Aktosun, Fall 2017, Math 5392

Instructor: Tuncay Aktosun, PKH 461, (817) 272-1545, aktosun@uta.edu

Course: Selected Topics in Mathematics: Mathematical Analysis, Math 5392, Section 002, Course number 91191

Office Hours: 3:50-4:50 pm, Monday and Wednesday

Classroom: PKH 485

Classtime: 2:30-3:50 pm, Monday and Wednesday

Textbook: No textbook will be used; some reading materials will be provided.

Coverage: We will cover some topics in Linear Algebra and Analysis with the goal of seeing Linear Algebra/Analysis/Differential Equations from a unified viewpoint as a part of Linear Functional Analysis. We will try to learn mathematics independently of any particular textbook by learning the concepts based on basic principles and intuition.

Exams: No exams will be given.

Prerequisites: Consent of the instructor (basic undergraduate mathematical training in mathematics or physics or engineering should be sufficient).

REFERENCES:

[1] T. Tao, Analysis I and II, 3rd ed., Hindustant Book Agency, 2014.

[2] T. Aktosun and R. Weder, Chapter 3 of The Inverse Scattering Problem for the Matrix Schrödinger Equation, arXiv:1708.03837 [math-ph].

TOPICS COVERED:
• real numbers, complex numbers, rational numbers
• almost everyhwere (a.e.), set of measure zero
• Lebesgue integral vs Riemann integral
• Lebesgue integral, integrability
• Riemann integral, continuity
• integrand, derivative of Lebesgue integral
• integrand, derivative of Riemann integral
• vector space, field, dimension
• vector space over real numbers, vector space over complex numbers
• norm in a vector space
• scalar product in a vector space
• Lp, L, Rn, Cn

Tuncay Aktosun aktosun@uta.edu