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Problem solving – analysis of mathematical behavior. Proof –Mathematical notation. Basic notions from formal logic. Nature and techniques of proof. Counterexamples.
Euclid's postulates. Fundamental theorems in Euclidean Geometry. Vectors; dot and cross products. Basics of matrix algebra and its applications to geometry; determinants, inverse matrices, linear algebra and row reduction.
Other topics may include:
Lines and planes; conic sections. Positive definite quadratic forms in two variables.