| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910455565403321 |
|
|
Autore |
Xu Jiagu |
|
|
Titolo |
Lecture Notes on Mathematical Olympiad Courses [[electronic resource] ] : For Junior Section (In 2 Volumes) - Volume 1 |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
River Edge, : World Scientific Publishing Company, 2009 |
|
|
|
|
|
|
|
ISBN |
|
1-282-76204-4 |
9786612762048 |
981-4293-56-3 |
|
|
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (183 p.) |
|
|
|
|
|
|
Collana |
|
Mathematical Olympiad Series ; ; v.6 |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Electronic books. -- local |
International Mathematical Olympiad |
Mathematics -- Competitions |
Mathematics -- Problems, exercises, etc |
Mathematics - General |
Mathematics |
Physical Sciences & Mathematics |
Electronic books. |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Description based upon print version of record. |
|
|
|
|
|
|
Nota di contenuto |
|
Contents; Preface; Acknowledgments; Abbreviations and Notations; Abbreviations; Notations for Numbers, Sets and Logic Relations; 1 Operations on Rational Numbers; 1. Basic Rules on Addition, Subtraction, Multiplication, Division; 2. Rule for Removing Brackets; 3. Ingenious Ways for Calculating; Examples; Testing Questions (A); Testing Questions (B); 2 Monomials and Polynomials; Definitions; Operations on Polynomials; Examples; Testing Questions (A); Testing Questions (B); 3 Linear Equations of Single Variable; Usual Steps for Solving Equations; Examples; Testing Questions (A) |
Testing Questions (B)4 System of Simultaneous Linear Equations; Examples; Testing Questions (A); Testing Questions (B); 5 Multiplication Formulae; Basic Multiplication Formulae; Generalization of Formulae; Derived Basic Formulae; Examples; Testing Questions (A); Testing Questions (B); 6 Some Methods of Factorization; Basic Methods of |
|
|
|
|
|
|
|
|
|
|
|
Factorization; Examples; Testing Questions (A); Testing Questions (B); 7 Absolute Value and Its Applications; Basic Properties of Absolute Value; Examples; Testing Questions (A); Testing Questions (B); 8 Linear Equations with Absolute Values; Examples |
Testing Questions (A)Testing Questions (B); 9 Sides and Angles of a Triangle; Basic Knowledge; Examples; Testing Questions (A); Testing Questions (B); 10 Pythagoras' Theorem and Its Applications; Examples; Testing Questions (A); Testing Questions (B); 11 Congruence of Triangles; Basic Criteria for Congruence of Two Triangles; Examples; Testing Questions (A); Testing Questions (B); 12 Applications of Midpoint Theorems; Examples; Testing Questions (A); Testing Questions (B); 13 Similarity of Triangles; Criteria for Similarity of Two Triangles; Basic Properties of Two Similar Triangles |
Important Proportional Properties of SegmentsExamples; Testing Questions (A); Testing Questions (B); 14 Areas of Triangles and Applications of Area; Basic formulae for area of a triangle; Comparison of areas of triangles; Examples; Testing Questions (A); Testing Questions (B); 15 Divisions of Polynomials; Examples; Testing Questions (A); Testing Questions (B); Solutions to Testing Questions; Solutions to Testing Questions 1; Testing Questions (1-A); Testing Questions (1-B); Solutions to Testing Questions 2; Testing Questions (2-A); Testing Questions (2-B); Solutions to Testing Questions 3 |
Testing Questions (3-A)Testing Questions (3-B); Solutions to Test questions 4; Testing Questions (4-A); Testing Questions (4-B); Solutions to Testing Questions 5; Testing Question (5-A); Testing Questions (5-B); Solutions to Testing Questions (6); Testing Questions (6-A); Testing Questions (6-B); Solutions to Test Questions 7; Testing Questions (7-A); Testing Questions (7-B); Solutions to Testing Questions 8; Testing Question (8-A); Testing Questions (8-B); Solutions to Testing Questions 9; Testing Questions (9-A); Testing Questions (9-B); Solutions to Testing Questions 10 |
Testing Question (10-A) |
|
|
|
|
|
|
Sommario/riassunto |
|
Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and exceeds the usual syllabus, but introduces a variety concepts and methods in modern mathematics. In each lecture, the concepts, theories and methods are taken as the core. The examples are served to explain and enrich their intension and to indicate their applications. Besides, appropriate num |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2. |
Record Nr. |
UNISA996565566203316 |
|
|
Autore |
Seelbach Daniel |
|
|
Titolo |
Der Herrscher im Massenmedium : Fränkische Bildpolitik auf Münzen und Siegeln im Kulturvergleich / / Daniel Seelbach |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Berlin ; ; Boston : , : De Gruyter, , [2023] |
|
2024 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (X, 466 p.) |
|
|
|
|
|
|
Collana |
|
Millennium-Studien / Millennium Studies : Studien zu Kultur und Geschichte des ersten Jahrtausends n. Chr. / Studies in the Culture and History of the First Millennium C.E. , , 1862-1139 ; ; 105 |
|
|
|
|
|
|
|
|
Soggetti |
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Nota di contenuto |
|
Frontmatter -- Vorwort -- Inhaltsverzeichnis -- 1 Einleitung -- 2 Frühe fränkisch-poströmische Medien (6. Jh. - 3. V. 7. Jh.) -- 3 Schwächung des Königtums? (4. V. 7. Jh. - M. 8. Jh.) -- 4 Beginn der neurömischen Kultur (M. 8. Jh. - 1. H. d. 9. Jhs.) -- 5 Regionalisierung des fränkischen Imperiums (9. Jh. - 1. H. 10. Jh.) -- 6 Die spätfränkische Zeit (10. Jh.) -- 7 Überblick über epigraphische und ikonographische Elemente -- 8 Fazit -- Abbildungen -- Chartae geographicae -- Abkürzungsverzeichnis -- Schriftquellenverzeichnis -- Literaturverzeichnis -- Glossar -- Register |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
Auch wenn im Zuge des Iconic-Turns Historiker vermehrt auf Bildquellen zurückgriffen, so blieben die verbreitetsten Bildmedien der poströmischen Zeit, nämlich Münzen und Siegel, in Handbüchern und Studien unterrepräsentiert. Zu europäischen Herrschersiegeln dieser Zeit existiert bis heute nicht einmal ein Corpus. Dieser Band greift ebendiese Lücke auf, um die politische Kommunikation mittels Herrscherbildern auf Massenmedien der Franken im ständigen Vergleich mit denen anderer poströmischen Kulturen (Oströmer, Angelsachsen, Langobarden, Westgoten etc.) zu untersuchen und die teils höchst unterschiedlichen Entwicklungen zu erklären. Dabei wird auch vor heißdiskutierten Themen wie dem "Monetarierwesen" oder der "arabo-byzantinischen" Münzprägung nicht haltgemacht. Die so |
|
|
|
|
|
|
|
|
|
|
entstandene Makrohistorie bietet zukünftigen Forschenden einen guten Ausgangspunkt für weitere Studien. |
This study on post-Roman Europe is the first to systematically examine and compare the media of seals and coins for diverse cultures, such as the Franks, Lombards, Anglo-Saxons, and Visigoths, over a period of 500 years. It focuses on political communication by means of the ruler's image and the question of how it developed in specific media, which took place in very different ways despite a common heritage. |
|
|
|
|
|
| |