Repository: UIHistories Project: Course Catalog - 1893-1894 [PAGE 128]

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UNIVERSITY OF ILLINOIS.

10. Theory of Equations.—The development of the general properties of equations; relations of the roots and coefficients of equations, with applications to symmetric functions; transformation of equations; solution of reciprocal and binomial equations; algebraic solution of cubics and biquadratics; propertiesof derived functions; the limits and separation of the roots of equations; the solution of numerical equations of the nth degree. Burnside and Panton's Theory of Equations. Fall term, full study. Assistant Professor

TOWNSEND.

Required: Math. 2, 4. 11. Theory of Determinants.—It is designed to give the student a thorough working knowledge of the subject and of its applications. It will, in general, cover the origin and notation of determinants, properties of •determinants, determinant minors, multiplication of determinants, determinants of compound systems, determinants of special forms—Jacobians, Hessians, Wronskians—with applications to algebra including linear transformations, and to analytic geometry. Weld's Theory of Determinants with selected chapters from Scott's Theory of Determinants. Winter term, full study. Assistant

Professor TOWNSEND.

Required:

Math. 2, 4, 6, 7.

12. Theory of Invariants.—The course will cover the general development of the theory of invariants from both the geometric and the algebraic side. Applications of invariants will be made to systems of conies and to higher plane curves. Salmon's Modern Higher Algebra will be followed in part, but frequent use will be made of Gordan's Invariantentheorie. Spring term, full study. Assistant

Professor TOWNSEND.

Required:

Math. 7, 10, 11.

13. Theory of Functions.—By way of introduction, considerable attention will be given to the geometric representation of the complex variable, including Argand's diagram, conformal representation, and harmonic ratios, and bilinear transformation. This will be followed by the development of the theory of infinite series, algebraic and transcendental functions, integration of uniform functions. Riemann's surfaces, and so much of elliptic functions as the time will permit. Harkness aud Morley's Theory of Functions. Fall tei'm, full study. Assistant Professor TOWNSEND. Required: Math. 8, 9, 12.