Thirtyth Annotation

12/16/08

http://owpdb.mfo.de/detail?photo_id=10027

This is a primary source. This is a photo of Shiing Shen Chern and was provied by Bergman, George M, in Berkeley.

Twenty-nineth Annotation

12/16/08

http://owpdb.mfo.de/detail?photo_id=7484

This is a primary source and it is a phtotgraph, which was taken by Jacobs Konrad in Oberwolfach.

Twenty-eighth Annotation

12/16/08

http://www.onpedia.com/encyclopedia/Shiing-shen-Chern

This is a website, which had a detailed information about Chern's life.

He was born in Kashing, Chekiang Province in China (today known as Jiaxing in Zhejiang province). He moved to Tientsin (today known as Tianjin) in 1922 to be with his father, and from 1926 he was a student at Nankai University in that city, graduating in mathematics in 1930. He was a master student under Dan SUN at Tsing Hua University from 1931 to 1934, working on projective differential geometry. He died at Nankai University, Tianjin at the age of 93. The asteroid 29552 Chern is named after him.

Twenty-seventh Annotation

12/16/08

http://www.math.columbia.edu/~woit/wordpress/archives/000118.html

This is a secondary source, people responsed to the death of our greatest mathematician Chern.


Anonymous says:
December 6, 2004 at 2:19 pm
Sad news indeed. He seems to have been generous and an excellent mentor as well. Among his many outstanding students was the Fields Medallist Shing-Tung Yau of Calabi-Yau fame.


D R Lunsford says:
December 12, 2004 at 10:06 pm
I love the mathematical asides - otherwise I’d probably never know what was happening out there.
-drl

Twenty-sixth Annotation

12/16/08

http://www.aps-pub.com/proceedings/1511/151109.pdf

This is article contain one of Chern's picture, but it was wrote by Hung Hsi Wu, a professor of mathematical, but was created after Chern was died.

The whole article most described the efforts Chern had done on mathematical, and it is a really good article.

Twenty-fifth Annotation

12/16/08

http://www.encyclopedia.com/doc/1E1-stringth.html

An website given the definition for string theory. And this is a secondary source.
String theory description of elementary particles based on one-dimensional curves, or "strings," instead of point particles. The strings are embedded in a space-time having as many as 10 dimensions—the three ordinary dimensions plus time and seven compactified dimensions.

Twenty-fourth Annotation

12/16/08

http://www.encyclopedia.com/doc/1E1-ChernSS.html

This is a secondary source, which had informed me the works Chern had done on geometry field.
Studying the curvature of surfaces in spaces with more than three dimensions, he devised mathematical quantities that he called characteristic classes—now known as Chern classes—that differentiated different types of surfaces. The fields on which he had the greatest impact, global differential geometry and complex algebraic geometry, are fundamental to many areas of mathematics and theoretical physics, and his work at the foundation of gauge theory and string theory, among the most important developments of modern theoretical physics.

Twenty-third Annotation

12/16/08

http://www.answers.com/topic/generalized-gauss-bonnet-theorem

This website gives me an idea of what generalized-Gauss-Bonnet theorem is, and this is a secondary source. In mathematics, the generalized-Gauss-Bonnet theorem ('also called Chern-Gauss -Bonnet theorem) presents the Euler characteristic of a closed even-dimensional Riemannian manifold as an integral of a certain polynomial derived from its curvature. It is a direct generalization of the Gauss-Bonnet theorem to higher dimensions.

Twenty- second Annotation

12/16/08

http://www.answers.com/topic/chern-simons-form

This is a secondary source, which tell me te definition of Chern-simons form, which form was named after Shiing Shen Chern and James Harris Simons.

In mathematics, the Chern-Simons forms are certain secondary characteristic classes, They have been found to be of interest in gauge theory, and they (especially the 3-form) define the action of Chern-Simons theory.

twenty-first Annotation

12/16/08

http://www.answers.com/topic/shiing-shen-chern#Research

This is a secondary source, which informed the works that Chern had done so far.

Chern's work spreads over all the classic fields of differential geometry. It includes areas currently fashionable (the Chern-Simons theory arising from a 1974 paper written jointly with Jim Simons), perennial (the Chern-Weil theory linking curvature invariants to characteristic classes from 1944, after the Allendoerfer-Weil paper of 1943 on the Gauss-Bonnet theorem), the foundational (Chern classes), and some areas such as projective differential geometry and webs that have a lower profile. He published results in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds.

Twentyth Annotation

12/16/08

http://www.shawprize.org/en shawprize/2004/presentation/speeches/wuwenjum.html

This is a primary source, and a speech on Professor Shiing Shen Chern by Professor Wen-Tsun Wu.


" Chern's contribution to mathematic is both deep and broad. The Shaw Foundation is hornerd to award its first Prize in Mathematical Science to Professor Chern."

Nineteenth Annotation

12/16/08

http://www.shawprize.org/en/laureates/2004/mathematical/Chern/announcement.html

This is a primary source and a announcement on that Shiing Shen Chern had awarded the Shaw Prize for the mathematical science in 2004.

Eighteenth Annotation

12/16/08

http://www.shawprize.org/en/laureates/2004/mathematical/Chern/citation.html

This is a primary source, which brieftly describe his success in his life.

Shiing-Shen Chern was born in 1911 in China. He graduated from Nankai University in 1930 and the graduate school of Tsinghua University in 1934. He then furthered studies at the University of Hamburg. He has been professor at the Southwest Associated University, Kunming, China, the University of Chicago, and the University of California at Berkeley. He founded the mathematics research institute at Nankai and is the honorary director since 1992.

Seventeenth Annotation

12/16/08

http://www.shawprize.org/en/laureates/2004/mathematical/Chern/autobiography.html

This is a autobiography wrote by Shiing Shen Chern himself, and it's a primary source. This autobiography tell us how his life goes.

And have been honored by many national academies in the world, as members or foreign members. Among them are the following:


- Academia Sinica 1948
- National Academy of Sciences US 1961
- American Philosophical Society 1989
- Royal Society of London 1985
- Academie des Sciences Paris 1989
- Russian Academy of Sciences 2001
- Chinese Academy of Sciences 1994
- Academia Nazionale dei Lincei 1988
- Third World Academy of Sciences 1983
- Brazilian Academy of Sciences 1971

Sixtennth Annotation

12/16/08
http://www.shawprize.org/common/img/laureates/2004/mathematical/Chern/autography.jpg

This is a primary source, which is a phtotgraph of Professor Shiiing Shen Chern, Laureate of the Shaw Prize in Mathematical Science in 2004.

Primary and Secondary Source

Secondary Source

12/11/08

http://mathworld.wolfram.com/ChernClass.html

This is a secondary source, which give me the definition of what Chern Class is.

A gadget defined for complex vector bundles.The Chern classes of a complex manifold are the Chern classes of its tangent bundle. The th Chern class is an obstruction to the existence of everywhere complex linearly independent vector fields on that vector bundle.The th Chern class is in the th cohomology group of the base space.

12/11/08

http://en.wikipedia.org/wiki/Chern-Simons_form

This secondary source give me an idea of what Chern Simons Theory is, ,which are certain secondary characteristic classes. And is found to be of interest in gauge theory, and they (especially the 3-form) define the action of Chern-Simons theory.The theory is named for Shiing-Shen Chern and James Harris Simons, co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose.


12/11/08

http://math.berkeley.edu/index.php?module=announce&ANN_user_op=view&ANN_id=31

This is a secondary source, on this website people appraise Chern about how his contribution to the mathematical field.


"He's a towering figure in 20th-century mathematics," said Dr. Calvin C. Moore, a professor of mathematics at the University of California, Berkeley.

"He is somebody that had a broad outlook toward people," said Hartshorne. "It's not a warm department, and he was a warm person."


12/11/08

http://www-history.mcs.st-andrews.ac.uk/Biographies/Chern.html

This is a secondary source, I found a list of awards that had been given to Chern during his lifetime.

Honours awarded to S S Chern

Speaker at Intenational Congress 1950
AMS Colloquium Lecturer 1960
Sperker at Intenational Congress 1970
MAA Chauvenet Prize winner 1970
AMS Steele Prize 1983
Fellow of the Royal Society 1985
LMS Honorary Menber 1986
Shaw Prize 2004
Wolf Prize 1983/4

12/11/08

http://www.britannica.com/EBchecked/topic/109409/Shiing-shen-Chern


born October 26, 1911, Jiaxing, China

died December 3, 2004, Tianjin

Chinese American mathematician and educator whose researches in differential geometry developed ideas that now play a major role in mathematics and in mathematical physics.

This is a secondary source, this website informed me what Chern had successed for in his whole life, a biography of him.

11/18/08

Third In ternational Congress of Chinese Mathematicians


A Chinese Essay in Tribute to Professor Shiing-Shen Chern, found this page in a book called Third In ternational Congress of Chinese Mathematicians. This essay expressed how sad people were for the death of our one of the greatest person.

This is a seondary source, and this book help me to understand more mathematician in the past decade, who had contribute their whole life in the mathematical.

10/24/08

http://journals.cambridge.org/action/displayAbstract;jsessionid=869ADDF818FB552D066D1FF56B0E39B7.tomcat1?fromPage=online&aid=441323

This website informed me that Shiing Shen Chern was born on October 26th, 1911 in JiaXin, in china, and died in 2004. His father works for government. He first shows his mathematical ability by doing all the exercises in classical English textbooks on algebra and trigonometry when he was in his middle school, and he later became really interesting in the Sun's subject, projective differential geometry, he works hard. At Tsinghua, he met his wife Shih-Ning, the daughter of a professor.

This website help me to recongnized a brief summarize of Chern's life.


This is a secondary source, because this website was not created by Shiing Shen Chern's lifetime.

10/24/08

http://en.wikipedia.org/wiki/Introduction_to_quantum_mechanics

This website introduced the basic definition of Quantum Mechanics, it helps me to understanding the meaning of it, which is a physical science dealing with the behavior of matter and energy on the scale of atoms and subatomic particles or waves. And it spends a century of experimentation and applied science, to made quantum mechanical theory been proven to be very successful and practical.

This website is a secondary source, because it was created after Chern was died.





Primary Source

12/11/08

http://www.shawprize.org/en/laureates/2004/mathematical/Chern/essay.html


This is a primary source, which is a essay on Shing-Shen Chern, the first Shaw Prize is awarded to Professor Chern in recognition of his singular contributions to, and influence on, the mathematical life of our time.

11/25/08

http://www.nim.nankai.edu.cn/sschern/jiangxiang.htm

This is a primary source, this website had list many Chern's scholarship for those who were very good at math, and he had subscribed a part of his money to some school. In 2004, he gain $1000 thousand for his efforts on math, and contributed these money to some college which he had been work and study before.

11/25/08

http://www.nim.nankai.edu.cn

This is a primary source, this article give me an idea of how the role of Chern Siomos theory in solving the fractional quantum Hall effect mystery. The Chern -Siomos theroy unifies the fractional quantum Hall with the well understood integral quantum Hall effect, in the process leading to the prediction and the subsequent discovery of a new class of topological fermions in nature.


11/21/08

Chern-Simons Theory, Matrix Models, and Topological Strings


This is a primary source, this is a book about the above things in math, which detail the fomular for how to solve the Chern-Simons Theory, also other two theory, and how they work in math, but the formular is really hard for me to read, ,and understand what they were wrote about.


11/06/08

http://www.ams.org/notices/199807/chern.pdf


This website gives me an interviews with Shing Shen Chern when he was still alive, and there was a poem written by Chern. This interview told a completed and detailed story of Chern's life.

Following is the poem written by Chern:


Physics and geometry are one family.

Together and holding hands they roam to the limits of outer space.

Black hole and monopole exhaust the secret of myths;

Fiber and connections weave to interlace the roseate clouds.

Evolution equations describe solitons;

Dual curvatures defines instantons.

Surprisingly, Math, has earned its rightful place for man and in sky;

Fondling flowers with a smile -- just wish nothing is said.



This is a primary source, because it had inclued some pictures which was taken by him, and this is a interview.


10/28/08

http://www.nucleares.unam.mx/~alberto/physics/string.html

This article gives me an idea of what is String Theory. First what is the world made of, ordinary matter is made of atoms, and atom is made of three part, proton, neutron, and with the electron arranged around them. But neutrons and protons are made of even smaller particles, known as quarks. There are four fundamental forces in this universe: gravity, electromagnetism, and the weak and strong nuclear forces. Each of these is produced by fundamental particles that act as carriers of the force. The essential idea behind string theory is this: all of the different 'fundamental ' particles of the Standard Model are really just different manifestations of one basic object: a string.


This is a primary source, it provided me some important information of the my project, and this article let me easier understand the basic meaning of String Theory.

10/25/08

http://www.universityofcalifornia.edu/senate/inmemoriam/shiingshenchern.htm


This article gives a main detailed biography of Chern's life, he only had one day of elementary education, and four years at middle high school, at aged 15, he skippe two greades to enter the Nankai University, and how he opened his eyes to the grand vistas in geometry. And three major decisions in the period 1934 to 1943 that shaped the rest of his life.

This article references primary and secondary source, including the picture of Chern's and this article was created after Chern was passed away.

Fifteenth Annotation

12/11/08

http://mathworld.wolfram.com/ChernClass.html

This is a secondary source, which give me the definition of what Chern Class is.

A gadget defined for complex vector bundles.The Chern classes of a complex manifold are the Chern classes of its tangent bundle. The th Chern class is an obstruction to the existence of everywhere complex linearly independent vector fields on that vector bundle.The th Chern class is in the th cohomology group of the base space.

Fourteenth Annotation

12/11/08

http://en.wikipedia.org/wiki/Chern-Simons_form

This secondary source give me an idea of what Chern Simons Theory is, ,which are certain secondary characteristic classes. And is found to be of interest in gauge theory, and they (especially the 3-form) define the action of Chern-Simons theory.The theory is named for Shiing-Shen Chern and James Harris Simons, co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose.

Thirteenth Annotation

12/11/08

http://math.berkeley.edu/index.php?module=announce&ANN_user_op=view&ANN_id=31

This is a secondary source, on this website people appraise Chern about how his contribution to the mathematical field.


"He's a towering figure in 20th-century mathematics," said Dr. Calvin C. Moore, a professor of mathematics at the University of California, Berkeley.

"He is somebody that had a broad outlook toward people," said Hartshorne. "It's not a warm department, and he was a warm person."

Twelveth Annotation

12/11/08

http://www-history.mcs.st-andrews.ac.uk/Biographies/Chern.html

This is a secondary source, I found a list of awards that had been given to Chern during his lifetime.

Honours awarded to S S Chern

Speaker at Intenational Congress 1950
AMS Colloquium Lecturer 1960
Sperker at Intenational Congress 1970
MAA Chauvenet Prize winner 1970
AMS Steele Prize 1983
Fellow of the Royal Society 1985
LMS Honorary Menber 1986
Shaw Prize 2004
Wolf Prize 1983/4

Eleventh Annotation

12/11/08

http://www.shawprize.org/en/laureates/2004/mathematical/Chern/essay.html


This is a primary source, which is a essay on Shing-Shen Chern, the first Shaw Prize is awarded to Professor Chern in recognition of his singular contributions to, and influence on, the mathematical life of our time.

Tenth Annotation

12/11/08

http://www.britannica.com/EBchecked/topic/109409/Shiing-shen-Chern


born October 26, 1911, Jiaxing, China

died December 3, 2004, Tianjin

Chinese American mathematician and educator whose researches in differential geometry developed ideas that now play a major role in mathematics and in mathematical physics.

This is a secondary source, this website informed me what Chern had successed for in his whole life, a biography of him.