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基本信息 The basic information
姓名: 申爽

学院: 数学与统计学院


学历: 博士研究生毕业

学位: 理学博士


职称: 讲师（高校）

职务:


学科: 数学-应用数学





工作经历 Work Experience
2017.8至今 西北工业大学应用数学系 助理教授
2016.11--2017.5 哥伦比亚大学数据实验室 访问
2015.9--2016.9 香港中文大学数学系 博士后




教育经历 Education Experience
2010.8--2015.7 清华大学数学系 博士
2006.8--2010.7 清华大学数理基科班 学士




教育教学 Education And Teaching
2020年秋 西北工业大学 本科生3学分课程 概率论与数理统计 选课人数192
2019年秋 西北工业大学 本科生3学分课程 概率论与数理统计 选课人数220
2018年秋 西北工业大学 本科生3学分课程 概率论与数理统计 选课人数235
2016年春 香港中文大学 本科生3学分英文课程 Introductory Probability 选课人数60




综合介绍 General Introduction
Updated 2020/11/11
We are happy to announce the launch of our Real Analysis Friday Seminars in fall 2020. This is a series of seminars aimed at discussing real analysis of undergraduate level. While in the first several weeks we recollect some basics taught in an introductory course, in a later stage we will be talking about John C Oxtoby's remarkable book "Measure and Category". Here is the info of the sessions. Feel free to join us!





#RAFS Session 8
Time：Nov. 20, 2020, 16:00--18:00
Location：434 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Li, Yulong (Class of 2022)
Title：The Banach-Mazur Game
Abstract：In this talk, we are mainly concerned witha mathematical game that was proposed by S. Mazur in 1935 and first appeared in “Scottish book”, the world-renowned collection of problems. It involves two players and is believed to be a first example of infinite positional game. Surprisingly, the solution to this game is related to Baire category theorem. We will first define the game and understand what is meant by strategy. Then we show an equivalent condition in terms of category for one player to be sure to win, that is, having a strategy. This gives new insight into the sense in which a set of first category is small. Snacks and drinks will be provided.


#RAFS Session 7

Time：Oct. 30, 2020, 16:00--18:00
Location：434 Qi Xiang Building, Chang'an Campus
Speaker：Mr.Gao, Chaoqun (Class of 2021)
Title：The property of Baire
Abstract：We have come to the stage where we could make a first comparison of category and measure: the property of Baire is a property analogous to the measurability of a set, sets of first category could play the role of Lebesgue null sets. In this talk, we focus on the class of sets having the property of Baire, and try to study in a parallel manner with the class of measurable sets. Despite the evident difference as illustrated by the example that a null set could be of second category, we remark that both of the two classes include the Borel sets, and each is invariant under translation. Snacks and drinks will be provided.


#RAFS Session 6

Time：Oct. 23, 2020, 16:00--18:00
Location：434 Qi Xiang Building, Chang'an Campus
Speaker：Mr.Gao, Chaoqun (Class of 2021)
Title：Lebesgue's one-dimensional density theorem
Abstract：The study of densities appears naturally in geometric measure theory, a subject where rigorous proofs are often intricate and difficult. In this talk, we work on the real line and first define the density of a measurable set E at some point x, then we prove the classical Lebesgue density theorem (1904), which tells us how much of the set E, in the sense of Lebesgue measure, is concentrated near x. The main tool is a Vitali-type covering theorem. Snacks and drinks will be provided.


#RAFS Session 5

Time：Oct. 16, 2020, 16:00--18:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr.Wu, Qingtong(Class of 2022)
Title：Liouville numbers
Abstract：The study of Liouville numbers plays an important role in the transcendence theory and diophantine approximation, which in turn is widely recognized as a first window to metric number theory. In this talk, we first define Liouville numbers and prove that every Liouville number is transcendental, then we show that the set of Liouville numbers is of zero measure and its complement is a countable union of nowhere dense sets, thus providing another partition of R which consists of two “small” sets in the sense of measure and category, respectively. Snacks and drinks will be provided.



#RAFS Session 4
Time：Oct. 4, 2020, 16:00--18:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Wu, Qingtong (Class of 2022)
Title：Measure and category on the real line
Abstract：We will be talking about Oxtoby’s book from this week onward. Its main subject is twofold, the Baire category theorem with various applications and the duality between measure and category, both of which are based on the notion of countability, thus making us start with Cantor’s theorem which says no interval of real numbers is countable. We then explore two more existence theorems of Baire and Borel, and finally construct a set on the real line that is small in one sense but large in the other sense. Snacks and drinks will be provided.


#RAFS Session 3
Time：Sep. 25, 2020, 16:00--18:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Yang, Rui (Class of 2022)
Title：Littlewood’s three principles
Abstract：The British mathematician J.E. Littlewood (1885-1977) once proposed three principles as guide for working in real analysis: every (measurable) set is nearly a finite sum of intervals, every (measurable) function is nearly continuous, and every convergent sequence is nearly uniformly convergent. As Littlewood himself wrote, “it is natural to ask if the ‘nearly’ is near enough, and for a problem that is actually soluble it generally is.” In this talk we will discuss these three “nearly” and try to construct counter-examples when certain conditions are violated.


#RAFS Session 2
Time：Sep. 18, 2020, 15:00--17:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Yang, Rui (Class of 2022)
Title：Revisiting introductory real analysis (Part II)
Abstract：This is the second half of a 4-hour presentation which serves as a quick overview of a standard real analysis course taught here at NWPU.


#RAFS Session 1
Time：Sep. 11, 2020, 15:00--17:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Li, Yulong (Class of 2022)
Title：Revisiting introductory real analysis (Part I)
Abstract：This is the first half of a 4-hour presentation which serves as a quick overview of a standard real analysis course taught here at NWPU.




Archive for Past Seminars -- 2019 #MATS
We are happy to announce the launch of our Mathematical Analysis Tuesday Seminars in fall 2019. This is a series of seminars aimed at discussing mathematical analysis of undergraduate level. While we now have independent topics for each session, in a later stage we might choose to talk about Terence Tao's book "Analysis I". Here is the info of the sessions. Feel free to join us!


#MATS Final Session 10
Time：Jan. 10, 2020, 15:00--17:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker 1：Mr. Xiong, Jing (Class of 2020)
Title 1：A study on Bayesian statistics and frequentist statistics
Abstract 1：In the field of statistical inference, 19th century science was broadly Bayesian in its methodology, while frequentism dominated 20th century scientific practice. The aim of this talk is to compare these two schools by first presenting a basic overview of Bayesian and frequentist statistics as well as the related background of the 270-year debate between them. Then we construct examples from common scenarios including point estimation, interval estimation and hypothesis testing and use specific questions and data to draw a comparison of the corresponding results.
Speaker 2：Mr. Yao, Jiahao (Class of 2021)
Title 2：Kakeya problem in finite fields
Abstract 2：The Japanese mathematician Soichi Kakeya posed his famous question in 1917, which could be expressed as follows: a line segment with length 1 moves continuously by rotation and translation on the plane, turns 180 degrees and returns to its original position, then what is the minimum area that has been swapt? Since the work of Besicovitch, Kakeya sets have been found to be related to many other mathematical fields, including harmonic analysis and geometric measure theory. In this talk we are going to present Zeev Dvir's stunningly simple proof in 2008 which gives a full affirmative answer to the Kakeya conjecture in finite fields.


#MATS Session 9
Time：Jan. 3, 2020, 9:00--11:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Yang, Rui (Class of 2022)
Title：Differentiation of functions
Abstract：We are to discuss Chapter 10 of Tao's Analysis I. This includes basic definitions, local maxima/minima and derivatives, monotone functions and derivatives, inverse functions and derivatives, and the well-known L'Hopital's rule.


#MATS Session 8
Time：Dec. 20, 2019, 9:00--11:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Li, Yulong (Class of 2022)
Title：Continuous functions on R (Part II)
Abstract：We continue to discuss Chapter 9 of Tao's Analysis I. This includes the intermediate value theorem, monotonic functions, uniform continuity, and limits at infinity.


#MATS Session 7
Time：Dec. 13, 2019, 9:00--11:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Li, Yulong (Class of 2022)
Title：Continuous functions on R (Part I)
Abstract：We are to discuss Chapter 9 of Tao's Analysis I. This includes the intermediate value theorem, monotonic functions, uniform continuity, and limits at infinity.


***Fall Break***


#MATS Session 6 (Guest Talk)
Time：Oct. 29, 2019, 13:30--15:30
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Miss Li, Zishang (Class of 2021)
Title：From Riemann integral to Henstock integral
Abstract：Despite being the primary integration technique taught at undergraduate level, the theory of Riemann integral turns out to be not fully satisfactory. To overcome the drawbacks, in this talk we will define and investigate properties of the Henstock integral, which is a generalization of Riemann's in the sense that in the construction of the filter base with respect to Riemann sum, we change the restriction for parameter of the partition from being less than a constant to some gauge function. This talk has no prerequisite for Lebesgue measure theory.


#MATS Session 5
Time：Oct. 22, 2019, 15:00--17:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Yao, Jiahao (Class of 2021)
Title：Limit along a filter base
Abstract：Our interest stems from the definition of Riemann integral, which is well known to be defined as the limit, if it exits, of the Riemann sum. However this limit seems to be neither a standard sequence limit nor function limit. In this talk we will define and investigate the limit along a filter base, which was introduced in the 1930s by the famous group of (mainly) French mathematicians under the collective pseudonym Nicolas Bourbaki, and which offers a very useful type of convergence to help fully understand the limit of Riemann sum. Properties in parallel with those of the standard limit will also be discussed.


#MATS Session 4
Time：Oct. 15, 2019, 15:00--17:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Yang, Rui (Class of 2022)
Title：An incomplete list of completeness axioms of R (Part II)
Abstract：We first present the well-known Theorems of Cauchy-Cantor, Borel-Lebesgue, and Bolzano–Weierstrass, all of which are classical equivalent completeness axioms of the real numbers. Another several propositions regarding existence of suprema/infima, connectedness, as well as convergence of sequences will also serve as members of this very much incomplete list. We will show the proof and briefly bring the role of Archimedean Property to the audience's attention, which is less discussed in the curriculum of mathematics department.


#MATS Session 3
Time：Oct. 8, 2019, 13:30--15:30
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Xiong, Jing (Class of 2020)
Title：Everywhere continuous nowhere differentiable functions
Abstract：Most of the mathematical world had believed that a continuous function could only fail to be differentiable at some collection of isolated points, until Weierstrass published his shocking article in 1872. In this talk, we are mainly concerned with these pathological functions, i.e. everywhere continuous but nowhere differentiable ones. We will discuss three kinds of functions along with the proof of their nowhere differentiability, including the classical Weierstrass function and those presented by Takagi (1903) & van der Waerden (1930), and Swift (1961).


#MATS Session 2
Time：Sep. 17, 2019, 15:00--17:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Yang, Rui (Class of 2022)
Title：An incomplete list of completeness axioms of R
Abstract：We first present the well-known Theorems of Cauchy-Cantor, Borel-Lebesgue, and Bolzano–Weierstrass, all of which are classical equivalent completeness axioms of the real numbers. Another several propositions regarding existence of suprema/infima, connectedness, as well as convergence of sequences will also serve as members of this very much incomplete list. We will show the proof and briefly bring the role of Archimedean Property to the audience's attention, which is less discussed in the curriculum of mathematics department.


#MATS Session 1
Time：Sep. 3, 2019, 15:00--17:00
Location：447 Qi Xiang Building, Chang'an Campus
Speaker：Mr. Li, Yulong (Class of 2022)
Title：Rolle's Theorem and zeros of generalized polynomials
Abstract：We recollect the classical Rolle's Theorem first and derive Descartes' rule of signs with its generalizations. Bounds of number of zeros of Dirichlet polynomials will be obtained in terms of sign changes in the sequence of coefficients, as well as, in a finer degree, the sequence of their partial sums.




My field of interest consists of fractal geometry and dynamic systems.
You are very welcome to contact me by shuangshen@nwpu.edu.cn for research, teaching, or even just coffee.





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