Course Description
The evolution of mathematics from prehistory up to the fall of Rome. The impact of history and culture on its development and an introduction to the mathematical knowledge, methodology, and techniques of antiquity.
Athena Title
A Panorama of Ancient Mathemat
Pre or Corequisite
MATH 1113 or MATH 1113E
Corequisite
MATH 2250 or MATH 2250E
Semester Course Offered
Offered summer semester every year.
Grading System
A - F (Traditional)
Student Learning Outcomes
- Students will analyze how mathematical ideas evolved in response to cultural, social, and practical needs across civilizations. Students will critically assess ancient problem-solving techniques and compare them to modern methods.
- Students will interpret and deconstruct ancient algorithms and methods, identifying patterns and underlying principles. Students will draw comparisons between mathematical developments in Mesopotamia, Egypt, Greece, India, and China, identifying shared influences and unique contributions. Students will engage in hands-on problem-solving exercises from historical contexts helps refine analytical reasoning skills.
- Students will develop well-structured essays, improving their ability to articulate complex ideas about mathematical history and its cultural relevance. Group discussions will foster clarity and precision in verbal communication, as students present and defend their interpretations of historical texts and mathematical concepts.
- Students will explore how mathematical advancements were driven by the needs of ancient societies (e.g., trade, agriculture, governance, and astronomy). By studying mathematical traditions from diverse civilizations, students will appreciate the global nature of mathematical development and recognize the interconnectedness of cultures. Discussions on the broader impact of mathematics—both in ancient times and its implications today—will encourage students to reflect on the social responsibilities of mathematicians and scholars.
Topical Outline
- 1. Mathematics, Culture, and Language
○ The relationship between mathematics and human culture
○ The role of language and symbolism in the development of mathematical concepts
○ Early number systems and their cultural significance
- 2. Prehistory: The Origins of Mathematics
○ Early counting systems and numerical artifacts (e.g., tally sticks, the Ishango bone)
○ Geometry in prehistoric art and architecture
○ Practical mathematics in early human societies
- 3. Mathematics in Mesopotamia
○ Introduction to Mesopotamian cuneiform texts and paleography
○ Base-60 number system and arithmetic techniques
○ Problem-solving in Babylonian algebra and geometry
○ Applications in administration, astronomy, and land measurement
- 4. Mathematics in Ancient Egypt
○ Introduction to Egyptian hieratic texts and paleography
○ Arithmetic operations using unit fractions
○ Geometry and practical mathematics in construction and surveying
○ Problem-solving in the Rhind and Moscow papyri
- 5. Mathematics in Ancient Greece
○ The Greek ‘miracle’
○ Early number theory
○ Euclid’s Elements and axiomatic geometry
○ Archimedes and advancements in calculus-like methods
- 6. Mathematics in Ancient India
○ Development of decimal place value and early use of zero
○ Solutions to quadratic equations and trigonometry
○ Influence on later Islamic and European mathematics
- 7. Mathematics in Ancient China
○ Counting rods and the Chinese remainder theorem
○ Methods for solving linear equations (Nine Chapters on the Mathematical Art)
○ Influence on East Asian mathematical traditions
- Each topic will include a combination of historical context, exploration of key mathematical texts and methods, and problem-solving exercises. Students will also engage in discussions and write essays to deepen their understanding of the material.
