Introduction to University Mathematics (2026)
James MunroJames Munro's seven-part Oxford Mathematics foundational sequence bridging pre-university calculus and algebra with rigorous university proof construction, set theory, equivalence relations, functions, and formal quantifier logic.
Syllabus
7Foundations of University Mathematics: From Calculation to Proof
This introductory session for incoming Oxford mathematics undergraduates reviews essential high-school concepts and outlines the formal rigor and abstract thinking required for university-level mathematics, setting the stage for proof-based courses.
Natural Numbers, Well-Ordering & Mathematical Induction
This lecture, part of Oxford's introductory mathematics course, prepares incoming students by reviewing high-school mathematics and introducing the foundational concepts and proof techniques critical for university-level study.
The Binomial Theorem, Combinatorial Identities & Set Notation
This lecture, part of Oxford's introductory mathematics sequence, reviews foundational high-school concepts and introduces rigorous university-level proof techniques for first-year students.
Algebra of Sets, De Morgan's Laws, Truth Tables & Cardinality
This lecture, part of Oxford's introductory course, reviews high-school mathematical concepts while introducing students to the rigor and style of university-level mathematics, focusing on foundational principles and proof strategies essential for advanced study.
Binary Relations, Partitions & Equivalence Relations
This lecture, part of Oxford's introductory course, reviews essential high-school mathematical concepts and introduces the formal rigor and proof-based reasoning expected in a university mathematics curriculum.
Functions, Injections, Surjections, Bijections & Inverses
This lecture for Oxford first-year undergraduates introduces the pedagogical approach and core topics of university mathematics, bridging high school curricula with advanced concepts and problem-solving methodologies encountered in higher education.
Formal Logical Notation, Quantifiers & Constructing Mathematical Proofs
This lecture, part of Oxford's introductory mathematics sequence, serves as a capstone to foundational concepts, bridging pre-university knowledge with the analytical rigor expected in a first-year undergraduate curriculum.






