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University of OxfordOXF-INTROMathematicsintroductory· 2025

Introduction to University Mathematics (2026)

James Munro

James 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.

Start Lecture 17 lectures · 9h total
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Oxford Mathematics: Introduction to University Mathematics (2026)

Syllabus

7
Lecture 1· 1:14:56

Foundations 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.

Lecture 2· 1:52:56

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.

Lecture 3· 42:36

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.

Lecture 4· 1:33:11

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.

Lecture 5· 2:14:26

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.

Lecture 6· 45:16

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.

Lecture 7· 51:59

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.