#
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.

** Grading: **
Letter grades will be assigned based on class participation.

**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
*L*^{p}, *L*^{∞}, **R**^{n}, **C**^{n}

*Tuncay Aktosun *
aktosun@uta.edu

Last modified: September 16, 2017