Titlebook: Algebraic Curves and Riemann Surfaces for Undergraduates; The Theory of the Do Anil Nerode,Noam Greenberg Textbook 2022 The Editor(s) (if a

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Decision Making in Soviet PoliticsThe definition and basic properties of algebraic curves in the affine plane, and more generally, algebraic hypersurfaces in affine space. Contains a proof of Study’s lemma, which relates containment of curves to divisibility of their defining polynomials. Introduces the resultant, an important tool of elimination theory.

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Paul Kalb,Paul E. Greenberg,Crystal T. PikeA review of some basic notions of topology, including completeness and compactness. Manifolds and subspaces of manifolds. Quotients of Euclidean space by discrete subgroups, which include the torus.

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Michael W. Bonney,Howard G. BirnbaumDefining the notion of a connected space, path-connected space, path homotopy, and simply connected spaces. The winding number of a path. A review of multivariable calculus, including the inverse function theorem. Path-connected manifolds are differentiably path-connected.

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Michael W. Bonney,Howard G. BirnbaumIntegration of generalised 1-forms. The length of a path. Vector fields; conservative and symmetric vector fields.

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Howard G. Birnbaum,Paul E. GreenbergDeveloping the theory of differentiation of functions of a single complex variable, based on integration of real vector fields. Analytic functions; Cauchy’s integral formula; theorems of Morera, Weierstrass, and Liouville.

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