This course is intended to provide an introduction to the conceptual basis underlying high school mathematics. Emphasis will be placed on the in-depth understanding of fundamental mathematical ideas and the associated modes of reasoning and proof rather than on superficial coverage of many topics. The course will also help bridge the conceptual gap between the pre-calculus/calculus sequence and more advanced courses in mathematics by fostering the mathematical maturity necessary for success in those courses.
- Classroom Behaviour
- On the use of electronic aparati
- Course Objectives
- Recomendaciones para Estudiantes Nuevos
- In Praise of Lectures
Semester II, 2017-18
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Miscellaneous Notes
- Review of Precalculus
- On Definition (Definition according to Aristotle)
- On Truth
- On Sets
- On implication
- Logic-Set theory Correspondence
- Truth tables
- Connectives
- A list of tautologies
- On validity
- Some Axioms for Set Theory
- The Symmetric Difference of two sets.
- Extension of Induction to Well-founded Sets
- Inverse Functions
- Introduction to digraphs
- Digraph taxonomy
- Equivalence Relations
- Lattices
- Edge unlabelled Multigraphs
- Elementary Combinatorial Formulae
- Multisets
- Balls in Boxes
- On the Number of Surjections
- Function Digraphs
- Max–min inequality
- Summary of Lecture on the GCD