Module #1 Introduction to Logic and Philosophy of Mathematics Course overview, importance of logic and philosophy of mathematics, and historical background
Module #2 Propositional Logic Introduction to propositional logic, syntax, semantics, and basic logical operators
Module #3 Predicate Logic Introduction to predicate logic, quantifiers, and predicate logic syntax
Module #4 Set Theory Introduction to set theory, basic set operations, and set notation
Module #5 Relations and Functions Introduction to relations and functions, types of relations, and function notation
Module #6 Induction and Recursion Principle of mathematical induction, recursive definitions, and proof by induction
Module #7 Philosophy of Mathematics:An Introduction Overview of philosophical issues in mathematics, mathematical truth, and the nature of mathematics
Module #8 Platonism and Mathematical Realism Platonic view of mathematics, mathematical realism, and the existence of mathematical objects
Module #9 Nominalism and Fictionalism Nominalist view of mathematics, fictionalism, and the nature of mathematical truth
Module #10 Logicism and Formalism Logicist view of mathematics, formalism, and the role of language in mathematics
Module #11 Intuitionism and Constructivism Intuitionist view of mathematics, constructivism, and the role of human intuition
Module #12 Gödels Incompleteness Theorems Gödels incompleteness theorems, their significance, and implications for mathematical truth
Module #13 Model Theory Introduction to model theory, structures, and the concept of truth in a model
Module #14 Proof Theory Introduction to proof theory, formal proofs, and the Curry-Howard correspondence
Module #15 Category Theory Introduction to category theory, categorical logic, and the concept of mathematical structure
Module #16 Philosophy of Logic Philosophical issues in logic, logical truth, and the nature of logical consequence
Module #17 Philosophy of Set Theory Philosophical issues in set theory, the foundations of set theory, and the concept of set
Module #18 Philosophy of Mathematics and Cognition The role of cognition in mathematical understanding, cognitive science, and the philosophy of mathematics
Module #19 Philosophy of Mathematics and Language The role of language in mathematics, linguistic structures, and the philosophy of language
Module #20 Philosophy of Mathematics and Science The relationship between mathematics and science, mathematical modeling, and the philosophy of science
Module #21 Philosophy of Mathematics and Epistemology The relationship between mathematics and epistemology, mathematical knowledge, and the nature of truth
Module #22 Philosophy of Mathematics and Metaphysics The relationship between mathematics and metaphysics, mathematical objects, and the nature of reality
Module #23 Case Studies in Philosophy of Mathematics In-depth analysis of specific mathematical concepts and theories from a philosophical perspective
Module #24 Current Debates in Philosophy of Mathematics Current research and debates in the philosophy of mathematics, including new developments and challenges
Module #25 Course Wrap-Up & Conclusion Planning next steps in Logic and the Philosophy of Mathematics career
