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Topics embrace rings, polynomial rings, matrix rings, modules, fields and semi-simple rings. This course will give an outline of geometry from a modern viewpoint. Axiomatic, analytic, transformational, and algebraic approaches to geometry will be used. The relationship between Euclidean geometry, the geometry of complex numbers, and trigonometry might be emphasised. Properties of two- and three-dimensional shapes, rigid motion transformations, similarity, spatial reasoning, and the process and strategies of measurement.

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This course is the first of a three-course sequence designed to develop deeper understanding of elementary school mathematics content material wanted for educating. The course topics embody entire numbers and integers, fractions, ratio, p.c, decimals and arithmetic operations within these methods. This course covers the identical materials as MATH 125 but in a depth acceptable for honors students. It is the first course in the three part honors calculus sequence for school kids majoring in mathematics, science or engineering. Topics embody limits, continuity, differentiation, purposes of differentiation, and integration. Applications of the derivative are lined in detail, including approximation of errors utilizing differentials, maxima and minima issues, curve sketching, optimization problems, and Newton’s methodology.

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