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

Philosophical Foundations of Mathematics
( 25 Modules )

Module #1
Introduction to Philosophical Foundations of Mathematics
Overview of the course and importance of philosophical foundations in mathematics
Module #2
Ancient Greek Contributions to Mathematics
Exploring the mathematical and philosophical ideas of ancient Greeks, such as Plato and Aristotle
Module #3
The Development of Mathematics in the Middle Ages
Mathematical and philosophical advancements during the Middle Ages, including the role of Islamic scholars
Module #4
The Emergence of Modern Mathematics
Key figures and discoveries that shaped modern mathematics, including the Renaissance and Enlightenment
Module #5
Philosophical Debates in the 19th and 20th Centuries
Influential philosophical discussions and debates on the nature of mathematics in recent centuries
Module #6
What is Mathematics?
Exploring the nature and definition of mathematics
Module #7
The Foundations of Arithmetic
Examining the foundations of arithmetic, including the axioms and principles of number theory
Module #8
Geometry and the Nature of Space
Philosophical discussions on the nature of geometric space and its relationship to mathematics
Module #9
The Foundations of Logic
Introduction to formal logic and its relationships to mathematics and philosophy
Module #10
The Role of Axioms in Mathematics
The significance and implications of axiomatic systems in mathematics
Module #11
Platonism and the Nature of Mathematical Truth
Exploring the Platonist perspective on the nature of mathematics and mathematical truth
Module #12
Formalism and the Limits of Mathematical Knowledge
The formalist perspective on the foundations of mathematics and its limitations
Module #13
Intuitionism and the Role of Human Experience
The intuitionist perspective on mathematics, emphasizing the role of human experience and intuition
Module #14
Social Constructivism and the Nature of Mathematical Reality
The social constructivist perspective on the nature of mathematics and its relationship to human culture
Module #15
Fictionalism and the Status of Mathematical Entities
The fictionalist perspective on the nature of mathematical entities and their ontological status
Module #16
The Philosophy of Probability and Statistics
Philosophical discussions on the nature of probability and statistics
Module #17
The Foundations of Computation and Algorithmic Thinking
Exploring the philosophical foundations of computation and algorithmic thinking
Module #18
The Role of Mathematics in Science
Philosophical discussions on the relationship between mathematics and science
Module #19
Mathematics and Cognition
Examining the relationship between mathematics and human cognition
Module #20
The Ethics of Mathematical Practice
Philosophical reflections on the ethical implications of mathematical practice and its applications
Module #21
Category Theory and the Philosophy of Mathematics
Exploring the philosophical implications of category theory
Module #22
The Philosophy of Mathematical Notation and Representation
Philosophical discussions on the role of notation and representation in mathematics
Module #23
The Status of Infinity in Mathematics
Examining the philosophical implications of infinity in mathematics
Module #24
The Philosophy of Mathematics Education
Philosophical reflections on the nature and goals of mathematics education
Module #25
Course Wrap-Up & Conclusion
Planning next steps in Philosophical Foundations of Mathematics career


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