Summary
The video introduces an optional course on the history of mathematics at Oxford University for third-year undergraduates. It discusses the structure of the course with lectures and readings based on primary sources, specifically highlighting complex numbers and complex analysis. The importance of complex numbers in mathematics is emphasized, tracing their development and acceptance through history with contributions from early mathematicians like Cardano and Bombelli. The transition of complex numbers from solutions to equations to independent mathematical objects is explored, showcasing the reasoning and analogies used by historical figures like Wallis. Additionally, reference is made to key textbooks utilized in the course, such as Victor Katz's 'History of Mathematics' and Jacqueline Stedall's sourcebook.
Chapters
Introduction to History of Mathematics Course
Background on the Mathematics Course
Lecture on Complex Numbers Part 1
Main Texts Used in the Course
Introduction to Complex Analysis
Historical Background of Complex Numbers
Early Notable Figures
Attempts to Validate Imaginary Numbers
19th Century Development
Analogies and Justifications
Introduction to History of Mathematics Course
Introduction to the optional course on the history of mathematics for third-year undergraduates at Oxford University.
Background on the Mathematics Course
Explanation of the course structure involving lectures and readings on the history of mathematics based on primary sources.
Lecture on Complex Numbers Part 1
Overview of a lecture on complex numbers, following a comprehensive course on complex analysis.
Main Texts Used in the Course
Reference to the main books utilized in the history of mathematics course, including Victor Katz's 'History of Mathematics' and Jacqueline Stedall's sourcebook.
Introduction to Complex Analysis
Transition to the study of complex analysis and complex numbers, highlighting their importance in mathematics.
Historical Background of Complex Numbers
Exploration of the development and acceptance of complex numbers as legitimate mathematical entities through history.
Early Notable Figures
Introduction to early mathematicians like Cardano, Bombelli, and Harriot who contributed to the understanding and use of complex and imaginary numbers.
Attempts to Validate Imaginary Numbers
Discussion on the efforts to justify and incorporate imaginary and complex numbers into mathematical study, including insights from various mathematicians.
19th Century Development
Transition of complex numbers from solutions to equations to independent mathematical objects of study in the 19th century.
Analogies and Justifications
Exploration of analogies and reasoning used to understand and justify complex numbers in mathematics, including insights from historical figures like Wallis and others.
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