Prerequisite: MATH 254, 352, 335 with grade C- or better or consent of the instructor; (highly) recommended: MATH 372, 435

Course Learning Outcomes: By the end of this course, students will be able to:

• Demonstrate a working knowledge of the theory of Hilbert spaces and the spectral theory of operators in Hilbert spaces that will enable them to study the integral and partial differential equations in the second part of this course.

Program Learning Outcomes and Mission Statement of the Department of Mathematics

Course Requirements

• Textbook (required): L. Debnath and P. Mikusinski, Introduction to Hilbert Spaces with Applications, Academic Press, 2005
• Lecture Notes
• Goals and Objectives of the Course: Mathematical Physics is an interplay between mathematics and physics. It is a tool with which the presentation of physics is facilitated and the only language through which physics can express itself. This is a course for beginning graduate (both physics and mathematics) students interested in more advanced mathematics than they usually study at the undergraduate level, which attempts to strike a balance between formalism and application, between abstract and concrete. The purpose of this course is to study the basic concepts of mathematical physics such as: Banach spaces, Banach fixed point theorem, Hilbert spaces, orthonormal systems, linear functionals, projections, compact operators, self-adjoint operators, unitary operators, spectral theory of operators.
• Class Procedures: The majority of each class period will be lecture oriented. You are expected to: attend the lectures and to take your own lecture notes, read the textbook and work out problems from that section covered in class, do the homework problems.
• Attendance Requirements: It is important that you attend every class scheduled for this course. You are responsible for all announcements and material covered in this class as well as material from the textbook which is assigned but not covered in class.
• Computers: Any electronic devices such as laptops, tablets and cell phones cannot be used during the class. Please set your cell phones on vibrate.

Grading

• Homework: There will be weekly homework assignments that will count for 75% of the grade.
• Tests: There will be a final exam that will count for 25% of the total grade.
• Make-ups: Make-up exams will be given only in cases of extremely properly documented emergencies. Late homework will not be accepted.
• Evaluation: Grades will be determined on a 100 point scale. Those point totals near cutoff will be individually considered for the next higher grade. I do reserve the right to add some extra points depending on the class participation and outstanding exam performance.

Changes: The course plan may be modified during the semester. Such modifications will be announced in advance during class periods. You are responsible for keeping abreast of such changes.

Remarks: It is important to note that this course is cumulative (builds on itself) and it is assumed that all earlier parts covered are liable for any exam. It is strongly advised that you start working on this course from the very beginning. The course moves at a fast place, so it is very hard to catch up if you get behind.

Counseling and Disability Services. Reasonable Accommodations: New Mexico Tech is committed to protecting the rights of individuals with disabilities. Qualified individuals who require reasonable accommodations are invited to make their needs known to the Office of Counseling and Disability Services (OCDS) as soon as possible. In addition, New Mexico Tech offers mental health and substance abuse counseling through the Office of Counseling and Disability Services. The confidential services are provided free of charge by licensed professionals. To schedule an appointment, please call 835-6619.