Contents: (14 pages)
1. Introduction
2. The axiomatic approach
3. Riemannian Geometry
4. Manifolds all of whose geodesics are lines
5. Conclusion
References

Contents: (22 pages)
1. Introduction
2. The Projective Plane
3. Projective space
4. Projective Geometry Applied to Computer Vision

Contents: (39 pages)
1. Introduction
2. Three dimensional space
3. Dot product
4. Lines
5. The angle between two vectors
6. The cross product of two vectors
7. Planes
8. Problems

Contents: (14 pages)
1. Introduction
2. Mathematical Background
3. Preferences and Demand
4. Local Determinacy of Equilibrium
References

Contents: (33 pages)
1. Theorems for Verification
1.1 Basic Geometrical terms
1.2 Axioms and Theorems on lines
1.3 Axioms and Theorems on a triangle
1.4 Congruent triangles
1.5 Properties of parallelogram
1.6 Concurrency of lines
2. Theorems with logical proofs

Contents: (15 pages)
1. Introduction
2. Geometry
    A. Phenomenology
    B. Derivation of the structure of C
    C. Riemannian Structure
3. Discussion
References

Contents:, (32 pages)
1. Affine Algebraic Varieties
2. Projective Algebraic Varieties
3. Sheaves and General Algebraic Varieties
4. Properties of Algebraic Varieties
5. Divisors
6. Algebraic Geometry Over Algebraically Closed Fields
7. Schemes
8. Applications
Glossary
Bibliography
Biographical Sketch

Contents: (49 pages)
Chapter 1. Introduction to Smooth Manifolds
1. Plain curves
2. Surfaces in R3
3. Abstract Manifolds
4. Topology of abstract manifolds
5. Submanifolds
6. Dierentiable maps, immersions, submersions and embeddings
Chapter 2. Basic results from Dierential Topology
1. Manifolds with countable bases
2. Partition of unity
3. Regular and critical points and Sard's theorem
4. Whitney embedding theorem
Chapter 3. Tangent spaces and tensor calculus
1. Tangent spaces
2. Vector elds and Lie brackets
3. Frobenius Theorem
4. Lie groups and Lie algebras
5. Tensors and dierential forms
6. Orientation and integration of dierential forms
7. The exterior derivative and Stokes Theorem
Chapter 4. Riemannian geometry
1. Riemannian metric on a manifold
2. The Levi-Civita connection
3. Geodesics and the exponential map
4. Curvature and the Gauss equation