Teaching Teaching

Jie Xiao

Department of Mathematics and Statistics
Memorial University of Newfoundland
St. John's, NL A1C 5S7, Canada

jxiao@mun.ca

My teaching is at both graduate and undergraduate levels. I have ever had more than ten graduate students, postdoctoral fellows and visiting scholars whose interests lie respectively in analysis, geometry and PDE. In addition to supervision at the graduate level and above, I offer courses related to analysis and PDE. Below are some comments on the courses (from high to low level) I have taught since joining Memorial University of Newfoundland, and on my general teaching philosophy.

M 6319 - Harmonic Analysis:    This graduate course, that I taught in 2012 Winter Semester, is designed to be an introduction to Harmonic/Fourier Analysis on Euclidean Spaces. The subject has been a considerable flowering during the past several decades. This course will concentrate on the real variable methods of the theory, and provides a solid background for other courses including PDE. L. Grafakos' book: Classical and Modern Fourier Analysis was used as a text.

M 6312 - Measure Theory:    This course, that I taught in Winter 2006 semester, is a regular graduate course about the basis of modern theories of integration treating Lebesgue integration as a special one. Since the theory is quite general, permitting many notions of integration on a broad family of mathematical spaces, but also being intimately tied to functional analysis and geometric analysis, I will, in this course, give a broad introduction to the subject, with some emphasis on the geometric aspects.

M 6311 - Complex Analysis:    This course, that I taught (Winter 2013), is offered for the first-year graduate students. This course will address complex valued functions of one complex variable using three approaches: Riemann's one based on differentiation with connection to Cauchy-Riemann equations; Cauchy's integration and its associated Cauchy's integral theorem and formula; Weierstrass's theory of power series.

M 6310 - Functional Analysis:    This course, that I taught in: Winter 2005; Fall 2006; Fall 2012, is designed to serve the needs of the graduate students. The material to be covered in the course includes metric spaces, continuous maps, normed linear spaces, Banach spaces, Hilbert spaces and their linear (bounded and compact) operators.

M 6160 - Partial Differential Equations:    This is a graduate course which I taught in 2011 Fall Semester with L. Evans' PDE book.

M 4170 - Partial Differential Equations II:    This is a undergraduate course which I am teaching this semester (2014-2015 Winter) with J. David Logan's text: Applied Partial Differential Equations, 2nd ed, Springer, 2004.

M 4000 - Lebesgue Integration:    This is a undergraduate course which I taught in 2013/2014 Fall Semester with WWL Chen's lecture notes: Introduction to Lebesgue Integration and J Xiao's text: Integral and Functional Analysis.

M 3370 - Introductory Number Theory:    This is a course introducting number theory at the undergraduate level. There are now a variety of textbooks available for this course. However, I followed my own development of the core material with reference to Don Rideout's lecture notes (and references therein). Here is my text: Elementary Number Theory, International Press, 2006.

M 3301 - Integration and Metric Spaces:    Since there was no suitable texts for such an advanced undergraduate course, I wrote a text shared with PM 4302/6310 in Fall 2002, Winter 2004 and Fall 2005. The problems and solutions of this course are given in my book: Integral And Functional Analysis, Nova Science Publishers, Inc., 2007.

M 3202 - Vector Calculus:    In Winter 2016 I taught this course. Below are solutions of the assignments:

Assig1s | Assig2s| Assig3s | Assig4s| Assig5s| Assig6s | Assig7s| Assig8s| Assig9s | Assig10s

M 3001 - Analysis II:    As a follow-up of M 3000, this course, which I taught in Fall 2004 and in Fall 2006, and am teaching in Winter 2011, deals with the convergence of sequences, series of constants and functions, power and Taylor series. Here are the handout and assignments:

M3001H

M3001A1 | M3001A2| M3001A3 | M3001MidT1| M3001A4| M3001A5 | M3001MidT2|M3001A6| M3001A7 | M3001A8| M3001MidT3| M3001A9 | M3001A10

M3001S1 | M3001S2| M3001S3 | M3001MidT1S| M3001S4| M3001S5 | M3001MidT2S| M3001S6| M3001S7 | M3001MidT3S| M3001S8| M3001S9 | M3001S10

M 3000 - Analysis I:    This is a theoretic course (regarded as Advanced Calculus) which I taught in Fall 2003. Since I present most of the theory in the familar real number system as opposed to a more general or abstract setting, a student who learns for the first time to discover and write mathematical proofs can more readily call upon his or her experience for examples that illustrate the situation at hand. Fortunately, I taught this course again in Fall 2005. Below are the handout and advice, as well as assignments, mid-term-test, and their solutions:

3000H | 3000A

3000A1 | 3000A2 | 3000A3 | 3000A4 | 3000A5 | MidtermTest | 3000A6| 3000A7 | 3000A8 | 3000A9 | 3000A10

3000S1 | 3000S2 | 3000S3 | 3000S4 | 3000S5 | MidtermTestSol | 3000S6 | 3000S7 | 3000S8 | 3000S9 | 3000S10

M 2320 - Discrete Mathemathics:    This is a one semester course aimed primarily at students who have not done a year of calculus. My experience is that students learn more from intuitive explanations, diagrams and examples than they do from theorems and proofs. In lectures I dealed quickly with the main points of theory, then spent most class time on problem solving and applications of the main ideas. Perhaps most valuable thing for students to learn (and the hardest thing to teach) in a course like this, is how to pick up a math problem in a new setting and relate it to the standard body of theory. The more students see this happen in class, and the more they do it themselves in exercises, the better they grasp the basic ideas. Since Winter 2003 I have developed a textbook for this course based on the above philosophy as well as the corresponding book by E. Goodaire and M. Parmenter.

M 1050/1051 - Finite Mathematics I & II:    I instructed this course four times (at Concordia). It is a required course for the degree bachelor of education (primary or elementary), but it is also desirable alternative to calculus for certain degree programs requiring two first year mathematics courses (e.g., physical education, nursing and others). One of my most satisfactory parts of teaching this course was the fact that I was able to engage all of the students in learning and discussing math, despite their disparate backgrounds.

M 2000 - Calculus III:    This is a follow-up of M1001, discussing infinite series, functions of several variables and multiple integrals. In Winter 2011 I am teaching this course. Here are the course handout: H0 , and the assignments A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, and their solutions: S1, S2, S3, S4, S5, S6, S7, S8, S9, S10.

M 1001 - Calculus II:    This is a continuation of M1000 with concentration on calculus of integration. In teaching calculus one must be realistic and enthusiastic. It seems to the students and myself that the most important points are: a set of well-organized and clear lectures that follow and complement the text, an effective mechanism to obtain feedback from the students, and a good coordination with the teaching assistants. Of course, appropriate examples and applications will be extremely useful sources of motivating the subject.

M 1000 - Calculus I:    Twice in the recent years I taught this large lower division course on calculus of differentiation. I found this a refreshing change from the more technical upper division and graduate courses which have been my steady diet. Hopefully I will continuously contribute to the course offerings (in the lower division) from the Department of Mathematics and Statistics at MUN.