COURSE SYLLABUS

1.

()

Course Title(Chinese and English)

Mathematical Writing in English

2.

Course Type

Required

3.

Originating Department

Department of Mathematics

4.

Open to Which Majors

5.

Credit Hours

32

6.

Credit Value

2

7.

Teaching Language

Textbook and lecture notes are written in a combination of Chinese and English. The languages of instruction are Mandarin and English.

8.

Instructor(s)

Tao TANG and Min TSAO

9.

Pre-requisites or Other Academic Requirements

Three years of university English courses Calculus, Linear Algebra

10.

Course Objectives

LaTeX

This course is designed for mathematics graduate students and researchers who need advanced training in English writing and communication skills. Topics include structures of English mathematical research papers, commonly used sentence structures and phrases, and tips on how to submit and revise papers in English. The course also covers how to give mathematics presentations in English and how to write research or grant proposals in English. It also introduces LaTeX, an open-source software for high-quality typesetting widely used for mathematical papers.

11.

Teaching Methods and Innovations

The textbook of this course is ``Mathematical Writing in English written by professors Tao TANG and Jiu DING. The course offers students a lot of opportunities to practice reading, writing and presenting in scientific English. It will help students develop a solid foundation in mathematical writing in English and acquire valuable skills in using English for research and teaching.

12.

Course Contents and Course Schedule

1. (2 weeks)

2. (3 week)

3. (1 weeks)

4. LaTeX (1 week)

5. (1 weeks)

6. (2 weeks)

7. (2 week)

8. (2 weeks)

9. (2 week)

13.

Course Assessment

Homework 20% + in class group presentation 40% + Final presentation 40%

14.

Textbook and Supplementary Readings

,2014 ISBN9787040368932

COURSE SYLLABUS

1.

()

Course Title(Chinese and English)

Algebra

2.

Course Type

Required

3.

Originating Department

4

Open to Which Majors

5.

Credit Hours

48

6.

Credit Value

3

7.

Teaching Language

/

8.

Instructor(s)

9.

Pre-requisites or Other Academic Requirements

10.

Course Objectives

11.

Teaching Methods and Innovations

+

12.

Course Contents and Course Schedule

1. Jordan-HolderSylow

2. Unique factorization domainsPrincipal ideal domains

3.

4.

13.

Course Assessment

14.

Textbook and Supplementary Readings

1. Algebra (GTM 211)Serge Lang.

2. Algebra (GTM 73), Thomas W. Hungerford.

COURSE SYLLABUS

1.

()

Course Title(Chinese and English)

Measure Theory and Integration

2.

Course Type

Required

3.

Originating Department

Department of Mathematics

4

Open to Which Majors

5.

Credit Hours

48

6.

Credit Value

3

7.

Teaching Language

English, or Chinese, or both depending on the need of the students.

8.

Instructor(s)

; ,

Linlin Su, Assistant ProfessorXuefeng Wang, Professor

9.

Pre-requisites or Other Academic Requirements

,

Undergraduate Lebesgue Theory Complex Analysis and Functional Analysis

10.

Course Objectives

LebesgueLp

Rn

11.

Teaching Methods and Innovations

()

The course will be taught in the standard way (chalk and board, in-class discussion, homework, office hours, closed-book exams).

12.

Course Contents and Course Schedule

1. General Measure Spaces: Their Properties and Construction

1.1. Measures and Measurable Sets

1.2. Signed Measures: The Hahn and Jordan Decompositions

1.3. The Carath6odory Measure Induced by an Outer Measure

1.4. The Construction of Outer Measures

1.5. The Caratheodory-Hahn Theorem: The Extension of a Premeasure to a Measure

2. Integration Over General Measure Spaces

2.1. Measurable Functions

2.2. Integration of Nonnegative Measurable Functions

2.3. Integration of General Measurable Functions

2.4. The Radon-Nikodym Theorem

3. The Construction of Particular Measures

3.1. Product Measures: The Theorems of Fubini and Tonelli

3.2. Lebesgue Measure on Euclidean Space R"

3.3. Cumulative Distribution Functions on R and Lebesgue-Stieltjes integral

4. General LP Spaces: Completeness, Duality, and Weak Convergence

4.1. The Completeness of LP(X, )

4.2. The Riesz Representation Theorem for the Dual of LP(X, ), 1 p <

4.3. The Kantorovitch Representation Theorem for the Dual of L (X, )

4.4. Weak Sequential Compactness in LP(X, p.), 1 < p