UBC Wiki - User contributions [en]

User:Ghs/QED

2012-03-28T22:20:18Z

Ghs: Created page with "<math>\mathcal{L}_{QED} = \bar\psi(i \not\!\! D -m)\psi - \frac{1}{4}(F_{\mu\nu})^2~</math> <math>\not\!\! D = \gamma^\mu D_\mu~</math> <math>\gamma^\mu D_\mu = \partial_\mu..."

<math>\mathcal{L}_{QED} = \bar\psi(i \not\!\! D -m)\psi - \frac{1}{4}(F_{\mu\nu})^2~</math>

<math>\not\!\! D = \gamma^\mu D_\mu~</math>

<math>\gamma^\mu D_\mu = \partial_\mu + ieA_\mu~</math>

<math>F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu~</math>

Euler-Lagrange equations:

<math>m\bar\psi + \bar\psi e\gamma^mu A_\mu + \partial_\mu\bar\psi i\gamma^\mu = 0~</math>

<math>(i\not\!\! D - m)\psi = 0~</math> :: ('''Dirac equation''')

<math>ej^\mu + \frac{1}{2}\partial_\nu F_{\mu\nu} = 0~</math> where <math>j^\mu=\bar\psi\gamma^\mu\psi~</math>

Bike Co-Op

2012-03-27T05:48:34Z

Ghs:

{{Infobox non-profit
| name = Bike Co-op
| image = [[File:Bikecoop-STICKERfull.png|200px|alt logo]]
| location = 6138 Student Union Boulevard Coast Salish Territories Vancouver BC, Canada V6T 1Z1
| coordinates = [http://g.co/maps/dxwd8 49.267752,-123.250415]
| num_members = ~ 150
| homepage = [http://bikecoop.ca/ http://bikecoop.ca/]
}}

The Bike Co-op is a student-run organization located on campus at UBC. Cycling empowers us, and our goal is to provide students and other campus members with an accessible environment where they can learn to fix bicycles, share resources, and build community. We engage in cycling advocacy and education to promote biking as a safe and sustainable means of transportation.

Organized as a student club under the AMS, the Bike Co-op is run by a Board of Directors and an executive elected by its members at an Annual General Meeting. The board is the heart of the Co-op, and develops and facilitates its programming and events. Members of the board of directors are charged with the direction of the Co-op and are entrusted to make decisions about how it is run. Important decisions are made by the entire board, which meets weekly. We employ a consensus based decision making model.

==History of The Club==

The AMS Bike Co-op was founded in the spring of 1998 by a group of very dedicated students. The venture was financially backed by the AMS Innovative Projects Fund, Trek, and other supporters. The original purpose of the co-op was to build a shared fleet of purple and yellow bicycles which could be used by students to reduce the number of car trips on campus. This initiative was hugely successful, and continues to be a foundation of the co-op’s programming. After the initial success of this program, the co-op continued to expand its operations, gained a core of dedicated volunteers and became a hub for cycling on campus.

==Programs==

All of our programs are open to everyone: This includes students, staff, faculty and on and off campus community members.
No student status needed – although student status will get you a discount sometimes.

* Bike Kitchen
* Volunteer Night
* Cycling Resource Centre

* Cycling Resource Centre
* BYOB Build Your Own Bike
* Mechanic Instruction/crash courses
* Women’s Night
* Bikes 101
* Cargo Bike Share Program
* Bike Co-op Resource Library
* Advocacy
* UTown Youth Bike Club
* Bike Lockers
* Market Cargo

==Members==

Memberships are $15 for students, and $20 for faculty, staff and community members.

Short on cash? No problem. Volunteer with us for six hours and your membership is '''free'''.

Membership comes with some great benefits, including:

* 2 hours of shop time
* access to BYOB (Build Your Own Bike)
* complementary shop time on Fridays

and (in addition to six volunteer hours)

* access to the Purple and Yellow community bike fleet!

[[Category:AMS]][[Category:Clubs]][[Category:Bike]]

Voltage and Spontaneity

2012-03-27T05:44:11Z

Ghs:

{{Projectbox ChemHelp}}
===Voltage and Spontaneity===
A redox reaction will occur spontaneously if its potential has a positive value. We also know from thermodynatmics that a reaction that occurs spontaneously has a negative value for free energy change. The relationship between reaction potential and free energy for a redox reaction is given by the equation below, which serves as a bridge between thermodynamics and electrochemistry.

===Voltage and equilibrium ===

The standard reaction potential is related to the equilibrium constant by the following expression

:<math>E = E~</math> (standard condition) <math> + \frac{R T}{n F}\ln(K)~</math>

===Galvanic Cells===
In a galvanic cell (also called a voltaic cell), a spontaneous redox reaction is used to generate a flow of current.

In galvanic cell, the two half reaction take place in separate chamber, and the electrons that are released by the oxidation reaction pass through a wire to the chamber where they are consumed in the reduction reaction. That's how the current is created. Current is defined as the flow of positive charge, so current is always in the opposite direction from the flow of electrons.

In any electric cell, oxidation takes place at hte electrode called the anode. Reduction takes place at the electrode called the cathode.

The salt bridge maintains electrical neutrality in the system by providing enough negative ions to equal the positive ions being created at hte anode and providing positive ions to replace the coppor ions being used up at the cathode. The slat bridge can be an actual slat or it can be a slim passage that allows ions to move between the two chambers.

=== Electrolytic cells ===
IN an electrolytic cells, an outside source of voltage is used to force a non-spontaneous redox reaction to take place. That is, E <0

[[Category:ChemHelp]]

Bike Co-Op

2012-03-27T05:31:31Z

Ghs: /* Members */

Bike Co-Op

2012-03-27T05:30:20Z

Ghs:

{{Infobox non-profit
| name = Bike Co-op
| image = [[File:Bikecoop-STICKERfull.png|200px|alt logo]]
| location = 6138 Student Union Boulevard Coast Salish Territories Vancouver BC, Canada V6T 1Z1
| coordinates = [http://g.co/maps/dxwd8 49.267752,-123.250415]
| num_members = ~ 150
| homepage = [http://bikecoop.ca/ http://bikecoop.ca/]
}}

The Bike Co-op is a student-run organization located on campus at UBC. Cycling empowers us, and our goal is to provide students and other campus members with an accessible environment where they can learn to fix bicycles, share resources, and build community. We engage in cycling advocacy and education to promote biking as a safe and sustainable means of transportation.

Organized as a student club under the AMS, the Bike Co-op is run by a Board of Directors and an executive elected by its members at an Annual General Meeting. The board is the heart of the Co-op, and develops and facilitates its programming and events. Members of the board of directors are charged with the direction of the Co-op and are entrusted to make decisions about how it is run. Important decisions are made by the entire board, which meets weekly. We employ a consensus based decision making model.

==History of The Club==

The AMS Bike Co-op was founded in the spring of 1998 by a group of very dedicated students. The venture was financially backed by the AMS Innovative Projects Fund, Trek, and other supporters. The original purpose of the co-op was to build a shared fleet of purple and yellow bicycles which could be used by students to reduce the number of car trips on campus. This initiative was hugely successful, and continues to be a foundation of the co-op’s programming. After the initial success of this program, the co-op continued to expand its operations, gained a core of dedicated volunteers and became a hub for cycling on campus.

==Programs==

All of our programs are open to everyone: This includes students, staff, faculty and on and off campus community members.
No student status needed – although student status will get you a discount sometimes.

* Bike Kitchen
* Volunteer Night
* Cycling Resource Centre

* Cycling Resource Centre
* BYOB Build Your Own Bike
* Mechanic Instruction/crash courses
* Women’s Night
* Bikes 101
* Cargo Bike Share Program
* Bike Co-op Resource Library
* Advocacy
* UTown Youth Bike Club
* Bike Lockers
* Market Cargo

==Members==

Memberships are $15 for students, and $20 for faculty, staff and community members.

Short on cash? No problem. Volunteer with us for six hours and your membership is '''free'''.

Membership comes with some great benefits, including 2 hours of shop time, access to BYOB (Build Your Own Bike), complementary shop time on Fridays, and (in addition to six volunteer hours), access to the Purple and Yellow community bike fleet!

Bike Co-Op

2012-03-27T05:29:02Z

Ghs:

{{Infobox non-profit
| name = Bike Co-op
| image = [[File:Bikecoop-STICKERfull.png|200px|alt logo]]
| location = 6138 Student Union Boulevard Coast Salish Territories Vancouver BC, Canada V6T 1Z1
| coordinates = [http://g.co/maps/dxwd8 49.267752,-123.250415]
| num_members = ~ 150
| homepage = [http://bikecoop.ca/ http://bikecoop.ca/]
}}

The Bike Co-op is a student-run organization located on campus at UBC. Cycling empowers us, and our goal is to provide students and other campus members with an accessible environment where they can learn to fix bicycles, share resources, and build community. We engage in cycling advocacy and education to promote biking as a safe and sustainable means of transportation.

Organized as a student club under the AMS, the Bike Co-op is run by a Board of Directors and an executive elected by its members at an Annual General Meeting. The board is the heart of the Co-op, and develops and facilitates its programming and events. Members of the board of directors are charged with the direction of the Co-op and are entrusted to make decisions about how it is run. Important decisions are made by the entire board, which meets weekly. We employ a consensus based decision making model.

==History of The Club==

The AMS Bike Co-op was founded in the spring of 1998 by a group of very dedicated students. The venture was financially backed by the AMS Innovative Projects Fund, Trek, and other supporters. The original purpose of the co-op was to build a shared fleet of purple and yellow bicycles which could be used by students to reduce the number of car trips on campus. This initiative was hugely successful, and continues to be a foundation of the co-op’s programming. After the initial success of this program, the co-op continued to expand its operations, gained a core of dedicated volunteers and became a hub for cycling on campus.

==Programs==

All of our programs are open to everyone: This includes students, staff, faculty and on and off campus community members.
No student status needed – although student status will get you a discount sometimes.

* Bike Kitchen
* Volunteer Night
* Cycling Resource Centre

* Cycling Resource Centre
* BYOB Build Your Own Bike
* Mechanic Instruction/crash courses
* Women’s Night
* Bikes 101
* Cargo Bike Share Program
* Bike Co-op Resource Library
* Advocacy
* UTown Youth Bike Club
* Bike Lockers
* Market Cargo

==Members==

Memberships are $15 for students, and $20 for faculty, staff and community members.
Short on cash? No problem. Volunteer with us for six hours and your membership is free.
Membership comes with some great benefits, including 2 hours of shop time, access to BYOB (Build Your Own Bike), complementary shop time on Fridays, and (in addition to six volunteer hours), access to the Purple and Yellow community bike fleet!

Bike Co-Op

2012-03-27T05:27:51Z

Ghs:

Bike Co-Op

2012-03-27T05:26:12Z

Ghs:

Bike Co-Op

2012-03-27T05:20:58Z

Ghs:

Bike Co-Op

2012-03-27T05:16:35Z

Ghs:

File:Bikecoop-STICKERfull.png

2012-03-27T05:12:59Z

Ghs: AMS bike coop sticker logo

== Summary ==
AMS bike coop sticker logo
== Copyright status: ==

== Source: ==
bikecoop website

Bike Co-Op

2012-03-27T05:09:12Z

Ghs:

{{Infobox non-profit
| name = Bike Co-op
| location = 6138 Student Union Boulevard Coast Salish Territories Vancouver BC, Canada V6T 1Z1
| coordinates = [http://g.co/maps/dxwd8 49.267752,-123.250415]
| num_members = ~ 150
| homepage = [http://bikecoop.ca/ http://bikecoop.ca/]
}}

The Bike Co-op is a student-run organization located on campus at UBC. Cycling empowers us, and our goal is to provide students and other campus members with an accessible environment where they can learn to fix bicycles, share resources, and build community. We engage in cycling advocacy and education to promote biking as a safe and sustainable means of transportation.

Bike Co-Op

2012-03-27T05:08:05Z

Ghs:

{{Infobox non-profit
| name = Bike Co-op
| location = 6138 Student Union Boulevard Coast Salish Territories Vancouver BC, Canada V6T 1Z1
| coordinates = [http://g.co/maps/dxwd8 49.267752,-123.250415]
| num_members = ~ 150
}}

The Bike Co-op is a student-run organization located on campus at UBC. Cycling empowers us, and our goal is to provide students and other campus members with an accessible environment where they can learn to fix bicycles, share resources, and build community. We engage in cycling advocacy and education to promote biking as a safe and sustainable means of transportation.

Bike Co-Op

2012-03-27T05:07:22Z

Ghs:

{{Infobox non-profit
| name = Bike Co-op
| location = 6138 Student Union Boulevard Coast Salish Territories Vancouver BC, Canada V6T 1Z1
| coordinates = [http://g.co/maps/dxwd8 49.267752,-123.250415]
| members = ~ 150
}}

The Bike Co-op is a student-run organization located on campus at UBC. Cycling empowers us, and our goal is to provide students and other campus members with an accessible environment where they can learn to fix bicycles, share resources, and build community. We engage in cycling advocacy and education to promote biking as a safe and sustainable means of transportation.

Bike Co-Op

2012-03-27T05:06:24Z

Ghs:

{{Infobox non-profit
| name = Bike Co-op
| location = 6138 Student Union Boulevard Coast Salish Territories Vancouver BC, Canada V6T 1Z1
| coordinates = [http://g.co/maps/dxwd8 49.267752,-123.250415]
}}

The Bike Co-op is a student-run organization located on campus at UBC. Cycling empowers us, and our goal is to provide students and other campus members with an accessible environment where they can learn to fix bicycles, share resources, and build community. We engage in cycling advocacy and education to promote biking as a safe and sustainable means of transportation.

Bike Co-Op

2012-03-27T05:04:05Z

Ghs:

{{Infobox non-profit
| name = Bike Co-op
| location = 6138 Student Union Boulevard Coast Salish Territories Vancouver BC, Canada V6T 1Z1
| coordinates = [http://g.co/maps/b8t37 49.267752,-123.250415]
}}

The Bike Co-op is a student-run organization located on campus at UBC. Cycling empowers us, and our goal is to provide students and other campus members with an accessible environment where they can learn to fix bicycles, share resources, and build community. We engage in cycling advocacy and education to promote biking as a safe and sustainable means of transportation.

Template:Coord

2012-03-27T05:01:27Z

Ghs: Created page with "<includeonly>{{Coord/display/{{{display|inline}}}|1={{Coord/input/{{#ifeq:{{{1|}}}||nolat|{{#ifeq:{{{4|}}}{{{5|}}}{{{6|}}}||dec|{{#if:{{#switch:{{{4}}}{{{8}}}|NE|NW|SE|SW=y}}|..."

<includeonly>{{Coord/display/{{{display|inline}}}|1={{Coord/input/{{#ifeq:{{{1|}}}||nolat|{{#ifeq:{{{4|}}}{{{5|}}}{{{6|}}}||dec|{{#if:{{#switch:{{{4}}}{{{8}}}|NE|NW|SE|SW=y}}|dms|{{#if:{{#switch:{{{3}}}{{{6}}}|NE|NW|SE|SW=y}}|dm|{{#if:{{#switch:{{{2}}}{{{4}}}|NE|NW|SE|SW=y}}|d|ERROR}}}}}}}}}}|1={{{1|}}}|2={{{2|}}}|3={{{3|}}}|4={{{4|}}}|5={{{5|}}}|6={{{6|}}}|7={{{7|}}}|8={{{8|}}}|9={{{9|}}}|10={{{10|}}}|format={{{format|}}}|name={{{name|}}}}}{{{notes|}}}}}{{#ifeq:{{{dim|μ}}}|μ||{{Coord/input/error2|msg=dim= should be dim:|sort_ch=D}}}}{{#ifeq:{{{globe|μ}}}|μ||{{Coord/input/error2|msg=globe= should be globe:|sort_ch=G}}}}{{#ifeq:{{{region|μ}}}|μ||{{Coord/input/error2|msg=region= should be region:|sort_ch=R}}}}{{#ifeq:{{{scale|μ}}}|μ||{{Coord/input/error2|msg=scale= should be scale:|sort_ch=S}}}}{{#ifeq:{{{source|μ}}}|μ||{{Coord/input/error2|msg=source= should be source:|sort_ch=s}}}}{{#ifeq:{{{type|μ}}}|μ||{{Coord/input/error2|msg=type= should be type:|sort_ch=T}}}}</includeonly><noinclude>{{Documentation}}</noinclude>

Template:Coor

2012-03-27T05:00:13Z

Bike Co-Op

2012-03-27T04:52:59Z

Ghs:

{{Infobox non-profit
| name = Bike Co-op
| location = 6138 Student Union Boulevard Coast Salish Territories Vancouver BC, Canada V6T 1Z1
}}

The Bike Co-op is a student-run organization located on campus at UBC. Cycling empowers us, and our goal is to provide students and other campus members with an accessible environment where they can learn to fix bicycles, share resources, and build community. We engage in cycling advocacy and education to promote biking as a safe and sustainable means of transportation.

Template:Infobox non-profit/doc

2012-03-27T04:49:09Z

Ghs: Created page with "For more information please visit [http://en.wikipedia.org/wiki/Template:Infobox_non-profit Template:Infobox_non-profit]"

For more information please visit [http://en.wikipedia.org/wiki/Template:Infobox_non-profit Template:Infobox_non-profit]

Template:Infobox non-profit

2012-03-27T04:46:25Z

Ghs: wikipedia's Infobox for non-profit

{{ infobox| bodyclass = vcard| titleclass = fn org| title = {{{name<includeonly>|{{{organization_name|{{{Non-profit_name|{{PAGENAME}}}}}}}}</includeonly>}}}| image = {{{image<includeonly>|{{{organization_logo|{{{Non-profit_logo|}}}}}}</includeonly>}}}| caption = {{{caption|}}}| label1 = Founder(s)| data1 = {{{founder<includeonly>|</includeonly>}}}| label2 = Type| data2 = {{{type<includeonly>|{{{organization_type|{{{Non-profit_type|}}}}}}</includeonly>}}}| class2 = category| label3 = Tax ID No.| data3 = {{{tax_id<includeonly>|</includeonly>}}}| label4 = Registration No.| data4 = {{{registration_id<includeonly>|</includeonly>}}}| label5 = Founded| data5 = {{{formation<includeonly>|{{{founded|{{{founded_date|}}}}}}</includeonly>}}}| class6 = label| label6 = Location| data6 = {{{location<includeonly>|</includeonly>}}}| label7 = Coordinates| data7 = {{{coordinates<includeonly>|</includeonly>}}}| label8 = Origins| data8 = {{{origins<includeonly>|</includeonly>}}}| label9 = Key people| data9 = {{{key_people<includeonly>|</includeonly>}}}| label10 = Area served| data10 = {{{area_served<includeonly>|</includeonly>}}}| label11 = [[Product (business)|Products]]| data11 = {{{products<includeonly>|</includeonly>}}}| label12 = Services| data12 = {{{services<includeonly>|</includeonly>}}}| label13 = Focus| data13 = {{{focus<includeonly>|</includeonly>}}}| class13 = category| label14 = Mission| data14 = {{{mission<includeonly>|</includeonly>}}}| label15 = Method| data15 = {{{fields<includeonly>|{{{method|}}}</includeonly>}}}| label16 = Revenue| data16 = {{{revenue<includeonly>|</includeonly>}}}| label17 = Endowment| data17 = {{{endowment<includeonly>|</includeonly>}}}| label18 = Volunteers| data18 = {{{num_volunteers<includeonly>|</includeonly>}}}| label19 = Employees| data19 = {{{num_employees<includeonly>|</includeonly>}}}| label20 = Members| data20 = {{{num_members<includeonly>|</includeonly>}}}| label21 = Subsidiaries| data21 = {{{subsid<includeonly>|</includeonly>}}}| label22 = Owner| data122 = {{{owner<includeonly>|</includeonly>}}}| class23 = note| label23 = Motto| data23 = {{{motto<includeonly>|{{{organization_motto|{{{Non-profit_slogan|{{{non-profit_slogan|}}}}}}}}}</includeonly>}}}| label24 = Formerly called| data24 = {{{former name<includeonly>|</includeonly>}}}| label25 = Website| data25 = {{{homepage<includeonly>|</includeonly>}}}| label26 = Dissolved| data26 = {{{extinction<includeonly>|{{{dissolved|}}}</includeonly>}}}| below = {{#if:{{{footnotes<includeonly>|</includeonly>}}}|'''References:''' {{{footnotes}}} }}}}<noinclude>{{documentation}}</noinclude>

Bike Co-Op

2012-03-27T04:35:49Z

Ghs: Created page with "The Bike Co-op is a student-run organization located on campus at UBC. Cycling empowers us, and our goal is to provide students and other campus members with an accessible env..."

The Bike Co-op is a student-run organization located on campus at UBC. Cycling empowers us, and our goal is to provide students and other campus members with an accessible environment where they can learn to fix bicycles, share resources, and build community. We engage in cycling advocacy and education to promote biking as a safe and sustainable means of transportation.

Course:RUSS 207

2012-01-05T23:31:37Z

Ghs:

{{Infobox_New_Course

|title=Twentieth-Century Russian Writers in Translation

|picture=Image:wiki.png

|subject code=RUSS

|course number=207

|section number=001

|instructor=Professor Peter Petro

|instructor 2=

|instructor 3=

|instructor 4=

|instructor 5=

|email=petro@interchange.ubc.ca,
petro@mail.ubc.ca

|office=Buchanan Tower 212

|office hours=TBA

|schedule=Mon Wed Fri 11:00 - 12:00

|classroom=Buchanan D218

}}


The course deals with major 20th century Russian writers, their works, lives, thought and impact in the West. While broader literary context is provided, particular attention is paid to [http://en.wikipedia.org/wiki/Yevgeny_Zamyatin Zamyatin], [http://en.wikipedia.org/wiki/Mikhail_Bulgakov Bulgakov], [http://en.wikipedia.org/wiki/Boris_Pasternak Pasternak], [http://en.wikipedia.org/wiki/Aleksandr_Solzhenitsyn Solzhenitsyn], [http://en.wikipedia.org/wiki/Vladimir_Nabokov Nabokov] and Tolstaya.

The course begins with a brief introduction to the ''historical, social, political and cultural'' background, as no prior knowledge of Soviet history or Russian literature is assumed. The introduction takes the form of an overview of the most important historical, social and cultural events between the rule of Lenin (1917-1922) and Gorbachev (1985-1991). The rest of the course is devoted to the presentation and discussion of selected works of the major writers. Lectures are supplemented with student class presentations and discussion. Students will write a short “diagnostic essay” at the beginning of the course, and the most interesting of the essays will be read in class, so as to establish the basic requirements of essay composition. Class participation is a major feature of the pedagogy of the course designed to make the work of the Russian writers relevant to students.

==Requirements==
Diagnostic essay ( 3 pages, not marked ), class presentations (voluntary), 2 term papers (6-8 pages), class participation.

Paper format: double spaced.

==Marking==

*Class participation: 20%
*1st term paper 40%
*2nd term paper 40%

==Required Books==

{| class="wikitable sortable"
|-
! Title !! Author !! ISBN
|-
| [http://www.worldcat.org/oclc/757420341 Doctor Zhivago] (Trans Pevear) || PASTERNAK || 9780307390950
|-
| [http://www.worldcat.org/oclc/124025270 Master & Margarita] (Trans Pevear) || BULGAKOV || 9780140455465
|-
| [http://www.worldcat.org/oclc/14865720 One Day in The Life of Ivan Denisovich] || SOLZHENITSYN || 9780553247770
|-
| [http://www.worldcat.org/oclc/28947953 Portable Twentieth Century Russian Reader] || BROWN || 9780142437575
|-
| [http://www.worldcat.org/oclc/69423318 We] (Trans Randall) || ZAMYATIN || 9780812974621
|}

Course:RUSS 207

2012-01-05T23:31:11Z

Ghs: /* Requirements */

Course:RUSS 207

2012-01-05T22:42:50Z

Ghs: /* Required Books */

{{Infobox_New_Course

|title=Twentieth-Century Russian Writers in Translation

|picture=Image:wiki.png

|subject code=RUSS

|course number=207

|section number=001

|instructor=Professor Peter Petro

|instructor 2=

|instructor 3=

|instructor 4=

|instructor 5=

|email=petro@interchange.ubc.ca,
petro@mail.ubc.ca

|office=Buchanan Tower 212

|office hours=TBA

|schedule=Mon Wed Fri 11:00 - 12:00

|classroom=Buchanan D218

}}


The course deals with major 20th century Russian writers, their works, lives, thought and impact in the West. While broader literary context is provided, particular attention is paid to [http://en.wikipedia.org/wiki/Yevgeny_Zamyatin Zamyatin], [http://en.wikipedia.org/wiki/Mikhail_Bulgakov Bulgakov], [http://en.wikipedia.org/wiki/Boris_Pasternak Pasternak], [http://en.wikipedia.org/wiki/Aleksandr_Solzhenitsyn Solzhenitsyn], [http://en.wikipedia.org/wiki/Vladimir_Nabokov Nabokov] and Tolstaya.

The course begins with a brief introduction to the ''historical, social, political and cultural'' background, as no prior knowledge of Soviet history or Russian literature is assumed. The introduction takes the form of an overview of the most important historical, social and cultural events between the rule of Lenin (1917-1922) and Gorbachev (1985-1991). The rest of the course is devoted to the presentation and discussion of selected works of the major writers. Lectures are supplemented with student class presentations and discussion. Students will write a short “diagnostic essay” at the beginning of the course, and the most interesting of the essays will be read in class, so as to establish the basic requirements of essay composition. Class participation is a major feature of the pedagogy of the course designed to make the work of the Russian writers relevant to students.

==Requirements==
Diagnostic essay ( 3 pages, not marked ), class presentations (voluntary), 2 term papers (6-8 pages), class participation.

==Marking==

*Class participation: 20%
*1st term paper 40%
*2nd term paper 40%

==Required Books==

{| class="wikitable sortable"
|-
! Title !! Author !! ISBN
|-
| [http://www.worldcat.org/oclc/757420341 Doctor Zhivago] (Trans Pevear) || PASTERNAK || 9780307390950
|-
| [http://www.worldcat.org/oclc/124025270 Master & Margarita] (Trans Pevear) || BULGAKOV || 9780140455465
|-
| [http://www.worldcat.org/oclc/14865720 One Day in The Life of Ivan Denisovich] || SOLZHENITSYN || 9780553247770
|-
| [http://www.worldcat.org/oclc/28947953 Portable Twentieth Century Russian Reader] || BROWN || 9780142437575
|-
| [http://www.worldcat.org/oclc/69423318 We] (Trans Randall) || ZAMYATIN || 9780812974621
|}

Course:RUSS 207

2012-01-05T22:39:08Z

Ghs: /* Required Books */

{{Infobox_New_Course

|title=Twentieth-Century Russian Writers in Translation

|picture=Image:wiki.png

|subject code=RUSS

|course number=207

|section number=001

|instructor=Professor Peter Petro

|instructor 2=

|instructor 3=

|instructor 4=

|instructor 5=

|email=petro@interchange.ubc.ca,
petro@mail.ubc.ca

|office=Buchanan Tower 212

|office hours=TBA

|schedule=Mon Wed Fri 11:00 - 12:00

|classroom=Buchanan D218

}}


The course deals with major 20th century Russian writers, their works, lives, thought and impact in the West. While broader literary context is provided, particular attention is paid to [http://en.wikipedia.org/wiki/Yevgeny_Zamyatin Zamyatin], [http://en.wikipedia.org/wiki/Mikhail_Bulgakov Bulgakov], [http://en.wikipedia.org/wiki/Boris_Pasternak Pasternak], [http://en.wikipedia.org/wiki/Aleksandr_Solzhenitsyn Solzhenitsyn], [http://en.wikipedia.org/wiki/Vladimir_Nabokov Nabokov] and Tolstaya.

The course begins with a brief introduction to the ''historical, social, political and cultural'' background, as no prior knowledge of Soviet history or Russian literature is assumed. The introduction takes the form of an overview of the most important historical, social and cultural events between the rule of Lenin (1917-1922) and Gorbachev (1985-1991). The rest of the course is devoted to the presentation and discussion of selected works of the major writers. Lectures are supplemented with student class presentations and discussion. Students will write a short “diagnostic essay” at the beginning of the course, and the most interesting of the essays will be read in class, so as to establish the basic requirements of essay composition. Class participation is a major feature of the pedagogy of the course designed to make the work of the Russian writers relevant to students.

==Requirements==
Diagnostic essay ( 3 pages, not marked ), class presentations (voluntary), 2 term papers (6-8 pages), class participation.

==Marking==

*Class participation: 20%
*1st term paper 40%
*2nd term paper 40%

==Required Books==

{| class="wikitable sortable"
|-
! Title !! Author !! ISBN
|-
| Doctor Zhivago (Trans Pevear) || PASTERNAK || 9780307390950
|-
| Master & Margarita (Trans Pevear) || BULGAKOV || 9780140455465
|-
| One Day in The Life of Ivan Denisovich || SOLZHENITSYN || 9780553247770
|-
| Portable Twentieth Century Russian Reader || BROWN || 9780142437575
|-
| We (Trans Randall) || ZAMYATIN || 9780812974621
|}

Course:RUSS 207

2012-01-05T22:34:11Z

Ghs:

{{Infobox_New_Course

|title=Twentieth-Century Russian Writers in Translation

|picture=Image:wiki.png

|subject code=RUSS

|course number=207

|section number=001

|instructor=Professor Peter Petro

|instructor 2=

|instructor 3=

|instructor 4=

|instructor 5=

|email=petro@interchange.ubc.ca,
petro@mail.ubc.ca

|office=Buchanan Tower 212

|office hours=TBA

|schedule=Mon Wed Fri 11:00 - 12:00

|classroom=Buchanan D218

}}


The course deals with major 20th century Russian writers, their works, lives, thought and impact in the West. While broader literary context is provided, particular attention is paid to [http://en.wikipedia.org/wiki/Yevgeny_Zamyatin Zamyatin], [http://en.wikipedia.org/wiki/Mikhail_Bulgakov Bulgakov], [http://en.wikipedia.org/wiki/Boris_Pasternak Pasternak], [http://en.wikipedia.org/wiki/Aleksandr_Solzhenitsyn Solzhenitsyn], [http://en.wikipedia.org/wiki/Vladimir_Nabokov Nabokov] and Tolstaya.

The course begins with a brief introduction to the ''historical, social, political and cultural'' background, as no prior knowledge of Soviet history or Russian literature is assumed. The introduction takes the form of an overview of the most important historical, social and cultural events between the rule of Lenin (1917-1922) and Gorbachev (1985-1991). The rest of the course is devoted to the presentation and discussion of selected works of the major writers. Lectures are supplemented with student class presentations and discussion. Students will write a short “diagnostic essay” at the beginning of the course, and the most interesting of the essays will be read in class, so as to establish the basic requirements of essay composition. Class participation is a major feature of the pedagogy of the course designed to make the work of the Russian writers relevant to students.

==Requirements==
Diagnostic essay ( 3 pages, not marked ), class presentations (voluntary), 2 term papers (6-8 pages), class participation.

==Marking==

*Class participation: 20%
*1st term paper 40%
*2nd term paper 40%

==Required Books==

Course:RUSS 207

2012-01-05T22:33:13Z

Ghs: Created page with "<!--Begin Infobox; Please add your parameters after the equal signs below. If you do not wish to use the infobox, you may remove it by deleting everything between the Begin a..."

{{Infobox_New_Course

|title=Twentieth-Century Russian Writers in Translation

|picture=Image:wiki.png

|subject code=RUSS

|course number=207

|section number=001

|instructor=Professor Peter Petro

|instructor 2=

|instructor 3=

|instructor 4=

|instructor 5=

|email=petro@interchange.ubc.ca,
petro@mail.ubc.ca

|office=Buchanan Tower 212

|office hours=TBA

|schedule=Mon Wed Fri 11:00 - 12:00

|classroom=Buchanan D218

}}


==Course Description==

The course deals with major 20th century Russian writers, their works, lives, thought and impact in the West. While broader literary context is provided, particular attention is paid to [http://en.wikipedia.org/wiki/Yevgeny_Zamyatin Zamyatin], [http://en.wikipedia.org/wiki/Mikhail_Bulgakov Bulgakov], [http://en.wikipedia.org/wiki/Boris_Pasternak Pasternak], [http://en.wikipedia.org/wiki/Aleksandr_Solzhenitsyn Solzhenitsyn], [http://en.wikipedia.org/wiki/Vladimir_Nabokov Nabokov] and Tolstaya.

The course begins with a brief introduction to the ''historical, social, political and cultural'' background, as no prior knowledge of Soviet history or Russian literature is assumed. The introduction takes the form of an overview of the most important historical, social and cultural events between the rule of Lenin (1917-1922) and Gorbachev (1985-1991). The rest of the course is devoted to the presentation and discussion of selected works of the major writers. Lectures are supplemented with student class presentations and discussion. Students will write a short “diagnostic essay” at the beginning of the course, and the most interesting of the essays will be read in class, so as to establish the basic requirements of essay composition. Class participation is a major feature of the pedagogy of the course designed to make the work of the Russian writers relevant to students.

==Requirements==
Diagnostic essay ( 3 pages, not marked ), class presentations (voluntary), 2 term papers (6-8 pages), class participation.
==Marking==

*Class participation: 20%
*1st term paper 40%
==Required Books==

*2nd term paper 40%.

Course:MATH600D

2011-11-22T07:42:31Z

Ghs: /* Announcements */

{{Course2

|title= Topics in Algebraic K-theory
|picture=File:K-theory-logo.svg‎
|subject code=MATH
|course number=600D
|section number=101
|instructor=Professor Sujatha Ramdorai
|email= sujatha at ...
|webpage=http://www.math.ubc.ca/~sujatha/
|office= Math Annex 1201
|office hours= Wednesday 11:00-13:00 or by appointment
|schedule= Tuesday/Thursday 11:00-12:30
|classroom= Math Annex 1102

}}

[http://en.wikipedia.org/wiki/Algebraic_K-theory Algebraic K-Theory] originated in the 1960's and has today grown into a vast, active
branch of mathematics. It has made inroads into other areas of mathematics like Algebraic
topology, Algebraic geometry and Algebraic Number Theory . After a brief introduction
to the K-groups, we shall largely focus on the groups <math>K_0~</math>, <math>K_1~</math> and <math>K_2~</math>. The preliminaries
will constitute a third of the course. We will provide various snapshots of the linkages of
K-theory to some of the areas mentioned above. We shall then study the groups <math>K_i(F)~</math> for
a field <math>F~</math> of characteristic not 2, and its connections with the algebraic theory of quadratic
forms over the field <math>F~</math>, and to the Galois cohomology groups <math>H_{\acute{e}t}^i(F, \mathbb{Z}/2\mathbb{Z})~</math>, leading to the
statement of the [http://en.wikipedia.org/wiki/Milnor_conjecture Milnor conjectures], now a theorem due to Voevodsky.
There will be no final exam for this course. I will try to make the course as self-contained
as possible, pointing to further readings as the course progresses. There will be periodic
assignments which will serve as a basis for assigning a final grade.

== Homeworks ==
* [[:File:Math600D-ass1.pdf|Homework 1]] ( Due date: Sep 27, 2011 )[[Thread:Course talk:Math 600D/Homework 1 corrections|corrections]]
* [[:File:Math600d-hw2.pdf|Homework 2]] ( Due date: Oct 11, 2011 )[[Thread:Course talk:Math 600D/Homework 2 corrections|corrections]]
* [[:File:Math600d-hw3.pdf|Homework 3]] ( Due Date: Oct 25, 2011 )
* [[:File:Ass4.pdf|Homework 4]] ( Due Date: Nov 15, 2011 )
*[[:File:Ass5.pdf|Homework 5]] (Due Date: Nov 29, 2011)

== References ==
* Atiyah, Michael F, and D W. Anderson. K-theory. New York: W.A. Benjamin, 1967.
* Bass, Hyman. 1968. Algebraic K-theory. New York: W.A. Benjamin.
* Bass, Hyman, and Amit Roy. 1967. Lectures on topics in algebraic k-theory. Bombay: Tata Institute of Fundamental Research.
* Milnor, John W. Introduction to Algebraic K-Theory. Princeton, N.J: Princeton University Press, 1971.
* Rosenberg, J. Algebraic K-Theory and Its Applications. New York: Springer-Verlag, 1994.
* Srinivas, V. Algebraic K-Theory. Boston: Birkhäuser, 2008
* Weibel, Charles. [http://www.math.rutgers.edu/~weibel/Kbook.html The K-book: An introduction to algebraic K-theory] (a graduate textbook in progress)..
* [[:File:Steiberg.pdf|Notes on Steinberg relations]]
*[[:File:galcoho.pdf|Notes on Profinite Galois cohomology]]

== External links ==
* [http://www.math.uiuc.edu/K-theory/ K-theory Preprint Archives]
* [http://www.math.ubc.ca/~marioga/math_600D.html Mario Garcia Armas's Math 600D webpage]
*[http://ebooks.cambridge.org/chapter.jsf?bid=CBO9780511661907&cid=CBO9780511661907A021/ Brauer groups]
[[Category:Mathematics]][[Category:Algebra]]

== Announcements ==

Jerome will lecture on Nov 8 and Shane on Nov 22. There will be no lectures on Nov 10 and Nov 17. There *will* be lecture by me on Nov 15.

===SUGGESTED ADDITIONAL READING===

Bass, H.; Tate, J.
The Milnor ring of a global field. Algebraic K-theory, II: "Classical'' algebraic K-theory and connections with arithmetic (Proc. Conf., Seattle, Wash., Battelle Memorial Inst., 1972), pp. 349–446. Lecture Notes in Math., Vol. 342, Springer, Berlin, 1973.

Milnor, John
Algebraic K-theory and quadratic forms.
Invent. Math. 9 1969/1970 318–344.

Course:MATH600D

2011-11-05T18:22:19Z

Ghs: /* Homeworks */

{{Course2

|title= Topics in Algebraic K-theory
|picture=File:K-theory-logo.svg‎
|subject code=MATH
|course number=600D
|section number=101
|instructor=Professor Sujatha Ramdorai
|email= sujatha at ...
|webpage=http://www.math.ubc.ca/~sujatha/
|office= Math Annex 1201
|office hours= Wednesday 11:00-13:00 or by appointment
|schedule= Tuesday/Thursday 11:00-12:30
|classroom= Math Annex 1102

}}

[http://en.wikipedia.org/wiki/Algebraic_K-theory Algebraic K-Theory] originated in the 1960's and has today grown into a vast, active
branch of mathematics. It has made inroads into other areas of mathematics like Algebraic
topology, Algebraic geometry and Algebraic Number Theory . After a brief introduction
to the K-groups, we shall largely focus on the groups <math>K_0~</math>, <math>K_1~</math> and <math>K_2~</math>. The preliminaries
will constitute a third of the course. We will provide various snapshots of the linkages of
K-theory to some of the areas mentioned above. We shall then study the groups <math>K_i(F)~</math> for
a field <math>F~</math> of characteristic not 2, and its connections with the algebraic theory of quadratic
forms over the field <math>F~</math>, and to the Galois cohomology groups <math>H_{\acute{e}t}^i(F, \mathbb{Z}/2\mathbb{Z})~</math>, leading to the
statement of the [http://en.wikipedia.org/wiki/Milnor_conjecture Milnor conjectures], now a theorem due to Voevodsky.
There will be no final exam for this course. I will try to make the course as self-contained
as possible, pointing to further readings as the course progresses. There will be periodic
assignments which will serve as a basis for assigning a final grade.

== Homeworks ==
* [[:File:Math600D-ass1.pdf|Homework 1]] ( Due date: Sep 27, 2011 )[[Thread:Course talk:Math 600D/Homework 1 corrections|corrections]]
* [[:File:Math600d-hw2.pdf|Homework 2]] ( Due date: Oct 11, 2011 )[[Thread:Course talk:Math 600D/Homework 2 corrections|corrections]]
* [[:File:Math600d-hw3.pdf|Homework 3]] ( Due Date: Oct 25, 2011 )
* [[:File:Ass4.pdf|Homework 4]] ( Due Date: Nov 15, 2011 )

== References ==
* Atiyah, Michael F, and D W. Anderson. K-theory. New York: W.A. Benjamin, 1967.
* Bass, Hyman. 1968. Algebraic K-theory. New York: W.A. Benjamin.
* Bass, Hyman, and Amit Roy. 1967. Lectures on topics in algebraic k-theory. Bombay: Tata Institute of Fundamental Research.
* Milnor, John W. Introduction to Algebraic K-Theory. Princeton, N.J: Princeton University Press, 1971.
* Rosenberg, J. Algebraic K-Theory and Its Applications. New York: Springer-Verlag, 1994.
* Srinivas, V. Algebraic K-Theory. Boston: Birkhäuser, 2008
* Weibel, Charles. [http://www.math.rutgers.edu/~weibel/Kbook.html The K-book: An introduction to algebraic K-theory] (a graduate textbook in progress)..
* [[:File:Steiberg.pdf|Notes on Steinberg relations]]
*[[:File:galcoho.pdf|Notes on Profinite Galois cohomology]]

== External links ==
* [http://www.math.uiuc.edu/K-theory/ K-theory Preprint Archives]
* [http://www.math.ubc.ca/~marioga/math_600D.html Mario Garcia Armas's Math 600D webpage]
*[http://ebooks.cambridge.org/chapter.jsf?bid=CBO9780511661907&cid=CBO9780511661907A021/ Brauer groups]
[[Category:Mathematics]][[Category:Algebra]]

Course:MATH600D

2011-11-05T18:21:07Z

Ghs: /* Homeworks */

{{Course2

|title= Topics in Algebraic K-theory
|picture=File:K-theory-logo.svg‎
|subject code=MATH
|course number=600D
|section number=101
|instructor=Professor Sujatha Ramdorai
|email= sujatha at ...
|webpage=http://www.math.ubc.ca/~sujatha/
|office= Math Annex 1201
|office hours= Wednesday 11:00-13:00 or by appointment
|schedule= Tuesday/Thursday 11:00-12:30
|classroom= Math Annex 1102

}}

[http://en.wikipedia.org/wiki/Algebraic_K-theory Algebraic K-Theory] originated in the 1960's and has today grown into a vast, active
branch of mathematics. It has made inroads into other areas of mathematics like Algebraic
topology, Algebraic geometry and Algebraic Number Theory . After a brief introduction
to the K-groups, we shall largely focus on the groups <math>K_0~</math>, <math>K_1~</math> and <math>K_2~</math>. The preliminaries
will constitute a third of the course. We will provide various snapshots of the linkages of
K-theory to some of the areas mentioned above. We shall then study the groups <math>K_i(F)~</math> for
a field <math>F~</math> of characteristic not 2, and its connections with the algebraic theory of quadratic
forms over the field <math>F~</math>, and to the Galois cohomology groups <math>H_{\acute{e}t}^i(F, \mathbb{Z}/2\mathbb{Z})~</math>, leading to the
statement of the [http://en.wikipedia.org/wiki/Milnor_conjecture Milnor conjectures], now a theorem due to Voevodsky.
There will be no final exam for this course. I will try to make the course as self-contained
as possible, pointing to further readings as the course progresses. There will be periodic
assignments which will serve as a basis for assigning a final grade.

== Homeworks ==
* [[:File:Math600D-ass1.pdf|Homework 1]] ( Due date: Sep 27, 2011 )[[Thread:Course talk:Math 600D/Homework 1 corrections|corrections]]
* [[:File:Math600d-hw2.pdf|Homework 2]] ( Due date: Oct 11, 2011 )[[Thread:Course talk:Math 600D/Homework 2 corrections|corrections]]
* [[:File:Math600d-hw3.pdf|Homework 3]] ( Due Date: Oct 25, 2011 )
* [[:File:Assignment5.pdf|Homework 4]] ( Due Date: Nov 15, 2011 )

== References ==
* Atiyah, Michael F, and D W. Anderson. K-theory. New York: W.A. Benjamin, 1967.
* Bass, Hyman. 1968. Algebraic K-theory. New York: W.A. Benjamin.
* Bass, Hyman, and Amit Roy. 1967. Lectures on topics in algebraic k-theory. Bombay: Tata Institute of Fundamental Research.
* Milnor, John W. Introduction to Algebraic K-Theory. Princeton, N.J: Princeton University Press, 1971.
* Rosenberg, J. Algebraic K-Theory and Its Applications. New York: Springer-Verlag, 1994.
* Srinivas, V. Algebraic K-Theory. Boston: Birkhäuser, 2008
* Weibel, Charles. [http://www.math.rutgers.edu/~weibel/Kbook.html The K-book: An introduction to algebraic K-theory] (a graduate textbook in progress)..
* [[:File:Steiberg.pdf|Notes on Steinberg relations]]
*[[:File:galcoho.pdf|Notes on Profinite Galois cohomology]]

== External links ==
* [http://www.math.uiuc.edu/K-theory/ K-theory Preprint Archives]
* [http://www.math.ubc.ca/~marioga/math_600D.html Mario Garcia Armas's Math 600D webpage]
*[http://ebooks.cambridge.org/chapter.jsf?bid=CBO9780511661907&cid=CBO9780511661907A021/ Brauer groups]
[[Category:Mathematics]][[Category:Algebra]]

Course:MATH600D

2011-10-23T19:18:20Z

Ghs:

{{Course2

|title= Topics in Algebraic K-theory
|picture=File:K-theory-logo.svg‎
|subject code=MATH
|course number=600D
|section number=101
|instructor=Professor Sujatha Ramdorai
|email= sujatha at ...
|webpage=http://www.math.ubc.ca/~sujatha/
|office= Math Annex 1201
|office hours= Wednesday 11:00-13:00 or by appointment
|schedule= Tuesday/Thursday 11:00-12:30
|classroom= Math Annex 1102

}}

[http://en.wikipedia.org/wiki/Algebraic_K-theory Algebraic K-Theory] originated in the 1960's and has today grown into a vast, active
branch of mathematics. It has made inroads into other areas of mathematics like Algebraic
topology, Algebraic geometry and Algebraic Number Theory . After a brief introduction
to the K-groups, we shall largely focus on the groups <math>K_0~</math>, <math>K_1~</math> and <math>K_2~</math>. The preliminaries
will constitute a third of the course. We will provide various snapshots of the linkages of
K-theory to some of the areas mentioned above. We shall then study the groups <math>K_i(F)~</math> for
a field <math>F~</math> of characteristic not 2, and its connections with the algebraic theory of quadratic
forms over the field <math>F~</math>, and to the Galois cohomology groups <math>H_{\acute{e}t}^i(F, \mathbb{Z}/2\mathbb{Z})~</math>, leading to the
statement of the [http://en.wikipedia.org/wiki/Milnor_conjecture Milnor conjectures], now a theorem due to Voevodsky.
There will be no final exam for this course. I will try to make the course as self-contained
as possible, pointing to further readings as the course progresses. There will be periodic
assignments which will serve as a basis for assigning a final grade.

== Homeworks ==
* [[:File:Math600D-ass1.pdf|Homework 1]] ( Due date: Sep 27, 2011 )[[Thread:Course talk:Math 600D/Homework 1 corrections|corrections]]
* [[:File:Math600d-hw2.pdf|Homework 2]] ( Due date: Oct 11, 2011 )[[Thread:Course talk:Math 600D/Homework 2 corrections|corrections]]
* [[:File:Math600d-hw3.pdf|Homework 3]] ( Due Date: Oct 25, 2011 )

== References ==
* Atiyah, Michael F, and D W. Anderson. K-theory. New York: W.A. Benjamin, 1967.
* Bass, Hyman. 1968. Algebraic K-theory. New York: W.A. Benjamin.
* Bass, Hyman, and Amit Roy. 1967. Lectures on topics in algebraic k-theory. Bombay: Tata Institute of Fundamental Research.
* Milnor, John W. Introduction to Algebraic K-Theory. Princeton, N.J: Princeton University Press, 1971.
* Rosenberg, J. Algebraic K-Theory and Its Applications. New York: Springer-Verlag, 1994.
* Srinivas, V. Algebraic K-Theory. Boston: Birkhäuser, 2008
* Weibel, Charles. [http://www.math.rutgers.edu/~weibel/Kbook.html The K-book: An introduction to algebraic K-theory] (a graduate textbook in progress)..

== External links ==
* [http://www.math.uiuc.edu/K-theory/ K-theory Preprint Archives]
* [http://www.math.ubc.ca/~marioga/math_600D.html Mario Garcia Armas's Math 600D webpage]

[[Category:Mathematics]][[Category:Algebra]]

Course:MATH600D

2011-10-16T23:37:17Z

Ghs: /* References */

{{Course2

|title= Topics in Algebraic K-theory
|picture=File:K-theory-logo.svg‎
|subject code=MATH
|course number=600D
|section number=101
|instructor=Professor Sujatha Ramdorai
|email= sujatha at ...
|webpage=http://www.math.ubc.ca/~sujatha/
|office= Math Annex 1201
|office hours= Wednesday 11:00-13:00 or by appointment
|schedule= Tuesday/Thursday 11:00-12:30
|classroom= Math Annex 1102

}}

[http://en.wikipedia.org/wiki/Algebraic_K-theory Algebraic K-Theory] originated in the 1960's and has today grown into a vast, active
branch of mathematics. It has made inroads into other areas of mathematics like Algebraic
topology, Algebraic geometry and Algebraic Number Theory . After a brief introduction
to the K-groups, we shall largely focus on the groups <math>K_0~</math>, <math>K_1~</math> and <math>K_2~</math>. The preliminaries
will constitute a third of the course. We will provide various snapshots of the linkages of
K-theory to some of the areas mentioned above. We shall then study the groups <math>K_i(F)~</math> for
a field <math>F~</math> of characteristic not 2, and its connections with the algebraic theory of quadratic
forms over the field <math>F~</math>, and to the Galois cohomology groups <math>H_{\acute{e}t}^i(F, \mathbb{Z}/2\mathbb{Z})~</math>, leading to the
statement of the [http://en.wikipedia.org/wiki/Milnor_conjecture Milnor conjectures], now a theorem due to Voevodsky.
There will be no final exam for this course. I will try to make the course as self-contained
as possible, pointing to further readings as the course progresses. There will be periodic
assignments which will serve as a basis for assigning a final grade.

== Homeworks ==
* [[:File:Math600D-ass1.pdf|Homework 1]] ( Due date: Sep 27, 2011 )[[Thread:Course talk:Math 600D/Homework 1 corrections|corrections]]
* [[:File:Math600d-hw2.pdf|Homework 2]] ( Due date: Oct 11, 2011 )[[Thread:Course talk:Math 600D/Homework 2 corrections|corrections]]
* [[:File:Math600d-hw3.pdf|Homework 3]] ( Due Date: Oct 25, 2011 )

== References ==
* Atiyah, Michael F, and D W. Anderson. K-theory. New York: W.A. Benjamin, 1967.
* Bass, Hyman. 1968. Algebraic K-theory. New York: W.A. Benjamin.
* Bass, Hyman, and Amit Roy. 1967. Lectures on topics in algebraic k-theory. Bombay: Tata Institute of Fundamental Research.
* Milnor, John W. Introduction to Algebraic K-Theory. Princeton, N.J: Princeton University Press, 1971.
* Rosenberg, J. Algebraic K-Theory and Its Applications. New York: Springer-Verlag, 1994.
* Srinivas, V. Algebraic K-Theory. Boston: Birkhäuser, 2008
* Weibel, Charles. [http://www.math.rutgers.edu/~weibel/Kbook.html The K-book: An introduction to algebraic K-theory] (a graduate textbook in progress)..
* [http://www.math.uiuc.edu/K-theory/ K-theory Preprint Archives]

[[Category:Mathematics]][[Category:Algebra]]

Course:MATH600D

2011-10-16T23:36:16Z

Ghs: /* References */

{{Course2

|title= Topics in Algebraic K-theory
|picture=File:K-theory-logo.svg‎
|subject code=MATH
|course number=600D
|section number=101
|instructor=Professor Sujatha Ramdorai
|email= sujatha at ...
|webpage=http://www.math.ubc.ca/~sujatha/
|office= Math Annex 1201
|office hours= Wednesday 11:00-13:00 or by appointment
|schedule= Tuesday/Thursday 11:00-12:30
|classroom= Math Annex 1102

}}

[http://en.wikipedia.org/wiki/Algebraic_K-theory Algebraic K-Theory] originated in the 1960's and has today grown into a vast, active
branch of mathematics. It has made inroads into other areas of mathematics like Algebraic
topology, Algebraic geometry and Algebraic Number Theory . After a brief introduction
to the K-groups, we shall largely focus on the groups <math>K_0~</math>, <math>K_1~</math> and <math>K_2~</math>. The preliminaries
will constitute a third of the course. We will provide various snapshots of the linkages of
K-theory to some of the areas mentioned above. We shall then study the groups <math>K_i(F)~</math> for
a field <math>F~</math> of characteristic not 2, and its connections with the algebraic theory of quadratic
forms over the field <math>F~</math>, and to the Galois cohomology groups <math>H_{\acute{e}t}^i(F, \mathbb{Z}/2\mathbb{Z})~</math>, leading to the
statement of the [http://en.wikipedia.org/wiki/Milnor_conjecture Milnor conjectures], now a theorem due to Voevodsky.
There will be no final exam for this course. I will try to make the course as self-contained
as possible, pointing to further readings as the course progresses. There will be periodic
assignments which will serve as a basis for assigning a final grade.

== Homeworks ==
* [[:File:Math600D-ass1.pdf|Homework 1]] ( Due date: Sep 27, 2011 )[[Thread:Course talk:Math 600D/Homework 1 corrections|corrections]]
* [[:File:Math600d-hw2.pdf|Homework 2]] ( Due date: Oct 11, 2011 )[[Thread:Course talk:Math 600D/Homework 2 corrections|corrections]]
* [[:File:Math600d-hw3.pdf|Homework 3]] ( Due Date: Oct 25, 2011 )

== References ==
* Bass, Hyman. 1968. Algebraic K-theory. New York: W.A. Benjamin.
* Bass, Hyman, and Amit Roy. 1967. Lectures on topics in algebraic k-theory. Bombay: Tata Institute of Fundamental Research.
* Weibel, Charles. [http://www.math.rutgers.edu/~weibel/Kbook.html The K-book: An introduction to algebraic K-theory] (a graduate textbook in progress).
* Rosenberg, J. Algebraic K-Theory and Its Applications. New York: Springer-Verlag, 1994.
* Milnor, John W. Introduction to Algebraic K-Theory. Princeton, N.J: Princeton University Press, 1971.
* Atiyah, Michael F, and D W. Anderson. K-theory. New York: W.A. Benjamin, 1967.
* Srinivas, V. Algebraic K-Theory. Boston: Birkhäuser, 2008.
* [http://www.math.uiuc.edu/K-theory/ K-theory Preprint Archives]

[[Category:Mathematics]][[Category:Algebra]]

Course:MATH600D

2011-10-16T23:31:57Z

Ghs: /* Homeworks */

File:Math600d-hw3.pdf

2011-10-16T23:30:43Z

Ghs: K-theory, SK_1, K_1, Mennicke symbol, Morita equivalence, math600d homework, unimodular row, Steinberg group

== Summary ==
K-theory, SK_1, K_1, Mennicke symbol, Morita equivalence, math600d homework, unimodular row, Steinberg group
== Copyright status: ==

== Source: ==

Course:MATH600D

2011-10-16T21:16:35Z

Ghs: /* Homeworks */

Course:MATH600D

2011-10-11T20:50:23Z

Ghs: /* References */

Thread:Course talk:Math 600D/Homework 2 corrections/reply (2)

2011-10-11T17:09:12Z

Ghs:

Look at the [http://www.math.rutgers.edu/~weibel/Kbook/Kbook.II.pdf K-book chapter 2] page 14 exercise 2.3 ( Excision for <math>K_0~</math> and how to make a non-unital ring unital)

In the exact sequence <math>K_0(R,I)\xrightarrow{\pi_{2*}} K_0(R)\to K_0(R/I)~</math>

<math>\pi_2:D_R(I)\to R~</math> is given by <math>\pi_2(x,y)=y~</math> and <math>\pi_{2*}[-]=[R\otimes_{D_R(I)}^{\pi_2}-]~</math>

Thread:Course talk:Math 600D/Excision in Algebraic K-Theory

2011-10-11T04:26:50Z

Ghs: New thread: Excision in Algebraic K-Theory

{{Citation
| last1 = Suslin
| first1 = Andrei A.
| last2 = Wodzicki
| first2 = Mariusz
| title = Excision in Algebraic K-Theory
| journal = Annals of Mathematics
| volume = 136
| issue = 1
| pages = 51-122
| date = 1992
| language =
| url = http://math.berkeley.edu/~wodzicki/prace/AM_136_51.pdf
| mr =
| zbl = }}

Thread:Course talk:Math 600D/Homework 2 corrections/reply (2)

2011-10-11T04:21:49Z

Ghs:

Look at the [http://www.math.rutgers.edu/~weibel/Kbook/Kbook.II.pdf K-book chapter 2] page 14 exercise 2.3 ( Excision for <math>K_0~</math> and how to make a non-unital ring unital)

Thread:Course talk:Math 600D/Homework 2 corrections/reply (5)

2011-10-11T03:36:23Z

Ghs: Reply to Homework 2 corrections

Question 3.

<math>(a)\nRightarrow(b)~</math> ===> So one needs to add more assumptions.

example. <math>(\mathbb{Z}\oplus\mathbb{Z}/2\mathbb{Z})\otimes_\mathbb{Z} 2\mathbb{Z}\simeq \mathbb{Z}~</math> but <math>\mathbb{Z}\oplus\mathbb{Z}/2\mathbb{Z}~</math> is not a projective <math>\mathbb{Z}~</math>-module.

This question is the exercise 3.1 of the [http://www.math.rutgers.edu/~weibel/Kbook/Kbook.I.pdf K-book chapter 1] on page 23, also look at pages 15-23 for the review of line bundles and the picard group.

Thread:Course talk:Math 600D/Homework 2 corrections/reply (4)

2011-10-10T22:40:23Z

Ghs:

Question 2.

One can define exterior powers over commutative rings + good properties. So if:

<math>P\oplus R^{n-1}\simeq R^n \Rightarrow P\simeq P\otimes_R R \simeq \wedge^1_R P \otimes_R \wedge^{n-1}_R R^{n-1}\simeq \wedge^n_R R^n\simeq R~</math>

since rank of <math>P~</math> is one ( so constant ) over <math>R~</math> then <math>\wedge^k_R P = 0 \;\forall\; k > 1~</math>. [ I have assumed in all this that <math>R~</math> is unital. ]

For reference you may look at the [http://www.math.rutgers.edu/~weibel/Kbook/Kbook.I.pdf K-book chapter 1], pages: 4 (ex 1.6), 15, 16

For discussion of rank look at the [http://www.math.rutgers.edu/~weibel/Kbook/Kbook.I.pdf K-book chapter 1], pages: 2, 9

Exercise. If <math>R~</math> has the invariant basis property (IBP), i.e. <math>R^n\simeq R^m \Leftrightarrow n=m~</math>, then the rank of a stably free <math>R~</math>-module <math>P~</math> defined by <math>\text{rank}_R(P)=m-n~</math> where <math> m, n\in \mathbb{N}\cup {0}~</math> are such that <math>P\oplus R^n\simeq R^m~</math> is well defined.

Thread:Course talk:Math 600D/Homework 2 corrections/reply (4)

2011-10-10T21:18:01Z

Ghs:

Question 2.

One can define exterior powers over commutative rings + good properties. So if:

<math>P\oplus R^{n-1}\simeq R^n \Rightarrow P\simeq P\otimes_R R \simeq \wedge^1_R P \otimes_R \wedge^{n-1}_R R^{n-1}\simeq \wedge^n_R R^n\simeq R~</math>

since rank of <math>P~</math> is one ( so constant ) over <math>R~</math> then <math>\wedge^k_R P = 0 \;\forall\; k > 1~</math>. [ to prove this local to global fact one might need the fact that <math>R~</math> should be noetherian. And I have assumed in all this that <math>R~</math> is unital. ]

For reference you may look at the [http://www.math.rutgers.edu/~weibel/Kbook/Kbook.I.pdf K-book chapter 1], pages: 4 (ex 1.6), 15, 16

For discussion of rank look at the [http://www.math.rutgers.edu/~weibel/Kbook/Kbook.I.pdf K-book chapter 1], pages: 2, 9

Exercise. If <math>R~</math> has the invariant basis property (IBP), i.e. <math>R^n\simeq R^m \Leftrightarrow n=m~</math>, then the rank of a stably free <math>R~</math>-module <math>P~</math> defined by <math>\text{rank}_R(P)=m-n~</math> where <math> m, n\in \mathbb{N}\cup {0}~</math> are such that <math>P\oplus R^n\simeq R^m~</math> is well defined.

Thread:Course talk:Math 600D/Homework 2 corrections/reply (4)

2011-10-10T21:15:47Z

Ghs:

Question 2.

One can define exterior powers over commutative rings + good properties. So if:

<math>P\oplus R^{n-1}\simeq R^n \Rightarrow P\simeq P\otimes_R R \simeq \wedge^1_R P \otimes_R \wedge^{n-1}_R R^{n-1}\simeq \wedge^n_R R^n\simeq R~</math>

since rank of <math>P~</math> is one ( so constant ) over <math>R~</math> then <math>\wedge^k_R P = 0 \;\forall\; k > 1~</math>. [ to prove this local to global fact one might need the fact that <math>R~</math> should be noetherian. ]

For reference you may look at the [http://www.math.rutgers.edu/~weibel/Kbook/Kbook.I.pdf K-book chapter 1], pages: 4 (ex 1.6), 15, 16

For discussion of rank look at the [http://www.math.rutgers.edu/~weibel/Kbook/Kbook.I.pdf K-book chapter 1], pages: 2, 9

Exercise. If <math>R~</math> has the invariant basis property (IBP), i.e. <math>R^n\simeq R^m \Leftrightarrow n=m~</math>, then the rank of a stably free <math>R~</math>-module <math>P~</math> defined by <math>\text{rank}_R(P)=m-n~</math> where <math> m, n\in \mathbb{N}\cup {0}~</math> are such that <math>P\oplus R^n\simeq R^m~</math> is well defined.

Thread:Course talk:Math 600D/Homework 2 corrections/reply (4)

2011-10-10T20:57:37Z

Ghs: Reply to Homework 2 corrections

Question 2.

One can define exterior powers over commutative rings + good properties. So if:

<math>P\oplus R^{n-1}\simeq R^n \Rightarrow P\simeq P\otimes_R R \simeq \wedge^1_R P \otimes_R \wedge^{n-1}_R R^{n-1}\simeq \wedge^n_R R^n\simeq R~</math>

since rank of <math>P~</math> is one ( so constant ) over <math>R~</math> then <math>\wedge^k_R P = 0 \;\forall\; k > 1~</math>.

For reference you may look at the [http://www.math.rutgers.edu/~weibel/Kbook/Kbook.I.pdf K-book chapter 1], pages: 4 (ex 1.6), 15, 16

For discussion of rank look at the [http://www.math.rutgers.edu/~weibel/Kbook/Kbook.I.pdf K-book chapter 1], pages: 2, 9

Exercise. If <math>R~</math> has the invariant basis property (IBP), i.e. <math>R^n\simeq R^m \Leftrightarrow n=m~</math>, then the rank of a stably free <math>R~</math>-module <math>P~</math> defined by <math>\text{rank}_R(P)=m-n~</math> where <math> m, n\in \mathbb{N}\cup {0}~</math> are such that <math>P\oplus R^n\simeq R^m~</math> is well defined.

Thread:Course talk:Math 600D/Homework 2 corrections/reply (3)

2011-10-10T18:50:53Z

Ghs: Reply to Homework 2 corrections

Question 1.

<math>(a)\Rightarrow(b)~</math> is fine.

but <math>(b)\Rightarrow(a)~</math> should be modified to:

if <math>R^n\xrightarrow{f} R\to 0 ~</math> is an exact sequence then <math>f~</math> is given by a unimodular row.

The simple example that makes statement of <math>(b)\Rightarrow(a)~</math> false is :

<math>0\to\mathbb{Z}\xrightarrow{\times 2}\mathbb{Z}~</math>

Thread:Course talk:Math 600D/Homework 2 corrections/reply

2011-10-10T18:43:29Z

Ghs:

Question 4.
We do not have usually left exactness in the stated short exact sequence, so that part should be dropped.

Thread:Course talk:Math 600D/Homework 2 corrections

2011-10-10T18:43:13Z

Ghs:

Question 2.

We should assume that the module is not simply stably free, but that it is also as good as possible in that regards. That is, <math>P\oplus R = R^2~</math>.

Thread:Course talk:Math 600D/Homework 2 corrections/reply (2)

2011-10-10T02:18:06Z

Ghs:

the correct form of the exact sequence we should try to proof is : [ again this was just a typo ]

<math>0 \to K_0(R,I) \to {\color{red}K_0(D_R(I))} \xrightarrow{[R/I\otimes_R(R\otimes_{D_R(I)}-)]} K_0(R/I)~</math>