This course, "Introduction to University Mathematics," offers a foundational exploration of essential mathematical concepts, starting with natural numbers, induction, and set theory, before building the number system from integers and rationals to the formal construction of real numbers. It introduces key ideas like relations, functions, and mathematical logic, concluding with a deep dive into the Axiom of Completeness and its significant implications for the properties of the real number line, ultimately aiming to establish a rigorous understanding of the fundamental structures and logic necessary for higher-level mathematics.
| Lecture | Topics Covered | Speaker | Resources (Notes/Problems) |
|---|---|---|---|
| Lecture 1 May 5 (Mon) |
Building the Number System: Integers, Rationals, and Their Gaps (arithmetic, algebraic properties, gaps). Constructing the Real Numbers (formal construction, filling the gaps, complete ordered field). | E K Narayanan TA: Renjith T. |
Problem Sheet |
| Lecture 2 May 5 (Mon) |
The Natural Numbers, Induction, and Sets (including operations and cardinality). | Krishna Hanumanthu TA: Gobinda Sau |
Problem Sheet |
| Lecture 3 May 6 (Tue) |
Relations, Functions, and Logic (relations, functions, mathematical logic, logical statements, connectives, quantifiers). | Krishna Hanumanthu TA: Gobinda Sau |
Problem Sheet |
| Lecture 4 May 6 (Tue) |
Axiom of Completeness: The Least Upper Bound Property, existence of square roots, density of rationals and irrationals in $\textbf{R}$. | E K Narayanan TA: Renjith T. |
Problem Sheet |