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Preface; Contents; What Are Mathematical Cultures?; 1 The Normative Senses of `Culture'; 2 The Descriptive/Scientific Senses of `Culture'; 3 Mathematics; 4 Hofstede; 5 Bishop; 6 Final Thoughts; Appendix: Recent Conferences on Mathematical Cultures; References; Philosophy or Not? The Study of Cultures and Practices of Mathematics ; 1 Introduction; 2 Our Community; 2.1 Subject Matter; 2.2 Research Methods; 2.3 Motivation; 2.4 Extrinsic Factors; 3 Philosophy; 4 Three Relevant Distinctions for Empirical Philosophy; 4.1 First Philosophy vs. Second Philosophy; 4.2 Empirical Methodology
4.3 The Source of Empirical Data5 The Availability of Data; 6 Conclusion; References; Abacus as a Programming Language: Computer Science and History of Mathematics; 1 Introduction; 2 Counting Rods as an Imperative Language; 2.1 Data Structure and Variable Assignment; 2.2 Imperative Languages; 3 Abacus as a Functional Language; 3.1 Data Structure of the Abacus; 3.2 The Representability of Arithmetical Properties; 3.3 Currying Operations; 4 Pedagogical Strategies and Semantics of Programming Languages; 5 Conclusion; References; Mathematics in Engineering and Science
1 The Nature of Mathematical Reasoning2 Some Historical Examples; 3 Computational Science: Emergence of a New Reasoning Style; References; A Fashionable Curiosity: Claudius Ptolemy's `Desire for Knowledge' in Literary Context; 1 Ptolemy Outside of Literary Context; 2 Ptolemy's `Desire for Knowledge'; 3 The Desire for Knowledge in Greek Literature: A Survey; 4 Ptolemy's Choice; 5 Ptolemy's Platonic Enthusiasm; 6 The Phaedrus in Greek Imperial Literature; 7 Ptolemy's Literary Ambition; 8 Mathematical Psychologies Prior to Ptolemy?; 9 Ptolemy's Timely Desires; References
Transmission and Interactions Among Different Types of Geometrical Argumentations: From Jesuits in China to Nam Pyŏng-Gil in Korea1 Introduction; 2 Sources and the Style of Argumentations of "Elements of Geometry" in Emperor Kangxi's Shuli jingyun; 3 Influences of the Shuli jingyun in Korea: The Case of Nam Pyŏng-Gil; 4 Concluding Remarks; References
4.3 The Source of Empirical Data5 The Availability of Data; 6 Conclusion; References; Abacus as a Programming Language: Computer Science and History of Mathematics; 1 Introduction; 2 Counting Rods as an Imperative Language; 2.1 Data Structure and Variable Assignment; 2.2 Imperative Languages; 3 Abacus as a Functional Language; 3.1 Data Structure of the Abacus; 3.2 The Representability of Arithmetical Properties; 3.3 Currying Operations; 4 Pedagogical Strategies and Semantics of Programming Languages; 5 Conclusion; References; Mathematics in Engineering and Science
1 The Nature of Mathematical Reasoning2 Some Historical Examples; 3 Computational Science: Emergence of a New Reasoning Style; References; A Fashionable Curiosity: Claudius Ptolemy's `Desire for Knowledge' in Literary Context; 1 Ptolemy Outside of Literary Context; 2 Ptolemy's `Desire for Knowledge'; 3 The Desire for Knowledge in Greek Literature: A Survey; 4 Ptolemy's Choice; 5 Ptolemy's Platonic Enthusiasm; 6 The Phaedrus in Greek Imperial Literature; 7 Ptolemy's Literary Ambition; 8 Mathematical Psychologies Prior to Ptolemy?; 9 Ptolemy's Timely Desires; References
Transmission and Interactions Among Different Types of Geometrical Argumentations: From Jesuits in China to Nam Pyŏng-Gil in Korea1 Introduction; 2 Sources and the Style of Argumentations of "Elements of Geometry" in Emperor Kangxi's Shuli jingyun; 3 Influences of the Shuli jingyun in Korea: The Case of Nam Pyŏng-Gil; 4 Concluding Remarks; References