Syllabus

Mathematics MA 2055

Instructor

Benjamin McKay
b.mckay{@fake.org)ucc.ie
School of Mathematical Sciences
University College Cork
Cork, Ireland

Telephone	353 21 420 5838
Fax	353 21 427 0813
Secretary	353 21 490 2542

Students with disabilities

University College Cork seeks to provide equal access to its programs, services and activities for people with disabilities. If you will need accomodations in this class, reasonable prior notice needs to be given to the instructor and to the college to make arrangements for accomodations. All written information in this course can be made available in alternative format with prior notification.

What you know already

You should already have studied linear algebra including matrices and vectors, matrix arithmetic, Gaussian elimination, determinants, eigenvectors and eigenvalues, linear independence, kernels and images.

Course objectives

By the end of this course, you should be able to

1. Verify the linearity of mappings on real and complex vector spaces,
2. and the linear independence of sets of vectors,
3. Evaluate bases, transition matrices and matrices representing linear transformations,
4. Compute eigenvalues and eigenvectors of linear operators,
5. Construct orthonormal bases for vector spaces,
6. Verify properties of projection mappings, adjoint mappings, self-adjoint operators and isometries.

Books

There is no textbook for this course. We will use ideas from the following recommended books:

• Oleg Bogopolski, Introduction to Group Theory, European Mathematical Society, 2008.
• Peter D. Lax, Linear Algebra and Its Applications, Wiley-Blackwell; 2nd edition, 2009.
• Jean-Pierre Serre, Linear Representations of Finite Groups, Springer-Verlag, 5th edition, 1996.

We will only use most of chapter 1 of Bogopolski, and some of part 1 of Serre.

You might like to learn the basic linear algebra material from the free book:

http://euclid.ucc.ie/pages/staff/Mckay/linear-algebra/fall-2009/MA2055/LADW.pdf

Equipment

We will use no computers or calculators. Neither notes nor tapes of lectures may be permitted for purposes of sale.

Marking

75% will come from the final exam and 12.5% each from two tests. Tests and exams are to be completed independently by each student; only original work of the student whose name is on the assignment may be submitted for marking. Any missed test or final exam can not be rescheduled. Attendance will not count toward the final mark, although the instructor reserves the right to refuse admission to the final exam or to refuse to mark the exam of any student who (in the instructor's opinion) was frequently absent, or performed poorly on the tests.

Tests will be held on Tuesday, October 18 and Tuesday, November 29.

Lectures

Office hours

I will be in my office, Western Gateway room G-39, Fridays 9:30am-11:30am, and you can drop by then to ask questions. The schedule may be changed; if so you will be notified in class.

Holidays

Students who anticipate the necessity of being absent from class due to the observation of a major religious observance must provide advance notice of the dates to the instructor in writing.

Old exams and tests

Exams and tests not collected by students will be kept by the instructor for a period of three months after the termination of the course, at which time they will be destroyed.