 12:30 - 2:30 pm | Final exam |

- P. Halmos,
*Finite dimensional vector spaces*, this wonderfully written classics has been through many editions over the years. Somewhat similar to the next Glazman and Ljubich's book. - I. Glazman and Y Ljubich,
*Finite-Dimensional Linear Analysis: A Systematic Presentation in Problem Form*(Dover Books on Mathematics) Paperback, 2006.

This is a very unusual book, which through the problems leads students not only through linear algebra, but also "covertly" prepares them for much more advanced topics, such as functional analysis. - R. Bellman,
*Introduction to matrix analysis*, A wonderful classics, with many applications. - T. W. Korner,
*Vectors, pure and applied*, Cambridge Univ. Press, 2013.

Some other good linear algebra textbooks -
**An outstanding book on linear algebra using Matlab:**

LLOYD N. TREFETHEN AND DAVID BAU, III,*Numerical Linear Algebra*, SIAM 1997. - G. Strang, An introduction to linear algebra, Wellesley-Cambridge Press; 5th edition, 2016.
- G. Shilov,
*Linear algebra*, Dover 1977. - S. Axler,
*Linear algebra done right*, 3rd edition, Springer 2014. -
**A classical treatise**F. Gantmacher,*The theory of matrices. vols. I and II*. New York, Chelsea, 1959. Freely available on-line. -
**A more contemporary treatise**R. Horn and C. Johnson,*Matrix analysis*. One of the older editions available on-line. - Also by F. R. Gantmacher,
*Applications of the theory of matrices*. New York, Interscience, 1959.

E-mail (kuchment AT math.tamu.edu) is the preferred way to contact me.

When writing to me, please include your full name and "Math 423". Use your tamu.edu e-mail account to send me e-mails.

Make-ups for missed quizzes, home assignments and exams will only be allowed for a university approved excuse in writing. Wherever possible, students should inform the instructor before an exam or quiz is missed. Consistent with University Student Rules , students are required to notify an instructor by the end of the next working day after missing an exam or quiz. If there are confirmed circumstances that do not allow this (a written confirmation is required), the student has two working days to notify the instructor. Otherwise, they forfeit their rights to a make-up.

Late work will not be accepted, unless there is an university approved excuse in writing. In the latter case student has a week to submit the work.

Sometimes the instructor might make a mistake grading your work. If you feel that this has happened, you have one week since the graded work was handed back to you to talk to the instructor. If a mistake is confirmed, the grade will be changed. No complaints after that deadline will be considered.

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Services for Students with Disabilities (Cain Hall, Room B118, or call 845-1637).

All printed materials disseminated in class or on the web are protected by Copyright laws. One xerox copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.

Copying work done by others, either in class or out of class,
looking on other student?s
papers during exams or quizzes, having possession of unapproved
information in your calculator/computer/phone, etc., and/or having
someone else do your work for you are all acts of scholastic
dishonesty. These acts, and other acts that can be classified as
scholastic dishonesty, will be prosecuted to the full extent allowed
by University policy. In this class, collaboration on graded
assignments, either in class or out of class, is forbidden unless
permission to do so is granted by the instructor. For more
information on university policy regarding scholastic dishonesty, see
University Student Rules at
http://studentrules.tamu.edu/.

"An Aggie does not lie,
cheat, steal, or tolerate those who do." Visit
http://www.tamu.edu/aggiehonor and follow the rules of the
Aggie
Honor Code.