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10 Modules / ~100 pages
Wizard Mode
~25 Modules / ~400 pages

Historical Perspectives in the Philosophy of Mathematics
( 25 Modules )

Module #1
Introduction to the Philosophy of Mathematics
Overview of the field, its main questions, and its significance
Module #2
Ancient Greek Roots:Plato and Aristotle
Exploring the mathematical philosophies of Plato and Aristotle
Module #3
The Development of Mathematics in the Middle Ages
The contributions of Islamic mathematicians and the transmission of knowledge
Module #4
Renaissance Humanism and the Rise of Modern Mathematics
The impact of humanism on mathematics, including the work of Regiomontanus and Tartaglia
Module #5
The Emergence of Modern Calculus:Fermat and Descartes
The contributions of Fermat and Descartes to the development of modern calculus
Module #6
Isaac Newton and the Method of Fluxions
Newtons development of calculus and his philosophical views on mathematics
Module #7
Gottfried Wilhelm Leibniz and the Calculus Rivalry
Leibnizs contributions to calculus and the dispute with Newton
Module #8
The Philosophy of Mathematics in the 18th Century:Kant and DAlembert
Kants transcendental idealism and DAlemberts views on mathematical rigor
Module #9
The Emergence of Non-Euclidean Geometry
The work of Nikolai Lobachevsky, János Bolyai, and Carl Friedrich Gauss
Module #10
The Foundations of Mathematics:Cauchy and Weierstrass
The contributions of Augustin-Louis Cauchy and Karl Weierstrass to the foundations of mathematics
Module #11
The Rise of Formalism:Frege and Hilbert
The development of formal systems and the role of Gottlob Frege and David Hilbert
Module #12
The Logicist Program:Russell and Whitehead
The logicist program of Bertrand Russell and Alfred North Whitehead
Module #13
Intuitionism and the Philosophy of L.E.J. Brouwer
Brouwers intuitionistic philosophy of mathematics and its implications
Module #14
The Vienna Circle and Logical Positivism
The influence of the Vienna Circle on the philosophy of mathematics
Module #15
Kurt Gödel and the Limits of Formal Systems
Gödels incompleteness theorems and their impact on the foundations of mathematics
Module #16
The Philosophy of Mathematics in the 20th Century:Quine and Putnam
The contributions of W.V. Quine and Hilary Putnam to the philosophy of mathematics
Module #17
Category Theory and the Philosophy of Mathematics
The development of category theory and its implications for the philosophy of mathematics
Module #18
Feminist and Cultural Perspectives on the Philosophy of Mathematics
Exploring the importance of diversity and inclusion in the philosophy of mathematics
Module #19
The Philosophy of Mathematical Practice
Analyzing the nature of mathematical practice and its relation to philosophy
Module #20
Mathematical Structuralism and Categorical Thinking
The philosophical implications of mathematical structuralism and categorical thinking
Module #21
The Role of Intuition in Mathematical Discovery
The role of intuition in mathematical discovery and its philosophical implications
Module #22
The Philosophy of Applied Mathematics
Exploring the philosophical issues surrounding applied mathematics
Module #23
The Philosophy of Mathematical Modeling
The philosophical implications of mathematical modeling and its applications
Module #24
Computational Philosophy of Mathematics
The impact of computation on the philosophy of mathematics
Module #25
Course Wrap-Up & Conclusion
Planning next steps in Historical Perspectives in the Philosophy of Mathematics career


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