MATH 10850 and 10860
Required for Honors Mathematics Majors. (See also:nd.edu/~sumr)
This course is for students with a prior knowledge of calculus, who want a more advanced treatment of calculus, and have a desire to develop their mathematical talents. It stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subjects under consideration. Students requesting this course should have a SAT Math score over 700 and grades of at least A- in recent mathematics courses.
MATH 10850 focuses on the calculus of real-valued functions of a single variable, paying attention to clear definitions and logical arguments. It covers methods of integration, and approximation of functions by Taylor polynomials. It includes geometric and mechanical applications of calculus.
MATH 10860 covers sequences and series of complex numbers, convergence of power series, vectors, inner products, and the rudiments of linear algebra. It then covers the calculus of vector-valued functions of one variable. It ends with Isaac Newton’s proofs of Kepler’s laws of planetary motion.