Topics include internal product spaces, norms, self adjoint and normal operators, orthogonal and unitary operators, orthogonal projections and the spectral theorem, bilinear and quadratic varieties, generalized eigenvectors, and Jordan canonical kind. Properties of two- and three-dimensional shapes, inflexible motion transformations, similarity, spatial reasoning, and the method and methods of measurement. Class actions provoke investigations of underlying mathematical structure in the exploration of shape and area. Emphasis is on the reason of the mathematical thought process.
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Technology particularly designed to facilitate geometric explorations is integrated throughout the course. This series supplies the mandatory mathematical background for majors in Computer Science, Economics, Mathematics, Mathematical and Computational Science, and most Natural Sciences and some Engineering majors. Those who plan to major in Physics or in Engineering majors requiring Math 50’s past Math fifty one are beneficial to take Math 60CM. This sequence provides the required mathematical background for majors in all disciplines, especially for the Natural Sciences, Mathematics, Mathematical and Computational Science, Economics, and Engineering. The division offers three sequences in multivariable arithmetic. Knowledge of Math 21 content material is prime to university-level quantitative work, and is anticipated by the surface world for anybody earning a degree in a quantitative subject here.