Teaching

Course Teaching in Fall 2023  :      MATH 325: Linear Algebra

                                                                MATH 370 Real Analysis 1

 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 on your own and asking right questions are the most important skills. I am collecting some books I read and learnt math from. Students who wants 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 historical perspective)

                                         2. Real and Complex Analysis, W. Rudin. 

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

                                         3. A course in Functional Analysis, J. Conway

                                         4. Functions of complex Variables, J. Conway.  

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. 

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. 

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.