Teaching

Course Teaching in Spring 2025  :      MATH 228: Calculus 3

                                                                MATH 730  Graduate Complex Analysis

 Previous Teaching :

1.   MATH 226  (Calculus I)

2.   MATH 227 (Calculus II)

3.   MATH 228 (Calculus III)

4.   MATH 301 (Introduction to Proof)

5.   MATH 325 (Linear Algebra)

6.   MATH 370 (Introduction to Real Analysis)

7.   MATH 380 (Introduction to Complex Analysis)

8.   MATH 470/770 (Real Analysis II)

9.   MATH 471/771 (Introduction to Fourier Analysis)

10.   MATH 495 (Wavelet and Frames)

11.   MATH 710 (Measure Theory and Integration)

12.   MATH 711 (Functional Analysis)

13.   MATH 725 (Advanced Linear Algebra)

14.  MATH 730 (Graduate Complex Analysis) 

15.   MATH 895 (Graduate Frame Theory)

Student Reports

For many years, I asked students in my different analysis classes to do some reading reports on some advanced topics. Some of them did excellent work. I am glad to share those here.

Kakeya-Bescovitch sets by Phil Coren and Aswin Venkatesan

Uncertainty Principles by Charlie McMenomy

Space-Filling Curves by Laura Nowark

Excellent Textbooks recommendation: 

For students to be successful in math, reading books independently and asking the right questions are the most important skills. I am collecting some books I read and learned math from. Students who want to work with me are expected to read or go through a portion of the following textbooks.

Basic Analysis:  1. An Introduction to Analysis, William Wades

                            2. Complex Variables and Application, Brown and Churchill.

                            3. Topology, Munkres. 

Advanced  Analysis:      1. Four series textbooks by E. Stein and R. Shakarchi.  (Fourier Analysis, Complex Analysis, Real Analysis, Functional Analysis).

                                              (Great Textbook series learning modern analysis from a historical perspective)

                                         2. Real and Complex Analysis, W. Rudin. 

                                               (Classical Analysis books. May be dry to read today, but it contains essentially all the results wanted)

                                         3. A course in Functional Analysis, J. Conway

                                         4. Functions of Complex Variables, J. Conway.  

Fractal  Geometry:  1. Fractal geometry mathematical foundations and applications, K. Falconer.

                                   2. Fractal sets in Probability and Analysis, C. Bishop and Y. Peres.  

                                   3. Fourier Analysis and Hausdorff dimension,  P. Mattila. 

Harmonic Analysis: 1. Classical and Modern Fourier Analysis, L. Grafakos.

                                   2. An introduction to harmonic analysis, Y. Katznelson. 

                                   3. Algebraic Numbers and Fourier Analysis, R. Salem 

                                       (Interesting textbooks talking about the connection of Fourier analysis and algebra). 

Frame Theory:  1. A basis Theory Primer, C. Heil

                            2. Introduction to Frame Theory and Riesz bases, O. Christensen.

                            3. Foundation of Time-Frequency Analysis, K.  Grochenig.

                            4. An Introduction to Compressive Sensing, H. Rauhat. 

Probability and Stochastic Processes:  1. Probability Essentials, J. Jacod and P. Protter.

                                                                    2. Brownian Motion, Martingales and Stochastic Processes,  J. Le Gall.

                                                                    3. Brownian Motion and Stochastic Calculus, S. Shreve and I. Karatzas.

Linear Algebra: 1.  Linear Algebra Done Right, S. Axler.

                            2.  Linear Algebra and applications, S. Friedberg, A. Insel, L. Spence.