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 Riemannian Geometry (PDF)
R3 and the Riemann sphere Ĉ are diffeomorphic. Exercise 2.8. Find a proof of Proposition 2.24. Exercise 2.9. Let the spheres S1, S3 and the Lie groups SO(n), O(n), SU(n), U(n) be equipped with their standard differentiable structures introduced above. Use Proposition 2.24 to prove the f...
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R3 and the Riemann sphere Ĉ are diffeomorphic. Exercise 2.8. Find a proof of Proposition 2.24. Exercise 2.9. Let the spheres S1, S3 and the Lie groups SO(n), O(n), SU(n), U(n) be equipped with their standard differentiable structures introduced above. Use Proposition 2.24 to prove the fol- lowing diffeomorphisms S1 ∼= SO(2), S3 ∼= SU(2), SO(n)×O(1) ∼= O(n), SU(n)×U(1) ∼= U(n). Exercise 2.10. Find a proof of Corollary 2.28. Exercise 2.11. Let (G, ∗) and (H, ·) be two Lie groups. Prove that the product
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http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf#page=22
www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf#page=22
R3 and the Riemann sphere Ĉ are diffeomorphic. Exercise 2.8. Find a proof of Proposition 2.24. Exercise 2.9. Let the spheres S1, <span class="highlight">S3</span> and the Lie groups SO(n), O(n), SU(n), U(n) be equipped with their standard differentiable structures introduced above. Use Proposition 2.24 to prove the fol- lowing diffeomorphisms S1 ∼= SO(2), <span class="highlight">S3</span> ∼= SU(2), SO(n)×O(1) ∼= O(n), SU(n)×U(1) ∼= U(n). Exercise 2.10. Find a proof of Corollary 2.28. Exercise 2.11. Let (G, ∗) and (H, ·) be two Lie groups. Prove that the product
'Standard Operating Procedure'
Movie Reviews Historical, Fictional Icons Take To The Big Screen David Edelstein reviews Lincoln and Skyfall — films that follow two icons of history and cinema. Movie Reviews Between Friends, Age Is Nothing But A Number Starlet follows a young porn star who becomes friends with...
science_pub2003
Vermont Department of Education (Science Grade Expectations) S19 Science — Scientific Inquiry: Vermont Standards and Evidences—Representing Data and Analysis 7.1 c, cc, d, dd, ddd, e, f, g; 1.17a, aa, aaa, b, bb, bbb, c, cc, ccc, d, dd; 1.18, 1.20; 2.2c, cc, d, dd Grades 3-4 Grades 5-...
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Vermont Department of Education (Science Grade Expectations) S19 Science — Scientific Inquiry: Vermont Standards and Evidences—Representing Data and Analysis 7.1 c, cc, d, dd, ddd, e, f, g; 1.17a, aa, aaa, b, bb, bbb, c, cc, ccc, d, dd; 1.18, 1.20; 2.2c, cc, d, dd Grades 3-4 Grades 5-6 Representing Data and Analysis S3-4:6 Students demonstrate their ability to ANALYZE DATA by… • Interpreting patterns or trends in data. AND • Relating data to the original question and prediction
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http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page=12
education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page...
Vermont Department of Education (Science Grade Expectations) S11 Science — Scientific Inquiry: Vermont Standards and Evidences—Scientific Questioning 7.1 a, aa, aaa; 2.1 a, b, c, d; Predicting and Hypothesizing 7.1 b, bb, bbb; Designing Experiments 7.1 c, cc, 7.2 a, aa, b, bb; 2.2 a, aa, aaa, b, bb, 3.10 Grades 3-4 Grades 5-6 Scientific Questioning <span class="highlight">S3</span>-4:1 Students demonstrate their understanding of SCIENTIFIC QUESTIONING by… • Identifying at least one variable that affects a system
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http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page=16
education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page...
Vermont Department of Education (Science Grade Expectations) S15 Science — Grades 3-4 Grades 5-6 Scientific Inquiry: Vermont Standards and Evidences—Conducting Experiments 7.1 c, cc, i; 7.2 c, cc, d; 2.2 e, ee, f, g; Rep- resenting Data and Analysis 7.1 c, cc, d, dd, ddd, e, f, g; 1.17a, aa, aaa, b, bb, bbb, c, cc, ccc, d, dd; 1.18, 1.20; 2.2c, cc, d, dd, 3.10, 3.11, 3.12, 3.13 Conducting Experiments <span class="highlight">S3</span>-4:4 Students demonstrate their ability to CONDUCT EXPERI- MENTS by… • Referring to and
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http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page=20
education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page...
Vermont Department of Education (Science Grade Expectations) S19 Science — Scientific Inquiry: Vermont Standards and Evidences—Representing Data and Analysis 7.1 c, cc, d, dd, ddd, e, f, g; 1.17a, aa, aaa, b, bb, bbb, c, cc, ccc, d, dd; 1.18, 1.20; 2.2c, cc, d, dd Grades 3-4 Grades 5-6 Representing Data and Analysis <span class="highlight">S3</span>-4:6 Students demonstrate their ability to ANALYZE DATA by… • Interpreting patterns or trends in data. AND • Relating data to the original question and prediction
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http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page=24
education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page...
Vermont Department of Education (Science Grade Expectations) S23 Science — Physical Science: Vermont Standards and Evidences—Properties of Matter 7.12 a, aa, aaa, b, bb, bbb, c, cc, ccc, 3.10, 3.11, 3.13 [See also connection with S: 14 Physical Science—Physical Change] Grades 3-4 Grades 5-6 Properties of Matter <span class="highlight">S3</span>-4:9 Students demonstrate their understanding of the Properties of Matter by… • Investigating and measuring how the total weight of the parts of a substance, no matter how they are
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http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page=28
education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page...
Vermont Department of Education (Science Grade Expectations) S27 Science — Physical Science: Vermont Standards and Evidences—Properties of Matter 7.12 a, aa, aaa, b, bb, bbb, c, cc, ccc, 3.10, 3.11, 3.13 [See also connection with S: 14 Physical Science—Physical Change] Grades 3-4 Grades 5-6 Properties of Matter <span class="highlight">S3</span>-4:12 Students demonstrate their understanding of the States of Matter by… • Identifying , describing and comparing the properties of selected solids, liquids and gases. Science
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http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page=32
education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page...
Vermont Department of Education (Science Grade Expectations) S31 Science — Physical Science: Vermont Standards and Evidences—Energy and Energy Transformation 7.12 b, bb, bbb; Chemical Change 7.12 b, bb, bbb, e, ee, eee, 2.2, 3.10, 3.11 [See also connection with S: 48 Universe, Earth, Environment—Weather] Grades 3-4 Grades 5-6 Properties of Matter <span class="highlight">S3</span>-4:14 Students demonstrate their understanding of Physical Change by… • Investigating and explaining what happens to liquids in open containers
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http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page=44
education.vermont.gov/new/pdfdoc/pubs/grade_expectations/science.pdf#page...
Vermont Department of Education (Science Grade Expectations) S43 Science — Grades 3-4 Grades 5-6 Physical Science: Vermont Standards and Evidences—Force 7.12 d, dd, ddd, 2.2a, aa, aaa, 3.11 Force <span class="highlight">S3</span>-4:21 Students demonstrate their understanding of Force by… • Investigating and describing how different amounts of force can change the direction and speed of an object in motion. Science Concepts: a. Changes in speed or direction of motion are caused by forces. b. The greater the force
Draft
European and Japanese imperialism Evaluate European and Japanese imperialism of the late 19 th and 20 th century and the independence movements in Africa and Asia: causes, reactions, short- and long-term consequences DOK 4 Standards SS3 1.9, 1.6, 3.8 O. Causes and consequences of m...
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European and Japanese imperialism Evaluate European and Japanese imperialism of the late 19 th and 20 th century and the independence movements in Africa and Asia: causes, reactions, short- and long-term consequences DOK 4 Standards SS3 1.9, 1.6, 3.8 O. Causes and consequences of major demographic changes Outline major demographic changes and migrations from prehistoric times to the present, including: their causes and consequences (e.g. rural to urban, less developed to more developed
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http://dese.mo.gov/divimprove/curriculum/GLE/documents/ss_cle_0907.pdf#page=10
dese.mo.gov/divimprove/curriculum/GLE/documents/ss_cle_0907.pdf#page=10
Missouri, United States and World History CONCEPTS 3b. Knowledge of continuity and change in the history of the world US History (Required by RSMO 170.011) Government (Required by RSMO 170.011) Geography World History Economics A. Culture of early river valley civilizations DOK Standards B. Contributions of Greek and Roman civilizations DOK Standards C. Institutions and events of European civilization during the Middle Ages DOK Standards D. <span class="highlight">Japanese</span>
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http://dese.mo.gov/divimprove/curriculum/GLE/documents/ss_cle_0907.pdf#page=12
dese.mo.gov/divimprove/curriculum/GLE/documents/ss_cle_0907.pdf#page=12
European and <span class="highlight">Japanese</span> imperialism Evaluate European and <span class="highlight">Japanese</span> imperialism of the late 19 th and 20 th century and the independence movements in Africa and Asia: causes, reactions, short- and long-term consequences DOK 4 Standards SS3 1.9, 1.6, 3.8 O. Causes and consequences of major demographic changes Outline major demographic changes and migrations from prehistoric times to the present, including: their causes and consequences (e.g. rural to urban, less developed to more developed
Draft
Missouri, United States and World History 15 CONCEPTS 3b. Knowledge of continuity and change in the history of the world GRADE K GRADE 1 GRADE 2 GRADE 3 GRADE 4 GRADE 5 GRADE 6 GRADE 7 GRADE 8 L. Causes and consequences of economic theories and practices DOK Standards M. Causes, comparisons and re...
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Missouri, United States and World History 15 CONCEPTS 3b. Knowledge of continuity and change in the history of the world GRADE K GRADE 1 GRADE 2 GRADE 3 GRADE 4 GRADE 5 GRADE 6 GRADE 7 GRADE 8 L. Causes and consequences of economic theories and practices DOK Standards M. Causes, comparisons and results of major twentieth-century wars DOK Standards N. Causes, reactions and consequences of European and Japanese imperialism DOK Standards O
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http://dese.mo.gov/divimprove/curriculum/GLE/documents/ss_gle_2.0_k8_0907.pdf#page=13
dese.mo.gov/divimprove/curriculum/GLE/documents/ss_gle_2.0_k8_0907.pdf#pa...
SS3 1.9 B. Contributions of Greek and Roman civilizations Distinguish between Greek civilization and the Roman Empire regarding: 1. origins of democracy 2. rule of law 3. governmental structures DOK 2 Standards SS3 1.9 C. Institutions and events of European civilization during the Middle Ages Investigate Europe in the Middle Ages, including: 1. rise of kingdoms 2. feudalism 3. the Crusades DOK 2 Standards SS3 1.10 D. <span class="highlight">Japanese</span> institutions and culture
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http://dese.mo.gov/divimprove/curriculum/GLE/documents/ss_gle_2.0_k8_0907.pdf#page=15
dese.mo.gov/divimprove/curriculum/GLE/documents/ss_gle_2.0_k8_0907.pdf#pa...
Missouri, United States and World History 15 CONCEPTS 3b. Knowledge of continuity and change in the history of the world GRADE K GRADE 1 GRADE 2 GRADE 3 GRADE 4 GRADE 5 GRADE 6 GRADE 7 GRADE 8 L. Causes and consequences of economic theories and practices DOK Standards M. Causes, comparisons and results of major twentieth-century wars DOK Standards N. Causes, reactions and consequences of European and <span class="highlight">Japanese</span> imperialism DOK Standards O
Indiana Academic Standards-US History
involvement in Afghanistan USH.9.4 Explain issues and problems of the past by analyzing the interests and viewpoints of those involved. Example: The Scopes Trial, the Red Scare, Japanese internment during World War II, Watergate hearings and the actions of President Nixon, and U.S. involvemen...
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involvement in Afghanistan USH.9.4 Explain issues and problems of the past by analyzing the interests and viewpoints of those involved. Example: The Scopes Trial, the Red Scare, Japanese internment during World War II, Watergate hearings and the actions of President Nixon, and U.S. involvement in Iran and Iraq USH.9.5 Use technology in the process of conducting historical research and in the presentation of the products of historical research and current events. Example: Use digital archives to research and
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http://dc.doe.in.gov/Standards/AcademicStandards/PrintLibrary/docs-socialstudies/2007-ss-ushistory.pdf#page=11
dc.doe.in.gov/Standards/AcademicStandards/PrintLibrary/docs-socialstudies...
involvement in Afghanistan USH.9.4 Explain issues and problems of the past by analyzing the interests and viewpoints of those involved. Example: The Scopes Trial, the Red Scare, <span class="highlight">Japanese</span> internment during World War II, Watergate hearings and the actions of President Nixon, and U.S. involvement in Iran and Iraq USH.9.5 Use technology in the process of conducting historical research and in the presentation of the products of historical research and current events. Example: Use digital archives to research and
Minnesota Academic Standards
3. Students will describe the impact of the war on people such as women, African Americans and Japanese Americans. 1.Treaty of Versailles, Hitler, Mussolini and the rise of fascism in Germany and Italy; breakdown of the League of Nations; Good Neighbor Policy; Isolationism; Japanese mi...
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3. Students will describe the impact of the war on people such as women, African Americans and Japanese Americans. 1.Treaty of Versailles, Hitler, Mussolini and the rise of fascism in Germany and Italy; breakdown of the League of Nations; Good Neighbor Policy; Isolationism; Japanese militarism, Lend Lease; Pearl Harbor 2. European Theater: Battle of Britain, the “second front,” Normandy Invasion; Holocaust and the Nuremberg Trials; Pacific Theater: Battle of Midway, Okinawa and the Philippines; The Big
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http://education.state.mn.us/mdeprod/groups/Standards/documents/LawStatute/006219.pdf#page=7
education.state.mn.us/mdeprod/groups/Standards/documents/LawStatute/00621...
Students will identify and understand the struggles and contributions of African American leaders of this period, including W.E.B. DuBois and Booker T. Washington, and compare their ideas. 1. The Battle of Manila Bay, the annexation of the Philippines, and the rise of the U.S. as a world power 2. Panama Canal, the annexation of Hawaii, Boxer Rebellion, the Russo-<span class="highlight">Japanese</span> War, and the guerilla war in the Philippines, “Banana Wars” 3. Tuskegee Institute, establishment of the NAACP, Ida B. Wells I. U.S. HISTORY H
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http://education.state.mn.us/mdeprod/groups/Standards/documents/LawStatute/006219.pdf#page=18
education.state.mn.us/mdeprod/groups/Standards/documents/LawStatute/00621...
3. Students will describe the impact of the war on people such as women, African Americans and <span class="highlight">Japanese</span> Americans. 1.Treaty of Versailles, Hitler, Mussolini and the rise of fascism in Germany and Italy; breakdown of the League of Nations; Good Neighbor Policy; Isolationism; <span class="highlight">Japanese</span> militarism, Lend Lease; Pearl Harbor 2. European Theater: Battle of Britain, the “second front,” Normandy Invasion; Holocaust and the Nuremberg Trials; Pacific Theater: Battle of Midway, Okinawa and the Philippines; The Big
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http://education.state.mn.us/mdeprod/groups/Standards/documents/LawStatute/006219.pdf#page=35
education.state.mn.us/mdeprod/groups/Standards/documents/LawStatute/00621...
British in India and the French in Indochina to the British in Hong Kong and China; French and British colonies in sub- Saharan Africa; <span class="highlight">Japanese</span> and American colonial expansion in Western Pacific III. WORLD HISTORY G. Age of Empires and Revolutions, 1640 AD - 1920 AD The student will demonstrate knowledge of the effects of the Industrial Revolution during the 19th century. 1. Students will explain industrial developments and analyze how they brought about urbanization as well as social and environmental changes
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(National Geography Standard 5, p. 192) analyzing the changes in Japanese society by describing the role of geography in the development of Japan, the policies of the Tokugawa Shogunate, and the infl uence of China on Japanese society (National Geography Standard 4, p. 190) 5.3.3 South...
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(National Geography Standard 5, p. 192) analyzing the changes in Japanese society by describing the role of geography in the development of Japan, the policies of the Tokugawa Shogunate, and the infl uence of China on Japanese society (National Geography Standard 4, p. 190) 5.3.3 South Asia/India through the 18th Century – Analyze the global economic signifi cance of India and the role of foreign infl uence in the political, religious, cultural, and economic transformations in India and South Asia
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http://www.michigan.gov/documents/mde/SS_HSCE_210739_7.pdf#page=25
www.michigan.gov/documents/mde/SS_HSCE_210739_7.pdf#page=25
(National Geography Standard 5, p. 192) analyzing the changes in <span class="highlight">Japanese</span> society by describing the role of geography in the development of Japan, the policies of the Tokugawa Shogunate, and the infl uence of China on <span class="highlight">Japanese</span> society (National Geography Standard 4, p. 190) 5.3.3 South Asia/India through the 18th Century – Analyze the global economic signifi cance of India and the role of foreign infl uence in the political, religious, cultural, and economic transformations in India and South Asia
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http://www.michigan.gov/documents/mde/SS_HSCE_210739_7.pdf#page=27
www.michigan.gov/documents/mde/SS_HSCE_210739_7.pdf#page=27
Africa, Central Asia, and East Asia (National Geography Standard 16, p. 216) describing the connection between imperialism and racism, including the social construction of race comparing British policies in South Africa and India, French polices in Indochina, and <span class="highlight">Japanese</span> policies in Asia (See 7.3.3) (National Geography Standard 13, p. 210) analyze the responses to imperialism by African and Asian peoples (See 6.6.3) (National Geography Standard 13, p. 210) Note: Teachers
Core Content For Mathematics Assessment
Temple– temple city complex with towers, Buddhist – e.g., Liurong Temple/pagoda or called a stupa in India, part of a temple city complex) Unique visual arts in Asian cultures (Japanese printmaking, Chinese and Japanese ink and brush paintings, calligraphy) Historical Peri...
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Temple– temple city complex with towers, Buddhist – e.g., Liurong Temple/pagoda or called a stupa in India, part of a temple city complex) Unique visual arts in Asian cultures (Japanese printmaking, Chinese and Japanese ink and brush paintings, calligraphy) Historical Periods and Styles: (in chronological order) (Basic understanding of society in the time period, influence of geographic location and philosophical beliefs of each historical period is necessary to meet this standard) Renaissance (Leonardo
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http://www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=46
www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=46
Temple– temple city complex with towers, Buddhist – e.g., Liurong Temple/pagoda or called a stupa in India, part of a temple city complex) Unique visual arts in Asian cultures (<span class="highlight">Japanese</span> printmaking, Chinese and <span class="highlight">Japanese</span> ink and brush paintings, calligraphy) Historical Periods and Styles: (in chronological order) (Basic understanding of society in the time period, influence of geographic location and philosophical beliefs of each historical period is necessary to meet this standard) Renaissance (Leonardo
History Social Science Content Standards - Content Standards (CA Dept of Education)
transmission of African history and culture. 7.5 Students analyze the geographic, political, economic, religious, and social structures of the civilizations of Medieval Japan. 1. Describe the significance of Japan’s proximity to China and Korea and the intellectual, linguistic, religious, and...
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transmission of African history and culture. 7.5 Students analyze the geographic, political, economic, religious, and social structures of the civilizations of Medieval Japan. 1. Describe the significance of Japan’s proximity to China and Korea and the intellectual, linguistic, religious, and philosophical influence of those countries on Japan. 2. Discuss the reign of Prince Shotoku of Japan and the characteristics of Japanese society and family life during his reign. 3. Describe the values, social customs
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http://www.cde.ca.gov/be/st/ss/documents/histsocscistnd.pdf#page=36
www.cde.ca.gov/be/st/ss/documents/histsocscistnd.pdf#page=36
transmission of African history and culture. 7.5 Students analyze the geographic, political, economic, religious, and social structures of the civilizations of Medieval Japan. 1. Describe the significance of Japan’s proximity to China and Korea and the intellectual, linguistic, religious, and philosophical influence of those countries on Japan. 2. Discuss the reign of Prince Shotoku of Japan and the characteristics of <span class="highlight">Japanese</span> society and family life during his reign. 3. Describe the values, social customs
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