ANALOGUE METHOD IN GEOMETRY COURSE

A course in Algebraic Geometry

A Course in Riemannian Geometry

Differential Geometry Course Notes

1.1. Review of topology. Definition 1.1. A topological space is a pair (X, T) consisting of a set X and a collection T = {U α } of subsets of X, satisfying the following: (1) ∅, X ∈ T , (2) if U α , U β ∈ T , then U α ∩ U β ∈ T , (3) if U α ∈ T for all α ∈ I, then ∪ α∈I U α ∈ T. (Here I is an indexing set, and is not necessarily finite.) T is called a topology for X and U α ∈ T is called an ope...

Geometry and Proof: Course Summary

This course is designed to explicate the following motto attributed to Hilbert. ”It must always be possible to substitute ’table’, chair’ and ’beer mug’ for ’point’, line’ and ’plane’ in a system of geometrical axioms.” We have considered this theme where ‘geometrical axioms’ are statements in Tarski’s world, various systems of geometry, and axioms for algebraic systems like the real numbers an...

Web-based Learning in a Geometry Course

This study concerns applying Web-based learning with learner controlled instructional materials in a geometry course. The experimental group learned in a Web-based learning environment, and the control group learned in a classroom. We observed that the learning method accounted for a total variation in learning effect of 19.1% in the 3 grade and 36.5% in the 6 grade. The main factor in the diff...